94
Instrumenta*on Chris Carr Monday 26 th November 2012 with thanks to Patrick Brown for many of the magnetometer slides
Instrumenta*on
Chris Carr Monday 26th November 2012
with thanks to Patrick Brown
for many of the magnetometer slides
PG Instrumenta*on Lectures 2012
• Monday 26th 10:00 -‐ 11:30 1. General principles and prac-ce for instrumenta-on 2. Design for the space environment
• Monday 26th 14:00 -‐ 15:30 3. Magne-c Field Instruments
• Wednesday 5th December Tutorial Session (Juliet) – See handout
2
The Scien*fic Method
3
The Scien*fic Method
4
General principles and Prac*ce for Instrumenta*on
General Design Considera*ons Linear Systems
• Transfer Func*on • Series systems and feedback
Characterisa*on • Sta*c Response, Frequency Response and Transient Response • Calibra*on
Digi*sa*on • Digital Signals • Aliasing
Feedback • Reason for using
Fourier • Bandwidth considera*ons
Noise • Sources and Characteris*cs
5
Fluxgate Magnetometer Instrument for the ESA/CNSA ‘Double Star’ Mission
6
Design Considera*ons
• Measurement Range • Resolu*on • Frequency Response • Noise • Calibrated accuracy • Stability (over *me and temperature) • Mass, power, telemetry • Reliability • Thermal and mechanical stresses • Radia*on • Cost • Schedule • Poli*cs!
7
Block Diagram – ‘Generic Instrument’
8
Sensor o`en kept apart from the rest of the instrument • Reduce interference • Because the environment is hos*le for the electronics • For user convenience
Sensor signal is usually small/weak Transmission line • Preserves the signal shape and strength • Prevents interference from outside signals
Condi*oning Electronics • Boosts the signal (amplifica*on) • Removes unwanted signals (filtering)
Converts from a voltage to a sequence of
numbers
We can do much more sophis*cated signal
processing in the ‘digital domain’
9
Desired characteris*cs of our func*onal elements
• Predictable input/output rela*onship (Transfer Func-on) for example – B to volts for a sensor – volts to volts for a filter, or amplifier – volts to ‘number’ for Analogue to Digital Converter
• Linear input/output response – Allows Fourier and related techniques to be applied
• Isola-on between blocks – Each block does not influence connected elements (no ‘loading’) – Low output impedance and high input impedance
Bolton: Mechatronics 10
Desired characteris*cs of our func*onal elements
• Predictable input/output rela*onship (Transfer Func-on) for example
• Linear input/output response • Isola-on between blocks
Physical Quan*ty
Low Zout High Zin Low Zout High Zin Low Zout High Zin
volts volts Filtering, Amplifica*on
More usually ADC and storage
11
The sensor shall not ‘load’ the quan*ty to be measured
Linear Systems and the Transfer Func*on
• System transfer func*on is Laplace-‐domain representa*on of the input/output rela*onship
G(s) =X(s)
Y (s)=
L{x(t)}L{y(t)}
Integral Laplace Transform Note similarity to Fourier Transform however • Is single-‐sided (t from zero to infinity) • Transforms to a func*on of the complex variable s • The Laplace transform has no direct physical
meaning
L{f(t)} = F (s) =
Z 1
0f(t)e�stdt
s = � + j!12
Generally required configura*ons: Systems in series and with feedback
13
X(s)
Y (s)= G1(s)G2(s)G3(s)
Bolton: Mechatronics
X(s)
Y (s)=
G(s)
1 +G(s)H(s)
U*lity of the Transfer Func*on
14 x(t) = L�1{G(s)Y (s)}
• Predict output x for any arbitrary input y – or vice-‐versa
Linearity requires func*onal blocks to be Linear Time-‐Invariant
• Governed by an n’th-‐order linear ordinary differen*al equa*on of the form
– y(t) is the input (forcing func-on) – x(t) is the output (response func-on)
• Most prac*cal system elements can be modeled as zero, first or second-‐order LTI
a0x+ a1dx
dt
+ a2d
2x
dt
2. . . an
d
nx
dt
n= b0y
15
Zero-‐order System
• No *me-‐dependence – Output responds instantly to input
• Characterised by Sta-c Sensi-vity • Examples: Poten*ometer, ideal amplifier
– Rare in reality, but many devices can be approximated as zero-‐order
a0x = b0y
Ks =b0a0
16
First-‐order System
• For the sta*c case • Exponen*al *me dependence
characterised by -me constant • Examples: First-‐order filter (e.g. RC), many sensors (e.g. any temperature
sensor), many instruments (e.g. magnetometer)
a0x+ a1dx
dt
= b0y
dx
dt
= 0 ! Ks =b0
a0
⌧ =a1a0
17
Second-‐order System
• Sta*c response
• Natural frequency
• Damping ra*o
• Examples: 2nd order filter, many mechanical, electrical and mechatronic systems
a0x+ a1dx
dt
+ a2d
2x
dt
2= b0y
dx
dt
= 0 ! Ks =b0
a0
!0 =
ra0a2
⇠ =a1
2pa0a2
18
Frequency Response for the Second-‐order System
• Recover Frequency Response from Transfer Func*on by sejng σ=0
• Bode Plot is log-‐log plot of G(jω) • For high-‐damping (ξ>1) second-‐
order system tends to first-‐order behaviour
X(s)
Y (s)= G(s) ! G(j!)
