I
Theoretical and Experimental Characterisation
of Energy in an Electrostatic Discharge
Yi-chuan Su
BEng, PhD Cand.
Submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy
Science and Engineering Faculty
Queensland University of Technology
March, 2013
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
II
Student: Yi-chuan Su
Student number: 04712382
Principal Supervisor
Prof. T. Steinberg
BE (Mech), MSc, PhD, CPEng, RPEQ, SMIEAust
Associate supervisor
Dr. J. Lyall
BE, BSc, ME, PhD
Associate Supervisor
Dr. M. Castillo
BE, PhD
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
III
Keywords:
Electrostatic discharge; High impedance measurement circuit, Minimum ignition energy, N-
pentane, Spark energy, and Spark discharge.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
V
Acknowledgements
This research work would not have been possible without the assistance and guidance of my
supervisors Prof. Ted Steinberg, A/Prof. Jim Lyall and Dr. Martin Castillo. Their support and
encouragement throughout the research journey is greatly appreciated.
Special thanks to Mate Frankic, Wolfgang Maier, Anthony Tofoni, Eric Klokman and Ken
McIvor of the Electrical Engineering Technician Team at SEF/QUT (EESE/BEE). Their
technical advice has allowed this project to succeed.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
VI
Abstract
Electrostatic discharges have been identified as the most likely cause in a number of incidents
of fire and explosion with unexplained ignitions. The lack of data and suitable models for this
ignition mechanism creates a void in the analysis to quantify the importance of static
electricity as a credible ignition mechanism. Quantifiable hazard analysis of the risk of
ignition by static discharge cannot, therefore, be entirely carried out with our current
understanding of this phenomenon.
The study of electrostatics has been ongoing for a long time. However, it was not until the
wide spread use of electronics that research was developed for the protection of electronics
from electrostatic discharges. Current experimental models for electrostatic discharge
developed for intrinsic safety with electronics are inadequate for ignition analysis and
typically are not supported by theoretical analysis.
A preliminary simulation and experiment with low voltage was designed to investigate the
characteristics of energy dissipation and provided a basis for a high voltage investigation. It
was seen that for a low voltage the discharge energy represents about 10% of the initial
capacitive energy available and that the energy dissipation was within 10 ns of the initial
discharge. The potential difference is greatest at the initial break down when the largest
amount of the energy is dissipated. The discharge pathway is then established and minimal
energy is dissipated as energy dissipation becomes greatly influenced by other components
and stray resistance in the discharge circuit. From the initial low voltage simulation work, the
importance of the energy dissipation and the characteristic of the discharge were determined.
After the preliminary low voltage work was completed, a high voltage discharge experiment
was designed and fabricated. Voltage and current measurement were recorded on the
discharge circuit allowing the discharge characteristic to be recorded and energy dissipation
in the discharge circuit calculated. Discharge energy calculations show consistency with the
low voltage work relating to discharge energy with about 30-40% of the total initial
capacitive energy being discharged in the resulting high voltage arc.
After the system was characterised and operation validated, high voltage ignition energy
measurements were conducted on a solution of n-Pentane evaporating in a 250 cm3 chamber.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
VII
A series of ignition experiments were conducted to determine the minimum ignition energy
of n-Pentane. The data from the ignition work was analysed with standard statistical
regression methods for tests that return binary (yes/no) data and found to be in agreement
with recent publications
The research demonstrates that energy dissipation is heavily dependent on the circuit
configuration and most especially by the discharge circuit’s capacitance and resistance. The
analysis established a discharge profile for the discharges studied and validates the
application of this methodology for further research into different materials and atmospheres;
by systematically looking at discharge profiles of test materials with various parameters (e.g.,
capacitance, inductance, and resistance). Systematic experiments looking at the discharge
characteristics of the spark will also help understand the way energy is dissipated in an
electrostatic discharge enabling a better understanding of the ignition characteristics of
materials in terms of energy and the dissipation of that energy in an electrostatic discharge.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
VIII
Table of Contents
1.0 Introduction .......................................................................................................................... 1
1.1 Introduction ...................................................................................................................... 1
1.2 Theory .............................................................................................................................. 3
1.3 Research Method ............................................................................................................. 4
1.3.1 High Voltage measurement....................................................................................... 6
1.3.2 Low Voltage Discharge Simulation and Measurement ............................................ 7
1.3.3 High Voltage Discharge Simulation and Measurement............................................ 7
1.3.4 Ignition Experiment .................................................................................................. 8
1.4 Application and Contributions ......................................................................................... 8
1.5 Conclusion ....................................................................................................................... 9
2.0 Literature Review............................................................................................................... 10
2.1 Introduction .................................................................................................................... 10
2.2 Electrostatics .................................................................................................................. 11
2.2.1 Charge transfer ........................................................................................................ 11
2.2.2 Conduction .............................................................................................................. 11
2.2.3 Induction ................................................................................................................. 11
2.2.4 Triboelectricity ........................................................................................................ 12
2.2.5 Electrostatics Summary .......................................................................................... 14
2.3 Human body model ........................................................................................................ 16
2.4 Charged Device Model .................................................................................................. 17
2.5 Machine Model .............................................................................................................. 18
2.6 Electrostatic Discharges as an Ignition Hazard ............................................................. 20
2.7 Discharge energy ........................................................................................................... 21
2.7.1 Capacitive Energy ................................................................................................... 23
2.7.2 Energy Dissipation .................................................................................................. 25
2.8 HV measurement ........................................................................................................... 26
2.8.1 Resistive Voltage Divider ....................................................................................... 26
2.8.2 Capacitor compensation .......................................................................................... 27
2.8.3 Oscilloscope ............................................................................................................ 29
2.8.4 Discussion/conclusion............................................................................................. 31
3.0 High Voltage Measurement Review .................................................................................. 32
3.1 High Resistance High Voltage-Voltage Divider............................................................ 32
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
IX
3.2 Frequency Response of Resistive Divider ..................................................................... 35
3.3 Equivalent Capacitor Voltage Divider ........................................................................... 37
3.3.1Resistor-Stray Capacitance Evaluation .................................................................... 39
3.3.2 High Voltage Capacitive Resistive Divider -Stray Capacitance Evaluation .......... 41
3.4 Oscilloscope Calibration ................................................................................................ 42
3.5 Current Measurement..................................................................................................... 44
3.6 Discharge Resistor High frequency Response ................................................................... 46
3.7 Measurement Errors and Absolute Errors ...................................................................... 47
3.8 Conclusion ..................................................................................................................... 48
4.0 Low Voltage Discharge Simulation and Measurement ..................................................... 49
4.1 Low Voltage Discharge Simulation and Measurement Experiment Method ................ 50
4.2 Low Voltage Discharge Simulation and Measurement Experiment Results and
Analysis................................................................................................................................ 52
4.3 Low Voltage Discharge Simulation and Measurement Experiment Discussion ........... 54
4.4 Low Voltage Discharge simulation and Measurement Experiment Conclusion ........... 57
5.0 High Voltage Discharge Simulation and Measurement..................................................... 58
5.1 High Voltage Measurement Circuit ............................................................................... 59
5.1.1 High Voltage Measurement Circuit Simulations .................................................... 59
5.1.2 High Voltage Measurement Circuit Evaluation ...................................................... 64
5.1.3 High Voltage Measurement Circuit Oscilloscope Compensation .......................... 65
5.1.4 High Voltage Measurement Circuit Overview ....................................................... 66
5.1.5 High Voltage Measurement Circuit Attenuation Calculation DC .......................... 72
5.1.6 High Voltage Measurement Circuit Attenuation Calculation High Frequency ...... 73
5.1.7 High Voltage Measurement Circuit Absolute Errors.............................................. 74
5.1.8 High Voltage Simulation ........................................................................................ 75
5.2 High Voltage discharge Experimental Method .............................................................. 77
5.2.1 High Voltage Experiment Circuit ........................................................................... 77
5.2.2 Experiment procedure ............................................................................................. 80
5.2.3 Energy Calculation.................................................................................................. 80
5.3 Results and Analysis ...................................................................................................... 81
5.3.1 Discharge Current and Voltage Waveforms ........................................................... 81
5.3.2 Experiment Calculations and Results ..................................................................... 85
5.3.3 Discharge Voltage ................................................................................................... 85
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
X
5.3.4 Energy in the Capacitor .......................................................................................... 89
5.3.5 Discharge Resistor Energy Dissipation .................................................................. 90
5.3.6 Discharge Point Energy Dissipation ....................................................................... 91
5.3.7 Unaccounted Energy Results Summary .................................................................. 93
5.3.8 Peak Current............................................................................................................ 93
5.4 Discussion ...................................................................................................................... 95
5.4.1 Discharge Current and Voltage Waveform Discussion .......................................... 95
5.4.2 Results Summary-Discussion ................................................................................. 97
5.4.3Discharge Voltage-Discussion ................................................................................. 97
5.4.4 Capacitor Energy-Discussion.................................................................................. 97
5.4.5 Discharge Resistor Energy Dissipation-Discussion................................................ 97
5.4.6 Discharge Point Energy-Discussion ....................................................................... 98
5.4.7 Unaccounted Energy-Discussion ............................................................................ 98
5.4.8 Peak Current-Discussion ......................................................................................... 99
5.5 High Voltage Discharge Simulation and Measurement- Conclusion ............................ 99
6.0 Materials Ignitions ........................................................................................................... 100
6.1 Introduction .................................................................................................................. 100
6.2 Method ......................................................................................................................... 101
6.3 Results and Analysis .................................................................................................... 102
6.3.1 Ignition Energy and Minimum Ignition Energy ................................................... 102
6.3.2 Ignition Probability Statistical Analysis ............................................................... 102
6.3.3 Ignition Discharge characteristics ......................................................................... 106
6.4 Material Ignition Discussion ........................................................................................ 107
6.4.1 Minimum Ignition Energy .................................................................................... 107
6.4.2 Ignition Probability ............................................................................................... 107
6.4.3 Ignition Discharge ................................................................................................. 108
6.4.4 Capacitance vs. Discharge Energy ........................................................................ 108
6.5 Material Ignition Conclusion ....................................................................................... 108
7.0 Contributions and Conclusions ........................................................................................ 110
7.1 High Voltage Measurement ......................................................................................... 110
7.2 Low Voltage Experiment ............................................................................................. 111
7.3 High Voltage Experiment ............................................................................................ 112
7.4 Material Ignition Experiment ....................................................................................... 114
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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7.5 Conclusions .................................................................................................................. 115
8.0 Future Work ..................................................................................................................... 117
9.0 References ........................................................................................................................ 118
10.0 Appendix ........................................................................................................................ 122
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
XII
List of Figures
Figure 2.2.1.1 Charge Transfer Conduction. ........................................................................... 11
Figure 2.2.1.2 Charge Transfer Induction. ............................................................................... 12
Figure 2.2.2.3Charge Transfer Triboelectricity. ...................................................................... 13
Figure 2.4.0.1CDM Current Waveform ................................................................................... 18
Figure 2.5.0.1 MM Current Waveform .................................................................................... 19
Figure 2.8.1.1 Resistor Voltage Divider .................................................................................. 27
Figure 2.8.2.1 Capacitor Coupled Voltage Divider. ................................................................ 28
Figure 2.8.3.1 Oscilloscope Schematic .................................................................................... 30
Figure 3.1.0.1 High Voltage Resistive Divider........................................................................ 35
Figure 3.2.0.1 1GΩ Frequency Response of Resistive divider in Linear Magnitude Ω .......... 36
Figure 3.3.0.1High Voltage Capacitive Resistive Divider ...................................................... 39
Figure 3.3.1.1 Plot of 1GΩ Stray Capacitance Over Frequency ............................................. 40
Figure 3.3.2.1 Plot of Coupled 2GΩ/1pF Capacitance over Frequency .................................. 41
Figure 3.4.0.1 Schematic of 1X Probe and Oscilloscope ........................................................ 43
Figure 3.4.0.2 Schematic of 10X Probe and Oscilloscope ...................................................... 43
Figure 3.5.0.1 Plot of 0.1Ω Current Measurement Section over Frequency ........................... 45
Figure 3.6.0.1 Plot of 1.5 kΩ Discharge Resistor over Frequency .......................................... 47
Figure 4.1.0.1 Schematic of the low voltage ESD simulation experiment .............................. 51
Figure 5.1.1.1 Initial High Voltage Divider ............................................................................. 61
Figure 5.1.1.3 Simulated Frequency Response for the Divider at 2MΩ Node ........................ 63
Figure 5.1.2.1 Coupled High Voltage Divider ......................................................................... 65
Figure 5.1.3.1 Compensated 2X Probe Oscilloscope Equivalent Circuit ................................ 66
Figure 5.1.4.1 Complete High Voltage Measurement Circuit ................................................. 68
Figure 5.1.4.2 Complete High Voltage Measurement Equivalent Circuit 1 ............................ 69
Figure 5.1.4.3 Complete High Voltage Measurement Equivalent Circuit 2 ............................ 70
Figure 5.1.4.4 Complete High Voltage Measurement Equivalent Circuit 3 ............................ 71
Figure 5.1.5.1 Complete High Voltage Measurement Equivalent Circuit 4 ............................ 72
Figure 5.1.6.1 Complete High Voltage Measurement Equivalent Circuit 5 ............................ 73
Figure 5.2.1.1 Overall Experiment Circuit .............................................................................. 79
Figure 5.3.1.1 Experiment Results- Discharge Voltage Waveform at Discharge Capacitor ... 83
Figure 5.3.1.2 Experiment Results- Discharge Current Waveform ......................................... 84
Figure 5.3.3.1 Plot of Discharge Voltage Results with absolute error .................................... 86
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
XIII
Figure 5.3.4.1 Plot of Initial Capacitive Energy with absolute error ....................................... 89
Figure 5.3.5.1 Plot of Discharge Resistor Energy Dissipation with absolute error ................. 91
Figure 5.3.6.1 Plot of Discharge Point Energy Dissipation with absolute error ...................... 92
Figure 5.3.8.1 Plot of Peak Current with absolute error .......................................................... 94
Figure 6.3.2.1 Plot of Ignition Results and Ignition Probability Curve for N-Pentane ......... 106
Appendix 10.2 Plot of 500MΩ Frequency Response in Linear Magnitude Ω ...................... 123
Appendix 10.3 Plot of 200MΩ Frequency Response in Linear Magnitude Ω ...................... 123
Appendix 10.4 Plot of 500MΩ Stray Capacitance over Frequency ...................................... 124
Appendix 10.5 Plot of 200MΩ Stray Capacitance over Frequency ...................................... 124
Appendix 10.6 Plot of 200MΩ/10pF Capacitance over Frequency ...................................... 125
Appendix 10.7 Plot of 2MΩ/220pF Capacitance over Frequency ........................................ 125
Appendix 10.10 High Voltage Experiment Setup ................................................................. 153
Appendix 10.11 High Voltage Experiment Discharge Point ................................................. 154
Appendix 10.12 High Voltage Experiment Measurement Equipment .................................. 155
Appendix 10.13 Ignition Experiment, Ignition Frame Extract from High Speed Camera .... 156
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
XIV
List of Tables
Table 3.3.1.0.1 Table of Stray Capacitance Results ................................................................ 40
Table 3.3.2.0.1 Table of Evaluated Capacitance Results ......................................................... 42
Table 4.1.0.0.1 Table of experimental variables matrix for the low voltage ESD simulation 51
Table 5.1.2.0.5 Table of High Voltage Divider-Stray Capacitance Results ............................ 65
Table 5.1.7.0.1 Resistive Measurement Error .......................................................................... 74
Table 5.1.7.0.2 Capacitive Measurement Error ....................................................................... 75
Table 5.3.2.0.1 Experiment Results-Summary of Discharge Energy Results for 100pF
simulation and experiment ....................................................................................................... 87
Table 5.3.6.1.1 Discharge Point Energy Dissipation Results .................................................. 93
Table 5.3.2.0.1 Unaccounted Energy Result Summary ........................................................... 93
Table 5.3.8.1.1 Peak current summary .................................................................................... 95
Table 6.3.0.0.1 Ignition and No Ignition Discharge Result Summary .................................. 103
Appendix 10.1 Table of Triboelectric Series ......................................................................... 122
Appendix 10.9 Simulation and Measurement of an Electrostatic Discharge Low Voltage
Experiment Results ................................................................................................................ 139
Appendix 10.14 Table of Ignition and No Ignition Results................................................... 160
Appendix 10.15 Data for Ignition Probability Plot, with Ignition Data ................................ 162
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
XV
Nomenclature
A Amperes
C Coulombs
Cm3 centi-Meter cubed
GΩ Giga-Ohm
GHz Giga-Hertz
kHz kilo-Hertz
kΩ kilo-Ohm
kV kilo-Volt
mA milli-Amperes
MHz Mega-Hertz
mJ milli-Joules
mm milli-Meter
mΩ milli-Ohm
nF nano-Farad
nH nano-Henry
nS nano-Second
pF pico-Farad
pS pico-Second
V Volt
W Watts
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
XVI
Eqn 1 Spark Energy Estimation Es = Ec − Er − Eresidual,
Eqn. 2 Coulomb’s Law
= 124 ∙
Eqn 3 Force
=
Eqn 4 Field Strength
=
Eqn 5 Field Strength
= 4 ∙
Eqn 6 Net Flux
Φ = ∙ = ∙ ! =
Eqn 7 Field strength for parallel plates
= "
Eqn 8 Voltage potential
# = $ , $ = # = ∮ ∙ & ∙ '
Eqn 9 Energy/work
( = 12 $ ∙ #, # = 1$ ) ∙ *
Eqn 10 Attenuation of resistor voltage divider
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
XVII
+ = ,1 + ,2,2
Eqn 11 Attenuation of capacitor coupled voltage divider
+ = $1 + $2$1
Eqn 12 Attenuation of coupled voltage divider
+ =,11 + ./,1$1 + ,21 + ./,2$2,21 + ./,2$2
Eqn 13 Attenuation ratio ,1,2 = $2$1
Eqn 14 Cut off frequency
01 = 12 ∙ ∙ , ∙ $
Eqn 15 Capacitance Reactance Equation
21 = 12 ∙ ∙ 0 ∙ $
Eqn 16 Capacitance-frequency and –j dependant
$ = −.2 ∙ ∙ 21 ∙ 0
Eqn17 Absolute Error
3456'7*8 6 = ± 12 :;<;=7= =8+578+4'8 >+'78
Eqn 18 Measurement Relative Error
,8'+*;>8 6% = ±+456'7*8 86=8+578 >+'78 × 100%
Eqn 19 Energy dissipated in resistor
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
XVIII
( = #, ∙ *
Eqn 20 Energy dissipated at the discharge point
( = (#1 − #) ∙ #, ∙ *
Eqn 21 unaccounted energy
(7<+1167<*8 = (1+D+1;*6 − (85;5*6 − (;51ℎ+F8
(7<+1167<*8 = 12 $ ∙ # − #, ∙ * − (#1 − #) ∙ #, ∙ *
Eqn 22 Ohm’s Law
# = ) ∙ ,, ) = #,
Eqn 23Natural Frequency RLC Circuit
/G = 1√I ∙ $ , /J = 2K
Eqn 24 Damping Factor RLC Circuit
L = ,2 M$I
Eqn 25 Logistic Regress Modelling Probability of Ignition/No Ignition
N = 8(OPQOR)(1 + 8OPQOR)
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
XIX
Definitions and Abbreviations
Charged Device Model (CDM)
Charge device model is a specified equivalent circuit that characterises a
device that is charged, and then discharges to ground or another object of less
or opposite charge.
Electrostatics (ES)
The study of static electrical charges & its effects and transfer (conduction,
induction or discharge).
Human Body Model (HBM)
Human body model is an equivalent circuit model of the human body, in terms
of resistance, capacitance and inductance.
Machine model (MM)
Machine model refers to an equivalent circuit where instead of the human
body to be the main item of interest, a particular machine is modelled.
Minimum Ignition Energy (MIE):
The minimal amount of energy required to ignite a particular material or
object in a particular environment. Ignition does not necessary imply
continuous combustion, propagation, or explosion.
Static Electricity (SE)
Similar meaning to Electrostatics. Adopted before Faraday demonstrated that
electricity is in the form of movement of positive and negative charges, and
static electricity is where electrons are stationary.
Stray Capacitance
Stray Capacitance in this document refers to the additional unexpected
capacitance that exhibits at high frequency. This is common as surface
capacitance across large resistances as the insulation exhibits parasitic
capacitance effects to ground at high frequency.
Stray Inductance
Stray Inductance refers to the additional unexpected inductance due to
manufacture/design of the components. Inductance is apparent at high
frequency and its effects can be seen as oscillatory ringing signals. This
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
XX
inductance derives from internal construction and conduction path within the
component. E.g. looping conductive paths.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
1.0 Introduction
1
1.0 Introduction
1.1 Introduction
Electrostatic discharges have been identified as one of the most likely cause in a number
of incidents of fire and explosions with unexplained ignitions [1-3]. The lack of data and
suitable models forms a void in the analysis to quantify the significances of static
electricity in these situations. Emphasis must be placed on the fact that electrostatic
charge build up is a natural phenomenon that will occur with any situation of charge
transfer. It is not limited to human interactions with our physical world. In industrial
scenarios, repetitive actions cause cyclic transfers of very small amounts of charge. A
charge build-up creates a significant combustion hazard that can lead to catastrophic
damage, destroy plants and cause harm to personnel.
Quantifiable hazard analysis of the risk of ignition by static discharge cannot be entirely
carried out with our current understanding and experimental results. Improved
experimental models need to be established using a systematic procedure in order to
characterise the energy associated with electrostatic discharge.
The study of electrostatics and the associated fundamental principles have been around
for a long time. However it was not until the wide spread application of electronics that
research was developed for the protection of these electronics from electrostatic
discharges. The ever increasing amount of newly created technology drives new research
to develop methods and experiments to assess the hazardousness of electrostatics to
materials. Currently, experimental models for electrostatic discharge developed for
intrinsic safety with electronics are inadequate for ignition analysis. As interest increased
in the area of hazardousness electrostatic discharge, research continues with the models
established for electronic safety testing.
Previous work presented in the Confirmation Document in Appendix 10.16 showed in
agreement with related work that a resistive characteristic could be drawn to characterise
the energy dissipation of the discharge [4-6]. This research entailed examining the voltage
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
1.0 Introduction
2
and current characteristic of the discharge, and a complete discharge characteristic for a
Human Body Model was created. From the initial simulation and experiments, it was seen
that discharge energy represents about 10% of the initial capacitive energy and that the
energy dissipation was within 10ns of the initial discharge, where potential breaks down
and current flows through the arc in the discharge [6]. This is expected considering the
discharge characteristic of voltage and current in relation to the energy dissipation. As the
initial break down occurs the potential difference is the greatest, allowing the majority of
the energy to be dissipated. The discharge arc is then established and minimal energy is
dissipated as energy dissipation becomes greatly influenced by other components and
stray resistance in the discharge circuit. From the initial work of low voltage simulations,
the importance of the energy dissipation and the characteristic of the discharge is
emphasised, as the discharge energy would be as high as 30-40% of the capacitive energy
in an actual resistor/capacitor discharge and the characteristics of the discharge will
determines the energy dissipation over the discharge period [6].
High voltage simulation and experimentation of the electrostatic discharge required an
accurate measurement setup in order to achieve the precise measurement of the energy
dissipation. Building on the model of electrostatic discharge from electronic intrinsic
safety, the human body model was used as a basis to simulate electronically the discharge
characteristics. Expanding on the results and understanding of energy dissipation in
preliminary work, energy dissipation of the discharge in comparison to the total initial
capacitive energy was investigated. Voltage and current measurement were recorded on
strategic positions on the discharge circuit, allowing the discharge characteristic to be
recorded and energy dissipation in the discharge circuit analysed. Discharge energy
calculation shows consistency from low voltage work with discharge energy representing
about 40% of the total initial capacitive energy.
Research shows that ignition energy needs to be investigated on a more complex system
in order to achieve an accurate quotation of the minimum ignition energy [4, 6]. However,
the more complex the discharge system becomes; the more difficult it is to achieve
precision in energy calculation. Effects of the measurement circuit plus any possible stray
capacitance, inductance and resistance need to be taken into account, as they greatly
impact on the energy dissipation.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
1.0 Introduction
3
High voltage ignition energy measurements were conducted on ignitions of n-Pentane
solution evaporated in a 250cm3 chamber. A series of ignition experiments was conducted
to determine the minimum ignition energy of n-Pentane. The lowest recorded ignition
energy was 0.352 mJ, with statistically results showing P=0.1 E=0.269 mJ, P=0.5
E=0.448 mJ and P=0.9 E=0.627 mJ. From the results, the importance of circuit
configuration on the discharge characteristic and ultimately the ignition energy can be
inferred.
Through this research, energy dissipation was found to be based heavily on the circuit
configuration of capacitance and resistance. Varying the capacitance varies the initial
energy plus the duration of discharge. Initial experiments showed that varying of
resistance varies the peak current and the duration of discharge. The analysis established a
discharge profile for the discharge that caused ignition for this set of experiments. This
methodology provides a base for further research into different materials and atmospheres,
by systematically looking at discharge profiles of test materials with various parameters
(e.g., capacitance, inductance, and resistance).
Systematic experiments looking at the discharge characteristics of the spark will help
understand the energy dissipation of the electrostatic discharge. This will allow us to
understand the ignition requirements in terms of energy and the dissipation of that energy
in an electrostatic discharge.
1.2 Theory
Static electricity is the build-up of static charges and presents an electrostatic hazard in
the potential unwanted release of energy [1]. This energy is built up by the transfer of
charges as described by the theories of conduction, induction and triboelectricity of
electrostatics. The release of this energy either to ground or an oppositely charged object
is what causes hazards. In most cases, the release of charges is undesired, unwanted and
unintentional. The usual form of release or dissipation of static electricity is in the form of
an electrical arc, which has the potential to lead to an ignition and consequently
combustion or explosion of nearby material/fuel.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
1.0 Introduction
4
Electrostatic build up and discharge has been categorised into models representing their
use and characteristic. Most widely known, is the Human Body Model (HBM), which is
simulated by capacitor and resistor[7]. It is the most common test model for electronics
protection, as human interaction is the most common form of damage to electronic
components whether in production or application. The human body is reduced down to an
equivalent electronic circuit of series connected resistor and capacitor, with R 1.5 KΩ and
C 100 pF [7].
Energy in the discharge has not been the main aspect in the previous studies for electronic
component testing. Recent research on discharge energy is related to electronics and uses
models developed for discharge energy consideration. A wholly discharged capacitive
energy is the approach taken where the total capacitive energy is the discharge energy,
with considerations to residual capacitive energy.
Measurement of high voltage discharge requires a complex design of circuits to allow
safe and accurate recording of voltages and currents. To achieve this, an extensive study
was conducted for the measurement of high voltages and extremely fast discharges. In
order to measure such a high voltage discharge, specially designed voltage dividers were
needed to step down the discharge voltage. However the voltage not only needs to step
down, it also needs to be matched capacitively to ensure correct ratio is retained.
Competency and understanding of the measurement equipment is required to ensure
recorded data is accurate. Accurate measurement will allow energy dissipation to be
calculated and an understanding of how the discharge energy compares to the initial
capacitive energy and the resistive dissipated energy.
1.3 Research Method
Through literature review, the advantages and disadvantages for each of the standardised
model for electrostatic simulation was determined. The models are Charged Device
Model (CDM), Human Body Model (HBM) and Machine Model (MM). These models
were first established as an electrical representation of what the expected discharge and
damage would be if discharged from the various possible scenarios. As the intended uses
of these models were to test intrinsic safety of electronic components; the major
difference in regard to investigate is the utilising of the model for energy calculation. The
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
1.0 Introduction
5
Charged Device Model (CDM) is based on the possible storage of charges and discharges
by an insulator on to an electronic component [8]. It is a pure capacitive representation
with no additional resistance or inductance. From literature, a Charged Device Modelled
discharge tends to have high peak current and extremely short time frames [8-10].
A Human Body Model (HBM) is derived from the simulation of the human body as
electrical component in order to observe the effects of discharges from a human to an
electronic component [7]. The human body from an electrical equivalent point of view is
composed of resistance and capacitance with minimal inductance. The values are quoted
to be 1.5k Ω and 100 pF for a standard body. From past work, discharge from a Human
Body Model tends to have a longer discharge time compared to Charged Device Model
and a lower peak current due to the resistance.
Machine Model (MM) came about from the possible storage of charges and discharges in
repetitive action on a mechanized system [11]. Due to the open ended-ness of application,
the only defining aspect is that discharges are calibrated through a 500 Ω resistor. There
is no limit for capacitance since possible charge storage is dependent on the system. For
general testing, the recommended value is 200 pF. With a resistive component, the peak
current is expected to be similar to the Human Body Model and with discharge time
frame to be dependent on the capacitance
Research on electrostatic discharge is limited as we lack sufficient understanding of the
phenomenon, in particular the dissipation of energy involved and the effects on ignition
by the equivalent electrical components. Electrostatics as a hazard has only gained focus
in the last 10 years, mainly due to the need for further understanding of unexplained
ignitions in various accidents. This created the need to understand the energy dissipation
of the discharge in order to comprehend the ignition probability. The models established
for electronics intrinsic safety provides a basis for further research into the energy aspect
of an electrostatic discharge. The Human Body Model is investigated in detail in this
study with ignition energy experimentations, as Human Body Model, represent the most
widely spread of the hazards with the addition of resistive component allowing greater
control over discharge.
