Low level seminar
A Greater Measure of Confidence
DC Voltage measurements, intro
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Voltage Measurements
VSource
of
Voltage
VoltmeterVs
Two main problems:
1. Source is not ideal, Vs is dependent upon load
2. Voltmeter is not ideal, it is not an absolute open
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Thevenin Equivalent Model
VoltmeterV
Rs
Ideal voltage
source Vs
• VS Open-Circuit Voltage
• RS Thevenin Equivalent Source Resistance
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Thevenin Equivalent Model
VoltmeterVRin
Rs
Source
of
Voltage
Vs
V = V
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S
Rin
R + RS in
Theoretical Limits of Voltage Measurement
The Rs provides a fundamental limit to how
well you can resolve Vs:
Vn = 4kTBRs
K - Boltzmann’s constant
T - absolute temperature of the source
B - noise bandwidth in hertz
R - resistance of the source in Ohms
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How to reduce Vn
• Reduce temperature
• Reduce the bandwidth:
– Increasing response time of the instrument
– Noise speed trade off
Vn = 4kTBRs
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Voltage Measurements
VsSource of
Voltage
RsHI
LO
En
In
Cin RinV Ideal
Voltmeter
Voltmeter
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Voltage Measurements
VsSource
of
Voltage
Rs
V
R2
R1
Voltmeter
V = VS
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R1+ R2
R1
Voltage Measurements
RsHI En Voltmeter
Source of In Ideal
VoltageVs
Cin RinV
Voltmeter
LO
VsSource
of
Voltage
Rs
V
R2
R1
Voltmeter
A Greater Measure of Confidence
Typical Parameters
Instr. type
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RIN eN IN
DMM 1GΩ 1µV 100pA
nVmeter 1GΩ 10nV 50pA
Electrometer 10TΩ 10µV 10fA
PROBLEM: Measure 1 mV to within 3%
Instr. Type RIN eN IN
DMM
nVmeter
Electrometer
1GΩ
1GΩ
10TΩ
1µV
10nV
10µV
100pA
50pA
10fA
10MΩ
1mV
A Greater Measure of Confidence
PROBLEM: Measure 1 mV to within 3%
Instr. Type RIN eN IN
DMM
nVmeter
Electrometer
1µV
10nV
10µV
100pA
50pA
10fA
1GΩ-1%1GΩ
10TΩ
10MΩ
1mV
A Greater Measure of Confidence
PROBLEM: Measure 1 mV to within 3%
Instr. Type RIN eN IN
DMM
nVmeter
Electrometer
1GΩ-1%1GΩ
10TΩ
1µV±0.1%10nV
10µV
100pA
50pA
10fA
10MΩ
1mV
A Greater Measure of Confidence
PROBLEM: Measure 1 mV to within 3%
Instr. Type RIN eN IN
DMM
nVmeter
Electrometer
1GΩ-1%1GΩ
10TΩ
1µV±0.1%10nV
10µV
100pA10-10 A* 107 Ω = 10-3 V
50pA
10fA
±100%!!
10MΩ
1mV
A Greater Measure of Confidence
PROBLEM: Measure 1 mV to within 3%
Instr. Type RIN eN IN
DMM
nVmeter
Electrometer
1GΩ-1%1GΩ-1%10TΩ
1µV±0.1%10nV
10µV
100pA10-10 A* 107 Ω = 10-3 V
50pA
10fA
±100%!!
10MΩ
1mV
A Greater Measure of Confidence
PROBLEM: Measure 1 mV to within 3%
Instr. Type RIN eN IN
DMM
nVmeter
Electrometer
1GΩ-1%1GΩ-1%10TΩ
1µV±0.1%10nV
±0.001%10µV
100pA10-10 A* 107 Ω = 10-3 V
50pA
10fA
±100%!!
10MΩ
1mV
A Greater Measure of Confidence
PROBLEM: Measure 1 mV to within 3%
Instr. Type RIN eN IN
DMM
nVmeter
Electrometer
1GΩ-1%1GΩ-1%10TΩ
1µV±0.1%10nV
±0.001%10µV
100pA
50pA5*10-11 *107 Ω= 5*10-4 V
10fA
10-10 A* 107 Ω = 10-3 V
±100%!!
±50%!!
10MΩ
1mV
A Greater Measure of Confidence
PROBLEM: Measure 1 mV to within 3%
Instr. Type RIN eN IN
DMM
nVmeter
Electromete
r
1GΩ-1%1GΩ-1%10TΩ
-0.0001%
1µV±0.1%10nV
±0.001%10µV
100pA
50pA5*10-11 *107 Ω= 5*10-4 V
10fA
10-10 A* 107 Ω = 10-3 V
±100%!!
±50%!!
10MΩ
1mV
A Greater Measure of Confidence
A Greater Measure of Confidence
PROBLEM: Measure 1 mV to within 3%
Instr. Type RIN eN IN
DMM
nVmeter
Electromete
r
1GΩ-1%1GΩ-1%10TΩ
-0.0001%
1µV±0.1%10nV
±0.001%10µV
±1%
100pA
50pA5*10-11 *107 Ω= 5*10-4 V
10fA
10-10 A* 107 Ω = 10-3 V
±100%!!
±50%!!
10MΩ
1mV
A Greater Measure of Confidence
PROBLEM: Measure 1 mV to within 3%
Instr. Type RIN eN IN
DMM
nVmeter
Electromete
r
1GΩ-1%1GΩ-1%10TΩ
-0.0001%
1µV±0.1%10nV
±0.001%10µV
±1%
100pA
50pA
10fA
10-10 A* 107 Ω = 10-3 V
±100%!!
5*10-11 *107 Ω= 5*10-4 V
±50%!!
10-14 A*107Ω =10-7V
=±0.01%!!
OK! ~ 1 % Error
10MΩ
1mV
Rs determines what instrument to choose
A Greater Measure of Confidence
• High Rs (Rs > 1 MΩ )– A limiting factor could be loading errors or voltage terms created by offset current In. Need a high input impedance voltmeter to reduce such errors: Electrometer. See high impedance voltage measurements.
• Low Rs (Rs < 1 MΩ )– For low Rs, very high input resistance not required, DMM could be a good solution. For low voltages, the limiting factor could be En. Use Nanovoltmeter
For More Information:
A Greater Measure of Confidence
Later segments of Keithley’s Low Level
Seminars:
• High impedance voltage measurements
• Low impedance voltage measurements
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A Greater Measure of Confidence
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