19
Bolton: Mechatronics
Proper*es of LTI Systems
1. Frequency Preserva*on
2. Superposi*on
• If elements are LTI then system will be LTI • Fourier and Laplace methods are applicable • Linear system will not distort signal
– Non-‐linearity will result in genera*on of new frequencies or Harmonic Distor-on
• Instrumenter’s goal is to ensure a linear design
Linear
Time Invariant
System
𝐴0 cos(𝜔0𝑡 + 𝜙0) 𝐴0′ cos(𝜔0𝑡 + 𝜙0′ )
Linear
Time Invariant
System
𝐴0 cos(𝜔0𝑡 + 𝜙0) + 𝐴1 cos(𝜔1𝑡 + 𝜙1) +…
𝐴0′ cos(𝜔0𝑡 + 𝜙0′ ) +
𝐴1′ cos(𝜔1𝑡 + 𝜙1′ ) +⋯
20
System Characterisa*on
• Conclude that we may fully characterise a system by measuring its 1. Transient Response
(typically step-‐input y(t)=u(t)) 2. Sta-c Response
(a`er transients decayed, typically for large t) 3. Frequency Response
(response to sinusoidal input swept over some range of input frequencies)
21
First order transient response
• E.g. temperature sensor suddenly placed in hot liquid
• Exponen*al response • Can measure the -me-‐
constant and sta-c sensi-vity • Also derive bandwidth
!c =1
⌧
22
Cluster Magnetometer Frequency Response
• Bode Plot (Magnitude part only) • Bandwidth is defined as response from DC to ωc
23
-‐3dB
ωc
Bandwidth ~20Hz
Sta*c Response: Devia*on from the ideal
Non-‐Linearity
Hysteresis
24
Offset
All may introduce non-‐linear effects resul*ng in artefacts in the data especially harmonic distor*on • Offset may be subtracted • Non-‐linearity and hysteresis more pernicious
Sta*c Response Measurement
• Comparison with reference measurement – Best es*mate of ‘True Value’ – Usually from a ‘higher quality’
instrument
• Quan*fy – Sta*c Sensi*vity – Linearity – Zero offset – Hysteresis
Doebelin: Measurment Systems 25
Calibra*on Hierarchy
Primary Standard Interna*onally Recognised
Secondary Standard e.g. NPL Accuracy *** Cost £££
Ter*ary Standard e.g. Specialist Calibra*on
Lab Accuracy ** Cost ££
In-‐House Calibra*on Lab e.g. in industry or university Accuracy * Cost £
Ter*ary Standard e.g. Specialist Calibra*on
Lab Accuracy ** Cost ££
Ter*ary Standard
Secondary Standard Other Na*onal
Ter*ary Standard Other Na*onal
26
Calibra*on is used to es*mate Systema*c Error
• “Truth” ≡ Reference Measurement • “Bias” ≡ Systema*c Error • “Precision” ≡ Std Devia*on of distribu*on
27
Precision is not the same as Accuracy
28
Uncontrolled External Input
• Temperature-‐dependent sta*c-‐sensi*vity and offset • Other environmental considera*ons
– Pressure, accelera*on, vibra*on, illumina*on – Dri`, ageing (electronic systems) – Wear (mechanical systems)
29
Calibra*on Principle
• Compare against reference measurement with other input factors controlled / constant – Cover parameter space – Control external factors such as
temperature
30
Calibra*on Principle
• Helmholtz coils null Earth’s field and apply test B
• Temperature-‐controlled Box houses Magnetometer under test
• Reference magnetometer mounted outside box
31
Sampling and Digi*sa*on
• Is a 2-‐stage process • Is not just a phenomenon of the digital age • All laboratory data is
1. Sampled (measurement taken every minute) 2. Digi*sed (number wriven in a lab-‐book)
32
1. Sample & Hold circuit (regular sampling)
2. Analogue to Digital Converter (linear approxima*on)
Electronic Digi*ser
33
Quan*sa*on
• Sampling quan*ses *me into a set of discrete values – Want regularly spaced samples (sampling *me Ts) – Variability or ‘noise’ on Ts is known as jiPer – Stable clock signal
(e.g. square-‐wave) will ensure regular, low-‐jiver sampling
• Digi-sa-on quan*ses the con*nuous analogue quan*ty (usually a voltage) as a discrete number – Introduces an error
to the digi*sed signal – Quan-sa-on Error
34
• Quan*sa*on error will be – over a long series of input values – uniformly distributed between ±½ the resolu*on of the digi*ser
• Quan*sa*on adds noise • RMS noise added is
35
NRMS =qp12
Nyquist Theorem
• A signal can only be properly sampled if it has frequency components below half the sample rate – Wagon-‐Wheel Effect – This is Aliasing
36
Aliasing
37
Frequency-‐domain Characteris*cs of the Digi*sed Signal next section. As an example of this, assume
fs
= 100 Hz and the input signal contains allof the frequencies 25, 70, 160 and 510 Hz addedtogether. The spectrum of the analogue signalwould show all these frequencies. The spectrumof the digital signal shows the frequencies 25,30, 40 and 10 Hz. The first is correct, but thelast 3 are aliases.