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1.0 Introduction
6
Through the literature, we have seen an increase in complexity in the measurement and
calculation of discharge energy [12-14]. From the rough estimation of total initial energy
in the capacitor as adopted in various standards to a more precise estimation of discharge
energy by measuring current and discounting the energy lost by other know components
in the discharge circuit. This research looks at the energy in the discharge by measuring
voltage and current of the discharge, in order to create a discharge profile.
Ignition energy needs to be investigated on a more complex system in order to achieve an
accurate quotation of the minimum ignition energy. However, the more complex the
discharge system becomes; the more difficult it is to achieve a precision energy
calculation. The effects of the measurement circuit plus any possible stray capacitance,
inductance and resistance impact greatly on the energy dissipation.
1.3.1 High Voltage measurement
In order to measure directly the high voltage at discharge, a specifically designed voltage
divider bridge is required. The bridge will need high voltage rated components with
compensation capacitors in order to maintain attenuation over the discharge event. This is
due to the impulse response of the discharge requiring the voltage divider bridge to have
response from DC to 1+ GHz. To maintain the DC response, the divider needs to be
compensated and all known components included in the compensation.
Investigation found that large resistances have a reduced effect at high frequencies and
will exhibit unwanted characteristics, unless these effects are taken into account. High
frequency from the discharge will induce stray inductance and capacitance, which
introduces ringing oscillations into the discharge and significantly alters the overall
experiment circuit characteristics.
High frequency characteristic analysis found that mega ohm resistors have reduced
resistance and have additional capacitance and inductance. These effects were limited
through a component selection process for a high voltage measurement circuit, via
selection by manufacturing method/type and quality of construction. However, the stray
capacitance and inductance were still present when examined with a network analyser
creating a complex impedance profile of the components. These stray values are not only
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
1.0 Introduction
7
present in the high resistance components, but also in the cables, connections,
oscilloscope and probes. The only viable solution is to account for them in a final analysis
of the measurement circuit as an overall measurement circuit characteristic.
1.3.2 Low Voltage Discharge Simulation and Measurement
A simple experiment involving lower voltage was setup to simulate and measure an ESD
at low voltages with the aim to see the energy dissipation throughout the circuit.
Simulations of electrostatic discharges specified by IEC standards [7], set parameter such
as rise time, discharge period and discharge current. This is typically based on the
residual voltage/charge on the discharge capacitor, whereas this research examines the
voltage and current in the actual spark in order to obtain a more precise comparative
measurement of the energy dissipated. This allows us to better understand the energies in
the discharge.
Results from the low voltage experiment showed a hypothesis for energy calculation with
80-90% discharge resistor energy dissipation recorded, along with 5-15% energy
dissipation by stray resistances and 5-10% by the discharge point. This experiment has
shown the significance of stray resistance in the energy dissipation. The energy
dissipation in a discharge is dissipated through all the resistances in the circuit, including
resistors, stray resistances and breakdown potential. Leading to the conclusion that energy
dissipation in a discharge is dynamic and is mainly dissipated at the initial discharge
through any resistance as a factor of the peak current.
1.3.3 High Voltage Discharge Simulation and Measurement
From the previous low voltage investigation and experiment, a high voltage discharge
experiment and measurement circuit was designed, constructed and characterised for
calibration. Measurement circuit was simulated and analysed with respect to impedances
at high frequency, to allow characteristic to be defined for energy dissipation calculation.
Attenuated voltage is recorded and processed for calculation and analysis. Energy
calculation is done using the recorded voltage and current, to obtain at initial capacitive
energy, discharge resistor energy and discharge point energy.
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The results showed an overview of the high voltage discharge, with specific detail to
discharge voltage, initial capacitive energy, discharge resistor energy, discharge energy
and peak current. The experiment presents a functional method for investigating the
energy dissipation in high voltage discharges and ignition energy of materials relevant to
electrostatic discharge.
1.3.4 Ignition Experiment
Utilising the experiment methodology for ignition energy calculation from previous
investigation with high voltage discharge measurement, systematic experiments were
conducted to determine the minimum ignition energy of n-Pentane.
A minimum ignition energy and probability of ignition was obtained from the ignition
experiments. Lowest recorded energy for successful ignition was 0.352 mJ, with
statistical result of 0.269 mJ for 1% probability of ignition. Comparison to related work
show close agreement to ignition results.
1.4 Application and Contributions
Investigations have identified the importance of characterisation of the measurement and
experiment circuit for discharge experiments. It is a requirement by recommendation of
this research to fully characterise the circuitry before experiment so analysis can be
conducted. Three main characteristic are required to be determined and they are, 1)
component and overall resistance at high frequency, 2) stray capacitance in the circuit and
3) impedance of cabling and current shunts used in analysis.
Low voltage experiment reiterated the importance of energy dissipation in the circuit as
the energy dissipated in the discharge would never be the initial capacitive energy since
components in the circuit and stray resistances will always dissipate a significant amount
of the energy.
An experiment methodology for measuring ignition energy in a high voltage discharge
was developed. The methodology allows the calculation of the energy dissipated
throughout the circuit and thus characterises the energy in the discharge. Characterisation
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
1.0 Introduction
9
done from the analysis of the data enables the particular properties of interest to be
defined and determined.
Utilizing the developed experimental system and methodology to calculate energy in the
discharge, the ignition characteristics of n-pentane have been explored. A minimum
ignition energy and probability of ignition was obtained from the ignition experiments
with comparison to related work show close agreement.
This application of consistent theory, validated through experiments that can be used to
identify hazards in the application domain, is fundamentally new due to the lack of
accurate data of electrostatics discharge (ESD) under the specific condition of hazardous
atmosphere and will thus contribute greatly to the scientific community. The significance
of this research will be use of the experiment system and experiment methodology to
determine ignition characteristic of materials. This allows the assessment of electrostatic
hazards in order to provide guidance for the avoidance of hazardous situations.
1.5 Conclusion
Investigations have identified key points of characterisation for the measurement of high
voltage discharge and have reinforced the importance of the distribution of energy
dissipation in an ignition energy calculation. Experimental methodology to calculate
ignition energy developed for this research has been successfully used to determine the
minimum ignition of n-Pentane as a validation.
This research and experimental work has provided a basis to assess electrostatic hazards
in a variety of situations not present in the current standards and safety practices. It brings
into focus the increased importance of hazardous atmosphere and material characteristics
in electrostatic hazard analysis. Therefore, it is essential that the experiment methodology
established and verified through a systematic procedure of experiments, contributing to
the current knowledge and standards for minimum ignition energy testing and
electrostatic discharge ignition testing.
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2.0 Literature Review
2.1 Introduction
Electrostatic charge is the build-up of static electricity and an electrostatic hazard is the
potential unwanted release of that energy [15]. This energy is built up by the transfer of
charges as described by the theories of conduction, induction and triboelectricity of
electrostatics [16]. The build-up and discharge have been documented in various
standards and safety documents for the protection of electronics against damage by the
electrostatic discharge. Past research categorised the electrostatic discharges into three
main models with regards to their occurrence and electrical equivalence in an electrical
simulated circuit [7, 8, 11]. The three models are Charged Device Model (CDM), Human
Body Model (HBM), and Machine Model (MM). The release of this energy either to
ground or an oppositely charged object is what causes hazards, as in most cases this
discharge is unwanted and unintentional [15]. The usual form of release or dissipation of
static electricity is in the form of an electrical arc, which can lead to an ignition and
consequently combustion or explosion of flammable materials or fuels. This created the
need to understand the energy dissipation of the discharge in order comprehends the
ignition probability. The estimation of the total initial energy in the capacitor as adopted
in various standards is inadequate. This research will more precisely estimate the
discharge energy by measuring current and voltage while including energy lost by other
known components in the discharge circuit. Ignition energy needs to be investigated on a
more complex system in order to achieve an accurate estimation of the minimum ignition
energy. As the discharge system becomes more complex, the more difficult it is to
achieve a precise energy calculation. The effects of the measurement circuit plus any
possible stray capacitance, inductance and resistance greatly impact on the energy
dissipation. Measurement of electrostatic discharge requires a specifically designed
circuit with consideration of the high frequency response as the discharge occurs and the
ability to withstand the high voltage prior to and after discharge.
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2.2 Electrostatics
2.2.1 Charge transfer
Conduction and electrostatic induction are important basic concepts in understanding
charge transfer in static electricity. This is also the case with triboelectricity, as it
describes the charge interaction when two objects are in contact and moved so that charge
from one object is transferred to the other object, leaving one object negatively charged
and the other positively charged [16]. This effect is dependent on the contact area, the
frequency of contact, the speed of movement, the material of the objects, and the
environment.
2.2.2 Conduction
Conduction is the transfer of charges when a charged object is brought into contact with a
neutral or oppositely charged object or the ground[16]. Conduction is shown below in
Figure 2.2.1.1, where a charge object is used to conductively charge a neutral object.
(A) (B) (C)
Figure 2.2.1.1 Charge Transfer Conduction.
The above illustration shows an example of conduction. A shows a
negatively charged object and a neutral object separated from each
other. B depicts the situation where the charged object is brought into
contact with the neutral object. The difference in charge is neutralized.
C depicts when the objects are moved apart and both object become
slightly negatively charged.
2.2.3 Induction
Induction is similar except no contact is made [16]. An example is when a charged object
placed next to a grounded object. If the ground link is broken and the charged object is
removed, the originally grounded object will now be charged oppositely to the original
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Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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charged object. This is shown in Figure 2.2.1.2, where a negative charged object in
brought into close proximity of the grounded object, then the ground link is severed while
the charged object is removed, leaving the grounded object positively charged.
(A) (B) (C)
Figure 2.2.1.2 Charge Transfer Induction.
The above illustration shows an example of induction. A shows a
negatively charged object separated from a neutral grounded object.
The negative charged object is brought into close proximity, as shown
in B. The negative charged object then repels the negative charges in
the lower object to flow into the ground. As the ground is severed and
the two objects are separated, the originally grounded object becomes
positively charged as shown in C.
2.2.4 Triboelectricity
Triboelectricity is the theory of charge transfer due to of the contact of materials together
rubbing, brushing, or any other physical contact that allows charges to be stripped from
one object and stored on other [16]. These different materials form a conductive adhesion
when brought into contact and forms an electrochemical bond on the atomic level. When
the materials are separated, one material losses electrons and is left with a positive charge
and the other material gains the electrons and is left with an overall negative charge. As
shown in Figure 2.2.2.3, where two different material are rubbed or repetitive contact
resulting in electrons being striped by one material leaving one material negatively
charged and the other positively charged.
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Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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(A) (B) (C)
Figure 2.2.2.3Charge Transfer Triboelectricity.
The illustration above demonstrates triboelectricity charge transfer.
The situation in A shows two neutral objects in contact. B illustrates
the rubbing and the creation of the negative charge build and the
positive charge build up on the opposing rubbing surfaces. As the
materials are separated, as shown in C, the surfaces maintain the
opposing oppositely charges.
The table of Triboelectric series is as shown in Appendix 11.1, and it presents the
material that are more likely to be positively charge on top and down to negatively
charged material. It can be seen from the table that it is the insulative material that are
more likely to be positively charge and the conductive materials to be negatively charged.
Therefore by bring into contact or rub.
There has been substantial work done in the past in relation to the chargeability of non-
metallic materials, in particular clothing [17-19]. The Textile Institute has series
publications called Textile Progress. In particular, Volume 28, Number 1 (Electrostatic
Charging of Textile) of this series, deals directly with the electrostatic charging of textile
material and methodologies to determine charge on the material [18]. The publication
covers extensively the properties of textiles and the characteristics to determine the
chargeability of them. There are other studies which explore the chargeability of non
metallic materials for the particular application in clean rooms to limit the electrostatic
build up in electronics manufacturing and handling [18, 20]. Other work explores at the
possibility of limiting electrostatic build up with additives in the materials to promote a
Negative series material
Positive series material
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Rubbing
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higher conductivity[21]. While work has been done on the contact electrification and
conduction in polymers, where an experiment of system was designed to place charges on
polymer fabrics by conduction [22]. Other than the above articles that deal specifically
with charging of non metallic materials, fundamental principles of triboelectricity are
covered in many extensive standards and guides to electrostatics [16, 23-25].
2.2.5 Electrostatics Summary
The principles of charging a non-metallic material are well known. However, there is a
need to calculate and measure the amount of charge capable of being deposited on a
material. This need is for the protection and prevention of electrostatic hazards, as the
minimum ignition energy (MIE) of materials can be formulated from the previous area.
Minimum ignition energy is not a property in electronic and triboelectricity investigation,
the collective investigation from theory to applied experiment in recent researches ties
together the MIE and hazardousness property to electrostatic discharge [11, 12, 26-28].
As an extended application of that focus the calculated MIE can be compared to the
measured MIE of the material, to determine whether the material could be an electrostatic
hazard in a simulated situation and then extend its application to real life scenarios. In a
real life scenario, many other variables will change the electrostatic build up and
ultimately the electrostatic discharge. These variables include humidity, air, elements in
the air, temperature, pressure, and materials involved in the contact charge transfer.
Past research has provided a wealth of information in the format of standards from
International and Australian standards on the topics of electrostatic control and
electrostatic protection. These are sources of electrostatic principles and general safe
practices; however they fail to address specific areas such as the increased effects of
oxidization on the ignition energy of the ignited material and the characterization of
materials in terms of electrostatic properties of chargeability, charge retention ability, and
the quantified energy for ignition.
Two Australian standards directly address this topic; namely AS/NZS 1020:1995 [23],
and AS/NZS 61000.4.2:2002 [29]. Standard AS 61000.4.2:2002 is a direct derivative of
IEC 61000-4-2 Ed 1.2B:2001 which covers the required protection and test methods for
electrical and electronic systems. The described test method uses a High Voltage Direct
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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Current power supply to charge a storage capacitor to discharge into a test system, testing
the tolerability of the system to ESD. Since the purpose of this standard is to test the
immunity of electrical and electronic systems to ESD, it does not consider the energy in
the discharge and relations of the ESD energy to possible ignitions. However, the test
method can be adapted to test the required ESD energy for ignition, testing for the
minimum ignition energy under the specific conditions of increased oxidization.
The standard AS/NZS 1020 addresses the control of undesirable static electricity and is
presented as a comprehensive guide to the control of undesired static electricity [23]. It
covers the basic principles of electrostatics from generation of static to control of static
electricity in solid objects, persons, liquid and etc. The standard also covered general
detection of electric potentials and basics of measurement equipment for measuring static
electricity. This standard provide an inclusive view on the topic of electrostatic control,
but it does not address specific issues such as effects of increasing oxidization,
quantifying energy for ignition in everyday materials and electrostatic characteristics of
those materials in terms of chargeability, charge retain ability and energy discharged.
NFPA 77: Recommended Practice on Static Electricity [25] is the most recognised
standard on the topic of electrostatic practices in relation to fire safety. It is a concise
standard covering a very broad field including fundamental theories, static safety
practices, and the evaluation of static hazards. However, as it is a guide to the practices
dealing with static electricity, it does not address specific issues such as effects of
increasing oxidization, quantifying energy for ignition in everyday materials and
electrostatic characteristics of those materials in terms of chargeability, charge retention
ability and energy discharged. The guide does provide valuable information in the
industrial sector, with charge accumulation and dissipation in liquid or semi liquid
transfers of products. There is also information on possible conduction, triboelectricity
charge transfers in industrial applications of moving parts and charge transfer between
vehicles/large objects and ground. As with the subsequent standards that referenced this
standard, such as the AS/NZS 1020, it overlooked the fields of increasing oxidization and
the quantifying characteristics of everyday materials, such as fabric and textiles. This
creates a void in the required knowledge in our abilities to assess hazards and provide
preventative measures.
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Noteworthy British standards include BS7506-1 and BS7506-2, whereas Part 2 provides a
series of test methods to determine electrical and electrostatic characteristics, which is a
basis for further studies, experiments and adaptations to achieve applicable results [9, 24].
Similar to its counterparts in the Australian Standard (AS) and the International
Electrotechnical Commission (IEC), in regards to the information it provides and the
depth of understanding, the BS 7506 series of standards also overlooks the specific issues
referred to above.
Standards make awareness to the potential danger, but lacks in depth investigation
required for definitive analysis of ignition hazards from electrostatic discharge. Results of
more recent research and this work, present a gap in the implementation of experiment
data to application of knowledge to hazard prevention [4, 27]. Literature on electrostatic
discharge (section 2.6) and discharge energy (Section 2.7) will further explore the issue at
hand.
2.3 Human body model
IEC61340-3-1[7] Electrostatics- Part3-1 Methods for simulating electrostatic effects-
Human body model (HBM) electrostatic discharge test waveforms[7], provides a model
of simulating and experiment with ESD with regards to HBM model. The standard
provides a standardised method of testing solid state electronics in terms of testing for
immunity from ESD from human operations. It provides an excellent point of
investigation as it provided current waveforms as to the ESD, as well as a method for
measurement. Current measurement described is to apply consistence to a human body
model discharge, with which the test would be repeated for a Device Under Test (DUT).
Expected current waveform for a no load and 500 Ω load were presented in the standard.
Although limited in the data that is drawn from this method of current measure of ESD, is
nonetheless an important stepping-stone in the investigation.
The Human Body Model is the most applicable model to this research in regards to
ignition probability and hazards. The standardised HBM model provides a basis for
experimentation and the defined variables allows measurement to be better defined. As in
consideration the added complexity of the discharge circuit due to addition resistance
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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reduces the effect of the stray resistance to the energy dissipation, HBM represents the
best consideration for ignition as the most unpredictable element is human contact.
The general consensus in the knowledge provided by the standards mentioned above is
that fundamental and general preventative and protective measures need to be provided,
and forming a basis for further studies and experiments in specified areas. However the
yet to be explored areas of increasing effects of oxidization on the ignition energy and
materials, and characterisation materials in terms of electrostatics properties of
chargeability, charge retention ability and the quantified energy for ignition greatly
identifies the void in the required knowledge in order to conduct quantifiable analysis
with respect to the specified materials.
2.4 Charged Device Model
The Charged Device Model (CDM) is the standard in integrated circuits (IC) intrinsic
testing. It is defined by the fast transient response on the order of nanoseconds and high
current due to lack of resistance. It is a simulation of pure capacitive discharge of the
charge stored by triboelectricity through manufacturing and handling.
Capacitance values ≤300 pF are used in the standard CDM ESD testing. The IC device
subject to testing is tested through its pins with the charges in the capacitance ≤1 kV. For
IC intrinsic testing, the procedure is for the IC device to be discharge 6 times with 3
positive and 3 negative charges. The residual charge is drained away to ground by a
ground plan with 1MΩ resistance.
The standard JESD22 provides an established test method for CDM ESD testing [8]. This
test is similar to ANSI/ESDA STM5.3.1 and AEC-Q100-011 [[9, 30]. JESD22 is the test
method for the evaluation of all packaged semiconductor components, thin film circuits,
surface acoustic wave components, optic-electronic components, hybrid integrated
circuits, and multi-chip modules of any of the above types of components. The testing
discharge is specified by the conditions voltage 100-2000 V, with rise time less than 400
pS, and compliance to the CDM current waveform as given below as an extract from the
stand [8].
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Figure 2.4.0.1CDM Current Waveform
Plot of a generic CDM current waveform denoting the rise time (Tr),
the 50% Ip undershoot (U-), the 25% Ip overshoot (U+), and the peak
current Ip ©JEDEC[8]
This model for ignition research utilises a less complex discharge circuit. The difference
of resistance in comparison to the HBM has a significant effect on the discharge
waveform and thus the energy dissipation. The absence of resistance unrestraint the
current flow and introduces stray resistances from cable, wires and circuit set up, that will
affect the energy dissipation as discharge occurs. Repeatability in testing with this model
would concern energy dissipation in the great uncertainty in the calculation of energy
dissipation due to the exact length of cable, exact thickness, and how cable actually lies
on the table. The energy calculation can be conducted with the assumption that the
measurement circuit will not impact greatly on the discharge circuit.
2.5 Machine Model
Machine Model is used to test electrical components that are prone to possible damage
from electrostatic build up and discharge in the production process. It simulates the
possible triboelectric effect of charge transfer onto a capacitive median for storage and
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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discharge with no resistive component. JESD22-A115C [11] provides a method for
testing with MM as with ANSI/ESDA STM5.2 [31] and AEC-Q100-003 [32].
Standard testing involves charging a capacitor up to 300 pF to voltages up to 400 V,
before switch discharging through the Device Under Test (DUT). Initially the discharge
needs to be calibrated with a 500 Ω resistor to give a underdamped oscillatory pulse as
shown in the extract from the stand as below in Figure 2.5.0.1 [11].
Figure 2.5.0.1 MM Current Waveform
Plot of a MM current waveform 500 Ω taken from an example
calibration where the peak current (Ipr) is shown in amperes and time
in nanoseconds ©JEDEC [11].
Similarly with the Charged Device model (CDM), the Machine model (MM) neglects the
energy aspect of the discharge. The focus of the test method is to test for intrinsic safety
for electronic component by simulation discharge of Triboelectric gained charges in an
experimental method. Energy is not considered and only peak current and current
waveforms are considered.
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2.6 Electrostatic Discharges as an Ignition Hazard
Electrostatic discharge hazards are well documented with the majority of investigation
deriving from the engineering of electronics and the electronic manufacturing industry.
Electronics are easily damaged when exposed to an ESD; therefore there is a great
amount of literature on the prevention, elimination, and protection of ESD in electronic
design, manufacturing, and use [33-35]. However, the research herein focuses on
electrostatics as a cause of accidents like the work of Taillet et al. [36]. Taillet et al
studied at great detail to find the possible cause of 3 major accidents and concluded that
electrostatic hazards was the most probable cause in all 3 cases.
As with all forces, the fundamental understanding of electrostatics by Masuda et al. has
lead to great inventions and applications [37]. Electrostatics is currently used in
applications ranging from droplet control in inkjet printers, electrostatic precipitators to
remove pollution, to force discharges to create plasma chemical effect to remove toxic
waste. In agreement with Castel et al. agrees with Masuda that the applications of
electrostatics are numerous and evolving.
The study of electrostatic hazards has gained greater importance in research in the last 50
years, as we began to understand the potential and potency of ESD. Gibson et al.
identified the lack work that defines the incendivity of discharges from non-conductors
consisting of solids, powders, or liquids and has lead to vast research in this area [38].
There have been a number of studies of the ignition probability of an ESD that exhibit a
broad range of variables. Wilson et al. explains that ignition of natural gas depends on the
following three factors: (1) the fragmentation of the discharges into discrete sparks, (2)
the loss of energy to the body resistance, and (3) the quenching effect of the electrodes.
The view that the loss of energy to the body resistance is shared by Butterworth et al. in
works that studied the incendivity of electrical discharges between planar resistive
electrodes [39]. Butterworth et al. determined that a resistance of 100 MΩ dramatically
decreased the possibility of ignition. Other ignition variables identified by Bailey et al.
include humidity and the container properties in studies conducted in power silos. The
test silo facility was described in detail and results from the experiments showed the
electrostatic potential built up as the experimental material was poured into the silo.
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Furthermore, there were numerous discharges as an earthing probe was inserted into the
silo. Although the discharges were not sufficient to ignite the material, they do have the
potential to ignite other materials such combustible fuel. Bailey’s article has shown that
there is a need to develop a procedure and system to determine the minimum ignition
energy (MIE) of particular materials under various environments and scenarios. This is
the focus of this research. There also is a greater need to develop this standard with
regards to ignition in saturated oxygen, pressurised oxygen, non metallic materials, and
unstable combustible atmospheres (inert conditions).
Substantial research has gone into investigating hazards arising from an ESD in an
environment where the MIE has been lowered. This arises from the amount of charge that
can be built up on materials and has lead to instances where ignition and combustion has
not previously occurred. This area examines a potential hazardous environment, where
the introduction of an additional fuel has lowered ignition energy. This is important in the
correlation to the work of Bailey et al. in the area of powders in silo as well as hazards in
dust, flammable gas conditions, flammable vapours, mist [40-42].
In regards to protection, Wilson et al researched the ignition of natural gas via spark
discharges from the human body where it was found that some ignitions are prevented by
increasing the resistance in the human body.
Electrostatic Discharge (ESD) as a hazard is a substantial claim; however a clear regime
has not been identified or established quantifying the hazardousness of ESD. The
understanding of the discharge energy and in particular the energy dissipated is
paramount in order to assess the ignition energy of materials and hazardousness. Thus
identify ESD as a hazard and ignition source under various conditions.
2.7 Discharge energy
The need to better understand the energy dissipated in the discharge has become apparent
with the limited research present in this particular area of Electrostatic Discharge (ESD).
The acknowledgement of the discharge profile, that is dependent on the discharge circuit
configuration, is paramount in the research to determine ignition energy. The
hazardousness of an ESD need to be quantified through the investigation of the discharge
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energy. Through the investigation of discharge energy we can develop a model and
hypothesis for ignition probability of flammable material and fuels. This model can also
reflect the energy lost in other parts of the simulation and present an estimation of the
actual discharge energy. This discharge energy then can be used for development of the
MIE of particular materials with specific to atmosphere and environmental conditions.
There have been extensive publications on the calculation and experimental measurement
of minimum ignition energies [13, 43]. However, these experiments have only dealt with
gases and fuel, where parameters such as the composition of gases, temperature, pressure
and enthalpy of the gases are known. These parameters play a major role in the
determination of the MIE. Outside of this body of work, there is a large gap in the
knowledge for the determination of the minimum ignition energy of materials through
electrostatic discharges.
There are a number of references that explore the minimum ignition of materials and
protection and prevention codes of practices of ESD. These include standards explored in
Section 2.2.3, and they provide a general description on the principles of electrostatics,
and the preventative and protective actions.
Lower energy for ignition of materials from ESD was investigated. These include
ignitions in oxygen, fuel environment, and the combination of the two. From the many
minimum ignition experiments and projects, only a few target the presence of the addition
of oxygen and its effect on the minimum ignition energy. The groups of interest in this
field are predominantly within Aerospace organisation such as NASA and the medical
health industries where hyperbaric chambers are used [44]. Smith et al. presented results
for spacesuit materials that went under extensive testing for the possible ignition due to
arcing of electrical wiring within the spacesuit [45]. It was shown that for given current
and voltage settings, materials used in spacesuits could readily ignite in the abundance of
oxygen. Other published work presents the importance in the of amount of energy, and
provided improvement to the calculation of actual energy dissipated in the electrostatic
discharge [25, 43, 46, 47] .
The focus of NASA’s investigation was to determine if the spacesuit materials would
ignite from exposed wiring and electrical arcing at levels present within the spacesuit
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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without quantification of the MIE [45]. Unfortunately, this study did not address the
lowest possible energy under which the test material would ignite and the atmosphere.
The experiment was operated under the assumption that there is continuous discharge and
that the electrical system would continue to provide power for an extended period of time
until a definitive ignition or no ignition has been recorded.
Ono et al. discusses the minimum ignition energy of hydrogen air mixture [4]. This was
an important aspect of research as hydrogen requires only a hundredth of the minimum
ignition energy of hydrocarbons. It was concluded by Ono that the residual energy in the
capacitor was insignificant as compared to the calculation of the overall energy. This can
also be done for the discharge resistance, so that the energy equation becomes:
Es = Ec − Er − Eresidual, (Eq. 1)
Ec is the energy in the discharge capacitor, Er is the energy dissipated in the discharge
resistance, and Eresidual is the capacitor residual energy.
The increasing use of oxygen in our daily lives from industrial applications, medical
applications to individual activities have placed a focus on the specific topic of discharge
energy. Electrostatic build up in our bodies are correctly assumed not sufficient to ignite
material that one might come into contact with in everyday life. However, the presence of
abundant oxygen changes the ignition energy requirement and hence further study to
avoid incident of hazards and accidents is demanded.
2.7.1 Capacitive Energy
Fundamentals of electrostatics are based upon the interactions of subatomic particles
consisting of a proton, neutron, and electron. Protons have a positive charge, while
electrons have a negative charge. Neutrons are neutral and thus are not important here.
Charges are measured in coulombs, C, which is 1 Ampere Second (As), and is used to
express a single electron’s or proton’s charge as ±1.608e-19
C. As like charges repel and
unlike charges attract, the force of the attraction or repulsion is expressed by Coulomb’s
law,
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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= 124 ∙
(Eq. 2)
where permittivity is given by orεεε = , Q1 and Q2 are charge 1 and charge 2
respectively, and r is the distance between the two charges. The applicability of
Coulomb’s law is limited to point charges. For a charge that experiences a force over a
region, Coulomb’s law can be rearranged to give the field strength E,
=
(Eq. 3)
=
(Eq. 4)
and thus,
= 4 ∙
(Eq. 5)
Gauss’ law applies the concept of electric flux and the assumption that the net flux of the
electric field equals the charge inside a closed surface,
Φ = ∙ = ∙ ! =
(Eq. 6)
This is the general equation used to calculate effects of charges in a typical numerical
analysis. The application of this equation and the derivative of the equation allows for the
estimation of the potential energy via discharge at a particular voltage potential across
two objects.