It gets worse. If we see a signal at 10 Hz inthe digital data we have no means of know-ing if the original analogue signal was 10 Hz,90 Hz, 110 Hz, 190 Hz etc. It could be thatall of these signals were present, so all of thealiases would add on top of the real 10 Hz sig-nal, thus destroying any knowledge we mightneed about the amplitude of the original 10 Hzsignal. This illustrates a key point about alias-ing: not only does it generate new false fre-quencies, it can also destroy information aboutthe correct, lower frequencies. Because it is soimportant, we will study this in more detail inthe first lab session.
The Frequency Characteristics ofSampled Signals
One important point to start with is that a sam-pled signal is fundamentally unlike any otherkind of continuous signal you will have comeacross before. According to equation 5.1, theoriginal signal has been multiplied by a series ofdelta functions to create what we might call an’impulse train’. It is non-zero for values of nT
s
,but zero in-between. This gives it a very com-plicated spectrum, which we can see by takingthe Fourier Transform of equation 5.1 to get3
3We will cover the integral Fourier transform in moredetail later on in the course. In general, the mathemat-ics for sampled signals and the equivalent transformsinto the frequency domain are rather involved and be-yond the scope of this course. The result is quoted hereto give an understanding of the behaviour of the sam-pled signal under the Fourier transform but you wouldnot be expected to know or derive this.
Fs
(!) =1
Ts
1X
n=�1F (! + n!
s
) (5.3)
!s
=2⇡
Ts
= 2⇡fs
This shows that the spectrum of the sampledsignal is the same as the original signal, but re-peated infinitely along the frequency axis. Fig-ure 5.3 gives a graphical illustration of this.Panels (a) and (b) show the original signal andits spectrum. We can see that the signal is lim-ited to a band of frequencies below the Nyquistfrequency, so we should be able to sample itproperly. In fact, we are sampling comfortablyabove this at about 3 times the highest fre-quency in the analogue signal. Note that thissignal and its spectrum is highly stylised; realsignals rarely have such neatly compact spec-tra, as we shall see later, however it illustratesa principle here.
Panel (c) shows the sampled version of the sig-nal, in the form of an impulse train, and inthe spectrum (d) we can see the new repeatingfrequencies generated by the sampling process.The reason for this is not straightforward butonce understood does provide a rather satisfy-ing explanation for aliasing. In equation 5.1we can see that the original signal was multi-plied by an infinite sequence of delta-functions(the so-called comb function). Now, the Fouriertransform of the comb function happens to beanother comb function4. Further, multiplica-tion in the time-domain is equivalent to con-volution in the frequency domain. Therefore,in the frequency-domain we expect that thespectrum of the sampled signal is the spectrumof the original signal convolved with a combfunction. This is why the spectrum repeats in-finitely. Note that in the figure only the posi-tive frequency range is shown. We know thatthe Fourier transform generates negative fre-quencies as well; this is what accounts for thepart of the spectrum labeled “lower-sideband”.The spectra “copies” repeat each multiple of thesample frequency. If we reduce the sample rate
4See the table of Fourier transforms in Poularikas
20
38 Figure 5.3: Sampled Signals in the Frequency Domain (from Smith, www.dspguide.com)
21
Proper Sampling (obeys Nyquist)
Improper Sampling
(aliasing)
Avoid Aliasing High design priority
– An*-‐alias filter • Filters the analogue signal • Removes frequencies higher than the Nyquist limit
39
Feedback
• Many sensors are non-‐linear over the input range we need
• However approximately linear over a limited range
• We can use Nega*ve Feedback to operate the sensor only in the linear regime
• Will see how this is applied to Magnetometers using magne-c feedback
40
Approximately linear range
Feedback: a Frac*on B of the output is fed-‐back to the input
If B is posi*ve then we have posi-ve feedback. This is usually Unstable
41
Example: Climate Feedback
42
If B is nega*ve then we have nega-ve feedback. This is usually Stable
• The output acts so as to reduce the input • The Gain of the system is reduced • This is also called Closed Loop Opera-on • Behaviour of the Feedback path becomes dominant
43
G =
A
1 +BA⇡ 1
Bfor BA � 1
Example: Mechanical Governor Maintain constant speed (independent of load)
44
Fourier Representa*on of Signals
• Mul*plica*on in the *me domain -‐> Convolu*on in the frequency domain • A signal which is finite in *me is theore*cally infinite in frequency • Real signals have large bandwidths 45
Discussion ques*on:
• How much does it cost to build an instrument to generate this waveform?