As simple model of parallel plates, gives an expression for;
= "
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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(Eq. 7)
which can be applied to the equations ;
# = $ , $ = # = ∮ ∙ & ∙ '
(Eq. 8)
to find the capacitance of the parallel plate model. With a calculated capacitance and a
known voltage the energy stored can be calculated by:
( = 12 $ ∙ #, # = 1$ ) ∙ *
(Eq. 9)
2.7.2 Energy Dissipation
Energy dissipation calculations rely on accurately measure the energy in the discharge
and the form of discharge (electrostatic discharge). Electrostatic discharges are low
energy discharges due to the circumstances in which the energy is discharged and
dissipated. The HBM models the human body into electrical components of capacitance,
inductance and resistance. These electrical components define the waveform in which the
discharge occurs and how the energy dissipated. Due to the extremely small time constant
in the equivalent circuit because of the low capacitance, the duration of an electrostatic
discharge is estimated to be about 10 ns. As charges build up on an object, the
potential/voltage of the object rises until a breakdown occurs.
# = $
(Eq. 8)
This breakdown occurs due to the weakness in insulation in air or the environment in
which the object is in. The breakdown voltage in air is 33kv per cm, which refers to the
voltage at which an arc will spark over the gap. From Ohm’s law, by increasing the
resistance the current flows at discharge would decrease [39]. It was shown by
Butterworth et al. that by increasing the resistance to 100 MΩ, it was possible to avoid
ignition in a grain silo. A large resistor, in which discharge occurs through, would provide
a low current and also a large time constant in which the built up energy in the capacitor
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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is dissipated. This is consistent with the finding of Ono[4], where Ono. concluded that in
the case of an ESD in a mixture of hydrogen and air that larger resistance values requires
a higher initial voltage in order to have an ignition. The delivery of the stored energy is a
factor in the ignition process and in the numerical calculation of an electrostatic build up
and discharge.
2.8 HV measurement
Direct measurement of high voltage requires rated components in a resistive voltage
divider. The principle involved is discussed in detail in High Voltage Measurement
Techniques by Schwab [48]. The use of a pure resistive voltage divider bridge creates
uncertainty in the measurement when a discharged is involved. The impulse effect of the
discharge affects the resistive divider as a high frequency distortion which then affects the
ratio of the divider. In order to retain accurate measurement, both Schwab and Douglas
suggested capacitive compensation to resolve high frequency effects [48, 49]. Ideally, the
ratio of the resistive voltage divider is retained in the compensation of capacitors, thus
allowing the time constant in each of the Resistor/Capacitor (RC) to remain the same.
2.8.1 Resistive Voltage Divider
In order to directly measure high voltage, a resistor bridge can be built allowing an
overall rating of the bridge to match or exceed the expected measured voltage. Neglecting
stray inductances and capacitances, it is expected that the ratio of the measured section to
the overall bridge to remain consistence throughout the measurement, as shown in Figure
2.8.1.1 where R1 and R2 are in series.
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Figure 2.8.1.1 Resistor Voltage Divider
Schematic voltage divider bridge with ratio of 1000:1 whereas resistor
1 (R1, 1,000 MΩ) and resistor 2 (R2, 1 MΩ) are in series.
The resistance of R1 is much greater than R2 in order to decrease the potential due to
resistance. The attenuation of the resistor divider is given by:
+ = ,1 + ,2,2
(Eq. 10)
Extremely large resistances are required in order to achieve step down voltage
measurement for the experimental voltage of 30kV.
2.8.2 Capacitor compensation
Due to the fast transient effect during an ESD, the large resistances used in the resistive
voltage divider bridge will exhibit an unexpected response as high frequency effects the
resistances. The resistors will exhibit stray capacitance and inductance phenomena at high
frequency. The phenomena are dependent on the design, construction, and quality of the
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resistors and capacitor compensation is required to limit their effects. This can be
achieved by coupling additional capacitor to the resistor bridge as shown in Figure 2.8.2.1.
The attenuation at high frequency levels in DC can be derived from the resistor values.
While high frequency levels, the attenuation would become a capacitive division equation
with the large resistance exhibiting stray capacitances that are coupled to the larger
known values of capacitors 1 and 2 (C1, C2).
Figure 2.8.2.1 Capacitor Coupled Voltage Divider.
Schematic of a resistive voltage divider bridge with capacitors C1 and
C2 coupled to maintain the resistive ratio of 1000:1.
Thus the equation becomes;
+ = $1 + $2$1
(Eq. 11)
and then the equation from the frequency dependence becomes;
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+ =,11 + ./,1$1 + ,21 + ./,2$2,21 + ./,2$2
(Eq. 12)
In the DC regime, only the resistive part of the bridge exhibits the steady state attenuation
of:
+ = ,1 + ,2,2
(Eq. 10)
Ideally R1, R2, C1 and C2 are selected to match the following equation in order avoid
overcompensation or under-compensation. The equation for the attenuation characteristic
is given by;
,1,2 = $2$1
(Eq. 13)
and in terms of the time constant characteristic is given by:
,1 ∙ $1 = ,2 ∙ $2
(Eq. 13)
The voltage divider bridge should maintain DC characteristics in the high frequency
domain thus allowing for accurate measurements to be made. The capacitor compensation,
the selection of capacitor and resistors to these ideal equations must be considered in the
design of the voltage divider bridge in order to accurately measure an ESD.
2.8.3 Oscilloscope
In order to achieve accurate measurements, the internal workings of an oscilloscope need
to be investigated. This must be done in order to compensate for the oscilloscope’s
interference in the measurement circuit. Figure 2.8.3.1 shows the internal arrangement of
components that make up the standard 12-16pF capacitance and 1MΩ resistance in a
standard oscilloscope.
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Figure 2.8.3.1 Oscilloscope Schematic
Schematic of a typical Oscilloscope depicting the input signal and resistor in series to sum to 1 MΩ ©HAMEG [50]
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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The configuration suggests that the capacitor and resistor are in parallel to the input signal
and the resistors are in series that create 1MΩ and allowing further reduction of the signal
voltage.
The internal 1 MΩ resistance of the oscilloscope is to be taken into account in the design
of a voltage divider bridge in order to reduce the voltage and maintain correct resistive
ratio (for this assessment: 1,000:1). The additional capacitances from the oscilloscope
will accumulate thus contributing to overall capacitance to be compensated. These
capacitances include capacitance in the probe, internal capacitance and stray capacitances.
The effect of the addition of the oscilloscope should be maintained at 16 pF, thus limiting
the probe compensation to 16 pF for the 1,000:1 ratio.
2.8.4 Discussion/conclusion
The complexity of circuit required to compensate each addition measurement component
grows exponentially with the accuracy of measurement required. Each component needs
to be characterised with respect to stray capacitance, inductance and frequency response.
Then the overall characteristic needs to be assessed with consideration of each individual
component. Full analysis is in the following Chapter 3 (High Voltage Measurement),
where component are assessed in regards to high frequency characteristics.
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3.0 High Voltage Measurement Review
Through preliminary experiments and literature, it was concluded that high voltage
discharge measurement is a challenge at best. Various effects from the fast response of
the discharge combined with the high potential at discharge make accurate measurement
difficult. From NFPA 77 [25] electrostatic build up can achieve hundreds of thousands of
volts with breakdowns/discharges occurring as voltage reaches ~30 kV per cm in air. Due
to this high voltage, measurement requires a specialised circuit, in which voltage recorded
become a fraction of the voltage measured. A simple resistive voltage divider with high
voltage components stepping down the voltage would be sufficient to measure the high
voltage at discharge. However, the transient effects of the discharge alter the expected
response of a resistive divider, and would require complex circuitry and modelling to
accurately derive the expected response. Thus a review of component and circuit to be
used in a high voltage experiment and measurement need to be review and analysed for
their effects at discharge.
3.1 High Resistance High Voltage-Voltage Divider
High voltage measurement requires specialised equipment in order to obtain an accurate
measurement. High voltage components are required to achieve this. Previous work by
Ryo Ono[4], describes the use of a high voltage high resistance voltage divider bridge to
measure the steady state voltage of the charging circuit. The voltage divider used a high
voltage high resistance resistor of 1 GΩs in series with a 110 kΩ resistor to achieve a step
down voltage reading of 10,000:1 of the actual voltage. At this ratio, the voltage recorded
would be in the vicinity of 1-3 V if the breakdown voltage was 10-30 kV. This means that
measurements are more difficult at low voltage values. The large ratio will minimise the
actual voltage to the point where a reading is not distinguishable from the background
noise. Adopting the principle used to measure high voltage, the ratio was lowered to
allowing comparable testing at lower voltages. Lowering the ratio not only benefits in the
scaling data collected, but also allows easier differentiation of signal to noise. The ideal
ratio is 1,000:1, where expected input of to the oscilloscope is then 0-30 V from 0-30 kV.
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There are a number of methods to construct the high resistance voltage divider, where the
main difference is the type of resistor used. The main types of resistors are Carbon
Composite, Wire-wound and Film [51]. The required criteria for the High Voltage High
Resistance Bridge are voltage rating up to 30 kV and resistances able provide to ratio up
to 1,000:1. To achieve this either a large number of lower rated component can be used in
series to provide the required rating or the preferred one or two components to provide
the rating and the voltage division. This is due to the fact that connections from 100 or so
component will become significant and induce possible stray capacitance and inductance
to the measurement circuitry. It is possible to compensate for the stray capacitance but it
is ideal to limit when appropriate. Stray inductance is to be avoided as inductance will
induce an oscillatory ringing effect which will require addition resistance to damp out,
adding further unnecessary complication to the measurement circuit.
Carbon composite resistors are made from carbon and ceramic dust moulded into solids
with the ratio of carbon to ceramic determining the resistance [51]. The quality of
manufacture will determine the stray capacitance and inductance. This method of
manufacture possesses the best possible method in limiting stray capacitance and
inductance. This is due to the presumed consistency in the resistance through the
component and because it’s made to a single conductive object with a simple path for
current flow. The limiting factor is the resistance and voltage rating achievable through
current technology in carbon composition manufacture[52]. Mega-ohm resistance in Kilo-
volt rating in carbon composite resistor are not possible or not readily available.
Wire wound resistors are constructed from conductors/wires wound on a solid insulator
usually in a spiral helix form [51]. Wire wound resistor provides the highest wattage
rating due to this construction. High wattage rating allows high peak current in operation.
However, this winding construction also induces a significant amount of induction which
is unavoidable even with the best non-inductive conductor/wires in the winding.
Therefore is it not suitable for the fast transient response of an ESD, as the stray
inductance from the resistor will induce a significant oscillation ringing to the discharge.
This can be overcome by damping with additional resistors, but the additional resistor
will further complicate the discharge circuit.
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Film resistor are made by depositing a thin film of conductive material on to a insulator
solid then laser etched to provide required resistance [51]. Due to this construction, film
resistors have less stray inductance compared to wire wound. They also have large
resistance range and lower tolerance. Specially designed film resistors are able to achieve
GΩ resistances with kV ratings, making them suitable with one limitation. This limitation
is the stray inductance, which can be reduced with better quality resistors. Ideally, the
resistor can be manufactured with thinner layer of film allowing less stray inductance.
This holds true as technology advances, allowing higher quality resistors to be
manufactured.
In selecting the resistors for the high resistance high voltage divider bridge, the factors in
consideration are the stray capacitance, stray inductance, resistance value and the voltage
rating. Stray capacitance and inductance need to be limited through the type of resistor
construction. Resistor selection needs also to be in consideration of the feasibility of
achieving the resistance value and voltage rating. For example, it is possible to use 1,000
shunts to achieve the required voltage rating and voltage division. However, the cost and
connection of each shunt will induce more stray capacitance and inductance, rendering it
less applicable for the experiment Resistances needed are as described in Chapter 2.8.2
and they are 1 GΩ and subsequent 100 MΩ and 2 MΩ.
To bring the discharge voltage into range for measurement with a oscilloscope, an
attenuation of 1000X is required as the maximum expected voltage from discharge is 30
kV and the oscilloscope have a standard 30 V input. The internal impendence of the
oscilloscope is 2 MΩ, and thus the high voltage side requires a 2 GΩ resistance or greater
to achieve 1000X.
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Figure 3.1.0.1 High Voltage Resistive Divider
The figure shows the high voltage resistive divider with 2GΩ
resistance in the high voltage side dropping 99.8% of the overall
voltage. The lower side is a 2MΩ estimation of the approximate
impendence of measurement equipment.
The high voltage resistive divider shows an example of the values required to meet the
measurement guideline. Further compensation is required to include the effect of the
measurement equipment into consideration.
3.2 Frequency Response of Resistive Divider
Due to the fast transient response of an ESD, the frequency response of the voltage
divider needs to be investigated. At steady-state or relative DC-state the expected
response of the high voltage divider is as it is expected. However, when recording the
discharge waveform, the fast response causes the high voltage divider to respond
unexpectedly. From the chosen resistors investigation is needed to determine their high
frequency response.
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The Ohmite Mox series resistors are a thick film resistor [53], they are able to provide the
resistance and voltage rating for the simulation of ESD. The Ohmite MOX 108 resistors
are 1 GΩ, 20 kV rated with stated capacitance of 0.6 pF. The capacitance was confirmed
with a LCR meter at 1 kHz with measurements of 0.6-0.7 pF. The lower values at 100
MΩ and 2 MΩ did not register a value beyond noise signal.
To further examine the resistors at higher frequency, for stray capacitance and response, a
network analyser was used. The analyser used was a Rohde & Schwarz ZVL Network
Analyser 9 kHz-6 GHz [54]. Utilizing the network analyser’s feature of analysing the
return signal, the results of a S11 Linear Magnitude plot of impedances is shown below.
S-parameter measurement are the basic measurement method for a network analyser, they
provide the resulting signal that is reflected or transmitted through a device under test
[54].
Figure 3.2.0.1 1GΩ Frequency Response of Resistive divider in Linear Magnitude
Ω
Plot of the S11 analysis from the network analyser showing the
frequency response from 9 kHz to 6 GHz in linear magnitude Ω.
y = 8682.6x-0.226
R² = 0.0701
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
0.E+00 2.E+08 4.E+08 6.E+08 8.E+08 1.E+09
Lin
ea
r M
ag
nit
ud
e,
Ω
Frequency, Hz
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The above plot of the 1 GΩ resistor frequency responses shows the drop from1 GΩ
magnitude almost immediately after DC and at the lowest measureable frequency of 9
kHz the magnitude has decreased to 6,500 Ω, effectively reduces the resistor to non
operation past 9 kHz. Using the cut off frequency equation,
01 = 12 ∙ ∙ , ∙ $
(Eq. 14)
01 = 12 ∙ ∙ 1S ∙ 0.7D = 227VW
which gives a theoretical cut off frequency at 227 Hz using the manufacturer’s datasheet
[53]. This is consistent of the results, as past 227 Hz resistance will drop inverse
proportionally towards 0 Ω.
Similar results were recorded for 500 MΩ and 100 MΩ resistors of the same
manufacturer. The plots for the 500 MΩ and 100 MΩ are in Appendix 11.2 and 11.3
respectively.
From the frequency response results it is not possible to achieve accurate results with the
resistor divider as the performance of the resistor deteriorate immediately after DC at 227
Hz and have reduced to 0.00065% of the original 1 GΩ by 9 kHz.
3.3 Equivalent Capacitor Voltage Divider
In order to achieve a flat response from all frequencies from DC to 1 GHz, the resistive
voltage divider needs to be paired with a capacitive voltage divider. Referring to chapter
2.8.2 (Capacitor Compensation) and continuing with the example of High voltage
resistive from Chapter 3.1 (High Resistance High Voltage-Voltage Divider), the best
option is a compensated voltage divider. In order to maintain the same attenuation the
capacitance were chosen to be 10 pF and 10 nF. Figure 3.3.0.1 is the schematic of the
voltage divider.
To investigate the capacitive effect of the voltage divider, the sections of the divider were
analysed. Using the network analyser, the imaginary component of each section’s can be
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plotted and capacitance calculated. The capacitance can be derived from the capacitance
reactance equation.
21 = −.2 ∙ ∙ 0 ∙ $
(Eq. 15)
Where f is the frequency and Xc and C are reactance and capacitance respectively. Since
capacitance is of interest here, only negative imaginary figures are of importance, they
will replace R in the frequency equation. Thus the equation becomes,
$ = −.2 ∙ ∙ 21 ∙ 0
(Eq. 16)
Using this capacitance equation, the capacitance as a frequency dependant can be
calculated and used for the voltage divider analysis. This method to evaluate the stray
capacitance can also be use to evaluate the overall capacitance of the voltage divider.
Results from the evaluation will allow a more precise measurement when attenuation and
measurement value is taken into consideration.
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Figure 3.3.0.1High Voltage Capacitive Resistive Divider
The figure shows the example of resistive divider from Section 3.1
compensated with C1 and C2 to maintain attenuation of 1000X and
increases frequency performance from 227 Hz. C1 and C2 are 10 pF
and 10 nF respectively.
3.3.1Resistor-Stray Capacitance Evaluation
The Ohmite MOX 1 GΩ, 500 MΩ and 100 MΩ resistors were evaluated for their stray
capacitance at high frequency using the method described in the previous section. Plot of
the capacitance over frequency is as shown in Figure 3.3.1.1, where only the capacitance
is plotted and mean of the plot calculated. From the results, the mean stray capacitance
for the 1GΩ resistor is 4.15 pF.
The plot for 500 MΩ and 100 MΩ are shown in Appendix 11.4 and Appendix 11.5. The
mean stray capacitances calculated are 4.95 pF and 5.6 pF, respectively for 500 MΩ and
100 MΩ
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Figure 3.3.1.1 Plot of 1GΩ Stray Capacitance Over Frequency
Plot of 1 GΩ resistor’s stray capacitance as evaluated over frequency
from 9 kHz to 1 Ghz. Capacitance value in F. Mean is calculated to be
4.15 pF
From the stray capacitance evaluation of Ohmite’s MOX series resistors, it is apparent
that further analysis is required for the final voltage divider. The results of 4.15 pF, 4.95
pF and 5.6 pF, for 1 GΩ, 500 MΩ and 100 MΩ were larger than expected and will affect
the attenuation of the voltage divider at high frequencies.
Table 3.3.1.0.1 Table of Stray Capacitance Results
Resistor Capacitance at high
frequency
1 GΩ 4.15 pF
500 MΩ 4.95 pF
200 MΩ 5.6 pF
0
2E-12
4E-12
6E-12
8E-12
1E-11
1.2E-11
0.00E+00 2.00E+08 4.00E+08 6.00E+08 8.00E+08 1.00E+09
Ca
pa
cita
nce
, F
Frequency, Hz
Mean=4.15E-12
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3.3.2 High Voltage Capacitive Resistive Divider -Stray Capacitance Evaluation
Evaluation of the combined capacitive and resistive component for the voltage divider is
required, as the effects of stray capacitance from the resistive components are larger than
expected. 2 GΩ with 1 pF were tested in regards to capacitance at high frequency. The
mean capacitance was calculated to be 5.85 pF and the Plot of the 2 GΩ/1 pF is as shown
in Figure 3.3.2.1.
Figure 3.3.2.1 Plot of Coupled 2GΩ/1pF Capacitance over Frequency
Plot of capacitance of 2 GΩ coupled with 1 pF evaluated over
frequency from 9 kHz to 1 GHz. Capacitance value in F. Mean is
calculated to be 5.85 pF
Additional coupled sections were evaluated and the results are as follows. For the 200
MΩ/10 pF, the resultant capacitance over frequency is 73.5 pF and the 2 MΩ/220 pF
coupled section 452 pF. Plot for 200 MΩ/10 pF and 2 MΩ/220 pF are in the Appendix
section, Appendix 11.6 and Appendix 11.7
The expected value of the coupled 2 GΩ/1 pF section is 3.075 pF, compared to the
evaluated value of 5.85 pF which is a 90% increase. For the two couple sections
evaluated 200 MΩ/10 pF and 2 MΩ/220 pF, the results are 12.8 pF to 73.5 pF, 474%
difference and 220 pF to 452 pF, 105% difference.
0
2E-12
4E-12
6E-12
8E-12
1E-11
1.2E-11
1.4E-11
1.6E-11
1.8E-11
0.00E+00 2.00E+08 4.00E+08 6.00E+08 8.00E+08 1.00E+09
Ca
pci
tan
ce,
F
Frequency, Hz
Mean=5.85E-12
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Table 3.3.2.0.1 Table of Evaluated Capacitance Results
RC pair Capacitance
2 GΩ/1 pF 5.85 pF
200 MΩ/10 pF 73.5 pF
2 MΩ/220 pF 452 pF
The capacitance of each evaluated coupled sections were significantly larger than
expected at high frequencies. The effects of this will need to be taken into consideration
when calculating the final attenuation for measurement calculation. This will have a
major impact on the measurement and will require each section to be tested in the final
design of the measurement circuit.
3.4 Oscilloscope Calibration
The oscilloscope is designed to match a probe of defined amount of resistance and
capacitance. This design is able to take that into account and correct for the true value of
the resistance and capacitance. A standard oscilloscope has a set internal resistance of 1
MΩ and an internal capacitance of up to 20 pF. This internal characteristic combined with
the measurement probe characteristic will create a significant error if not compensated
properly.
Standard probes 1X are terminated with a 50 Ω resistance with the cable contributing
additional 50 Ω and about 75 pF to ground. The oscilloscope is tuned to accept the
specifications of the probe and the capacitance can be trimmed to give a flat attenuation
to the frequency response. The simplified equivalent circuit is as shown in Figure 3.4.0.1.
This is the same for a 10X probe, where in addition to the terminating resistance and
cable capacitance and resistance, the probe also has a 9 MΩ resistor and ~10 pF in the
head of the probe. This allows an attenuation of 10X to be established with the 1 MΩ
internal resistance and ~90 pF cable plus internal capacitance. This allows the
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oscilloscope to operate to higher frequency with DC response. The simplified equivalent
circuit is as shown in Figure 3.4.0.2.
Figure 3.4.0.1 Schematic of 1X Probe and Oscilloscope
Figure of 1X probe and oscilloscope, with equivalent components as
drawn. C1 and R1 are internal capacitance and resistance of the
oscilloscope. C2 and R2 are the probe characteristics, cable
capacitance and resistance, and terminating 50Ω resistor
Figure 3.4.0.2 Schematic of 10X Probe and Oscilloscope
Figure of 10X probe and oscilloscope with equivalent component as
drawn. It has the 1X probe configuration of C1 and R1 internal
capacitance and resistance of the oscilloscope, and C2 and R2 are the
probe cable characteristics. The addition components are the probe
head with C3 and R3 at 10 pF and 9 MΩ to give the 10X attenuation.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
3.0 High Voltage Measurement Review
44
Using the Figure 3.4.0.1, it is possible to design the measurement circuit with
consideration to the oscilloscope. This will entail design considerations from frequency
response, attenuation, voltage ratings to input characteristic to the oscilloscope.
Component selection will be a key issue to complete this measurement circuit and
compensated it with regards to the oscilloscope.
3.5 Current Measurement
Current can be measured by using a small resistance in the discharge path. Using ohm’s
law current is given by
# = ) ∙ X, ) = #X
(Eq. 22)
A 0.1 Ω was to be used in the discharge return path to record the current flow during
discharge. The resistor along with cable and connection was evaluated using a network
analyser to record the frequency response in regards to impedance. The impedance
analysis of the section showed a varied response from 9kHz to 1GHz. The response is
split into 3 band for analysis and means for each band calculated. The low frequency band
is from DC to 200MHz where discharge has past the initial breakdown and has been
establish for some time. The calculated mean is 0.69+.972iΩfor the low frequency band.
The medium frequency band is from 200MHz to 500MHz and it occurs in the time period
immediately after breakdown and could contain continuous arcing period of the discharge,
with low distortions from breakdown or break off of arcing. The calculated mean is
0.50+4.20i for the medium frequency band. The initial breakdown is show as the high
frequency band with expected frequency at 500MHz and spikes of up to 1GHz. The high
frequency band has a mean calculated at 9.20+1.5iΩ. The response of the current
measurement section is show in figure 3.5.0.1, with frequency band showing means of
each band. This analysis has effectively banded the response of the component into
smaller frequency band in regard to the assumed characteristics of an electrostatic
discharge. The bands are the initial breakdown in high frequency, medium frequency
where arcing has been established and low frequency as arcing continues and breaks off.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
3.0 High Voltage Measurement Review
45
From the mean value of the current measurement section, a characteristic of the current
measurement section can be recorded when used in combination with a compensated
oscilloscope and probe.
The increase in impedance as frequency increases in cable is described in various
literatures [55-57]. The 10 cm cable forming part of the current measurement section has
a profound effect on the overall characteristic and must be taken into consideration when
used for calculations.
Figure 3.5.0.1 Plot of 0.1Ω Current Measurement Section over Frequency
Plot of impedance of the current measurement section as evaluated by a network
analyser over frequency 9 kHz to 1 GHz. Impedance in Ω Ohms shown in 3
bands, Low, Medium and High Frequency Bands, with their respective means
0.69+9.72iΩ, 0.50+4.20iΩ and 9.20+1.53iΩ. Real values in red and imaginary
values in blue
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
3.6 Discharge Resistor High frequency Response
46
3.6 Discharge Resistor High frequency Response
The discharge resistor is assessed for high frequency response due to the possible effect
of high frequency deteriorating the resistance value. Figure 3.6.0.1, is the plot of
discharge resistor over frequency. Similarly with the current measurement section, there
are distinct bands of frequency in which a single response is dominant. The low
frequency band is from DC to 100MHz and has the mean impedance of 38.72+107.38i Ω.
Medium frequency band is from 100MHz to 500MHz, with the mean impedance of
8.15+13.90i Ω. From 500MHz to 1GHz is the high frequency band and it has a mean of
5.68-0.78i
The results of the discharge resistor high frequency response warrant inclusion in the final
calibration and calculation of energy dissipation. The decrease from 1.5 kΩ to 5.68-0.78i
Ω, is significant to be utilised in the calculations. This analysis has effectively banded the
response of the component into smaller frequency band with respect to the assumed
characteristics of an electrostatic discharge. The three bands used are, the initial
breakdown in high frequency, medium frequency where arcing has been established and
low frequency as arcing continues and breaks off. Similarly with the current measurement
section, the analysis has identified key values in each band of frequency for the purpose
of estimating the discharge. By using the values to estimate response of components
during discharge, as discharge becomes both time and frequency dependent. This method
of approximating the component value for discharge response (high frequency response)
can be thought of as an extension of the numeric method for approximating an integrate,
but in the frequency analysis. Calculation of discharge energy is the integration of power
over time, the three frequency band estimation of component response allow a constant to
be used for their respective frequency response during discharge; thus simplifies the
discharge waveform to time dependant instead of both frequency and time dependant.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
3.6 Discharge Resistor High frequency Response
47
Figure 3.6.0.1 Plot of 1.5 kΩ Discharge Resistor over Frequency
Plot of impedance of the 1.5k Ω discharge resistor as evaluated by a network
analyser over frequency 9 kHz to 1 GHz. Impedance in Ω Ohms shown in 3
bands, Low, Medium and High Frequency Bands, with their respective means
38.72+107.38iΩ, 8.15+13.90iΩ and 5.68+0.78iΩ. Real values in red and
imaginary values in blue
3.7 Measurement Errors and Absolute Errors
From the measurement point of view, in terms of the measurement equipment to be used,
the errors can be limited and carried to the final measurement point. Measurement error
of component contains the absolute error of the multimeter used to test the components;
they are carried on to the measurement of the data with the oscilloscope’s own absolute
error. The relative errors can be tabulated for the measurement circuit and overall error
derived from the table. The overall error can be calculated from the following:
3456'7*8 6 = ± 12 :;<;=7= =8+578+4'8 >+'78
(Eq. 17)
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
3.6 Discharge Resistor High frequency Response
48
,8'+*;>8 6% = ±+456'7*8 86=8+578 >+'78 × 100%
(Eq. 18)
Relative error in percentages can be added together to give the overall percentage error of
the final measurement. The final measurement’s absolute error can be calculated from the
overall error in percentages, by using equation 18.
±+456'7*8 86 = ,8'+*;>8 6% × =8+578 >+'78100%
So the final value should become measured value ± absolute error (final).
3.8 Conclusion
Analysis for the components to be used in a high voltage measurement circuit has found
that high frequency have a drastic de-rating effect on the component values. Stray
capacitance and inductance were present even after component criteria selection to limit
them. Analysis by a network analyser allows the establishment of an average value for
calculation purpose.
The analysis on the components in the discharge path has allowed an effective response to
be calculated when responding to the different periods in the discharge. Though crude,
the 3 band effectively signify the acting response of the component in their particular
frequency band with respect to the assumed characteristics of an electrostatic discharge.
This analysis simplifies a complex multivariable discharge waveform to a time dependant
waveform able to be integrated for energy.
Therefore, the only viable solution is to account for component values as assessed by a
network analyser as a final calibration of the measurement circuit, and the use those
values in the assessment for the overall measurement circuit characteristics
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
4.0 Low Voltage Discharge Simulation and Measurement
49
4.0 Low Voltage Discharge Simulation and Measurement
In order to clarify the energy dissipations of an electrostatic discharge (ESD), a simple
experiment involving lower voltage was set-up to simulate and measure an ESD at low
voltages. The aim of this experiment is to investigate the energy dissipation throughout
the circuit, especially during the initial high frequency and high impedance discharge at
the discharge point. This was done by measurements at the capacitor and discharge
resistor, which give us the differential voltage at the simulated discharge point.
Simulations of electrostatic discharges specified by IEC standards[7], has set parameters
such as rise time, discharge period and discharge current. Energy dissipation is calculated
from the general energy work equation, where C is capacitor, V is voltage and I is current.
( = 12 $ ∙ #, # = 1$ ) ∙ *
(Eq. 9)
However due to the low voltage and thus low energy of this experiment, energy
dissipated by other components of the circuit will be significant. As an extension to
research on hydrogen minimum ignition energy research [4], this experiment aims to look
at the discharge characteristics of the components in the circuit, where the spark energy is
the residual energy when energy in the resistor and capacitor residual energy is taken
away from the energy in the capacitor.
Es = Ec − Er − Eresidual, (Eq. 1)
In addition to measuring the voltage drop across the storage capacitor, the voltage drop
across the discharge resistor was also recorded. By combining the two measurements the
voltage drop across the discharge point can be recorded and energy calculated from the
voltage difference and current in the discharge.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
4.0 Low Voltage Discharge Simulation and Measurement
50
Reference is made to conference paper “Simulation and Measurement of an Electrostatic
Discharge” in Appendix 10.8. This paper showed that the energy dissipated in the
discharge by the switch decreased in relation to the energy in storage capacitor, but rose
in relation to the peak current. The peak current increased as the resistor value decreased;
this increase of energy dissipation in the switch is more apparent than in discharge
resistor. The paper also showed that the characteristics of the connections impacted on the
data collected. No perfect discharges were recorded, where all energy was accounted for.
Therefore, if total energy present in the discharge circuit is in the storage capacitor then
the total energy dissipated in the switch and discharge resistor should equal the capacitor
energy. From the paper 5-15% energy was unaccounted presumed lost in the resistances
of the connections.
4.1 Low Voltage Discharge Simulation and Measurement Experiment
Method
By taking measurements prior and after the discharge point, the voltage drop and current
of the discharge can be recorded. This measurement of VI characteristic of the discharge
can be used to calculate the energy of the discharge and relate the energy to energy in the
capacitor.
A low voltage experiment designed to simulate the discharge was completed to provide
preliminary data on energy calculation. The experiment used a standard 30 V DC power
supply, charging a discharge circuit through a 560 KΩ resistor as show in Figure 4.1.0.1.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
4.0 Low Voltage Discharge Simulation and Measurement
51
Figure 4.1.0.1 Schematic of the low voltage ESD simulation experiment
The capacitors ranged from 220 pF to 1.5 nF and the resistor from 330 Ω to 1.8
kΩ, values used for each set of tests are listed in Table 4.1.0.0.1.
Table 4.1.0.0.1 Table of experimental variables matrix for the low voltage ESD
simulation
# of Experiments R discharge
C storage 1.8kΩ 1.5kΩ 1kΩ 330Ω
1.5nF 10 10 10 10
1.2nF 10 10 10 10
1nF 10 10 10 10
680pF 10 10 10 10
470pF 10 10 10 10
220pF 10 10 10 10
Through the experiment matrix, the discharge characteristic can be investigated and the
effects of capacitance and resistance on energy dissipation can be recorded. It is expected
that large capacitance will deliver much higher energy dissipation and the range of
resistors should provide a choking effect to the flow of energy as the resistance is
decreased. This experiment is aimed to provide a trend characteristic to that effect, and
also derive the energy dissipation at the discharge point.
RDischarge
300 Ω~1.8 KΩ CStorage
220 pF~1.5 nF
30V
RCharge 560kΩ
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
4.0 Low Voltage Discharge Simulation and Measurement
52
Due to the low voltage, a spark over would not be possible and a switch was used to
simulate spark discharge. The discharge is measured by 100X voltage probes over the
storage capacitor and discharge resistor. The difference in these two reading gives the
voltage difference across the switch and gives a VI characteristic of the discharge.
For each variable set in the matrix 10 experiment results were recorded. Iteration
procedure is as follows,
1. The power supply is energised and a potential difference is seen on the oscilloscope.
2. The oscilloscope is set up to record on trigger when voltage on the storage capacitor
drops below 90%.
3. The switch is triggered, causing the discharge to occur and data recorded.
4. The system is reset for new iteration or new variable set
4.2 Low Voltage Discharge Simulation and Measurement Experiment
Results and Analysis
Referring to Appendix 10.8, voltage measurements at the two points Vc and Vr were
recorded. The difference of the two measured voltages gives the voltage drop across the
discharge point during discharge. Given the energy dissipated in the discharge resistor is
calculated from,
( = #Y, ∙ *
(Eq. 19)
and the energy dissipated at the discharge point is,
( = (#1 − #) ∙ #, ∙ *
(Eq. 20)
the unaccounted energy is given by
(7<+1167<*8 = (1+D+1;*6 − (85;5*6 − (;51ℎ+F8
(Eq. 21)
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
4.0 Low Voltage Discharge Simulation and Measurement
53
(1+D+1;*6 = 12 $ ∙ #
(Eq. 9)
(7<+1167<*8 = 12 $ ∙ # − #Y, ∙ * − (#1 − #) ∙ #, ∙ *
(Eq. 21)
Therefore, if total energy present in the discharge circuit is in the storage capacitor then
the total energy dissipated in the switch and discharge resistor should equal the capacitor
energy. From the paper 5-10% energy was unaccounted presumed lost in the resistances
of the connections.
Referring to Appendix 10.9, the results from the paper showed that the energy dissipated
in the discharge by the switch decrease in relation to the energy in storage capacitor, but
rose in relation to the peak current. It is expected that a larger capacitor will store a larger
amount of energy and therefore raises the overall energy dissipation in the discharge.
Therefore as the capacitance is decreased the energy dissipated at the discharge point
decreases. Overall, 80-90% of the total energy stored in the capacitor at discharge is
dissipated by the discharge resistor. In comparison, from Appendix 10.9, the largest
recorded average values for energy dissipated are 624nJ and 16.5nJ for the discharge
resistor and discharge point respectively. These results were for the 1.5nF capacitor
paired with 1kΩ. The stray resistance dissipated 35.5nJ of the initial 676nJ. However, the
results also showed that the peak current plays a major role in energy dissipation at the
discharge point.
The peak current increased as the resistor value decreased and increases the initial energy
dissipation in the resistive components. With a smaller resistance the inrush current will
peak at a higher point. The increase in peak current is inversely proportional to the
decrease of resistance. The results showed approximately a 600% increase in peak current
compare to 1/6 decrease in resistance. This is as expected as per ohm’s law,
# = ) ∙ ,, ) = #,
(Eq. 22)
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
4.0 Low Voltage Discharge Simulation and Measurement
54
as voltage remains constant, change in resistance will change the current. In this case the
discharging circuit initial voltage is V and discharge resistor is R. The initial current will
be relatively close in magnitude to the peak current.
Higher peak current will increase the energy dissipation at the initial discharge but should
deliver the same amount of overall energy as the initial energy in the capacitor remains
the same. However, the increase of peak current has been shown to increase the energy
dissipation at the discharge point as the discharge occurs. This increase of energy
dissipation is more apparent at the discharge point than at discharge resistor. However,
this phenomena accounts for only about 10% of the total discharge period and should be
more apparent for the high voltage simulations and experiments.
The main factor for the larger increase in energy dissipation at the discharge point
compared to at the discharge resistor, is that as discharge occurs the discharge point goes
from open circuit to short circuit, and effectively bridges the resistance from ∞ to 0 Ω.
Through ohm’s law it is clear that the larger peak current dissipates more energy as the
discharge point acts as a resistance in the transient phase
The fixed value components, the storage capacitor and discharge resistor, performed to
expectation with capacitors recording energy stored proportional to capacitor size and
independent of the resistor pair. Energy dissipation in the resistor responded according to
the size of capacitor with larger capacitor providing more energy for dissipation. There
slight increases in energy dissipated as the resistance is lowered; this is due to the effect
of peak current on the initial discharge. This is seen in figure 5 of Appendix 11.8, where
large peak current caused by the lower discharge resistance allowed a steeper trend of
energy dissipation at the discharge, as initial energy is decreased.
4.3 Low Voltage Discharge Simulation and Measurement Experiment
Discussion
The unaccounted energy mentioned in the previous section would be present in all
electronic circuits; it is only significant due to the relatively high amount with respect to
the low energy of the experiment. The peak current, 120mA in this experiment when
compared with the expected 30A in high voltage experiment, would cause the stray
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
4.0 Low Voltage Discharge Simulation and Measurement
55
resistance in the circuit to dissipate a more significant amount of energy in relation to the
milli-joule energy discharges. However, this resistance in comparison to the discharge
point and the discharge resistor would be much less than 5-15% of total resistance. As the
current is the same for a series circuit, energy dissipated by the resistance can be viewed
as percentage of total resistance, however this relationship is not apparent in the results.
At the smallest value of discharge resistor, the stray resistance was found to be 15-45 Ω.
It is not reasonable for stray resistance in the circuitry to accumulate to such large
resistance; therefore, it is possible that at the discharge, the transient effect of the
discharge effectively causes the discharge resistor to be a reduced resistance at high
frequency. If the resistance of the discharge resistor drops to a much lower value, a higher
percentage of energy would be dissipated at the discharge point and through the
connections and cables in the experiment. This phenomenon was investigated in Chapter
3.2 (Frequency Response of Resistive Divider), where resistors of high resistance stopped
performing at their rated value at high frequency. This requires further investigation for
confirmation and is further explored in chapter 5.
The increase in energy dissipation as capacitance increases is expected, however the ratio
of energy dissipated between the discharge point, the discharge resistor and the stray
resistance, is not proportional. The discharge resistor showed relatively consistent energy
dissipation when compared with difference size resistances of the discharge resistor. This
is somewhat expected as the majority of the energy is going to be dissipated by the
discharge resistor as the discharge resistor will continue to dissipate energy until the
charges of the storage capacitor are dispersed. The overall time will be much longer than
the initial discharge period, where the peak current will alter the energy dissipation. From
the analysis about 80-90% of the energy is dissipated by the discharge resistor and the
remaining 10-20% by the discharge point and the stray resistances. Furthermore it was
seen from the results in Appendix 10.9 that as the discharge resistance is decreased the
percentage of the energy dissipated by the discharge point increased. The increase at the
discharge point reduces the amount of energy dissipated by the stray resistance which
accounts for all the unaccounted energy lost from the initial capacitive energy. The
unaccounted energy is the residual energy after the discharge resistor and discharge point
energy dissipation has been subtracted from the initial capacitive energy.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
4.0 Low Voltage Discharge Simulation and Measurement
56
The discharge resistor affects the peak current and the time constant of the overall
discharge. A smaller resistance will give a larger peak current and a shorter time constant
for discharge. It was seen from the results that there is a linear relationship between the
peak current and the resistance.
Overall energy dissipation should not be effected by the larger peak current with smaller
discharge resistor. The overall energy is determined by the stored charges in the storage
capacitor, which is derived from the capacitor size and voltage to which the capacitor is
charged. The higher peak current results in higher energy dissipation at the discharge
point. The discharge point can be considered to be an open circuit prior to discharge and a
short circuit after discharge. Therefore the discharge point would dissipate relatively large
energy in the transition period from open to short circuit. This is as expected as prior to
discharge there is infinite resistance across the discharge point. As the discharge connects,
the resistance at the discharge point approaches 0 Ω, and with the peak current flowing
will generate significant energy at that instant. The energy dissipation happens as
discharge occurs. During an actual discharge, energy would be converted to light and heat
as the discharge occurs, in which charges as electrical energy is dissipated. It is also noted
that energy will be radiated by the high frequency current flowing in the circuit.
The storage capacitor contains the majority of the energy discharged. It is possible for
charges to be flowing from the power supply during discharge, but this is limited due to
the large charging resistor selection. By selecting resistor values combined with the
storage capacitor to give a much longer charging time constant than the discharge period,
it is possible to limit this charging while the capacitor discharges. Therefore is expected
that the energy in the capacitor is independent of charging resistor and power supply, as
seen in the results of Appendix 10.9. Recorded waveform indicated the difference in the
charge and discharge time constants, with the slow ramp up to charged voltage at
significant time after discharge has occurred.
Energy dissipated by the discharge resistor is dependent on the initial amount of charges
in the capacitor. From the results in Appendix 10.9, the resistor will dissipate up to 90%
of the initial energy in the capacitor. Peak current has little effect on this energy
dissipated as the discharge period is much longer than the initial breakdown and majority
of the energy dissipated after the initial breakdown will occur at the discharge resistor. In
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
57
comparison, the overall discharge period is 200-300 ns, while the initial breakdown is 1
ns-10 ns. The breakdown and initial discharge is expected to have a large peak power,
however due to the duration of the initial discharge in the proportion to the overall
discharge. Energy dissipated will be relatively small and dependent on the peak current,
circuit stray resistance and initial breakdown transient duration.
4.4 Low Voltage Discharge simulation and Measurement Experiment
Conclusion
This low voltage discharge simulation and measurement experiment has provided the
basis for investigation of the energy dissipation in a discharge circuit. The importance of
inclusive energy dissipation in the discharge investigation is established, which is the
consensus of current literature.
The simplification of the discharge circuit and simulating discharge through a switch has
provided additional understanding and expectation of the discharge phenomena. This
simulation has also provided the basis for investigating the effects of varying capacitance
and resistance in the discharge circuit. Underlines the significance of the discharge
resistor on the induced peak current and the initial energy at discharge of the capacitor.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
58
5.0 High Voltage Discharge Simulation and Measurement
Subsequent to the low voltage discharge simulation, theory and principles from previous
findings were considered to design the high voltage discharge simulation experiment. The
importance of discharge measurement, in particular the energy dissipation was reviewed
in previous chapters, Chapter 2.2 (Electrostatics) and Chapter 2.7 (Discharge Energy).
The discharge energy measurement needed to be investigated on a specifically designed
measurement system in order to achieve an accurate estimation of the minimum ignition
energy. However complexity of the measurement circuit will affect the measured values
as the effects of all the capacitance, inductance and resistance will impact on the energy
dissipation. In order to measure the high voltage at discharge, measurement circuit will
need to be tuned and compensated for the high frequency transient distortions. Referring
to Chapter 3 (High Voltage Measurement), each component and section of the
measurement circuit will need to be accounted for and investigated in relation to its
effects on the overall measurement. The aim is to achieve a flat response at high
frequencies and to be able to attenuate the high voltage to be captured by an oscilloscope.
This will allow an accurate capture of the voltage at discharge and allow the energy
dissipated to be evaluated.
Energy dissipation is the main focus of this simulation and experiment. From Chapter 2.7
(Discharge Energy), the initial capacitive energy of a discharge simulation can be
dissipated via the various components and the stray resistances. As seen in Chapter 4
(Low Voltage Discharge Simulation and Measurement), the discharge energy is not the
initial capacitive energy and the majority of the capacitive energy will be dissipated by
resistances in the discharge circuit. These resistances are the known discharge resistor,
unknown stray resistance and the equivalent resistance across the discharge point. The
aim of this simulation and experiment is to accurately assess the energy dissipation in a
simulated electrostatic discharge and allow discharge energy to be calculated for
minimum ignition energy investigations.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
59
From the previous sections and investigations, a high voltage discharge experiment and
measurement circuit was designed, constructed and characterised for calibration.
Measurement circuit was simulated and analysed with respect to resistances and
capacitances at high frequency, to define the characteristic for energy dissipation
calculation. Attenuated voltage is recorded and converted for calculation and analysis.
Energy calculation is done on the recorded voltage and current, to calculate the initial
capacitive energy, discharge resistor energy and discharge point energy.
The results showed an overview of the high voltage discharge, with specific detail to
discharge voltage, initial capacitive energy, discharge resistor energy, discharge energy
and peak current. The experiment presents a functional method for investigating the
energy dissipation, high voltage discharges and ignition energy of materials.
5.1 High Voltage Measurement Circuit
5.1.1 High Voltage Measurement Circuit Simulations
Due to this high voltage, measurement requires a specialised circuit, in which voltage
recorded becomes a fraction of the voltage measured. A simple resistive voltage divider
with high voltage components stepping down the voltage would be sufficient to measure
the high voltage before discharge. However, the transient effects of the discharge alter the
expected response of a resistive divider, and would require complex circuitry and
modelling to accurately derive the expected response. Special considerations need to be
taken into account as investigations showed in Chapter 3 (High Voltage Measurement).
The specific aspects that need to be assessed are the high frequency response of the
resistive divider, coupling compensation of the capacitive divider and the inclusion of
probe and oscilloscope into the overall assessment of the high voltage measurement
circuit.
To achieve the required attenuation for the high voltage measurement Ohmite’s Thick
Film resistors were chosen. These resistors were evaluated in Chapter 3 using a network
analyser and for the resistor values used 1 GΩ, 500 MΩ and 100 MΩ, the resistance was
found to have been reduced to less than 10 kΩ at 9+ kHz.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
60
As the measurement is to the ground at the node with the discharge capacitor and at the
discharge point, the measurement circuit will need to have sufficient resistance to the
charging resistor to allow the capacitor to charge to high voltage. For example, if 500 MΩ
resistor was used as the charging resistor, a 1 GΩ voltage divider bridge will only allow
the experiment to operate at 66% of the input voltage at the high voltage power supply.
Therefore it was decided to use 500 MΩ and a divider of 2.2 GΩ to allow the maximum
voltage to rise up to 81% of the high voltage power supply.
As the discharge capacitor reduces as energy for discharge requirement decreases, a
minimum ratio of 50:1 was sought to be maintained, resulting in using a 1 pF capacitance
for the coupling of the 2.2 GΩ divider. This is in consideration to the charges stored in
the capacitive divider; the charges in the divider should be relatively small compared to
the charges in the discharge capacitor. By limiting a minimum ratio of 50:1, the effects of
the capacitive divider would be 2% or less.
The initial design of the measurement circuit is as shown in the Figure 5.1.1.1, the 2 GΩ
resistor coupled to a 1 pF capacitance, 200 MΩ coupled to 10 pF and a 2 MΩ coupled to
220 pF
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
61
Figure 5.1.1.1 Initial High Voltage Divider
The above is a schematic of the initial high voltage divider with only
consideration to the capacitive coupling and resistive division. The additional 200
MΩ section is for the use of a 100X probe.
The inclusion of a 200 MΩ coupled section is for the use of a 100X probe, where the
measured voltage is reduced to max of 1 kV from expected 10 kV discharge. This allows
the 100X probe to use its internal resistance to step down the voltage for the oscilloscope.
Standard oscilloscope will have a maximum ± 50 V input, which gives the voltage at DC,
based on the resistive divider a value of 917 V and for 100X probe 9.17 V. At high
frequency, using the capacitive divider the discharge will have increased to 946V and the
100X probe will further reduce it to 9.46 V. Due to the high frequency transient effects of
the discharge, as explored in Chapter 2.8 (HV Measurement) and Chapter 3 (High
Voltage Measurement), it is expected the resistive divider to cut out immediately after DC
and the capacitive divider to continue providing a flat response to high frequency. Figure
5.1.1.2 is the simulated frequency response of the divider at the 200 MΩ node using Spice.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
62
Figure 5.1.1.2 Simulated Frequency Response of the Divider at 200MΩ node
Plot of the frequency response of the divider at 200MΩ, the divider out puts a flat
response from DC to 100GHz at the value of 917V, and switches to 946V for
1THz+
For a standard probe, the coupled capacitance of 220pF was used to allow better
resolution of the measured wave. At DC the expected voltage is 9V, calculated through
the resistive divider. Using the capacitive divider for high frequency, the discharge
expected would be 45 V at the 2 MΩ node. Similar to the results for the 200 MΩ node,
the resistive divider is expected to cut off immediately after DC and the capacitive divider
is expected to provide a flat response for high frequency. The Spice simulated response is
as shown in Figure 5.1.1.3.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
63
Figure 5.1.1.3 Simulated Frequency Response for the Divider at 2MΩ Node
Plot of the frequency response of the divider at 2MΩ, the divider out puts a flat
response from DC to 100GHz at the value of 9V, then switches to 45V from
1THz+
Both simulations show relative flat response at high frequency, with a step up at 1THz.
This is not expected as the cut off frequency for the 2.2 GΩ resistors is 58 Hz. With the
resistive section to cut off at 58Hz when coupled with the 1pF capacitor and the series
stray capacitance of 0.7 pF from two 1GΩ resistors:
01 = 12 ∙ ∙ 2S ∙ 1.35D = 58VW
(Eq. 14)
The simulated result of resistive divider cut off at 1 THz is unexpected and with
consideration of resistor construction, the resistive divider should cut off at the estimated
58 Hz or lower. From Chapter 3.2 (Frequency Response of Resistive Divider), the 1 GΩ
resistors’ magnitude reduces from its initial 1 GΩ down to less than 6.5 kΩ by 9 kHz.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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The resistive divider won’t be able to maintain the same ratio without the capacitive
divider holding up the ratio. The capacitor coupling retains the divider ratio as impedance
continues to fall and resistance effective becomes null after 10 kHz. Therefore it’s
assumed that after the cut off frequency of 58 Hz for the 2 GΩ divider section, the
response will rise to the capacitive divider response and by 10 kHz only the capacitive
divider will provide a response giving a flat output for high frequency.
5.1.2 High Voltage Measurement Circuit Evaluation
To investigate the response, a network analyser was used to evaluate the capacitive
component of each of the sections in the divider. Referring to Chapter 3.3 (Equivalent
Capacitor Voltage Divider) and using the results from the evaluation, the high voltage
divider is reassessed as show in Figure 5.1.2.1.
The stray capacitances were evaluated in Chapter 3.3.2 (High Voltage Capacitive
Resistive Divider- Stray Capacitance Evaluation) and the results are tabulated in 5.1.2.0.5
along with consideration to the coupling capacitor.
The capacitance of each evaluated coupled sections were significantly larger than
expected at high frequencies. The effect of the stray capacitance will be taken into
account in the following sections along with the effect to the overall attenuation. This is a
major impact on the measurement but the measurement calculations can be adjusted to
accommodate the effect.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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Figure 5.1.2.1 Coupled High Voltage Divider
The above is a schematic of the coupled high voltage divider with the stray
capacitance evaluated by the network analyser. The stray capacitance adds an
additional 4.85 pF to the 2 GΩ/1 pF section, 63.5 pF to the 200 MΩ/10 pF section
and 252 pF to the 2 MΩ/220 pF section.
Table 5.1.2.0.5 Table of High Voltage Divider-Stray Capacitance Results
RC pair Total Evaluated Capacitance Stray Capacitance
2 GΩ/1 pF 5.85 pF 4.85 pF
200 MΩ/10 pF 73.5 pF 63.5 pF
2 MΩ/220 pF 452 pF 252 F
5.1.3 High Voltage Measurement Circuit Oscilloscope Compensation
Referring to Chapter 3.4 (Oscilloscope Calibration), oscilloscope can be reduced to a
parallel resistor and capacitor pair with probe cable resistance and capacitance. The
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oscilloscope and probe cable need to be compensated for high frequency and the final
compensation and design need to be evaluated in the overall attenuation of the divider. A
1X probe will have a high frequency cut off at 6 MHz. By matching the capacitance and
resistances of the equivalent measurement circuit, a high frequency 2X probe can be
constructed. Figure 5.1.3.1 shows the compensated standard BNC/Alligator 1X probe and
oscilloscope with measured values of resistance and capacitance. Measurement of
resistance and capacitance was done with a LCR meter at 1 kHz. The probe
characteristics were 300 Ω cable resistance and 105 pF capacitance measured across the
line to ground with open circuit at one end. The oscilloscope was left floating and
measured to give 1 MΩ and 15 pF across the inputs. To obtain a 2X attenuation for the
probe and oscilloscope, the compensation was chosen to be 1 MΩ and 120 pF as the
probe tip.
Figure 5.1.3.1 Compensated 2X Probe Oscilloscope Equivalent Circuit
Figure shows the compensation for a 2X measurement probe oscilloscope
equivalent circuit. Compensation matched the probe cable and oscilloscope
resistance and capacitance creating a 2X probe for high frequency.
5.1.4 High Voltage Measurement Circuit Overview
From the investigation of this chapter, an assumed schematic is drawn for the
measurement circuit. The results from the evaluation of stray capacitance (Section 5.1.2)
300
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and oscilloscope compensation (Section 5.1.3) are used to compile the final overview of
the equivalent measurement circuit. Figure 5.1.4.1 is the complete schematic of the high
voltage measurement circuit. The figure shows the complete schematic of the
measurement circuit, from the high voltage divider to oscilloscope including the
compensation and cable characteristic.
As mentioned previously probe cable and oscilloscope were measured for capacitance
and resistance, which allowed them to be compensated with a probe tip of 120 pF and 1
MΩ, creating a 2X attenuation. The capacitance and resistance from the compensation,
probe cable and oscilloscope will affect the high voltage divider and alter the attenuation.
To determine the final measurement circuit characteristic, the measurement circuit is
reduced to an equivalent circuit as show in Figure 5.1.4.2.
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Figure 5.1.4.1 Complete High Voltage Measurement Circuit
Figure shows the schematic of the complete high voltage divider from the investigations. Sections shown are High Voltage Divider,
Compensation, Probe Cable and Oscilloscope. Values presents include measured values and compensated values.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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Figure 5.1.4.2 Complete High Voltage Measurement Equivalent Circuit 1
Schematic of the complete high voltage measurement circuit with the simplified
oscilloscope, probe tip and probe cable equivalent.
Therefore, it is convenient to divide the attenuation assessment into DC response and high
frequency response. For the DC attenuation, only the resistance will be in effect and
provide an equivalent circuit as shown in Figure 5.1.4.3.
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Figure 5.1.4.3 Complete High Voltage Measurement Equivalent Circuit 2
Schematic of the complete high voltage measurement circuit with simplified
oscilloscope, probe tip and probe cable equivalent in a DC assessment.
At high frequency the cable resistance of 300 Ω will still provide response to the high
frequency discharge. The cut off frequency of the probe cable is calculated by equation
14, assuming that the 1 MΩ resistor has null effect and the section then equates to a low
pass filter.
01 = 12 ∙ ∙ , ∙ $
(Eq. 14)
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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01 = 12 ∙ ∙ 300 ∙ 120D = 4.4:VW
(Eq. 14)
Therefore at 4.4 MHz the cable response will drop and provide a stray capacitance in
which at high frequency will be seen as a short circuit across the cable resistance. Thus at
the high frequency attenuation, only the capacitor will be in effect and provide an
equivalent circuit as shown in Figure 5.1.4.4.
Figure 5.1.4.4 Complete High Voltage Measurement Equivalent Circuit 3
Schematic of the complete high voltage measurement circuit with simplified
oscilloscope, probe tip and probe cable equivalent in a high frequency assessment.
Assuming high frequency at 4.4+ MHz, in which cable resistance act as short
circuit.
From Figures 5.1.4.3 and 5.1.4.4, the attenuation can be derived at which the measured
voltages at the oscilloscope need to be multiplied.
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5.1.5 High Voltage Measurement Circuit Attenuation Calculation DC
Continuing on from Section 5.1.4 (High Voltage Measurement Circuit Overview), for an
attenuation at DC, the equivalent circuit as shown in Figure 5.1.4.3 can be further reduced
to a two value divider with the point of interest at the CRO, Probe & Cable node. This is
as shown in Figure 5.1.5.1.
Figure 5.1.5.1 Complete High Voltage Measurement Equivalent Circuit 4
Schematic of the complete high voltage measurement circuit with equivalent
values for DC analysis. Measurement side consist of oscilloscope, probe tip,
probe cable and low voltage side of high voltage divider.
Referring to Chapter 2.8.1 (Resistive Divider), the attenuation of the resistor divider is
given by,
+ = ,1 + ,2,2
(Eq. 10)
+ = 2.2S + 1:1: = 2201
(Eq. 10)
Therefore the DC attenuation is 2201X at the “CRO, Probe & Cable” node, with a 2X
probe compensation and adjusted for the oscilloscope.
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5.1.6 High Voltage Measurement Circuit Attenuation Calculation High
Frequency
Similarly with the DC assessment (Chapter 5.1.5 High Voltage Measurement Circuit
Attenuation Calculation DC), the high frequency equivalent circuit can be further reduced
to a two value capacitive divider with the point of interest at the “CRO, Probe & Cable”
node. The result schematic is as shown below in Figure 5.1.6.1.