46
t
f(t)
2
0 1.5 3 4.5 6 7.5
Answer
• A mathema*cally perfect voltage output is not possible • Bandwidth roughly ∝ cost • We will always lose some frequencies and corrupt the signal
• Engineering: “The Art of Compromise” – Fidelity ∝ bandwidth but – Noise ∝ bandwidth and – Bandwidth costs money – Etc…
• We must analyse all the trade-‐offs when designing the instrument
47
Noise
• Is usually the limi*ng factor in our measurement ability • Comes from
– The sensor (physics of the measurement) – The electronics – Digi*sa*on – Interference
• We will consider 1. Thermal Noise 2. Shot Noise 3. Flicker Noise (1/f)
48
Sources of noise in experimental data
Total noise in measurement
Intrinsic Noise
Sensor physics
E.g. Barkhausen noise from magne*c materials
Sensor electronics
Thermal noise Shot noise
Measurement noise
Quan*sa*on noise
Flicker or 1/𝑓 noise
Extrinsic Noise
Sensor Pickup
Environmental Interference e.g. magne*c
sources
Electronic Interference
Conduc*ve pickup through
power/signal wires
Radia*ve pickup by
Magne*c field (induc*ve) or Electric Field (capaci*ve)
49
Noise comes from stochas*c processes
• Can only be described sta*s*cally • Amplitude probability func*on
– Normal (Gaussian) for shot, thermal, flicker – Uniform (flat) for quan*sa*on noise
• Power Spectrum – Flat (white) for thermal, shot – ∝1/𝑓 (pink)
for flicker
50
Thermal Noise
51
• Random thermal mo*on of conduc*on electrons
• Any resistance allows the material to support an electric field resul*ng in noise voltage
• Model as ideal (noiseless) resistor in series with ideal (zero-‐resistance) voltage source
• RMS noise voltage measured across any resistance R with a meter bandwidth B is
• Reduce thermal noise by – Reducing measurement bandwidth – Reduce temperature
VNRMS =p
4RkBTB
Shot Noise
• Sta*s*cal fluctua*on in number of charge carriers crossing a poten*al barrier – Prevalent in semiconductor or electron tube devices – Seen as noise in the current signal from the device – Due to quan*sa*on of charge, so only observed with small currents – Not present wires or resis*ve devices where long-‐range E-‐field interac*ons act
to ‘smooth’ the charge-‐carrier sta*s*cs
• RMS current noise on a DC current I measured with bandwidth B
52
INRMS =p2eIB
Flicker or 1/𝑓 noise
• A fundamental property of measurement
• Ubiquitous • Source generally unknown • Technology dependent
53
Pf1. . . f2 = k
Z f2
f1
1
fdf = k ln
fhfl
Power / 1
f
Composite Noise Power Spectrum
54
Consequences and Mi*ga*on • Noise is a func*on of physical parameters such as temperature,
resistance, current but always bandwidth • Reducing bandwidth reduces total noise measured
– Use filtering – Recall though that bandwidth reduc*on impacts signal fidelity – Consider more sophis*cated techniques such as phase sensi*ve
detec*on
55
2. Design for the Space Environment
– Accommoda*on – Mechanical Stresses – Thermal Stresses – Radia*on – Reliability/Redundancy
Fluxgate Magnetometer Instrument: Imperial College, IGeP Braunschweig, IWF Graz, NASA-‐GSFC
• Radia*on hard • Hi-‐Rel • Dual-‐redundant bus
architecture • Fault-‐tolerant by
design • 12-‐years con*nuous
opera*on (4 instruments)
• No degrada*on
56
Instrument Accommoda*on
on the Satellite Pla|orm
57
• Sensor – Boom-‐mounted – Removed from magne*c
sources on the pla|orm – But thermally challenging
and exposed to radia*on
• Electronics Box – Pla|orm-‐mounted – Benign thermal/radia*on
environment
58
Sensor and Electronics Accommoda*on
Mechanical Stress
• Test design for – Sta*c load
• 10’s g – Random load
• General ‘strength’ test – Sinusoidal load
• Search for resonances – Acous*c load
• Exhaust reflec*on from pad – Shock test
• Stage separa*on, especially upper-‐stage pyro-‐separa*on from satellite
• Mission-‐specific test levels 59
Thermal Stress • 1361 Wm-‐2 at 1RE • x10 at Mercury (BepiColombo) or Solar Orbiter perihelion • Local cooling by conduc*on and radia*on only • Conversely, shadowed
structure down to 100K • Rota*on or eclipses
results in extreme thermal cycling
• Poten*al for cracking or deforma*on
• Material selec*on to match thermal expansion coeffs
• Electronics and solder joints par*cularly vulnerable
60
Radia*on Electron, proton and heavy-‐ion effects
• Primarily CMOS and bipolar transistor effects
1. Total dose effects – 2kRad LEO – 20-‐100kRad polar Earth orbit
(Cluster) – 1MRad at Jupiter
2. Single event effects – High-‐energy par*cles – Transient effects such as
memory ‘bit-‐flips’ – ‘Latch-‐up’ – Catastrophic gate rupture
3. Displacement Damage – Crystal lajce corrup*on – Op*cs and optoelectronics
specially vulnerable
61
Total Dose Effects in MOS Gate Oxides
Holes are trapped at interface between VG
Electron-hole pairs
n+ n+ Source Drain
- -+
+ ++ +
+
+
from ionization in gate oxide gate oxide and channel
Ionization produces electron-hole pairs within the gate
Holes are trapped at oxide-silicon interface – Changes gate threshold voltage – Two types of traps: hole traps and interface traps
2008 Detector Workshop 8
Displacement Damage
Effects of Displacement Damage in Semiconductors – Minority carrier lifetime is degraded
• Reduces gain of bipolar transistors • Also affects optical detectors and some types of light-emitting diodes • Effects become important for proton fluences above 1010 p/cm2
– Mobility and carrier concentration are also affected Incident • Only important for high fluences particle
Particles Producing Displacement Damage – Protons (all energies) – Electrons with energies above 150 keV – Neutrons (from on-board power sources)
2008 Detector Workshop 22
Galactic Cosmic Rays
Extremely energetic particles – Produced by inter-galactic acceleration – They occur everywhere in space
GCR particles produce an intense track of electron-hole pairs along their path Charge collected in p-n junctions can cause a basic storage cell to change state (SEU)
Charge ~ Z2
+ + -
+ -+ -
+
+ + +
-
n
p-substrate + -
Incoming particle
Note the longer path length for strikes at angle
2008 Detector Workshop 37
Johnstone/NASA-‐JPL
Reliability
• Hi-‐Rel or established reliability components
• Highest level of fabrica*on scru*ny and tes*ng
• ‘Burn-‐in’ to avoid ‘infant mortality’
• Special processes for reliability and radia*on-‐hardness
• Circuit design prac*ce to mi*gate ‘single-‐point failures’
• Formal methodologies: – Worst-‐case analysis – De-‐ra*ng – Failure Modes Effects and Cri*cality
Analysis (FMECA)
62
63
FGMOUTBOARD
SENSOR
FGMINBOARDSENSOR
DUALMULTIPLEXER
& ADC
FGM-OBELECTRONICS
FGM-IBELECTRONICS
bus #2
bus #1
DPU-1DPU-2 MSA
INTERFACE#1
INTERFACE#2DUAL
POWERSUPPLY
UNIT
DUALPOWER
MANAGEMENTUNIT
INTERNALPOWER
DISTRIBUTION
COMMAND &DATA
INTERFACE(REDUNDANT)
INTER-EXPERIMENT
LINKPOWERINTERFACES
REDUNDANTPRIME COMMAND &DATA
INTERFACE(PRIME)
NASA/GSFC IWF GRAZ TU-BS ICSTM
Cluster FGM Instrument Block
Diagram
Redundancy
3. Magne*c Field Instruments
• Block Diagram for Spacecra` Mounted Instrument • Magnetometers: requirements for space science • Proton magnetometers • Op*cally pumped magnetometers (Helium and related) • Induc*ve magnetometers
– Rota*ng coil – AC ‘Search-‐Coil’ type – DC ‘Fluxgate’ type
• Magnetoresis*ve magnetometers • Calibra*on and magne*c cleanliness
64
65
Generic Spacecraft-Mounted Instrument
Instrument
Analogue
Spacecraft Instrument
Digital
66
Sensor Technology Range (T) Suitable for space
SQUID 10-14 – 10 No – Cryostat needed
Optically Pumped 10-14 – 10-4 Yes – B and |B|
Fluxgate 10-10 – 10-4 Yes – B
Nuclear Precession 10-11 – 10-2 Yes - |B|
Hall Effect 10-3 – 10-2 No
Search Coil 10-12 – 106 Yes for AC fields
• Three B field components • Bandwidth typically DC to 30Hz • Wide dynamic range typically 0.01nT – 50,000nT • High fidelity (low noise, linear, stable offsets) • Low resources (mass, power, telemetry) • Robust (radiation, thermal environment, vibration, shock and static load) • Sensors fitted to a boom away from S/C magnetic disturbance
Requirements on a ‘DC magnetometer’ for space science
67
Proton Precession Magnetometers
• Proton rich material eg water, kerosine • Surrounded by induction coil • Large external field applied to align
proton magnetic moments • When applied field is removed abruptly,
protons will precess in phase around ambient field
• This induces a small AC signal in coil • Proportional to ambient field
• Low-bandwidth instrument • Used for absolute measurement of B • A variation used on Earth-field mapping
missions eg Oested, CHAMP
Huggard 1970
68
Optically Pumped Magnetometers • Vector and Scalar Operation (on Cassini)
• Vector Mode – Light from a He lamp, 1.08um – Directed into a He absorption cell – He cell atoms are in meta-stable state by RF discharge – Presence of ambient field causes Zeeman splitting – Emergent radiation is measured by IR detector – The measured absorption depends on efficiency of the
optical pumping which is a function of the magnetic field – Helmholtz coils around cell apply rotating sweep fields – Signal modulated by rotating sweep fields applied by
surrounding Helmholtz coils – Output is a sinusoid whose magnitude and phase give the
size and direction of the field
• Scalar mode – AC field applied. – Absorption greatest when AC frequency = Larmor
frequency. – Larmor frequency related to |B| by fundamental constants – Result is a very accurate measure of absolute field
Smith 1975
69
Fluxgate MGMs
Rota*ng coil MGMs
Search Coil MGMs
Induction Magnetometers Faraday induc*on law → Vi = dΦ / dt
= d(BA) / dt= d(NAµoµr(t)H (t)) / dt
Since B = µoµrHExpanded
dttHdNAdttHdANdttdHNA rororo /)( /)( /)(Vi µµµµµµ ++=
Search-Coil Magnetometer
• Core of high magne*c permeability wound with coil
• 3 orthogonal axes • Bandwidth 100mHz to 100’s kHz (typical)
70
Rotating Coil Magnetometer
• Imprac*cal for space • Obsolete for Earth-‐field measurement 71
Fluxgate Magnetometer
• First developed by by Aschenbrenner and Goubau [1936]
• Rapid development during 40’s and 50’s for military and geophysical applica*ons
• Fluxgate signal in Vind is second harmonic of the excita*on frequency Iexc
72 Ripka (2003)
P. Ripka / Sensors and Actuators A 106 (2003) 8–14 9
Fig. 1. Fluxgate principle.