Figure 5.1.6.1 Complete High Voltage Measurement Equivalent Circuit 5
Schematic of the complete high voltage measurement circuit with equivalent
values for high frequency analysis. Measurement side consist of oscilloscope,
probe tip, probe cable and low voltage side of high voltage divider.
Referring to Chapter 2.8.2 (Capacitor Compensation), the attenuation of the resistor
divider is given by,
+ = $1 + $2$1
(Eq. 11)
+ = 5.419D + 512D5.419D = 95.48
(Eq. 11)
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Therefore the high frequency attenuation is 95.48X at the “CRO, Probe & Cable” node,
with a 2X probe compensation and adjusted for the oscilloscope.
5.1.7 High Voltage Measurement Circuit Absolute Errors
Referring to Chapter 3.7 (Measurement Error and Absolute Errors), the measurement
errors are tabulated in the following Tables 5.1.7.0.1 and 5.1.7.0.2 along with the
accumulative relative errors for the final measurement. Absolute error calculation is used
for figures in section 5.3.2 (Experiment calculation and results), showing error bars in the
respective graphs.
Table 5.1.7.0.1 Resistive Measurement Error
Measurement
Point Measured
Value Absolute error of the
measurement
equipment
Relative
Error % Cumulative
Relative Error %
2 G/1 pF NA NA NA 0.00%
200 M/10 pF 200 MΩ 0.05 Ω 0.00% 0.00%
2 M/220 pF 2 MΩ 0.05 Ω 0.00% 0.00%
Probe Tip 1 MΩ 0.05 Ω 0.00% 0.00%
Probe Cable 300 Ω 0.05 Ω 1.67% 1.67%
Oscilloscope 1 MΩ 0.05 Ω 0.00% 1.67%
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Table 5.1.7.0.2 Capacitive Measurement Error
Measurement
Point Measured
Value Absolute error of the
measurement
equipment
Relative
Error % Cumulative
Relative Error %
2 G/1 pF 5.85 pF 0.0005 pF 0.01% 0.01%
200 M/10 pF 73.5 pF 0.0005 pF 0.01% 0.02%
2 M/220 pF 452 pF 0.0005 pF 0.01% 0.03%
Probe Tip 120 pF 0.005 pF 0.01% 0.03%
Probe Cable 105 pF 0.005 pF 0.01% 0.04%
Oscilloscope 15 pF 0.005 pF 0.01% 0.05%
From the tables, the errors for resistive measurement will be ±1.67% and for capacitive
measurement ±0.05%. Using equation 18 the absolute values of the recorded values can
be derived.
±+456'7*8 86 = ,8'+*;>8 6% × =8+578 >+'78100%
(Eq. 18)
5.1.8 High Voltage Simulation
In the progress of developing sources of high voltage, three types generators were
evaluated and include the Van de Graff Generator, step-up transformers and switch mode
power.
Van De Graff Generators are based on the theory of triboelectricity and by using a
floating spherical conductor; charge can be stored and potential raised by triboelectricity.
Referring to the triboelectric table in Appendix 10.1, positive series materials are used in
conjunction with negative series material to strip charges from the positive series and
store the charges on the floating spherical conductor. An example of such setup is with
rubber in the form of a rubber band as the positive series material and a brass sphere as
the spherical conductor and the negative series material. The rubber band losses charges
to the brass through triboelectric effects and because the brass sphere is floating its able to
store the charges to an amount determined by the diameter of the sphere. The amount of
charge is limited by the materials used and the design of generator. It is quite able to
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achieve high potential by increasing the amount of insulation and increasing the size of
the sphere to store more charges. However, to discharge the amount of charge for
experiments this generator is not feasible and manipulation of the charges would become
hazardous.
Transformers are able to provide step-up voltage to the required high voltage. A simple
premade setup is available that uses on a 555-timer that controlled the charging of a
1000:1 ignition coil acting as a step up transformer, taking power from a standard 12 V
battery. By using the IC controller, a bridge of Zener Diodes is used to hold the low side
voltage up to 225 V allowing pluses of high voltage up to 225 kV to be generated on the
high side. The simplicity of the design allows the charging process to be manipulated by
allowing a capacitor to be charged and discharged without restriking or continual voltage
supplied. The use of an ignition coil as the step up transformer allows the high voltage to
be achieved but adds a large amount of addition inductance. Additional inductance will
induce an oscillatory ringing effect in the discharge and significantly affect the discharge
waveform and energy. Significant alteration and design will need to be developed in order
to accommodate additional damping measures to combat the inductance from the ignition
coil. Induction would be best to avoided but is possible to be limited using damping.
Therefore the use of transformer would not be suited for short discharges with low energy,
but it might be suited for initial testing due to it cost and ease of setup.
Switch mode power supplies minimises the inductor required compared to using
traditional step-up transformer, and in a charge pump topology, only capacitors are used.
It is a specially designed circuit that controls the charging and discharging of an energy
storage device. The device is usually an inductor/transformer or capacitors in a charge
pump. By switching and controlling the charging and discharge process, voltage output
can be adjusted. Only a charge pump or switch capacitor topology can deliver high
voltage in the kilo voltage region. By switching between charging capacitors the
switching regulator creates an effect similar to a Cockroft Walton Voltage multiplier or a
Marx generator. As the capacitors are charged, additional capacitors start charging adding
the potential drop across each capacitor as the series charges. By using a switching
regulator, the charging process can be closely controlled and efficiency increased.
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Switch mode power supply would be the ideal choice for the high voltage simulation
requirement of electrostatic discharge ignition experiments. It is possible to avoid or limit
inductance in the power supply and provide ease of control over the voltage and energy.
A specialist designed switch mode power supply is available at the specification required
for experiment. Those specification are ≥20 kV and ≥20 W, allowing the generator to
deliver 1 mA load current for charging. UltraVolt manufactured 30A24-30 high voltage
power supply was sourced for the experiment as it is most suited [58]. For this experiment
in high voltage measurement experiment a lower 10-12 kV is required, along with
reduced gap to simulate a lower energised discharge.
5.2 High Voltage discharge Experimental Method
5.2.1 High Voltage Experiment Circuit
From the design process of the last section, a measurement circuit is able to be
incorporated into the overall experimental circuit. The experiment setup includes a high
voltage power supply, charging resistor, discharge capacitor, discharge resistor, discharge
point, current measurement and the measurement circuit. Referring to Section5.1.8 (High
Voltage Simulation), switch mode power supply of a charge pump design was chosen as
the main power supply. This type of power supply is ideal for this experiment, due to the
relative low inductance introduced to the experiment circuit and the concise construction
compared to similar generators such as Cockroft Walton Voltage multiplier or a Marx
generator.
Referring to Chapter 5.1.1 (High Voltage Measurement Circuit Simulations), a 500 MΩ
charging resistor is required to charge the discharge capacitor and allow sufficient time
between charging to prevent continual discharge from the high voltage power supply. The
500 MΩ is in affect connected in series with the 2.2 GΩ measurement circuit, and by
using 500 MΩ will allow the voltage to be charged up to 81% of the power supply
voltage to be charged, while maintaining a large time constant in comparison to the
discharge.
The discharge capacitor is the main source of energy in the discharge. To ensure this, the
discharge capacitor will need to be at least 10 times larger than the capacitance in the
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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78
measurement circuit. From Figure 5.1.6.1, the overall capacitance in the measurement
circuit is 5.362 pF, which will contribute about 10% more capacitance to the overall
energy storage capacity for a 50 pF discharge capacitor. Thus, the discharge capacitor
selection needs to be take account for the effect of the measurement circuit when deciding
the size of the discharge capacitor.
Discharge resistor was selected to simulate the Human Body Model (HBM) simulation of
an electrostatic discharge (ESD). The resistor restrains the flow of current at discharge
simulating a longer discharge period, compared to a Charged Device Model (CDM)
simulation of an ESD. The resistor value as per HBM model is 1.5 kΩ.
Two electrodes manufactured to provide a parallel plate with a sharp point on the
discharge side of the electrode, were used as the discharge point. The electrodes were
used for easy modelling of the electric field induced prior to discharge. The effects of the
electric field prior to discharge have not been explored.
To calculate the energy dissipation in the discharge, current and voltage measurements
are required. From Chapter 3.5 (Current Measurement), the current measurement section
can be used with the compensated 2X probe and oscilloscope to acquire the current
measurement.
From the last section, Chapter 5.1 (High Voltage Measurement Circuit), a 2.2 GΩ high
voltage divider was designed. Referring to Figure 5.1.4.1 (Complete High Voltage
Measurement Circuit), the circuit consists of a high voltage divider, probe tip
compensation, probe cable characteristic and oscilloscope input impedances. The design
and evaluation of the high voltage measurement circuit response concluded that the final
attenuations are 2201 at DC and 95.48 at frequencies above 4.4 MHz from section 6.1.5
and 6.1.6 respectively. The measurement is to be taken via a compensated 2X probe and
oscilloscope.
The current measurement is conducted via the measurement of voltage across the current
shunt and recorded through a compensated 2X probe and oscilloscope. The current shunt
provides a small voltage drop across the resistance allowing current to be derived. The
current shunt is a 0.1 Ω shunt and with an 8.04 Ω magnitude at high frequency.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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79
Figure 5.2.1.1 Overall Experiment Circuit
Figure is a schematic of the experiment circuit. It shows all section of the experiment from power supply, charging, discharge sections
and measurement circuit.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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80
The overall experiment circuit is as show in Figure 5.2.1.1; it shows the high voltage
power supply, charging resistor, discharge capacitor, discharge resistor, discharge point,
current measurement and the voltage measurement circuit.
5.2.2 Experiment procedure
The procedure for experiment is as follow
1. Set discharge parameters such as atmosphere, discharge electrode separation and
discharge voltage, as shown in Appendix 10.10-12.
2. Initialise oscilloscope and set for trigger capture
3. Initialise high voltage power supply
4. Remove safety ground short
5. Trigger high voltage power supply to charge
6. Wait for discharge to occur and measurement recorded on the oscilloscope
7. Replace safety ground short if experiment concluded or repeat step 5 and 6
5.2.3 Energy Calculation
Referring to Section 4.4.2 (Low Voltage Discharge Simulation and Measurement
Experiment Results and Analysis), the energy in a discharge can be calculated from
( = (#1 − # − #;) ∙ #;X; ∙ *
(Eq. 20)
where Vc is the voltage at the capacitor and Vi is the voltage across the current measuring
resistor section, Zi. Vr is the voltage drop across the 1.5kΩ discharge resistor, impedance
Zr. Vr is given by,
# = ) ∙ X
(Eq. 22)
I is given by
) = #;X;
(Eq. 22)
Where Zi and Vi is the current shunt and voltage drop across the shunt. Vr becomes
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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81
# = #;X; ∙ X
And discharge energy equation (Eq. 20) becomes
(;1ℎ+F8 = (#1 − #;X; ∙ X − #;) ∙ #;X; ∙ *
Where Zr is 1.5kΩ and I is consistent due to series circuit arrangement for discharge
resistor and current measurement resistor
Energy in the capacitor is given by
(1+D+1;*6 = 12 $ ∙ #, # = 1$ ) ∙ *
(Eq. 9)
Energy dissipated in the discharge resistor is given by,
(85;5*6 = ) ∙ X ∙ *
(Eq. 19)
5.3 Results and Analysis
5.3.1 Discharge Current and Voltage Waveforms
Results were recorded from the two measurement points Vc and Vi, representing voltage
at the discharge capacitor and the voltage at the current measurement resistor. Referring
to the previous section Vr can be derived from the measurement of Vi. Plot of discharge
capacitor voltage and discharge current are as shown in Figures 5.3.1.1 and 5.3.1.2. The
plots show 15 discharges out of 17 recorded discharges. Two discharges were not
included due to measurement capture error.
Figure 5.3.1.1 also show a means plot of the 15 discharges, this was added to indicate the
similarities between all the discharges. The plots of the means identify the key features of
the discharge, namely, the charging voltage before discharge, the sharp transient at
discharge, the oscillations in the discharge and the state after the discharge.
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The current plot, Figure 5.3.1.2, has two additional max and min plot in addition to the
means plots. The reason for the inclusion of a maximum and minimum plot is to identify
the peak current and current characteristic. The means plot identifies the key features of
the current waveform, namely, the initial peak current, the oscillation in the discharge and
the discharged state after the discharge.
The voltage at the discharge capacitor as shown in Figure 5.3.1.1 shows the voltage
before discharge and the sharp transient discharge in which the voltage falls. The voltage
was measured via a high voltage divider and a compensated measurement circuit with
oscilloscope. The recordings showed the stable voltage before discharge and discharge
itself with the final state charging back up to high voltage. Inductance cannot be avoided
but the circuit was designed to minimise its effect. However it was not expected the
limited inductance would induce the significant amount of oscillations seen in the
recorded waveforms. This inductance and associated oscillation derivate from the HBM
specifications but has minimal effect on the overall aim of the experiment. The overall
aim of the experiment is to simulate a high voltage discharge and measure it. The added
inductance complicates the assessment for energy dissipation, due to voltage and current
oscillation, dissipating the energy over a longer period of time.
The discharge current as shown in Figure 5.3.1.2 represents the measured current
waveforms from the discharges. Similar with the voltage waveform analysis, oscillation
in the discharge was unavoidable; even through inductance was limited through design
process. However, oscillation does not affect analysis as energy continues to be dissipated
in the oscillation. Inductance caused in the experiment, is a result of the simulation using
a HBM, but does not affect the aim of the experiment to measure the dissipated energy.
However, energy dissipation will be more complex as dissipation in the reverse path will
also need to be considered.
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Figure 5.3.1.1 Experiment Results- Discharge Voltage Waveform at Discharge Capacitor
Plot of the discharge voltage at the discharge capacitor during the discharge period. 100 pF Discharge
-15000
-10000
-5000
0
5000
10000
15000
20000
25000
-1.00E-06 -5.00E-07 -3.00E-20 5.00E-07 1.00E-06
Vo
lta
ge
, V
olt
s
Time, Seconds
Exp. 275
Exp. 276
Exp. 277
Exp. 278
Exp. 279
Exp. 280
Exp. 281
Exp. 282
Exp. 283
Exp. 284
Exp. 285
Exp. 292
Exp. 293
Exp. 295
Exp. 296
Average
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84
Figure 5.3.1.2 Experiment Results- Discharge Current Waveform
Plot of the discharge current over time during the discharge period. 100 pF Discharge
-15
-10
-5
0
5
10
15
-6.00E-08 -1.00E-08 4.00E-08 9.00E-08 1.40E-07 1.90E-07
Cu
rre
nt,
Am
ps
Time, Seconds
275
276
277
278
279
280
281
282
283
284
285
292
293
295
296
means
max
min
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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5.3.2 Experiment Calculations and Results
Summary of the discharge results are shown in Table 5.3.2.0.1. Results for each set of the
experiment are tabulated with the voltages at discharge, the energy in the capacitor, the
energy dissipated by the discharge resistor, the energy dissipated at the discharge point,
the unaccounted energy, and the peak current. Due to the effect of inductance on the
discharge, the results include negative value representing reverse path dissipation by the
reversed current.
The results include set of discharges (285 and 292) that appear to have re-strike after
initial discharge. This assessment is based on the lower voltage at discharge and the large
amount of unaccounted energy. The large percentage of unaccounted energy can be due
to initial overestimate of the capacitive energy, or a continued discharge, where the
previous discharge essentially have established a discharge path lowering the potential
required for discharge.
5.3.3 Discharge Voltage
Average voltage at discharge is 8,921.38 V, with maximum at 10,564.8 V and minimum
at 7,043.2 V. Due to the large attenuation in the DC measurement, Voltage at discharge
can vary greatly due to the limited resolution of the results captured. The smallest
increment is 0.4 V, which equates to 880.4 V. Therefore, assuming the maximum value
for DC measurement is ±3 V then 0.2 V measurement errors by the oscilloscope adds
addition 3.33% relative error to the overall measured value, make the overall relative
error 5%. The measured values would become 8,921.38±446.07 V for average,
10,564.8±528.24 V for maximum and 7,043.2±352.16 V for minimum, as shown in
Figure 5.3.3.1.
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Figure 5.3.3.1 Plot of Discharge Voltage Results with absolute error
Figure of discharge voltages plotted with voltage and respective absolute error
for the measured result. Plots of 8,921.38±446.07 V average, 10,564.8±528.24V
max and 7,043.2±352.16 V min.
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Table 5.3.2.0.1 Experiment Results-Summary of Discharge Energy Results for 100pF simulation and experiment
275 real imag 276 real imag 277 real imag 278 real imag 279 real imag
Vpeak 8804 Vpeak 10564.8 Vpeak 10564.8 Vpeak 8804 Vpeak 8804
Capacitor 3.80E-03 Capacitor 5.47E-03 Capacitor 5.47E-03 Capacitor 3.80E-03 Capacitor 3.80E-03
Resistor -4.92E-08 -1.11E-05 Resistor -7.43E-06 -3.92E-05 Resistor -7.05E-06 -3.83E-05 Resistor -1.10E-05 -4.80E-05 Resistor -1.29E-05 -5.33E-05
Discharge 8.14E-04 4.99E-04 Discharge 1.45E-03 1.46E-03 Discharge 1.45E-03 1.42E-03 Discharge 1.40E-03 1.64E-03 Discharge 1.43E-03 1.78E-03
Losses 65.70% 2.50E-03 Losses 47.69% 2.61E-03 Losses 48.34% 2.64E-03 Losses 21.41% 8.13E-04 Losses 17.33% 6.58E-04
Ipeak + 10.57 5.45 Ipeak + 10.83 12.77 Ipeak + 10.83 12.02 Ipeak + 10.83 14.46 Ipeak + 10.83 15.59
Ipeak - -9.56 -7.51 Ipeak - -10.83 -15.59 Ipeak - -10.83 -15.40 Ipeak - -10.83 -17.09 Ipeak - -10.83 -17.46
280 real imag 281 real imag 282 real imag 283 real imag 284 real imag
Vpeak 8804 Vpeak 8804 Vpeak 10564.8 Vpeak 10564.8 Vpeak 7043.2
Capacitor 3.80E-03 Capacitor 3.80E-03 Capacitor 5.47E-03 Capacitor 5.47E-03 Capacitor 2.43E-03
Resistor -1.06E-05 -4.70E-05 Resistor -2.61E-07 -1.00E-05 Resistor -1.24E-06 -1.77E-05 Resistor -7.30E-07 -1.62E-05 Resistor 1.63E-06 -3.98E-06
Discharge 1.40E-03 1.63E-03 Discharge 6.82E-04 4.96E-04 Discharge 1.04E-03 7.89E-04 Discharge 1.01E-03 7.23E-04 Discharge 5.95E-04 2.84E-04
Losses 21.68% 8.23E-04 Losses 69.26% 2.63E-03 Losses 66.95% 3.66E-03 Losses 68.56% 3.75E-03 Losses 63.97% 1.55E-03
Ipeak + 10.83 15.21 Ipeak + 9.98 5.63 Ipeak + 9.30 7.14 Ipeak + 10.06 6.76 Ipeak + 9.39 3.19
Ipeak - -10.83 -16.52 Ipeak - -7.27 -8.26 Ipeak - -10.83 -11.08 Ipeak - -10.49 -10.14 Ipeak - -8.12 -4.51
285 real imag 292 real imag 293 real imag 295 real imag 296 real imag
Vpeak 8804 Vpeak 7043.2 Vpeak 8804 Vpeak 7043.2 Vpeak 8804
Capacitor 3.80E-03 Capacitor 2.43E-03 Capacitor 3.80E-03 Capacitor 2.43E-03 Capacitor 3.80E-03
Resistor 9.23E-07 -5.45E-06 Resistor 9.45E-07 -2.46E-06 Resistor 2.66E-06 -1.04E-05 Resistor 2.20E-06 -3.49E-06 Resistor 8.09E-07 -1.69E-05
Discharge 5.76E-04 3.41E-04 Discharge 3.52E-04 1.49E-04 Discharge 1.18E-03 5.45E-04 Discharge 6.56E-04 2.41E-04 Discharge 1.28E-03 7.34E-04
Losses 75.96% 2.88E-03 Losses 79.45% 1.93E-03 Losses 54.73% 2.08E-03 Losses 63.14% 1.53E-03 Losses 47.39% 1.80E-03
Ipeak + 9.47 3.38 Ipeak + 6.51 2.82 Ipeak + 10.83 7.32 Ipeak + 8.80 3.94 Ipeak + 10.83 8.26
Ipeak - -7.27 -5.07 Ipeak - -6.26 -5.82 Ipeak - -10.83 -6.38 Ipeak - -9.05 -3.76 Ipeak - -10.83 -9.95
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
88
Summary Vpeak Capacitor Resistor- r I Discharge-r i Losses % Ipeak + Ipeak -
Average 8921.387 3.97E-
03 -2.81E-
06 -2.16E-
05 1.02E-
03 8.44E-
04 54.10% 2.12E-
03 9.99 -9.64
Max 10564.8 5.47E-
03 2.66E-
06 -2.46E-
06 1.45E-
03 1.78E-
03 79.45% 3.75E-
03 10.83 -10.83
Min 7043.2 2.43E-
03 -1.29E-
05 -5.33E-
05 3.52E-
04 1.49E-
04 17.33% 6.58E-
04 6.51 -6.26
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
89
5.3.4 Energy in the Capacitor
Energy in the capacitor is dependent on the voltage at and after discharge as capacitance
is fixed for this experiment. Referring to previous sections methods, the capacitive energy
is given by,
( = 12 $ ∙ #
(Eq. 9)
With capacitance constant, only voltage is a variable. As assessed above, limited
resolution of the results contributed to a larger measurement error for this measurement of
voltage at DC prior to discharge. The 5% DC voltage relative measurement error equates
to 10% error on capacitive energy calculation. The capacitive energies recorded were
3.97±0.397 mJ average, 5.47±0.547mJ maximum and 2.43±0.243 mJ minimum, as shown
in Figure 5.3.4.1.
Figure 5.3.4.1 Plot of Initial Capacitive Energy with absolute error
Figure of initial capacitive energy in mJ with respective absolute error for the
calculated result. Plots of 3.97±0.397 mJ average, 5.47±0.547 mJ max and
2.43±0.243 mJ min.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
90
5.3.5 Discharge Resistor Energy Dissipation
Energy dissipated by the discharge resistor is determined by the current as voltage over
the resistor was not measured. Current is derived from the voltage over the current
measurement resistor via Ohm’s law.
) = #;X;
(Eq. 22)
The current is then used to calculate the energy dissipation in the discharge resistor
through the use of Ohm’s law and energy dissipation in a resistor
# = ) ∙ X
(Eq. 22)
( = #X ∙ * = ) ∙ X
X ∙ * = ) ∙ X ∙ *
(Eq. 19)
This gives the following equation for energy dissipated in the discharge resistor through
calculation of current from the current measurement resistor.
( = (#; X;⁄ ) ∙ X ∙ *
(Eq. 19)
Energy dissipation calculated using the above equation is tabulated in Table 6.3.2.0.1.
Given real power dissipation is of interest, only the real energy dissipated is mentioned
and plotted here. The results show an average of -2.811 uJ dissipated, with maximum as
high as 2.66uJ and minimum as low as -12.897 uJ.
Additional measurement error caused by absolute error 0.2 V in the oscilloscope accounts
for a much smaller error as the resolution of the discharge is ±50 V. The relative error to
be added is 0.2% to give the overall relative error 0.25% and 0.5% for energy calculation.
This amends to the results to -2.811±0.014 uJ average, 2.66±0.013 uJ maximum and
-2.897±0.064 uJ minimum as shown in Figure 5.3.5.1.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
91
Figure 5.3.5.1 Plot of Discharge Resistor Energy Dissipation with absolute error
Figure of discharge resistor energy dissipation in mJ with respective absolute
error for the calculated results. Plots of -2.811±0.014 uJ average, 2.66±0.013 uJ
max and -2.897±0.064 uJ min.
5.3.6 Discharge Point Energy Dissipation
Referring to the previous section, discharge point energy dissipation is given by,
( = (#1 − #;X; ∙ X − #;) ∙ #;X; ∙ *
(Eq. 20)
Where Vc is the voltage at the capacitor, Vi/Ri is the current flowing during the discharge
and R is the discharge resistance. Due to the method of calculating energy dissipation,
both real and imaginary values need to be included. The real values represent real energy
dissipation by resistive elements, while the imaginary values represent energy being
stored or discharged by inductive and/or capacitive elements.
The same overall relative error of 0.25% is maintained giving the energy calculation a
relative error of 0.5%. The results for real energy dissipation are 1.023±0.005 mJ average,
1.454±0.007 mJ maximum and 0.352±0.002 mJ minimum. For the imaginary energy
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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92
dissipation, average is 0.844±0.004 mJ, maximum is 1.78±0.009 mJ and minimum is -
1.49±0.007 mJ. The energy dissipation values are plotted in Figure 5.3.6.1 along with
results tabulated in Table 5.3.6.1.1.
Figure 5.3.6.1 Plot of Discharge Point Energy Dissipation with absolute error
Figure of discharge point energy dissipation in mJ with respective absolute error
for the calculated results. Plots of 1.023±0.005 mJ average real, 1.454±0.007 mJ
max real 0.352±0.002 mJ min real. 0.844±0.004 mJ average imaginary,
1.78±0.009 mJ max imaginary and 1.49±0.007 mJ min imaginary.
Average real,
1.02E-03
Maximum real,
1.45E-03
Minimum real,
3.52E-04
Average imaginary,
8.44E-04
Maximum
imaginary, 1.78E-
03
Minimum
imaginary, 1.49E-
04
0.00E+00
2.00E-04
4.00E-04
6.00E-04
8.00E-04
1.00E-03
1.20E-03
1.40E-03
1.60E-03
1.80E-03
2.00E-03
En
erg
y i
n m
illi
-Jo
ule
s, m
J
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
93
Table 5.3.6.1.1 Discharge Point Energy Dissipation Results
Real Energy in mJ Average real Maximum real Minimum real
Discharge Point 1.0234E-03 1.4542E-03 3.5234E-04
± 5.1170E-06 7.2709E-06 1.7617E-06
Imaginary Energy in mJ Average imaginary Maximum imaginary Minimum imaginary
Discharge Point 8.4395E-04 1.7788E-03 1.4911E-04
± -4.21977E-06 -8.89417E-06 -7.4553E-07
5.3.7 Unaccounted Energy Results Summary
The unaccounted energy is the difference between the energy supplied by the capacitor
and the energy being dissipated in the discharge resistor and discharge point. Since all
energy is from the capacitor, unaccounted energy is the residual energy after both real and
imaginary energy in the circuit as been accounted. The overall equation with respect to
the above energy calculation equation is,
(7<+1167<*8 = 12 $ ∙ # − (#; X;⁄ ) ∙ , ∙ * − (#1 − #;X; ∙ X − #;) ∙ #;X; ∙ *
(Eq. 21)
The unaccounted energy or lost energy is tabulated in Table 5.3.2.0.1. The results were
shown both as in joules and in percentage of the initial capacitive energy.
Due to the limited resolution of the discharge voltage, the unaccounted energy record
varies greatly as it depends on the calculated capacitive energy. The results from Table
5.3.2.0.1 show the average unaccounted energy at 2.12 mJ/54.10% of the initial
capacitive energy, with max at 3.75mJ/79.54% and min at 0.658mJ/17.33%.
Table 5.3.2.0.1 Unaccounted Energy Result Summary
Energy in mJ Average Maximum Minimum
Unaccounted 2.12E-03 3.75E-03 6.58E-04
% of initial Cap 54.10% 79.45% 17.33%
5.3.8 Peak Current
The peak discharge current is the maximum value recorded by the current measurement
resistor. Peak current has a significant effect on the energy dissipation during the initial
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
94
discharge. Referring to Chapter 4 (Low Voltage Discharge Simulation and Measurement),
the high peak current dissipates significantly larger amount of energy when compared to
overall energy dissipation throughout the discharge. Only real current is of interest as
imaginary current is either charging or discharging storage elements in the circuit.
Peak current results from Table 5.3.2.0.1 are shown with positive and negative peaks,
giving two sets of peak current results. Positive peak currents are 9.99 A average, 110.83
A maximum and 6.51 A minimum. Negative peak currents are -9.64 A average, -10.83 A
maximum and -6.26 A minimum.
From Table 5.1.7.0.1, measurement error from the oscilloscope is 4.33%. The peak
current with absolute error is as show in Table 5.3.8.1.1 and plotted in Figure 5.3.8.1.
Figure 5.3.8.1 Plot of Peak Current with absolute error
Figure of Peak current during discharge in amperes with absolute error from
measurement. Plots of peak currents, 9.99±0.43 A average+, 10.83±0.47 A max+,
6.51±0.28 A min+, -9.64±0.42 A average-, -10.83±0.47 A max-, and
-6.26±0.27 A min.