1 ppm/!C. If they work in the feedback mode, the result-ing magnetometer linearity error may be as low as 10"5
[10].If resolution in the nanotesla range is required, fluxgates
are the best selection. Compared to high-temperature su-perconducting quantum interference device they may havesimilar noise level, but the measurement range of fluxgateis much larger. If pT or even smaller fields are measured,a low-temperature SQUID should be used. Magnetoresis-tors, mainly anisotropic magnetoresistance sensors, are themain competitors of fluxgate sensors. Commercially avail-able AMRmagnetoresistors such as Philips KMZ have a res-olution worse than 10 nT, but they are smaller and cheaperand may consume less energy. Linearity of the best presentcompensated AMR sensors is 0.05% [11,12].The mostly used modern low-noise fluxgate sensor is the
“parallel” type with ring-core. “Parallel” type means that theexcitation and the measured field have the same direction.Orthogonal type is rarely used, mostly in thin-film devices.The second harmonic in the induced voltage is extracted bya phase-sensitive detector, and the pick-up coil often servesalso for the feedback. Current-output is also used in somedesigns. Other designs are used for special purposes, suchas rod-type sensors for non-destructive testing or positionsensing [13].
2. Core shapes of fluxgates
The main problem of using the basic single-core designis the large signal on the excitation frequency at the sen-sor output, because the sensor acts as a transformer. Thus,the single-core design is used mainly for simple devicesand special applications. Pulse-position type sensors alsohave single-core [14]. Some simple magnetometers such as[15] are based on autooscillation circuits. These devices aresmall, low-power and cheap; however, they have strong com-petitors in AMR magnetoresistors. Orthogonal single-corefluxgate sensor for defectoscopy was developed by Sasada[16]. For precise fluxgates, double cores (either double-rodor ring-core) are normally used.Moldovanu et al. developed a number of double-rod
(Vacquier—Foerster type) core sensors. They report 120 pTp–p noise and 0.42 nT/K offset in the temperature range of"20 to +70 !C for tensile-stress annealed amorphous core[17,18].
Fig. 2. Race-track fluxgate.
2.1. Ring-core sensors
While the pick-up coil is a straight solenoid with thering-core in its center, the excitation coil is toroidally woundaround it. Ring-core sensors can be regarded as a form ofbalanced double sensor. The closed magnetic circuit is con-sisting of two half-cores. The core is usually made of severalturns of thin tape of soft magnetic material. The ring-coregeometry is advantageous for the low-noise sensors, eventhough that the ring-core sensors have low sensitivity, dueto the large demagnetization. Ring-core sensors also allowfine balancing of the core symmetry by rotating the corewith respect to the sensing coil.
2.2. Race-track sensors
Their sensitivity is higher and the race-track sensor isless sensitive to perpendicular fields, due to the lower de-magnetization factor (Fig. 2). Race-tracks, on the other side,still have the advantages of the closed-type sensors, mainlylow-noise—6 pT/
#Hz@1Hz was reported for sensor hav-
ing 65mm long race-track amorphous core [19]. Sensitivityand noise for smaller sensors is studied in [20]. Modifiedrace-track sensor design allows final adjustment of the sen-sor balance by sliding the pick-up coil along the core [21].
3. The effect of demagnetization
If the constant pick-up coil area in the general inductionsensor equation is assumed, we get:
"Vi = d!dt
= NAµ0µ dH(t)
dt+ NAµ0H dµ(t)
dt
where µ is relative permeability.The basic induction effect (first term) is still present in
fluxgate sensors, and causes interference. But the most im-portant component is the second term caused by fluxgateeffect. The core permeability is periodically changing withthe excitation field. The given formula can be used for longrod-type sensors, but for the more often used ring-cores,the demagnetization effect should be considered. Demag-netization means that H in the core material is lower than
73
Ring-core Fluxgate • Operating Principle
– Soft permeable core driven around hysteresis loop at frequency f0
– Field-proportional voltage at 2f0 induced in sense winding
– Output signal rectified, integrated and used to drive magnetic feedback
– Sensor operates as a null-detector – Closed-loop operation improves linearity
• Advantages – Low noise <10pT/ √Hz @1Hz – Wide dynamic range – Mature technology and robust – Relatively inexpensive
• Disadvantages – Sensor mass – Power ~ 1W – Calibration drift with time and temperature
• Offset, gain, angles
74
HD Vi 2f0
B
H
C1
C2 HD
B
H
Drive (f0)
Φ CASE A: Zero external DC field Half cores saturate synchronously – no net change of flux seen by sense winding CASE B: Non-‐zero external DC field Half cores do not saturate synchronously – a net change of flux seen by sense winding
Change of flux in sense winding at the 4 crossing of the B-‐H infec*on points in each drive period à induced voltage at 2 x fo according to Faraday
CASE A
CASE B
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Field magnitude determined by 2f magnitude Field direction determined by 2f phase relative to reference
Reference 2f
Measured 2f
Fluxgate Electronics: Open Loop
76
Fluxgate Electronics: Closed Loop
• Rectified signal is integrated and converted to a current to back-off the ambient field
• Magnetic negative feedback • Benefits include improved linearity and temperature stability • Scale factor depends only on feedback resistor/gain stage and coil constant.
77
Measured signal
Feedback signal
(Magnes 1999)
78
Equating terms and re-arranging
And if kSFLG2G1 >> 1
Two conclusions
Measurement range only set by feedback circuit
Output noise is dominated by input amplifier and sensor noise only
(Very low noise analogue pre-amps available)
79
Fluxgate Electronics: ‘Digital’
– Analogue signal processing moved to the digital domain – ADC and DAC within sensor control loop – Offers increased flexibility -‐ programmable – First Missions late 90s -‐ ROMAP, VEX, Astrid, Oersted – First Imperial digital design will fly on Solar Orbiter
Sensor core
Serial link to PC 22Hz
V to I converter
Sense winding
Drive winding
48kHzf (12kHz)
¸ 4Drive circuitry
ADC48/96kHz(AD1835)
DAC6kHz
(AD1835)
ΣIntegrator
Field Correlation
(ADSP-21262)
ADSP 21262 Ex-Kit Eval. Board
A digital fluxgate control loop
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Fluxgate Electronics: Delta-Sigma Design
O’Brien (2007)
Replace
+ + with
81
Fluxgate Noise
• Best expressed as a Noise Spectral Density (NSD) often at1Hz • Characteristic 1/f fall off
• 1/f dominant • Calculate RMS noise in any
band fL…fH
• Fluxgate ‘minimum’ noise spectral density at 1Hz
Ripka (2003)
NRMS =
sZ fH
fL
P (f)df =
s
P (1) ln
✓fHfL
◆
NSD ⇡ 5pTpHz
10 P. Ripka / Sensors and Actuators A 106 (2003) 8–14
the measured field H0 in the open air. Thus, the flux densitywithin the core must be written:
B = µ0µH0
[1+ D(µ ! 1)]= µ0µaH0
where D is the effective demagnetization factor and µa isthe apparent permeability, µa = µ/[1+D(µ!1)], for veryhigh µ, µa " 1/D.If demagnetization is considered, the equation for fluxgate
output voltages becomes more complex:
Vi = NAdBdt
= NAµ0H01! D
{1+ Dµ(t) ! 1}2dµ(t)
dt
Demagnetisation of ring-cores was studied by Clarke [22],study of the ring-core internal field was also performed byPrimdahl et al. [23].From this equation, and also from practical experience,
general practical rules for achieving high sensitivity can bededuced:
1. Voltage sensitivity increases with number of turns N (ifN is very high, other factors, such as coil parasitic capac-itance, limits the sensitivity).
2. Sensitivity decreases with demagnetization factor D.3. The sensitivity is high for materials having rectangularshape of the hysteresis loop, as they have a steep changeof permeability dµ/dt, when the core is coming into sat-uration. But these materials cannot be used because oftheir high noise level.
4. Until eddy currents (which change the shape of the hys-teresis loop) become important, voltage sensitivity in-creases with excitation frequency (because (dHexc/dt) #f ).
The voltage output is often tuned. Tuning may be inten-tional by parallel capacitance to utilize parametric amplifi-cation or unintentional (by parasitic coil capacitance).