Average +, 9.99
Maximum +, 10.83
Minimum +, 6.51
Average -, -9.64
Maximum -, -10.83
Minimum -, -6.26
-15.00
-10.00
-5.00
0.00
5.00
10.00
15.00
Cu
rre
nt
Am
pe
res,
A
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
95
Table 5.3.8.1.1 Peak current summary
Current,
Amps Peak Current ±
Average + 9.99 0.43
Maximum + 10.83 0.47
Minimum + 6.51 0.28
Average - -9.64 -0.42
Maximum - -10.83 -0.47
Minimum - -6.26 -0.27
5.4 Discussion
5.4.1 Discharge Current and Voltage Waveform Discussion
Looking at the captured waveforms in Section 5.3.1 (Discharge Current and Voltage
Waveform), significant oscillation is present, which suggest the design process to limit
inductance was not entirely successful. Inductance can be derived with the assumption
that capacitance total is 105.85 pF (discharge capacitor in parallel with measurement
circuit capacitance) and that the oscillation at 20 nS period is natural frequency. The
equation for natural frequency is,
/G = 1√I ∙ $ , /J = 2K
(Eq. 23)
I = 1$ ∙ /J = 1105.85D ∙ 220< = 95.81<V
By the above assumption an inductance of 95.81 nH is calculated. If the above inductance
is assumed, from the damping factor equation using a damping factor of 1.0, R would be,
L = ,2 M$I
(Eq. 24)
, = 2L_$I
= 2_105.85D95.81<
= 60.17Ω
Assuming period of oscillation at 20 nS, the frequency of the oscillations at discharge
would be 50 MHz for this experiment. Therefore, 60.17Ω resistance is required to
critically damp the circuit. This reinforced the theory that at initial discharge the high
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
5.0 High Voltage Discharge Simulation and Measurement
96
response transient effectively renders the resistor in the circuit null, since there a 1.5kΩ
discharge resistor in series with the inductance and capacitance, which with respect the
above analysis would suggest it has to drop below 60.17 Ω at the discharge. This
confirmed by the discharge resistor assessment in section 3.7 (Discharger Resistor High
Frequency Response), where high frequency response at 250MHz + is less than 10 Ω.
This adds to the already large frequency disruption from the transient discharge, with
initial peak frequency of 500 MHz-1GHz from the >1 nS rise time seen in the experiment.
In regards to energy dissipation, oscillations would not affect the overall energy
dissipation. Energy dissipation would be considered in absolute; in both positive and
negative directions.
The lack of resolution at DC for the voltage waveform induced a significant error to the
measurement, as shown in Figure 5.3.1.1. Relative measurement error from the
oscilloscope is 3.33%, calculated from the maximum value of 3V with 0.2V measurement
error. The relative error equates to 440V at the final reading and compared to the 5kV
difference between the minimum to maximum recorded voltage, the lack of resolution
become apparent.
The high frequency sections of the voltage waveform include a large number of
oscillations. This emphasises the importance of limiting inductance in the experiment
circuit. The use of capacitive divider for the high frequency response is show as effective
as the 50 MHz oscillation from the discharge has been captured with limited distortion.
Looking at the current waveform, there is significant oscillation present due to stray
inductance. Inductance was limited during design and modelling of the investigation,
however through the analysis it was found that a small amount 95.81nH estimated is
present at discharge. Every component will have some inductance; the inductance could
be due to effect of high frequency response of the component, induced through the design
and manufacture the individual components. Another source of possible inductance
would be the arrangements of the connections and connecting cables.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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97
5.4.2 Results Summary-Discussion
The tabulated results in Table 5.3.2.0.1, is a summary of the experimental results and
calculations. The tabulated results show where possible real and imaginary parts of the
represented values. The inclusion of complex calculation through the impedance allows a
closer look at the energy interactions in this circuit. Imaginary energy dissipation is not
real energy dissipated, it signifies the energy being used to charge or discharge from
storage element such as inductors and capacitors.
5.4.3Discharge Voltage-Discussion
Due to the large attenuation in the DC voltage measurement, resolution of the
measurement is significantly limited. Smallest increment in measurement is 880 V for the
overall max ±30 kV measurement setup, representing 3.33% relative measurement error
to the oscilloscope and taking the overall relative error to 5% for DC voltage
measurements. Results showed average of 8,921 V, which is close to the estimated 9 kV
for a 3mm gap. The experiment is set up to charge till break down across the gap. The
high voltage is reduced by the charging resistor to 81% of the high voltage at the supply.
Therefore, if maximum recorded voltage was 10,564 V then the maximum supply voltage
is 13,041 V.
5.4.4 Capacitor Energy-Discussion
The 10% relative error for the energy in the capacitor energy calculation represents a
significant amount of disputable energy. This is a direct result of the limited resolution on
the DC measurement. As the energy is dependent on the capacitance and voltage, the
large increment in the voltage measurement reduces the accuracy of the initial energy
evaluation. Capacitance is constant for this experiment, thus the wide range in energy
calculated is due to the voltage variation. Energy calculated ranged from 2.43 mJ to 5.43
mJ; voltage volatility is thus noted.
5.4.5 Discharge Resistor Energy Dissipation-Discussion
Energy dissipation in the discharge resistor is dependent on the resistance and current in
the discharge. Given that resistor is constant for this experiment, the current is the main
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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98
variable. The current is derived from the current measurement results and it is used in
equation 19 to calculate the energy dissipation.
( = ) ∙ X ∙ *
(Eq. 19)
Current measurement derived from measured voltage over the current measurement
resistor give a low measurement error of 0.45%. The current measurement section
contains just the resistor acting as a current shunt in which voltage drop is measured. It
was unexpected that such low resistance would be affected by the high frequency but as
evidenced in Section 3.5 (Current Measurement) the resistor exhibited higher impedance
as frequencies increased. There will be a large increase in resistance at high frequency
due to skin effect which is a result of the limitation on the design and manufacture, an
adverse effect to high frequency. Further research would be required to determine high
frequency component for measurement.
5.4.6 Discharge Point Energy-Discussion
Discharge point energy is calculated by the voltage difference at the discharge point and
the current through the discharge. Absolute values were used for the final calculation and
the importance of polarity of the energy was noted. Results indicate that a higher voltage
was recorded at the discharge resistor due to inrush of current from ground as discharge
occurs; this creates a negative readings. However, the reverse orientation and oscillatory
ring does not impact on the overall measurement as the absolute energy dissipation
reading is recorded and overall absolute value of the energy dissipation is calculated from
the recordings.
5.4.7 Unaccounted Energy-Discussion
Due to the complex calculation, we can see that not all the initial energy is dissipated by
resistance. Significant complex imaginary energy is used from the initial energy to charge
other storage elements in the discharge circuit. These elements are either inductive or
capacitive. The energy is the remaining unaccounted energy from calculation and can be
up to 80% of the initial energy. Average of 54% is high considering energy unaccounted
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
99
dissipation due to stray resistances in the circuit and accuracy of measurement. The ±10%
measurement error contributes greatly to the accuracy of this outstanding energy
calculation. However, even with the consideration of absolute measurement error, there is
no doubt unaccounted elements in the circuit dissipates a significant amount of the initial
discharge energy. Further investigation would be required to understand the effect on this
minuscule time frame of an electrostatic discharge.
5.4.8 Peak Current-Discussion
Currents were calculated at 0.4pS measurement periods by the measurement circuit
through the arrangement of oscilloscope, probe and current measurement circuit. 0.4 pS is
the minimum time increment on the oscilloscope. This provided a relatively accurate
measurement at ±4.33% relative measurement error.
5.5 High Voltage Discharge Simulation and Measurement- Conclusion
Through this investigation, a high voltage discharge experiment was designed constructed
and characterised for calibration and energy dissipation calculation. The circuit was
defined in accordance to impedance and capacitance with respect to high frequency,
which allows the characterisation of the circuit for energy dissipation measurement and
calculation.
The findings showed an overview of the high voltage discharge, allowing details such as
discharge voltage, initial capacitive energy, discharge resistor energy, discharge energy
and peak current to be investigated. The resulting experiment presents a functional
method for investigating the energy dissipation in high voltage discharges and ignition
energy of materials.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
6.0 Materials Ignitions
100
6.0 Materials Ignitions
6.1 Introduction
The design, fabrication and validation of the developed discharge system described,
enables the study of the energy required to ignite a material. Chapter 5 (High Voltage
Discharge Simulation and Measurement) validates the developed system, capable of
determining the discharge energy required for ignition. Systematic experiments were
conducted to determine the minimum ignition energy for a simulated electrostatic
discharge on a liquid phase fuel.
The discharge capacitor is the main variable in which energy is stored and discharged. As
successful ignitions of the fuel are confirmed, capacitor values are decreased till no
ignition occurs. The discharges are recorded to calculate energy dissipation as described
in Chapter 5, in particular Section 5.2.2 (Energy Calculation). Energy dissipation results
are then used in a probability analysis to determine the minimum ignition energy.
The fuel material chosen for this experiment is liquid n-Pentane and was chosen due to its
insulative properties and its low ignition energy requirement. It was determined during
the initial search for appropriate fuel material that insulative properties are required for
ignition to occur in a simulated electrostatic discharge (ESD). Additionally, the previous
and related recent works on n-Pentane and associated researchers would allow some
indication to the validity of the results.
A suitable material was sought with the following parameters, low electrical conductive
factor, low ignition energy, and readily available. Hydrocarbons were ideal, with low
ignition energy required [59] and n-pentane matching the low electrical conductive factor
[25] and readily available in the laboratory.
.
High voltage ignition energy measurements of n-Pentane were conducted for 0.5ml n-
Pentane solution evaporated in a 250 cm3 chamber. It was determined that the minimum
require energy for ignition of n-Pentane from the experiments conducted was 0.352mJ,
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
6.0 Materials Ignitions
101
and statistical analysis result for a 1% probability of ignitions (P=0.01) the energy is
0.269 mJ, for a 50% ignition (P=0.5) the energy is 0.448 mJ and for 99% ignition (P=0.99)
the energy is 0.627 mJ. From the results, the importance of circuit configuration on the
discharge characteristic and ultimately the ignition energy can be determined.
6.2 Method
This investigation of the ignition energy requirement for n-Pentane carries on from
Chapter 5, using the same measurement setup described in Section 5.2.1 (Experiment
Circuit) and using the energy calculation method in Section 5.2.3 (Energy Calculation).
The ignition energy calculated is then used to determine the probability of ignition
through the collected data of discharges. The ignition energy is controlled through the
careful variation of discharge capacitor value. By decreasing the capacitance, it is
possible to approach and determine the minimum value of capacitance in which ignition
will occur and from the results calculate the ignition energy in the discharge and the
ignition probability.
The n-Pentane was deposited in the base of the glass chamber shown in Appendix 10.11
and allowed to evaporate in the chamber. Ignition test then were conducted with the
following procedure.
1. Set discharge parameters such as atmosphere, discharge electrode separation and
discharge voltage, as shown in Appendix 10.10-12
2. Initialise oscilloscope and set for trigger capture
3. Initialise high voltage power supply
4. Deposit 0.5mL of n-Pentane solution to discharge point.
5. Remove safety ground short
6. Trigger high voltage power supply to charge
7. Wait for discharge to occur and measurement recorded on the oscilloscope
8. Replace safety ground short if experiment concluded or repeat Steps 6 and 7
9. If ignition does not occur after 3 tests, chamber is flushed, ground link replaced
and repeat Steps 4-8.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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6.3 Results and Analysis
Ignitions experiment results are tabulated in the Table 6.3.0.0.1. The results are split into
ignition and no ignition sections, with the summarised analyses on the right. First set of
results in blue are the ignited results. The second set of results in red is the non-ignition
results. A Summary of the two sets of result is at the end of the table. Twenty-one sets of
data were used in the ignition analysis of the overall 49 set of results. The ignition results
are a mix of all the ignition experiments with focus only on the energy dissipated instead
of capacitor value. An example of the discharge can be found in the frame extracts from
the high speed camera in Appendix 10.13. The entire experiment result can be located in
Appendix 10.14.
6.3.1 Ignition Energy and Minimum Ignition Energy
As shown in Section 6.3.6, the ignition energy is calculated via
( = (#1 − #;X; ∙ X − #;) ∙ #;X; ∙ *
(Eq. 20)
The results are tabulated in Table 6.3.0.0.1. The lowest recorded confirmed ignition and
its ignition energy is 0.352 mJ with exclusion to re-strike arcing. In comparison the
standardised testing derived from Lewis and von Elbe stated a 1% probability of ignition
requires 0.28 mJ [60], results from Moorhouse [59] stated 0.5mJ and work by Calcote [61]
show 0.6 mJ lowest ignition energy.
6.3.2 Ignition Probability Statistical Analysis
Probability of ignition was analysed with respect to a binomial statistical modelling, using
Logistic Regression Method to analyse a Bernoulli ignition/no ignition statistic of the
ignition results [62]. The resultant S-Curve gives a good indication of the probability of
ignition from the binary (True/False) ignition/no ignition results. The S-curve defines the
probabilities of ignition with a mid-transition zone, where probability of ignition
increases exponentially from no ignition to ignition. This analysis is ideal solution for a
statistical analysis of ignition results as the data are not normally distributed. The
probability of ignition is given as:
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
6.0 Materials Ignitions
103
Table 6.3.0.0.1 Ignition and No Ignition Discharge Result Summary
275 real imag 292 real imag 293 real imag 295 real imag 296 real imag
Vpeak 8804 Vpeak 7043.2 Vpeak 8804 Vpeak 7043.2 Vpeak 8804
Capacitor 3.80E-03 Capacitor 2.43E-03 Capacitor 3.80E-03 Capacitor 2.43E-03 Capacitor 3.80E-03
Resistor -4.92E-08 -1.11E-05 Resistor 9.45E-07 -2.46E-06 Resistor 2.66E-06 -1.04E-05 Resistor 2.20E-06 -3.49E-06 Resistor 8.09E-07 -1.69E-05
Discharge 8.14E-04 4.99E-04 Discharge 3.52E-04 1.49E-04 Discharge 1.18E-03 5.45E-04 Discharge 6.56E-04 2.41E-04 Discharge 1.28E-03 7.34E-04
Losses 65.70% 2.50E-03 Losses 79.45% 1.93E-03 Losses 54.73% 2.08E-03 Losses 63.14% 1.53E-03 Losses 47.39% 1.80E-03
Ipeak + 10.57 5.45 Ipeak + 6.51 2.82 Ipeak + 10.83 7.32 Ipeak + 8.80 3.94 Ipeak + 10.83 8.26
Ipeak - -9.56 -7.51 Ipeak - -6.26 -5.82 Ipeak - -10.83 -6.38 Ipeak - -9.05 -3.76 Ipeak - -10.83 -9.95
334 real imag 336 real imag 338 real imag 341 real imag 360 real imag
Vpeak 8804 Vpeak 7043.2 Vpeak 7043.2 Vpeak 7043.2 Vpeak 10564.8
Capacitor 2.64E-03 Capacitor 1.69E-03 Capacitor 1.69E-03 Capacitor 1.69E-03 Capacitor 3.24E-03
Resistor 2.04E-06 -8.56E-06 Resistor -2.62E-06 -1.00E-05 Resistor -1.52E-06 -5.42E-06 Resistor 8.65E-07 -3.12E-06 Resistor 1.74E-06 -1.14E-05
Discharge 9.16E-04 4.73E-04 Discharge 2.47E-04 4.52E-04 Discharge 1.01E-04 2.29E-04 |Discharge| 3.52E-04 1.97E-04 Discharge 1.02E-03 6.15E-04
Losses 47.54% 1.25E-03 Losses 59.35% 1.00E-03 Losses 80.82% 1.36E-03 Losses 67.59% 1.14E-03 Losses 49.74% 1.61E-03
Ipeak + 10.83 7.14 Ipeak + 6.17 3.38 Ipeak + 3.72 4.69 Ipeak + 7.02 5.63 Ipeak + 10.83 7.89
Ipeak - -10.32 -6.38 Ipeak - -4.40 -11.27 Ipeak - -2.03 -6.20 Ipeak - -7.02 -3.19 Ipeak - -10.83 -9.20
361 real imag 362 real imag 363 real imag
Vpeak 8804 Vpeak 8804 Vpeak 8804
Capacitor 2.25E-03 Capacitor 2.25E-03 Capacitor 2.25E-03
Resistor 1.64E-06 -8.34E-06 Resistor -2.54E-06 -1.90E-05 Resistor -5.93E-06 -2.39E-05
Discharge 7.73E-04 5.17E-04 Discharge 8.50E-04 8.60E-04 Discharge 6.24E-04 1.04E-03
Losses 42.91% 9.65E-04 Losses 24.89% 5.59E-04 Losses 27.13% 6.10E-04
Ipeak + 10.83 5.63 Ipeak + 10.83 8.07 Ipeak + 10.83 4.13
Ipeak - -9.47 -6.76 Ipeak - -10.15 -10.14 Ipeak - -5.33 -17.65
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
6.0 Materials Ignitions
104
337 real imag 352 real imag 353 real imag 357 real imag 358 real imag
Vpeak 7043.2 Vpeak 5282.4 Vpeak 5282.4 Vpeak 10564.8 Vpeak 10564.8
Capacitor 1.69E-03 Capacitor 8.09E-04 Capacitor 8.09E-04 Capacitor 3.24E-03 Capacitor 3.24E-03
Resistor -1.34E-06 -5.12E-06 Resistor 6.15E-07 -3.85E-06 Resistor 2.53E-07 -3.87E-06 Resistor -7.31E-07 -1.94E-05 Resistor 5.70E-07 -1.27E-05
Discharge 1.27E-04 2.40E-04 Discharge 3.30E-04 2.45E-04 Discharge 2.73E-04 2.22E-04 Discharge 1.15E-03 8.92E-04 Discharge 8.89E-04 6.49E-04
Losses 78.60% 1.33E-03 Losses 29.26% 2.37E-04 Losses 39.28% 3.18E-04 Losses 37.46% 1.21E-03 Losses 52.87% 1.71E-03
Ipeak + 4.31 5.45 Ipeak + 6.17 5.26 Ipeak + 6.94 4.51 Ipeak + 10.83 11.27 Ipeak + 10.83 7.70
Ipeak - -2.79 -6.57 Ipeak - -7.70 -3.76 Ipeak - -5.50 -4.51 Ipeak - -10.83 -9.01 Ipeak - -9.05 -10.89
311 real imag 312 real imag 313 real imag 316 real imag 318 real imag
Vpeak 5282.4 Vpeak 5282.4 Vpeak 7043.2 Vpeak 7043.2 Vpeak 7043.2
Capacitor 6.28E-04 Capacitor 6.28E-04 Capacitor 1.12E-03 Capacitor 1.12E-03 Capacitor 1.12E-03
Resistor 6.40E-07 -2.15E-06 Resistor -6.40E-07 -4.47E-06 Resistor 3.02E-07 -3.20E-06 Resistor -7.09E-07 -6.24E-06 Resistor -1.69E-08 -4.98E-06
Discharge 2.52E-04 1.19E-04 Discharge 1.92E-04 2.57E-04 Discharge 2.49E-04 1.66E-04 Discharge 2.94E-04 3.05E-04 Discharge 3.20E-04 2.93E-04
Losses 41.05% 2.58E-04 Losses 29.38% 1.84E-04 Losses 63.01% 7.03E-04 Losses 46.99% 5.24E-04 Losses 45.53% 5.08E-04
Ipeak + 5.24 3.57 Ipeak + 4.65 2.07 Ipeak + 6.51 3.38 Ipeak + 7.19 4.32 Ipeak + 7.70 3.57
Ipeak - -6.43 -3.57 Ipeak - -4.57 -7.89 Ipeak - -4.65 -4.51 Ipeak - -4.65 -7.14 Ipeak - -5.33 -5.26
Ignition Average Max Min No Ignition Average Max Min
Vpeak 8483.855 10564.8 7043.2 Vpeak 7043.2 10564.8 5282.4
Capacitor 2.78E-03 3.80E-03 1.69E-03 Capacitor 1.44E-03 3.24E-03 6.28E-04
Resistor 3.98E-07 -1.08E-05 2.66E-06 -2.46E-06 -5.93E-06 -2.39E-05 Resistor -1.06E-07 -6.59E-06 6.40E-07 -2.15E-06 -1.34E-06 -1.94E-05
Discharge 8.02E-04 5.34E-04 1.28E-03 1.04E-03 3.52E-04 1.49E-04 Discharge 4.08E-04 3.39E-04 1.15E-03 8.92E-04 1.27E-04 1.19E-04
Losses 51.84% 1.45E-03 79.45% 2.5E-03 24.89% 5.59E-04 Losses 46.34% 6.98E-04 78.60% 1.71E-03 29.26% 1.84E-04
Ipeak + 9.88 6.03 10.83 8.26 6.51 2.82 Ipeak + 7.04 5.11 10.83 11.27 4.31 2.07
Ipeak - -9.06 -7.89 -10.83 -17.65 -5.33 -3.19 Ipeak - -6.15 -6.31 -10.83 -10.89 -2.79 -3.57
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
6.0 Materials Ignitions
105
N = 8(OPQOR)(1 + 8OPQOR)
(Eq. 25)
where, P is the probability, E is the ignition energy, and β0 and β1 are coefficients derived
by Method of Maximum Likelihood [63].
From the ignition results in Table 6.3.0.0.1, the coefficients are derived to be -11.34 and
25669, β0 and β1 respectively. The plot of the ignition result with the probability of
ignition is as shown in Figure 6.2.2.1. Using the probability equation,
N = 8(OPQOR)(1 + 8OPQOR)
(Eq. 25)
N = 8(bcc.deQfggh)(1 + 8(bcc.deQfggh))
Data plots including the probability plot for Figure 6.2.2.1 is in Appendix 10.15.
The results shows 1% probability of ignitions P=0.01, energy to be 0.269mJ, 50%
ignition P=0.5, energy is 0.448mJ and 99% ignition probability at 0.627mJ. A probability
of ignition S-curve is shown with the ignition data, showing the transition zone from
0.269 mJ to 0.627 mJ.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
6.0 Materials Ignitions
106
Figure 6.3.2.1 Plot of Ignition Results and Ignition Probability Curve for N-
Pentane
Figure shows the plot of ignition results from Table 6.3.0.0.1 and the ignition
probability S-curve for n-pentane
6.3.3 Ignition Discharge characteristics
Average voltage at discharge voltage is 8,483 V for ignited experiments compared to
7,043 V for non ignited experiments. And this trend for larger values in average ignited
experiment verses non ignited experiment is common for initial capacitor energy,
discharger resistor energy, discharge energy, and peak current values.
The effect of lowering capacitor is present and expected in all the analysis as the energy
dissipation or peak current is expected to drop with discharge capacitor value. With
decrease of capacitor value the overall energy for discharge decreases, leading to no
ignition as the energy drop below the minimum ignition energy.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.00E+00 2.00E-04 4.00E-04 6.00E-04 8.00E-04 1.00E-03 1.20E-03
Pro
ba
bil
ity
of
Ign
itio
n,
P
Discharge Energy in joules. J
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
6.0 Materials Ignitions
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6.4 Material Ignition Discussion
6.4.1 Minimum Ignition Energy
Comparisons made in the current results to Lewis and Moorhouse shows that there is still
a significant amount of knowledge required in order to fully understand the energy
dissipation in the discharges to determine the minimum ignition energy. Attention is also
drawn to Eckhoff’s [14] conclusion on minimum ignition values reported by Lewis to be
unnecessarily conservative [60], which is nearly twice the lowest recorded value. This
experiment calculated 1% probability of ignition of Pentane at 0.269 mJ, 4 percent less
than the 0.28 mJ reported by Lewis. However, a lower value would have been expected as
only energy dissipated at the discharge point is considered, which identifies the
dissipation characteristics in the discharges. The lowest confirmed ignition energy is
0.352 mJ which only represent 33% of the initial energy. The resulting 67% of the initial
energy unaccounted is assumed to have been used to charge other storage elements in the
circuit or dissipated by resistances other than those measured. Since no measurement or
characteristic was done on the stray capacitance, inductance and resistance, there is no
method to identify the energy usage other than at the measured points.
Standardised testing method described by the “ASTM: Standard Test Method for
Minimum Ignition Energy and Quenching Distance in Gaseous Mixtures” [64] was not
implemented in this ignition experiment. Therefore, minimum ignition results can only
act as an indication for the development of the high voltage measurement and ignition
energy experiment for research. It would be for future development to amend this
experiment to the described standardise testing method for the purpose of investigating
the energy dissipation in accordance to defined parameters for testing gaseous mixtures.
6.4.2 Ignition Probability
For a general comparison, Lewis [60] used a 1% probability for the minimum ignition
energy, which gave the reported value of 0.28 mJ at 3.3% volume. Using a 1%
probability this set of ignition results gave a probability of 1% ignition at 0.269mJ. The
low sample count in the ignition results and different experiment setup would be likely
causes of the accuracy in ignition energy at 1% probability. More data and experiment is
required to obtain confident statistically analysed ignition probability results that can be
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
6.0 Materials Ignitions
108
compared with the standardised testing method. More experiments will also reduce the
amount of data point outside the upper region of the s-curve, ignition and non-ignition
respective.
6.4.3 Ignition Discharge
The data from the summarised ignition results is as expected, with respect to the lowering
of energy dissipation when comparing the ignition and no ignition sets. The discharge
voltage varied greatly which was not expected as the same experiment setup is used. The
same gap of 3 mm is maintained which would indicate a fixed potential required for
breakdown and discharge. This volatility in discharged voltage warrants future
investigation where the discharge period can be identified and the respective voltage at
discharge more accurately assessed. A possible reason for the discrepancy in this trend for
discharge voltage could be because at proximity to the transition zone of ignition an extra
600V is required for ignition [65]. Another possible reason is the low data count for the
ignition results.
6.4.4 Capacitance vs. Discharge Energy
A full investigation of the capacitance in relation to the discharge energy was not able to
be completed with the available results. More data are needed to identify the significance
of additional capacitance on the minimum ignition energy. An investigation of
capacitance verse the minimum ignition energy would allow further understanding of the
significance of circuit configuration and the waveform or discharge characteristic, on the
probability of ignition.
6.5 Material Ignition Conclusion
Using the developed experiment method developed in previous investigations, a
systematic experiment for investigating the ignition energy of n-Pentane was conducted.
Through the lowering of ignition energy in the discharge, a lowest ignition value was
established. Collected data was also able to be analysed statically to determine ignition
probabilities at various levels of ignition energies.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
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Lowest ignition energy recorded was 0.352 mJ, and the statically result of 0.269 mJ for 1
% probability of ignition. The results showed close agreement to related published values.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
7.0 Contributions and Conclusions
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7.0 Contributions and Conclusions
The work performed has resulted in the design, fabrication and validation of a system to
characterise the energy in an electric discharge and permits the characterisation of
Minimum Ignition Energy for materials in a well characterised electrostatic discharge.
The following presents a summary of the results and analyses that have been performed
and their associated contributions.
7.1 High Voltage Measurement
The initial assessment that a high voltage electrostatic discharge will be difficult to record
with a high degree of accuracy was proven true. The investigation described in Chapter 3
demonstrated large discrepancies between DC and high frequency response of the
components used to construct a high voltage measurement circuit. This created the need
to fully characterise the components to be used for the discharge measurement with
respect to both DC and high frequency responses. The results showed the rapid decrease
of impedance with respect to high frequency for large resistance and increase of
impedance for current shunts and cables. These effects were explained as high frequency
effects of the stray capacitance decreasing resistance, and the skin effect on the
conductors inducing higher impedance. This resulted in a difference between the
measured value and discharge circuit value during the discharge period. A revised
characteristic of the measurement circuit will need to be identified and used for
experiments as a final step to prevent any additional resistance and capacitance altering
the circuit characteristics. This assessment should include high frequency resultant for
impendence and stray capacitance, for all the connected components including high
voltage measurement points, probes, cables and oscilloscope.
Results from this investigation have identified the importance of carefully characterising
the measurement and experiment circuit. The key characteristics to determine are:
- Resistances at high frequency and the underlining effects of stray capacitance.
Large resistance values are reduced as a high frequency dependant, with
capacitance becoming significant factor in circuit.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
7.0 Contributions and Conclusions
111
- Stray capacitance from the handling, connection, design and manufacture of the
resistors and other components produce unwanted stray capacitance at high
frequency. This stray capacitance needs to be accounted for in the final
assessment of the experiment circuit as it cannot be eliminated and will affect the
circuits discharge characteristics.
- Impedance of cabling and current shunts cannot be assumed, as high frequency is
shown to affect the impedance. An assessment must be conducted to determine
the high frequency characteristics of the cabling and current shunts.
7.2 Low Voltage Experiment
In Chapter 5, a low voltage experiment designed for preliminary assessment of the effects
an electrostatic discharge was described, that provided good indication of the energy
dissipation and discharge waveform in a high voltage electrostatic discharge. Discharge
point energy dissipation methodology for the associated energy calculation was
implemented. Due to the simplicity of the circuit it was possible to measure the node
before and after the discharge point, allowing a potential difference to be derived from
two independent voltage measurements. Energy dissipations from all significant
components were able to be calculated from the two voltage measurement as well as their
dissipation in respect to initial energy in the capacitor.
The two energy dissipations calculated from the measurements are 1) the discharge
resistor dissipation and 2) the discharge point dissipation. The initial energy is calculated
from the capacitor and, with a lossless simulation, there should be no unaccounted energy
when the two energy dissipations from the initial energy are considered. However, from
the results obtained there is 5-10% of energy unaccounted, with 5-10% dissipated by the
discharge point and 80-90% dissipated by the discharge resistor. The unaccounted energy
is small but significant when compared to the energy dissipated at the discharge point,
indicating a similar overall resistance value. As for the large 80-90% energy dissipation
by the discharge resistor; this is expected since the experiment does not involve actually
arcing to ground and thus the majority of the energy is dissipated through the components
in the circuit.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
7.0 Contributions and Conclusions
112
Current waveforms from the simulated discharges were also evaluated for their peak
current in order to determine energy dissipation. High peak current induced large
instantaneous energy dissipation at the initial peak discharge period, as a result of the
influx of current due to discharge. This period was short at a few nano-seconds and
comparatively short when compared to the overall discharge period.
This investigation reiterates the importance of this energy dissipation calculation for
ignition energy work, as the energy dissipated in the discharge would never be the initial
capacitive energy since components in the circuit and stray resistances will always
dissipate a significant amount of the energy.
7.3 High Voltage Experiment
A high voltage experiment was used to develop a method of measuring and calculating
the ignition energy was described in Chapter 6. Using the theory developed in Chapter 3,
a measurement circuit for high voltage measurement was designed and constructed. Final
characterisation of the measurement circuit found the initial DC response to be vastly
different to the high frequency response. This phenomenon meant energy calculations
could only be conducted in a distinct period of the discharge. Energy calculations were
done from the first point of the fast transient and continued up to 200 nS into the
discharge. It was assumed that the majority of the energy in the discharge was dissipated
by 200 nS. Prior to this time the discharge voltage was recorded for the calculation of the
initial capacitive energy present.
Captured waveforms indicated a significant amount of inductance in the circuit that added
ringing oscillations to the current and voltage waveforms. Further analysis concluded that
95 nH of inductance was induced by components at high frequency which are present
despite limitation of the inductance in design and component selection phase. Analysis
also found that critical damping was achieved with a resistance of 60Ω, indicating that the
resistance in the circuit had fallen to below that figure during the high frequency
discharge. This lack of resistance is indicated in the discharge resistor high frequency
response analysis completed in section 3.6.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
7.0 Contributions and Conclusions
113
It was found the large attenuation for reducing the high voltage provided insufficient
resolution for precise voltage reading. A measurement error of 3.33% was therefore
added to the resulting voltage readings. Voltage measurements gave an average of 8.9 kV,
which is approximately 81% of high voltage from the power supply. The voltages are
consistent with the expected 3.3 kV per mm breakdown across air and 9-10 kV across the
experiment 3mm gap.
Voltage was used in the analysis to determine the initial energy, through the use of the
capacitive energy equation and assuming all energy in the discharge derived from the
energy stored in the capacitor. Due to the use of voltage prior to discharge the inherent
DC voltage measurement error is carried forward, resulting in a 10% error with the
capacitor energy calculation. On average, 3.97 mJ was present in the capacitor for
discharge.
The current present in the discharge is measured through the use of a current shunt, via
Ohm’s law with the voltage drop across the current shunt. The current is then used to
calculate the energy dissipated in the discharge resistor with an average of -2.81 uJ
recorded... This figure is negative and much lower than the results from the low voltage
experiment, where 80-90% of the initial energy is dissipated by the discharge resistor; this
indicates that at the discharge discharger resistor is affected by the high frequency of
discharge and has idyllically performed as a storage element as either or both inductive
and capacitive capacity.
By using the current in the discharge, the potential difference at the discharge point was
found from the voltage at the capacitor and the voltage drop over the discharge resistor.
An average of 1.03 mJ was recorded, approximately 26% of the average initial energy.
This figure is much higher than the results from the low voltage experiment, where only
5-10% of the initial energy is dissipated. This increase is thought to be due to the actual
breakdown where electrical energy is converted to heat and light, and due to the influence
of peak current on the energy dissipation. Since the peak current in the discharge
dissipated a large amount of energy during the initial breakdown, when effective
impedance across the discharge point approaches 0 Ω from ∞ Ω.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
7.0 Contributions and Conclusions
114
The unaccounted for energy remains after energy dissipated by the discharge resistor and
discharge point has been taken into account comes to 2.12 mJ, representing 54% of the
average initial energy. As was present in the low voltage experiment, there is a noticeable
amount of unaccounted for energy that can’t be discounted as measurement error. The
significance of this energy is apparent as it contains up to 54% of the initial energy and is
not counted toward energy dissipation in the circuit. The unaccounted for energy cannot
be estimated, it can only be deduced when energy dissipation has been analysed. This
energy is assumed to have been utilized to charge other storage element in the discharge
path, for example stray capacitance and inductance not measured or assessed.
Unaccounted energy could also be dissipated by stray resistance or storage till after
discharge where they then are used to charge the discharge capacitor again.
This investigation has developed an important and validated test method for measuring
ignition energies in a high voltage discharge simulating an electrostatic discharge. The
robust measurement methodology allows the calculation of the energy dissipated
throughout the circuit and thus characterises the energy in the discharge. Characterisation
done from the analysis of the data enables the particular properties of interest to be
defined and determined.
7.4 Material Ignition Experiment
Using the method of calculating energy dissipation in a high voltage discharge developed
in Chapter 6, materials ignition experiments to find the ignition energy for n-pentane were
conducted. A series of experiments with different capacitors to deliver different amount
of energy were conducted to determine the minimum ignition energy. The lowest ignited
energy recorded was 0.352 mJ which is in good agreement with the results from Calcote
[61] after considering unaccounted energy losses, and also in good agreement with the
value stated by Lewis [60]. The results of Lewis are for 1% probability of ignition by
Lewis is 4 percent under at 0.269mJ.
In comparison, the statistical analysis of the data by logistic regression predicted ignition
energy of 0.269 mJ at 1% probability of ignition. This is a good indication of the
functionality of the system but should not be accepted for comparison as the experiment
was not conducted in accordance with any standardised methodologies such as ASTM
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
7.0 Contributions and Conclusions
115
International. Testing consistency with ASTM Int. standards for gases and vapour would
be a valuable further study.
The analysis of the ignition data identified an interesting point that also warrants further
investigation. This was that the discharge voltage for successful ignitions, as compared to
unsuccessful ignitions, showed an increase of 600 V. This difference is unexpected as the
same gap for discharge and experiment setup was present. This difference could be due to
the insufficient amount of data for full statistical analysis, or it could be due to the large
measurement error of the DC voltage measurement. Further tests are required to identify
the cause of this.
Utilizing the developed experimental system and methodology to calculate energy in the
discharge, the ignition characteristics of n-pentane have been explored. A minimum
ignition energy and probability of ignition was obtained from the ignition experiments.
Comparison to related work show agreement to published values. Future work should be
done to calculate solid, liquid and gases minimum ignition energy for a wide range of
materials.
Further investigation is required to obtain a better understanding of how energy other than
the discharge energy is dissipated in the circuit.
7.5 Conclusions
Through this investigation of the characterisation of the minimum energy for ignition in
an electrostatic discharge the following conclusions can be drawn:
- High voltage discharge measurement involving fast transient response will be
difficult to record with a high degree of accuracy. Significant design, assessment
and calibration of the high voltage measurement circuit would be required to
perfect the measurement obtained. This study has shown that this is possible.
- Three key characteristics are required to be assessed for the high voltage
measurement circuit. They are,
o Resistance of the resistors at high frequency.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
7.0 Contributions and Conclusions
116
o Stray capacitance from components and connections
o Impedances of the cabling and current shunts used in the circuit that would
be required for the analysis calculations.
- Previous work and the low voltage experiment have reiterated the importance of
energy dissipation in the discharge circuits. Investigation is required as in depth as
possible to determine only the discharge energy.
- Inductance must be limited for a high voltage discharge to prevent oscillatory
ringing in the discharge waveforms. However, it is not possible to eliminate all
inductance.
- Capacitive energy from initial charging is not equal to the ignition energy. From
this experiment data
o Impedance in the circuit will dissipate significant energy, either real or
imaginary when reacted to the high frequency discharge.
o Ignition energy represents approximately 26% of the capacitive energy
o Average 54% of the energy is unaccounted, dissipated by stray capacitance,
inductance and resistance in the circuit.
- Ignition experiment validated the functionality of the high voltage measurement
and ignition energy calculation method.
- N-Pentane ignition energy measurement show close agreement to published value
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
8.0 Future Work
117
8.0 Future Work
Two potential areas related to this work would benefit from further work.
Firstly, the material ignition experiment in this work should be amended to become
consistent with a standardised methodology for materials ignition test. This would allow
minimum ignition energy results from this measurement methodology to be contributed
to minimum ignition energy data.
Secondly, it would be of significant interest to collate a discharge resistance versus
ignition energy relation to determine a discharge characteristic based on resistance. It has
been shown that a large resistance in the discharge would prevent ignition through the
slow dissipation of energy due to the limited current flow from the large resistance. This
would present as an informative characteristic for a material hazard assessment. A
methodology for investigating this characteristic is required, to make the assessment to
determine if resistance is a significant criterion for ignition.
Similar, a correlation between ignition energies and capacitances of the discharge
capacitor would be of interest. The aim is to investigate the reduced discharge period as
capacitance is decreased with the voltage constant. Also to characterisation of the ignition
energy in relation to the minimum ignition energy, would allow further analysis for
ignition. This work has the methodology developed for this assessment; further work is
required to establish this characteristic as criteria for ignition.
The establishment of a resistance and capacitance relationship of a material for minimum
ignition would allow criteria to be drawn for hazardous analysis for that material. Precise
preventative measures can be deduced from the established correlation, such as placing
additional resistance in ground path or developing imbedded capacitance meter with set
parameters for warning to ignition hazard.
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
9.0 References
118
9.0 References
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121
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Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
122
10.0 Appendix
Appendix 10.1 Table of Triboelectric Series
Table of Triboelectric Series [16] Positive Air
Loses Human Skin
Electrons Asbestos
Rabbit Fur
Glass
Human Hair
Mica
Nylon
Wool
Lead
Cat Fur
Silk
Aluminum
Paper
Cotton
Steel
Wood
Lucite
Sealing Wax
Amber
Rubber Balloon
Hard Rubber
Mylar
Nickel
Copper
Silver
UV Resist
Brass
Synthetic Rubber
Gold, Platinum
Sulfur
Acetate, Rayon
Polyester
Celluloid
Polystyrene
Orlon, Acrylic
Cellophane Tape
Polyvinylidene Chloride (Saran)
Polyurethane
Polyethylene
Polypropylene
Polyvinylchloride (Vinyl)
Kel-F (PCTFE)
Gains Silicon
Electrons Teflon
Negative Silicone Rubber
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
123
Appendix 10.2 Plot of 500MΩ Frequency Response in Linear Magnitude Ω
Plot of 500MΩ Frequency Response in Linear Magnitude Ω
Appendix 10.3 Plot of 200MΩ Frequency Response in Linear Magnitude Ω
Plot of 200MΩ Frequency Response in Linear Magnitude Ω
y = 629797x-0.474
R² = 0.2019
0.00
1,000.00
2,000.00
3,000.00
4,000.00
5,000.00
6,000.00
7,000.00
8,000.00
9,000.00
0.E+00 2.E+08 4.E+08 6.E+08 8.E+08 1.E+09
Lin
ea
r M
ag
nit
ud
e,Ω
Frequency,Hz
y = 1E+06x-0.515
R² = 0.2184
0.00
2,000.00
4,000.00
6,000.00
8,000.00
10,000.00
12,000.00
0.E+00 2.E+08 4.E+08 6.E+08 8.E+08 1.E+09
Lin
ea
r M
ag
nit
ud
e,Ω
Frequency, Hz
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
124
Appendix 10.4 Plot of 500MΩ Stray Capacitance over Frequency
Plot of 500MΩ Stray Capacitance over Frequency. Mean capacitance is 4.95 pF
Appendix 10.5 Plot of 200MΩ Stray Capacitance over Frequency
Plot of 500MΩ Stray Capacitance over Frequency. Mean capacitance is 5.6 pF
0
2E-12
4E-12
6E-12
8E-12
1E-11
1.2E-11
0.00E+00 2.00E+08 4.00E+08 6.00E+08 8.00E+08 1.00E+09
Ca
pa
cita
nce
, F
Frequency, Hz
Mean=4.95E-12F
0
2E-12
4E-12
6E-12
8E-12
1E-11
1.2E-11
1.4E-11
1.6E-11
1.8E-11
0.00E+00 2.00E+08 4.00E+08 6.00E+08 8.00E+08 1.00E+09
Ca
pa
cita
nce
, F
Frequency, Hz
Mean=5.6E-12
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
125
Appendix 10.6 Plot of 200MΩ/10pF Capacitance over Frequency
Plot of 200MΩ/10pF Capacitance over Frequency. Mean capacitance is 73.5pF
Appendix 10.7 Plot of 2MΩ/220pF Capacitance over Frequency
Plot of 2MΩ/220pF Capacitance over Frequency. Mean capacitance is 452pF.
0
1E-10
2E-10
3E-10
4E-10
5E-10
6E-10
0.00E+00 2.00E+08 4.00E+08 6.00E+08 8.00E+08 1.00E+09
Ca
pa
cita
nce
, F
Frequency, Hz
Mean=73.50E-12
0.00E+00
2.00E-09
4.00E-09
6.00E-09
8.00E-09
1.00E-08
1.20E-08
1.40E-08
1.60E-08
0.00E+00 2.00E+08 4.00E+08 6.00E+08 8.00E+08 1.00E+09
Ca
pa
cita
nce
, F
Frequency, Hz
Mean=452E-12
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
126
Appendix 10.8 Simulation and Measurement of Electrostatic Discharge
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
127
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
128
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
129
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
130
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
131
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
132
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
133
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
134
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
135
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
136
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
137
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
138
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
139
Appendix 10.9 Simulation and Measurement of an Electrostatic Discharge Low Voltage Experiment Results
560k1.5n1.8
k
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 6.57E-07 6.75E-07 6.39E-07 5.23E-07 6.39E-07 5.07E-07 6.37E-07 6.75E-07 6.75E-07 6.57E-07 6.75E-
07
5.07E-
07
6.28E-
07
Resistor 6.21E-07 6.19E-07 6.15E-07 4.66E-07 6.02E-07 4.34E-07 5.96E-07 6.19E-07 6.22E-07 6.15E-07 6.22E-
07
4.34E-
07
5.81E-
07
Switch 6.48E-09 7.26E-09 7.62E-09 4.37E-09 8.76E-09 1.23E-08 1.31E-08 8.6E-09 1.15E-08 7.36E-09 1.31E-
08
4.37E-
09
8.74E-
09
Losses 2.98E-08 4.91E-08 1.67E-08 5.23E-08 2.88E-08 6.08E-08 2.8E-08 4.72E-08 4.15E-08 3.52E-08 6.08E-
08
1.67E-
08
3.89E-
08
% losses 0.04537
6
0.07271 0.02615 0.10015
5
0.04497
9
0.11994
5
0.04399 0.06997
4
0.06144
4
0.05361
2
11.99
%
2.61% 6.38%
Ipeak 0.01784 0.02163
1
0.01761
7
0.01717
1
0.01850
9
0.01672
5
0.01605
6
0.02073
9
0.01940
1
0.02007 2.16E-
02
1.61E-
02
1.86E-
02
560k1.2n1.8
k
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 5.61E-07 5.76E-07 5.46E-07 5.76E-07 5.61E-07 5.60E-07 5.46E-07 5.76E-07 5.76E-07 5.76E-07 5.76E-
07
5.46E-
07
5.65E-
07
Resistor 5.23E-07 5.33E-07 5.10E-07 5.29E-07 5.20E-07 5.15E-07 5.14E-07 5.27E-07 5.20E-07 5.27E-07 5.33E-
07
5.10E-
07
5.22E-
07
Switch 5.72E-09 8.67E-09 5.83E-09 5.01E-09 1.41E-08 1.74E-08 6.15E-09 8.93E-09 1.16E-08 4.97E-09 1.74E-
08
4.97E-
09
8.85E-
09
Losses 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 4.39E-
08
2.59E-
08
3.46E-
08
% losses 5.72E-02 5.97E-02 5.51E-02 7.27E-02 4.75E-02 4.92E-02 4.75E-02 7.00E-02 7.62E-02 7.58E-02 7.62% 4.75% 6.11%
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
140
Ipeak 0.02051
6
0.02007 0.02051
6
0.01806
3
0.01828
6
0.01672
5
0.01850
9
0.01984
7
0.01850
9
0.01917
8
2.05E-
02
1.67E-
02
1.90E-
02
560k1n1.8k I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 4.43E-07 4.2E-07 4.31E-07 4.43E-07 4.43E-07 4.43E-07 4.55E-07 4.55E-07 4.31E-07 4.31E-07 4.55E-
07
4.20E-
07
4.40E-
07
Resistor 4.07E-07 3.98E-07 3.97E-07 4.08E-07 3.76E-07 4.1E-07 3.85E-07 4.14E-07 3.88E-07 4E-07 4.14E-
07
3.76E-
07
3.98E-
07
Switch 9.21E-09 6.37E-09 8.27E-09 8.42E-09 6.11E-09 5.59E-09 1.28E-08 1.34E-08 5.9E-09 7.22E-09 1.34E-
08
5.59E-
09
8.33E-
09
Losses 2.75E-08 1.58E-08 2.59E-08 2.64E-08 6.07E-08 2.79E-08 5.77E-08 2.78E-08 3.78E-08 2.45E-08 6.07E-
08
1.58E-
08
3.32E-
08
% losses 0.06211
5
0.03757
6
0.06009
2
0.05961 0.13694
7
0.06299
2
0.12665
3
0.06104
7
0.08765
8
0.05681
9
13.69
%
3.76% 7.52%
Ipeak 0.01850
9
0.02163
1
0.01694
8
0.01850
9
0.01694
8
0.02163
1
0.01717
1
0.02185
4
0.02118
5
0.01917
8
2.19E-
02
1.69E-
02
1.94E-
02
560k680p1.8
k
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 2.93E-07 3.01E-07 3.01E-07 3.01E-07 2.93E-07 3.01E-07 2.93E-07 2.93E-07 3.01E-07 2.93E-07 3.01E-
07
2.93E-
07
2.97E-
07
Resistor 2.55E-07 2.63E-07 2.62E-07 2.36E-07 2.58E-07 2.4E-07 2.54E-07 2.58E-07 2.65E-07 2.59E-07 2.65E-
07
2.36E-
07
2.55E-
07
Switch 7.67E-09 7.06E-09 4.49E-09 5.34E-09 3.73E-09 3.6E-09 9.98E-09 4.34E-09 5.23E-09 3.11E-09 9.98E-
09
3.11E-
09
5.45E-
09
Losses 3E-08 3.13E-08 3.48E-08 5.91E-08 3.08E-08 5.73E-08 2.93E-08 3.02E-08 3.12E-08 3.1E-08 5.91E-
08
2.93E-
08
3.65E-
08
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
141
% losses 0.10252
1
0.10402
6
0.11568
4
0.19641
1
0.10501
3
0.19044
5
0.09991
1
0.10318
5
0.10374
2
0.10577
6
19.64
%
9.99% 12.27%
Ipeak 0.01627
9
0.02073
9
0.01940
1
0.01717
1
0.01784 0.02073
9
0.01806
3
0.01984
7
0.01940
1
0.02163
1
2.16E-
02
1.63E-
02
1.91E-
02
560k470p1.8
k
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 2E-07 1.89E-07 1.89E-07 1.89E-07 1.94E-07 2E-07 1.89E-07 1.89E-07 1.89E-07 2.00E-
07
1.89E-
07
1.73E-
07
Resistor 1.55E-07 1.59E-07 1.77E-07 1.83E-07 1.84E-07 1.86E-07 1.79E-07 1.69E-07 1.78E-07 1.86E-
07
1.55E-
07
1.57E-
07
Switch 2.09E-09 2.78E-09 4.25E-09 3.19E-09 3.42E-09 4.06E-09 2.93E-09 2.82E-09 4.75E-09 4.75E-
09
2.09E-
09
3.03E-
09
Losses 4.25E-08 2.69E-08 7.62E-09 2.73E-09 6.77E-09 9.37E-09 6.69E-09 1.78E-08 6.35E-09 4.25E-
08
2.73E-
09
1.27E-
08
% losses 0.21267
2
0.14245
5
0.04028
4
0.01444
4
0.03480
2
0.04690
5
0.03536
6
0.09403
3
0.03356
3
21.27
%
1.44% 6.55%
Ipeak 0.02073
9
0.02073
9
0.01516
4
0.02140
8
0.02118
5
0.01627
9
0.02118
5
0.02029
3
0.01940
1
2.14E-
02
1.52E-
02
1.76E-
02
560k220p1.8
k
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 9.03E-08 8.53E-08 8.29E-08 8.78E-08 8.53E-08 8.04E-08 9.03E-08 8.53E-08 7.81E-08 8.53E-08 9.03E-
08
7.81E-
08
8.51E-
08
Resistor 8.61E-08 8.12E-08 8.07E-08 8.41E-08 7.32E-08 6.52E-08 8.6E-08 8.13E-08 7.47E-08 8.26E-08 8.61E-
08
6.52E-
08
7.95E-
08
Switch 1.53E-09 1.77E-09 1.61E-09 1.67E-09 1.22E-09 9.7E-10 1.78E-09 2.34E-09 1.72E-09 1.72E-09 2.34E- 9.70E- 1.63E-
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
142
09 10 09
Losses 2.73E-09 2.34E-09 5.49E-10 2E-09 1.09E-08 1.43E-08 2.57E-09 1.71E-09 1.59E-09 9.77E-10 1.43E-
08
5.49E-
10
3.96E-
09
% losses 0.03022
5
0.02744
3
0.00662
7
0.02276 0.12719
5
0.17752
3
0.02840
2
0.02001
6
0.02041
8
0.01145
3
17.75
%
0.66% 4.72%
Ipeak 0.01962
4
0.01984
7
0.01962
4
0.02007 0.01962
4
0.01917
8
0.01917
8
0.01940
1
0.01895
5
0.01984
7
2.01E-
02
1.90E-
02
1.95E-
02
560k1.5n1.5
k
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 6.75E-07 6.57E-07 6.57E-07 6.75E-07 6.75E-07 6.75E-07 6.75E-07 6.75E-07 6.75E-07 6.75E-
07
6.57E-
07
6.04E-
07
Resistor 6.15E-07 6.09E-07 6.2E-07 6.08E-07 6.23E-07 6.14E-07 6.15E-07 5.84E-07 6.15E-07 6.23E-
07
5.84E-
07
5.50E-
07
Switch 9.18E-09 7.92E-09 9.94E-09 2.03E-08 8.3E-09 1.38E-08 1.58E-08 6.44E-09 9.22E-09 2.03E-
08
6.44E-
09
1.01E-
08
Losses 5.11E-08 3.97E-08 2.76E-08 4.65E-08 4.38E-08 4.71E-08 4.41E-08 8.41E-08 5.08E-08 8.41E-
08
2.76E-
08
4.35E-
08
% losses 0.07571 0.06049 0.04205
3
0.06887
3
0.06492
5
0.06976 0.06536
7
0.12462
2
0.07527
7
12.46
%
4.21% 6.47%
Ipeak 0.02573
7
0.02252 0.02225
2
0.02118 0.02627
3
0.02010
7
0.02252 0.02654
2
0.02091
2
2.65E-
02
2.01E-
02
2.08E-
02
560k1.2n1.5
k
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 5.61E-07 5.61E-07 5.61E-07 5.6E-07 5.76E-07 5.76E-07 5.76E-07 5.61E-07 5.76E-07 5.76E-07 5.76E-
07
5.60E-
07
5.68E-
07
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
143
Resistor 5.25E-07 5.23E-07 5.25E-07 5.26E-07 5.26E-07 5.26E-07 5.27E-07 5.33E-07 5.32E-07 5.27E-07 5.33E-
07
5.23E-
07
5.27E-
07
Switch 9.29E-09 6.66E-09 9.34E-09 7.15E-09 5.94E-09 1.25E-08 8.7E-09 8.3E-09 9.88E-09 7.94E-09 1.25E-
08
5.94E-
09
8.57E-
09
Losses 2.64E-08 3.13E-08 2.62E-08 2.7E-08 4.36E-08 3.71E-08 4.03E-08 1.97E-08 3.43E-08 4.11E-08 4.36E-
08
1.97E-
08
3.27E-
08
% losses 0.04702
6
0.05577
1
0.04670
6
0.04811
5
0.07563
7
0.06436
5
0.07001 0.03517 0.05951
2
0.07127
5
7.56% 3.52% 5.74%
Ipeak 0.02493
3
0.02171
6
0.02546
9
0.02627
3
0.02627
3
0.02037
5
0.02600
5
0.02520
1
0.02305
6
0.02225
2
2.63E-
02
2.04E-
02
2.42E-
02
560k1n1.5k I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 4.43E-07 4.43E-07 4.43E-07 4.43E-07 4.43E-07 4.31E-07 4.2E-07 4.55E-07 4.55E-07 4.43E-07 4.55E-
07
4.20E-
07
4.42E-
07
Resistor 4.11E-07 3.94E-07 4.09E-07 4.1E-07 4.13E-07 3.73E-07 3.76E-07 4.01E-07 4.16E-07 4.11E-07 4.16E-
07
3.73E-
07
4.01E-
07
Switch 5.14E-09 9.59E-09 6.98E-09 8.21E-09 7.04E-09 6.88E-09 1.29E-08 6.77E-09 9.31E-09 7.61E-09 1.29E-
08
5.14E-
09
8.05E-
09
Losses 2.77E-08 3.94E-08 2.74E-08 2.46E-08 2.31E-08 5.15E-08 3.11E-08 4.73E-08 3E-08 2.47E-08 5.15E-
08
2.31E-
08
3.27E-
08
% losses 0.06237
6
0.08884
7
0.06174
3
0.05557
5
0.05211
8
0.11929
6
0.07409 0.10385
4
0.06585
5
0.05565
4
11.93
%
5.21% 7.39%
Ipeak 0.02010
7
0.02118 0.02305
6
0.02412
9
0.02627
3
0.02386
1
0.02010
7
0.02520
1
0.02439
7
0.02493
3
2.63E-
02
2.01E-
02
2.33E-
02
560k680p1.5 I II III IV V VI VII VIII IX X Max Min Averag
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
144
k e
Capacitor 2.85E-07 2.85E-07 2.61E-07 2.85E-07 2.85E-07 2.85E-07 3.09E-07 2.62E-07 3.01E-07 3.01E-07 3.09E-
07
2.61E-
07
2.86E-
07
Resistor 2.63E-07 2.59E-07 2.57E-07 2.45E-07 2.55E-07 2.21E-07 2.63E-07 2.56E-07 2.55E-07 2.57E-07 2.63E-
07
2.21E-
07
2.53E-
07
Switch 6.43E-09 5.06E-09 5.33E-09 4.54E-09 4.02E-09 9.06E-09 7.06E-09 7.92E-09 1.09E-08 8.34E-09 1.09E-
08
4.02E-
09
6.86E-
09
Losses 1.51E-08 2.08E-08 -1.3E-09 3.56E-08 2.62E-08 5.52E-08 3.93E-08 -2.6E-09 3.53E-08 3.54E-08 5.52E-
08
-
2.57E-
09
2.59E-
08
% losses 0.05309
7
0.07301
2
-0.00491 0.12500
6
0.09204
4
0.19371
5
0.12725
4
-0.00981 0.11726
9
0.11762
6
19.37
%
-0.98% 8.84%
Ipeak 0.02118 0.02493
3
0.02520
1
0.02520
1
0.02466
5
0.02198
4
0.02654
2
0.02600
5
0.02010
7
0.02600
5
2.65E-
02
2.01E-
02
2.42E-
02
560k470p1.5
k
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 1.89E-07 1.79E-07 1.89E-07 2.05E-07 1.89E-07 1.89E-07 1.89E-07 1.89E-07 1.89E-07 1.89E-07 2.05E-
07
1.79E-
07
1.90E-
07
Resistor 1.76E-07 1.67E-07 1.79E-07 1.58E-07 1.73E-07 1.68E-07 1.82E-07 1.71E-07 1.79E-07 1.72E-07 1.82E-
07
1.58E-
07
1.73E-
07
Switch 6.16E-09 7.42E-09 6.26E-09 6.5E-09 5.56E-09 5.42E-09 5.91E-09 9.19E-09 5.76E-09 8.59E-09 9.19E-
09
5.42E-
09
6.68E-
09
Losses 6.9E-09 3.92E-09 3.36E-09 4.1E-08 1.04E-08 1.54E-08 1.09E-09 8.62E-09 3.9E-09 8.12E-09 4.10E-
08
1.09E-
09
1.03E-
08
% losses 0.03647
7
0.02195
2
0.01778
8
0.20003 0.05520
3
0.08124
4
0.00578
9
0.04559
7
0.02059
8
0.04295 20.00
%
0.58% 5.28%
Ipeak 0.02439
7
0.02225
2
0.02466
5
0.02412
9
0.02493
3
0.02546
9
0.02573
7
0.01876
7
0.02573
7
0.01876
7
2.57E-
02
1.88E-
02
2.35E-
02
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
145
560k220p1.5
k
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 8.29E-08 8.78E-08 8.53E-08 8.29E-08 8.28E-08 8.29E-08 8.53E-08 7.57E-08 8.53E-08 8.78E-
08
7.57E-
08
7.51E-
08
Resistor 8.06E-08 8.3E-08 8.23E-08 8.25E-08 7.68E-08 8E-08 8.13E-08 7.45E-08 8.13E-08 8.30E-
08
7.45E-
08
7.22E-
08
Switch 3.09E-09 3.46E-09 3.93E-09 4.38E-09 3.55E-09 3.38E-09 3.12E-09 3.16E-09 3.52E-09 4.38E-
09
3.09E-
09
3.16E-
09
Losses -8.2E-10 1.34E-09 -9.3E-10 -4E-09 2.53E-09 -5.4E-10 9.23E-10 -1.9E-09 5.34E-10 2.53E-
09
-
3.98E-
09
-2.88E-
10
% losses -0.00993 0.01530
1
-0.0109 -0.04803 0.03050
2
-0.00656 0.01081
6
-0.02547 0.00625
8
3.05% -4.80% -0.38%
Ipeak 0.02412
9
0.02412
9
0.02225
2
0.02037
5
0.01903
5
0.02386
1
0.02412
9
0.02278
8
0.02386
1
2.41E-
02
1.90E-
02
2.05E-
02
560k1.5n1k I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 6.75E-07 6.73E-07 6.93E-07 6.75E-07 6.69E-07 6.75E-07 6.75E-07 6.75E-07 6.75E-07 6.73E-07 6.93E-
07
6.69E-
07
6.76E-
07
Resistor 6.34E-07 6.29E-07 6.24E-07 6.33E-07 6.24E-07 6.33E-07 6.16E-07 6.14E-07 6.25E-07 6.06E-07 6.34E-
07
6.06E-
07
6.24E-
07
Switch 1.54E-08 1.63E-08 2.41E-08 1.42E-08 1.69E-08 1.43E-08 1.89E-08 1.48E-08 1.28E-08 1.78E-08 2.41E-
08
1.28E-
08
1.65E-
08
Losses 2.51E-08 2.79E-08 4.45E-08 2.81E-08 2.83E-08 2.78E-08 4.02E-08 4.67E-08 3.77E-08 4.88E-08 4.88E-
08
2.51E-
08
3.55E-
08
% losses 0.03717
7
0.04138
9
0.06422
9
0.04169
5
0.04233
3
0.04120
7
0.05952
5
0.06921
9
0.05584
1
0.07257
4
7.26% 3.72% 5.25%
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
146
Ipeak 0.03518
2
0.03785
9
0.03021 0.03556
4
0.03365
2
0.03709
4
0.03747
6
0.03059
3
0.03594
6
0.03021 3.79E-
02
3.02E-
02
3.44E-
02
560k1.2n1k I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 5.76E-07 5.61E-07 5.76E-07 5.76E-07 5.76E-07 5.76E-07 5.76E-07 5.76E-07 5.74E-07 5.76E-07 5.76E-
07
5.61E-
07
5.74E-
07
Resistor 5.13E-07 5.18E-07 5.31E-07 5.34E-07 5.26E-07 5.29E-07 4.95E-07 5.29E-07 5.26E-07 5.3E-07 5.34E-
07
4.95E-
07
5.23E-
07
Switch 1.14E-08 1.47E-08 1.38E-08 1.23E-08 1.17E-08 1.07E-08 1.02E-08 1.07E-08 1.44E-08 1.26E-08 1.47E-
08
1.02E-
08
1.23E-
08
Losses 5.13E-08 2.78E-08 3.13E-08 3.01E-08 3.78E-08 3.59E-08 7.03E-08 3.64E-08 3.42E-08 3.29E-08 7.03E-
08
2.78E-
08
3.88E-
08
% losses 0.08911
6
0.04962
9
0.05428
1
0.05223
3
0.06560
3
0.06237
3
0.12199 0.06312
3
0.05955
8
0.05713
4
12.20
%
4.96% 6.75%
Ipeak 0.03174 0.03097
5
0.03518
2
0.03288
7
0.03785
9
0.03212
2
0.03403
4
0.03479
9
0.02753
3
0.03059
3
3.79E-
02
2.75E-
02
3.28E-
02
560k1n1k I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 4.43E-07 4.43E-07 4.43E-07 4.55E-07 4.55E-07 4.55E-07 4.55E-07 4.2E-07 4.55E-07 4.43E-07 4.55E-
07
4.20E-
07
4.47E-
07
Resistor 3.67E-07 4.09E-07 4.04E-07 3.81E-07 4.07E-07 4.13E-07 4.18E-07 3.53E-07 4.13E-07 4.04E-07 4.18E-
07
3.53E-
07
3.97E-
07
Switch 7.74E-09 9.23E-09 1.07E-08 1.2E-08 1.02E-08 8.05E-09 1.05E-08 7.65E-09 9.39E-09 9.65E-09 1.20E-
08
7.65E-
09
9.51E-
09
Losses 6.83E-08 2.48E-08 2.88E-08 6.27E-08 3.84E-08 3.46E-08 2.69E-08 5.95E-08 3.28E-08 2.96E-08 6.83E- 2.48E- 4.06E-
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
147
08 08 08
% losses 0.15407
8
0.05602
5
0.06489
5
0.13759
9
0.08430
7
0.07594
6
0.05906
1
0.14180
3
0.07195
6
0.06685
2
15.41
%
5.60% 9.13%
Ipeak 0.03709
4
0.03709
4
0.03097
5
0.02944
6
0.03556
4
0.03785
9
0.03709
4
0.03594
6
0.03747
6
0.03556
4
3.79E-
02
2.94E-
02
3.54E-
02
560k680p1k I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 3.01E-07 2.93E-07 2.93E-07 3.01E-07 2.93E-07 3.01E-07 3.01E-07 3.01E-07 3.01E-07 3.01E-07 3.01E-
07
2.93E-
07
2.99E-
07
Resistor 2.59E-07 2.53E-07 2.52E-07 2.23E-07 2.51E-07 2.58E-07 2.55E-07 2.45E-07 2.19E-07 2.57E-07 2.59E-
07
2.19E-
07
2.47E-
07
Switch 8.51E-09 8.4E-09 7.95E-09 6.97E-09 8.39E-09 9.15E-09 8.9E-09 8.59E-09 7.11E-09 8.64E-09 9.15E-
09
6.97E-
09
8.26E-
09
Losses 3.39E-08 3.19E-08 3.34E-08 7.05E-08 3.32E-08 3.41E-08 3.7E-08 4.74E-08 7.47E-08 3.52E-08 7.47E-
08
3.19E-
08
4.31E-
08
% losses 0.11256
9
0.10892
5
0.11411
6
0.23420
5
0.11335
6
0.11343
3
0.12308
8
0.15735
4
0.24830
9
0.11705
1
24.83
%
10.89
%
14.42%
Ipeak 0.03785
9
0.03671
1
0.03671
1
0.03671
1
0.03632
9
0.03709
4
0.03747
6
0.03709
4
0.03671
1
0.03747
6
3.79E-
02
3.63E-
02
3.70E-
02
560k470p1k I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 1.89E-07 1.89E-07 1.89E-07 1.94E-07 1.89E-07 1.94E-07 1.89E-07 1.94E-07 1.94E-07 1.89E-07 1.94E-
07
1.89E-
07
1.91E-
07
Resistor 1.75E-07 1.8E-07 1.79E-07 1.83E-07 1.66E-07 1.8E-07 1.8E-07 1.82E-07 1.8E-07 1.8E-07 1.83E-
07
1.66E-
07
1.78E-
07
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
148
Switch 6.75E-09 6.51E-09 6.39E-09 6.05E-09 6.2E-09 6.33E-09 6.68E-09 5.74E-09 8.01E-09 6.6E-09 8.01E-
09
5.74E-
09
6.53E-
09
Losses 7.52E-09 2.52E-09 4.12E-09 5.71E-09 1.66E-08 7.6E-09 2.27E-09 6.59E-09 6.78E-09 2.77E-09 1.66E-
08
2.27E-
09
6.25E-
09
% losses 0.03975
3
0.01333
8
0.02180
7
0.02936
9
0.08761
5
0.03908
9
0.01203 0.03391
5
0.03489
5
0.01465
3
8.76% 1.20% 3.26%
Ipeak 0.02944
6
0.03632
9
0.03632
9
0.03632
9
0.03632
9
0.03671
1
0.03632
9
0.03594
6
0.02791
6
0.03632
9
3.67E-
02
2.79E-
02
3.48E-
02
560k220p1k I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 8.29E-08 8.53E-08 8.53E-08 8.78E-08 8.53E-08 8.29E-08 8.78E-08 8.78E-08 8.53E-08 9.03E-08 9.03E-
08
8.29E-
08
8.61E-
08
Resistor 7.77E-08 8.11E-08 7.43E-08 8.31E-08 7.25E-08 7.22E-08 8.14E-08 8.12E-08 8.16E-08 8.28E-08 8.31E-
08
7.22E-
08
7.88E-
08
Switch 3.01E-09 3.13E-09 3E-09 3.1E-09 3.1E-09 3E-09 3.71E-09 4.48E-09 3.1E-09 3.32E-09 4.48E-
09
3.00E-
09
3.29E-
09
Losses 2.15E-09 1.12E-09 8.05E-09 1.64E-09 9.72E-09 7.7E-09 2.73E-09 2.09E-09 6.38E-10 4.25E-09 9.72E-
09
6.38E-
10
4.01E-
09
% losses 0.02591
8
0.01307
1
0.09437
9
0.01867
8
0.11388
3
0.09288 0.03109
7
0.02376
1
0.00748
1
0.04706
2
11.39
%
0.75% 4.68%
Ipeak 0.03327 0.03441
7
0.03288
7
0.03441
7
0.03327 0.03288
7
0.03097
5
0.02447
4
0.03403
4
0.03441
7
3.44E-
02
2.45E-
02
3.25E-
02
560k1.5n330 I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 6.75E-07 6.75E-07 6.75E-07 6.93E-07 6.75E-07 6.75E-07 6.75E-07 6.39E-07 6.75E-07 6.75E-07 6.93E- 6.39E- 6.73E-
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
149
07 07 07
Resistor 6.1E-07 6.07E-07 6.1E-07 6.15E-07 6.05E-07 6.08E-07 6.09E-07 5.78E-07 6.13E-07 6.06E-07 6.15E-
07
5.78E-
07
6.06E-
07
Switch 2.28E-08 2.31E-08 1.96E-08 2.73E-08 2.85E-08 2.39E-08 2.35E-08 2.54E-08 2.13E-08 2.44E-08 2.85E-
08
1.96E-
08
2.40E-
08
Losses 4.18E-08 4.53E-08 4.53E-08 5.12E-08 4.16E-08 4.32E-08 4.26E-08 3.59E-08 4.11E-08 4.47E-08 5.12E-
08
3.59E-
08
4.33E-
08
% losses 0.06196
9
0.06713
3
0.06715
1
0.07382
8
0.06160
3
0.06395
1
0.06316
4
0.05615
7
0.06083 0.06623
7
7.38% 5.62% 6.42%
Ipeak 0.11638
6
0.11516
1
0.11638
6
0.11516
1
0.11271
1
0.11516
1
0.11516
1
0.11026 0.11638
6
0.11516
1
1.16E-
01
1.10E-
01
1.15E-
01
560k1.2n330 I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 5.76E-07 5.76E-07 5.76E-07 5.76E-07 5.76E-07 5.76E-07 5.46E-07 5.76E-07 5.76E-07 5.61E-07 5.76E-
07
5.46E-
07
5.71E-
07
Resistor 5.13E-07 5.13E-07 5.07E-07 5.17E-07 4.98E-07 5.11E-07 5.04E-07 4.92E-07 4.96E-07 5.05E-07 5.17E-
07
4.92E-
07
5.06E-
07
Switch 2.22E-08 2.32E-08 2.11E-08 1.91E-08 2.12E-08 2.06E-08 2.31E-08 2.03E-08 2.27E-08 2.95E-08 2.95E-
08
1.91E-
08
2.23E-
08
Losses 4.06E-08 4E-08 4.81E-08 4.01E-08 5.65E-08 4.43E-08 1.81E-08 6.39E-08 5.72E-08 2.67E-08 6.39E-
08
1.81E-
08
4.36E-
08
% losses 0.07043
6
0.06951
5
0.08352
6
0.06958
4
0.09809
9
0.07692
8
0.03321
7
0.11098
8
0.09934
4
0.04761
7
11.10
%
3.32% 7.59%
Ipeak 0.11393
6
0.11393
6
0.11516
1
0.11516
1
0.11393
6
0.11638
6
0.11393
6
0.11393
6
0.10658
5
0.08820
8
1.16E-
01
8.82E-
02
1.11E-
01
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
150
560k1n330 I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 4.55E-07 4.55E-07 4.55E-07 4.43E-07 4.55E-07 4.55E-07 4.43E-07 4.31E-07 4.55E-07 4.55E-07 4.55E-
07
4.31E-
07
4.51E-
07
Resistor 3.76E-07 3.95E-07 4.04E-07 4.01E-07 3.99E-07 4E-07 4.06E-07 4E-07 4.02E-07 4.02E-07 4.06E-
07
3.76E-
07
3.99E-
07
Switch 2.16E-08 1.68E-08 1.56E-08 1.83E-08 1.81E-08 1.75E-08 1.42E-08 1.69E-08 1.7E-08 1.77E-08 2.16E-
08
1.42E-
08
1.74E-
08
Losses 5.75E-08 4.38E-08 3.62E-08 2.37E-08 3.85E-08 3.74E-08 2.37E-08 1.42E-08 3.6E-08 3.6E-08 5.75E-
08
1.42E-
08
3.47E-
08
% losses 0.12623 0.09611
4
0.07955
2
0.05335
4
0.08453
8
0.08214 0.0534 0.03290
9
0.07895
1
0.07908
2
12.62
%
3.29% 7.66%
Ipeak 0.08330
8
0.11271
1
0.11516
1
0.10291 0.11271
1
0.11393
6
0.11393
6
0.11271
1
0.11393
6
0.11393
6
1.15E-
01
8.33E-
02
1.10E-
01
560k680p33
0
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 3.01E-07 2.85E-07 3.01E-07 3.01E-07 3.01E-07 3.01E-07 2.93E-07 3.09E-07 2.93E-07 3.01E-07 3.09E-
07
2.85E-
07
2.99E-
07
Resistor 2.49E-07 2.37E-07 2.46E-07 2.31E-07 2.5E-07 2.5E-07 2.42E-07 2.48E-07 2.43E-07 2.29E-07 2.50E-
07
2.29E-
07
2.43E-
07
Switch 1.03E-08 1.05E-08 1.14E-08 9.31E-09 1.08E-08 1.01E-08 1.08E-08 1.14E-08 1.09E-08 1.45E-08 1.45E-
08
9.31E-
09
1.10E-
08
Losses 4.14E-08 3.75E-08 4.32E-08 6.1E-08 4E-08 4.06E-08 4E-08 4.95E-08 3.93E-08 5.73E-08 6.10E-
08
3.75E-
08
4.50E-
08
% losses 0.13754
1
0.13144
5
0.14350
4
0.20265
2
0.13286
4
0.13493
6
0.13661
6
0.16003
8
0.13405
6
0.19044 20.27
%
13.14
%
15.04%
Ipeak 0.11393
6
0.11026 0.11393
6
0.11148
5
0.11393
6
0.11393
6
0.11026 0.11393
6
0.11148
5
0.08453
3
1.14E-
01
8.45E-
02
1.10E-
01
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
151
560k470p33
0
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 1.89E-07 1.89E-07 1.89E-07 1.94E-07 1.89E-07 1.84E-07 1.94E-07 1.94E-07 1.94E-07 1.94E-07 1.94E-
07
1.84E-
07
1.91E-
07
Resistor 1.79E-07 1.73E-07 1.76E-07 1.72E-07 1.79E-07 1.69E-07 1.81E-07 1.83E-07 1.79E-07 1.7E-07 1.83E-
07
1.69E-
07
1.76E-
07
Switch 7.09E-09 8.29E-09 7.81E-09 7.3E-09 8.57E-09 8.52E-09 8.43E-09 7.37E-09 9.07E-09 8E-09 9.07E-
09
7.09E-
09
8.05E-
09
Losses 3.46E-09 7.82E-09 4.83E-09 1.47E-08 1.93E-09 6.85E-09 5.14E-09 4.04E-09 6.29E-09 1.65E-08 1.65E-
08
1.93E-
09
7.16E-
09
% losses 0.01830
6
0.04137
1
0.02553
3
0.07541
8
0.01020
8
0.03726
8
0.02644
9
0.02080
3
0.03238
1
0.08511
5
8.51% 1.02% 3.73%
Ipeak 0.10903
5
0.10536 0.10903
5
0.11026 0.10781 0.10413
5
0.10168
5
0.11026 0.09310
9
0.10781 1.10E-
01
9.31E-
02
1.06E-
01
560k220p33
0
I II III IV V VI VII VIII IX X Max Min Averag
e
Capacitor 8.04E-08 8.53E-08 8.53E-08 9.03E-08 8.78E-08 8.53E-08 8.78E-08 8.53E-08 8.04E-08 8.78E-08 9.03E-
08
8.04E-
08
8.56E-
08
Resistor 7.68E-08 7.17E-08 8.36E-08 8.28E-08 7.37E-08 7.27E-08 7.74E-08 8.22E-08 7.64E-08 8.23E-08 8.36E-
08
7.17E-
08
7.79E-
08
Switch 3.13E-09 3.16E-09 2.36E-09 3.59E-09 2.63E-09 2.76E-09 3.27E-09 3.43E-09 3.06E-09 2.77E-09 3.59E-
09
2.36E-
09
3.02E-
09
Losses 5.43E-10 1.05E-08 -6.61E-
10
3.99E-09 1.15E-08 9.90E-09 7.12E-09 -2.87E-
10
1.01E-09 2.74E-09 1.15E-
08
-
6.61E-
10
4.63E-
09
% losses 0.67% 12.28% -0.78% 4.42% 13.07% 11.60% 8.11% -0.34% 1.25% 3.12% 13.07
%
-0.78% 5.34%
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
152
Ipeak 9.92E-02 9.92E-02 1.04E-01 1.03E-01 1.02E-01 1.02E-01 1.02E-01 1.00E-01 9.80E-02 1.02E-01 1.04E-
01
9.80E-
02
1.01E-
01
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
153
Appendix 10.10 High Voltage Experiment Setup
Photo of High Voltage Experiment Setup, Img_2595.jpg
HV Power Supply
HV Return
HV output
Discharge circuit
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
154
Appendix 10.11 High Voltage Experiment Discharge Point
Photo of the Discharge Point, Img_2596.jpg
HV Return
HV output
Discharge electrodes
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
155
Appendix 10.12 High Voltage Experiment Measurement Equipment
Photo of the Measurement Equipment, Img_2597
Oscilloscope Tektronix DPO 4034
DC Power supply 30VDC
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
156
Appendix 10.13 Ignition Experiment, Ignition Frame Extract from High Speed
Camera
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
157
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
158
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
159
Pictures of ignition extracted from high speed camera video
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
160
Appendix 10.14 Table of Ignition and No Ignition Results
100pF(98pF) 275 276 277 278 279 280 281 282 283 284 285 292 293 295 296
Voltage at discharge8804 12325.6 12325.6 10564.8 10564.8 10564.8 8804 8804 8804 8804 8804 7043.2 8804 7043.2 8804
Capacitor 3.80E-03 7.44E-03 7.44E-03 5.47E-03 5.47E-03 5.47E-03 3.80E-03 3.80E-03 3.80E-03 3.80E-03 3.80E-03 0.002431 3.80E-03 2.43E-03 3.80E-03
Resistor 1.25E-03 2.84E-03 3.04E-03 1.66E-03 1.66E-03 1.58E-03 1.22E-03 1.45E-03 1.43E-03 1.25E-03 7.93E-04 6.30E-04 1.01E-03 6.81E-04 1.04E-03
Discharge + 9.17E-04 1.71E-03 1.70E-03 1.79E-03 1.87E-03 1.80E-03 7.66E-04 1.16E-03 1.13E-03 6.06E-04 6.34E-04 3.61E-04 1.30E-03 6.94E-04 1.44E-03
Discharge - -1.05E-03 -2.34E-03 -2.54E-03 -1.24E-03 -1.24E-03 -1.17E-03 -1.01E-03 -1.11E-03 -1.11E-03 -1.06E-03 -6.27E-04 -5.29E-04 -7.37E-04 -5.30E-04 -7.08E-04
1.96E-03 4.06E-03 4.24E-03 3.04E-03 3.11E-03 2.98E-03 1.78E-03 2.27E-03 2.24E-03 1.66E-03 1.26E-03 8.90E-04 2.03E-03 1.22E-03 2.14E-03
Losses 5.84E-04 5.48E-04 1.69E-04 7.76E-04 7.00E-04 9.18E-04 8.01E-04 8.26E-05 1.25E-04 8.88E-04 1.74E-03 9.11E-04 7.49E-04 5.26E-04 6.15E-04
Losses % 15.38% 7.36% 2.27% 14.19% 12.80% 16.78% 21.10% 2.17% 3.29% 23.38% 45.93% 37.46% 19.72% 21.63% 16.20%
Ipeak + 12.44 12.74 12.73592 12.73592 12.73592 12.73592 11.74129 10.94527 11.8408 11.04478 11.14428 7.66 12.73592 10.34826 12.73592
Ipeak - -11.24 -12.74 -12.7359 -12.7359 -12.7359 -12.7359 -8.55721 -12.7359 -12.3383 -9.55224 -8.55721 -7.36318 -12.7359 -10.6468 -12.7359
72pF(68pF) 331 332 333 334 335 336 337 338 339 340 341
Voltage at discharge8804 10564.8 8804 10564.8 7043.2 8804 7043.2 8804 8804 8804 7043.2
Capacitor 2.64E-03 3.79E-03 2.64E-03 3.79E-03 1.69E-03 2.64E-03 1.69E-03 2.64E-03 2.64E-03 2.64E-03 1.69E-03
Resistor 7.69E-04 1.06E-03 7.86E-04 1.03E-03 2.95E-04 9.99E-04 3.18E-04 1.12E-03 5.68E-04 9.79E-04 3.71E-04
Discharge + 7.58E-04 1.06E-03 6.75E-04 9.85E-04 1.29E-04 3.09E-04 1.66E-04 9.29E-05 6.24E-04 9.31E-04 3.78E-04
Discharge - -5.60E-04 -7.93E-04 -5.80E-04 -7.54E-04 -2.37E-04 -8.17E-04 -2.19E-04 -9.70E-04 -3.63E-04 -7.05E-04 -2.49E-04
1.32E-03 1.85E-03 1.25E-03 1.74E-03 3.65E-04 1.13E-03 3.85E-04 1.06E-03 9.87E-04 1.64E-03 6.27E-04
Losses 5.48E-04 8.89E-04 5.95E-04 1.02E-03 1.03E-03 5.11E-04 9.83E-04 4.55E-04 1.08E-03 2.08E-05 6.88E-04
Losses % 20.81% 23.42% 22.58% 26.94% 60.83% 19.40% 58.31% 17.27% 41.00% 0.79% 40.79%
Ipeak + 11.54229 12.73592 10.84577 12.73592 5.074627 7.263682 5.074627 4.378109 11.44279 12.73592 8.258706
Ipeak - -11.8408 -12.7359 -9.55224 -12.1393 -3.8806 -5.97015 -3.48259 -3.28358 -9.45274 -11.8408 -8.25871
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
161
60pF(58pF) 352 353 354 355 356 357 358 359 360 361 362 363
Voltage at discharge7043.2 7043.2 8804 8804 8804 12325.6 12325.6 8804 8804 8804 8804 8804
Capacitor 1.44E-03 1.44E-03 2.25E-03 2.25E-03 2.25E-03 4.41E-03 4.41E-03 2.25E-03 2.25E-03 2.25E-03 2.25E-03 2.25E-03
Resistor 5.16E-04 4.58E-04 5.56E-04 8.62E-04 8.74E-04 1.23E-03 1.34E-03 3.23E-04 4.79E-04 4.95E-04 5.08E-04 4.62E-04
Discharge + 3.51E-04 2.98E-04 7.29E-04 3.92E-04 3.81E-04 1.37E-03 9.86E-04 1.20E-04 1.22E-03 9.40E-04 1.11E-03 9.58E-04
Discharge - -3.55E-04 -3.22E-04 -3.75E-04 -6.63E-04 -6.87E-04 -8.82E-04 -1.00E-03 -2.44E-04 -2.38E-04 -2.71E-04 -2.49E-04 -2.37E-04
7.06E-04 6.20E-04 1.10E-03 1.05E-03 1.07E-03 2.25E-03 1.99E-03 3.64E-04 1.45E-03 1.21E-03 1.36E-03 1.20E-03
Losses 2.16E-04 3.61E-04 5.88E-04 3.32E-04 3.06E-04 9.25E-04 1.08E-03 1.56E-03 3.14E-04 5.42E-04 3.83E-04 5.90E-04
Losses % 15.01% 25.09% 26.15% 14.76% 13.62% 20.99% 24.54% 69.43% 13.95% 24.12% 17.04% 26.26%
Ipeak + 7.263682 8.159204 11.54229 8.059701 7.661692 12.73592 12.73592 4.278607 12.73592 12.73592 12.73592 12.73592
Ipeak - -9.05473 -6.46766 -11.9403 -8.1592 -7.9602 -12.7359 -10.6468 -3.9801 -12.7359 -11.1443 -11.9403 -9.35323
50pF(45pF) 307 309 310 311 312 313 316 317 318 319 320
Voltage at discharge8804 7043.2 7043.2 5282.4 7043.2 7043.2 7043.2 10564.8 7043.2 12325.6 12325.6
Capacitor 1.74E-03 1.12E-03 1.12E-03 6.28E-04 1.12E-03 1.12E-03 1.12E-03 2.51E-03 1.12E-03 3.42E-03 3.42E-03
Resistor 5.91E-04 3.45E-04 2.00E-04 1.41E-04 4.13E-04 2.95E-04 3.38E-04 6.88E-04 3.86E-04 8.07E-04 8.57E-04
Discharge + 6.74E-04 3.14E-04 6.06E-04 2.84E-04 2.29E-04 2.81E-04 3.59E-04 8.79E-04 3.77E-04 1.18E-03 1.16E-03
Discharge - -4.30E-04 -2.54E-04 -8.44E-05 -8.32E-05 -2.83E-04 -2.10E-04 -2.14E-04 -4.44E-04 -2.41E-04 -5.00E-04 -5.52E-04
1.10E-03 5.68E-04 6.90E-04 3.67E-04 5.13E-04 4.91E-04 5.73E-04 1.32E-03 6.18E-04 1.69E-03 1.71E-03
Losses 4.86E-05 2.03E-04 2.26E-04 1.20E-04 1.90E-04 3.30E-04 2.05E-04 5.00E-04 1.12E-04 9.27E-04 8.48E-04
Losses % 2.79% 18.19% 20.28% 19.04% 17.02% 29.58% 18.33% 19.91% 10.05% 27.11% 24.80%
Ipeak + 11.24378 6.865672 10.84577 6.169154 5.472637 7.661692 8.457711 12.1393 9.054726 12.73592 12.73592
Ipeak - -11.4428 -8.0597 -10.2488 -7.56219 -5.37313 -5.47264 -5.47264 -11.9403 -6.26866 -12.7359 -12.7359
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
162
Appendix 10.15 Data for Ignition Probability Plot, with Ignition Data
B0 -11.5038
B1 25660
Energy Probability
0 1.01E-05
0.00005 3.64E-05
0.0001 0.000131
0.00015 0.000474
0.0002 0.001706
0.00025 0.006128
0.0003 0.021757
0.00035 0.074275
0.0004 0.224471
0.00045 0.510798
0.0005 0.790211
0.00055 0.931451
0.0006 0.980007
0.00065 0.994377
0.0007 0.998435
0.00075 0.999566
0.0008 0.99988
0.00085 0.999967
0.0009 0.999991
0.00095 0.999997
0.001 0.999999
0.00105 1
0.0011 1
0.00115 1
0.0012 1
0.00125 1
0.0013 1
0.00135 1
0.0014 1
0.00145 1
0.0015 1
0.00155 1
0.0016 1
0.00165 1
0.0017 1
0.00175 1
0.0018 1
0.00185 1
0.0019 1
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
163
0.00195 1
0.002 1
0.00205 1
0.0021 1
0.00215 1
0.0022 1
0.00225 1
0.0023 1
0.00235 1
0.0024 1
0.00245 1
0.0025 1
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
164
Appendix 10.16 Confirmation of Candidature Document, Sections: Concept and Literature
Review
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
165
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
166
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
167
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
168
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
169
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
170
Theoretical and Experimental Characterisation of Energy in an Electrostatic Discharge
10.0 Appendix
171