4. Core materials
High permeability and low coercivity, but non-rectangularshape of the magnetization curve is preferred for the corematerial. The material should have low number of structuralimperfections, low internal stresses, uniform cross-section,smooth surface and high homogeneity of the parameters.Low saturation magnetization (for low-power) and high elec-trical resistivity (for low eddy current losses) are advanta-geous. The minimum noise is achieved for alloys possessingvery low magnetostriction. Materials suitable for fluxgatecores are permalloys (with 78–81% of nickel) and amor-phous alloys. Ferrites are used only exceptionally, as theygive low sensor sensitivity.Amorphous magnetic materials, whose use for fluxgate
cores started from the early 1980s, are magnetic “metallicglasses” produced by rapid quenching. Cobalt-based amor-phous alloys with low magnetostriction are particularly suit-
Fig. 3. Noise of Billingsley Magnetics fluxgate sensor. The sensor coreis 17mm diameter amorphous ring (from [32]).
able for fluxgate applications. Annealing may further de-crease the noise level of a tape for fluxgate core. Using amor-phous 17mm ring-core, Nielsen et al. reached noise levelof 4.2 pT/vHz@1Hz, which corresponds to 11.1 nT rms inthe frequency range of 60mHz–10Hz [24]. It was recentlyshown that also the tape surface treatment such as chemicaletching may improve the core properties [25]. Fig. 3 showsthe typical noise spectrum and time plot measured on flux-gate sensor manufactured by Billingsley Magnetics.Single-domain fluxgates proposed by Koch are theoret-
ically free of magnetic noise [26]. Noise level achievedso far was 1.4 pT/vHz@1Hz for 25mm ring-core and3.5 pT/vHz@1Hz for 13 cm long rod-core, but predictedvalues are even lower.
5. Principles of fluxgate magnetometers
The most frequently used principle of fluxgate magne-tometers is second-harmonic detection of the output volt-age. The other principles also appeared, but until now theywere not fully proved to bring substantial advantages exceptsimplification of the circuitry. We give only three recentexamples of these devices. Robertson presented a 1mmlong single-core sensor. Using differential peak detection, asimilar sensor excited at 40MHz had 250 pT/
$Hz@10Hz
noise [27,28]. The relaxating-type magnetometer uses asingle-core saturated by unipolar pulses and measures thelength of the relaxation pulse after the excitation field isswitched-off. The instrument has +/!200mT range, 5%linearity error and about 0.5 nT p–p noise [29]. Dimitropou-los suggests a new sensor principle combining fluxgate withMateucci effect [30]. The amorphous 6 cm long wire isexcited by flat coil pair. Although the precision of the firstprototype is reported to be 60 nT, the device can be scaleddown to 5mm and further optimised.
Quantization Noise
82
– Use oversampling plus digital filtering to reduce Quan*sa*on Noise – Quan*sa*on noise should be matched to intrinsic sensor noise
83
Ultra Electronics Ltd
– Industrial partner -‐ Ultra Electronics – Cassini/Double Star Heritage – Two core sensor – Tuned second harmonic detec*on – Combined sense and feedback windings – Offset stability < 0.05 nT/°C – Scale factor dri` < 40 ppm/°C – Noise density < 8pT/root Hz @1Hz – Opera*ng range
• -‐80oC to 70oC (opera*onal) • -‐130oC to 90oC (non-‐opera*onal)
84
Anisotropic Magnetoresistance
• Magneto Resistance Effect – Field-dependent resistance – Thin permalloy layer (Ni/Fe) – ΔR/R of order 1- 2% – AMR offers lowest noise – Thermal noise limited
• Barber Poles – Max sensitivity & linearity
at M v H 45o – Conductive strips for
linear operation
• AMR Sensors – Thin film solid state devices – Implemented as Wheatstone
bridge – Mass <1g, Ceramic package
( )( )Hθ2cos0ΔR0RR +=
Philips
85
Integrated ‘coils’ • Set - Reset Coils
– Planar ‘coil’ acts on each bridge resistor – Parallel to Easy axis – Used to re-align the magnetisation – Large current spike needed – Can extract sensor offset (unlike fluxgate) – Compensates for offset and offset drift
• Offset coils
– Planar ‘coil’ parallel to Hard (sensitive) axis
– Permits magnetic feedback – Used in closed loop back off measured
field – Improves linearity and variation of
gain with temperature – Suppresses Barkhausen noise
COIL
FByo ARHV ×=
86
Single axis AMR magnetometer
87
Fluxgate vs AMR • Three layer Mu-‐Metal shield • 3Hz sine wave – 5nT ptp • Op*mal AMR configura*on • Closed loop, RFB=9kΩ • Bridge voltage 12V • Offset compensa*on • Flip frequency, 1.1kHz • Sensi*vity ~ 11mV/nT • Sensi*vity not linear with
increasing RFB • Some residual offset in closed
lop • Temperature measurement
outstanding
DSP (20mV/div)
AMR (20mV/div)
Calibra*on • Each instrument
– 3 sensors • Offset • Gain • 2 angles
• 12 parameters to find – All measured pre-‐launch – Evolu*on in 10 can be inferred
from in-‐flight data
88
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89
Imperial’s Magnetic Test Facility
3 axis Helmholtz Coils
Sensor thermal chamber
Pit for long terms offset and noise measurement
90
Sensor under test
• Facility dynamically backs of Earth’s field using two Earth Field Reference Magnetometers (EFR) located either side of the hut
• EFR located in pits either side of hut • Sum (average) of EFRs used to cancel Earths
field inside coil system • Difference (gradient) of EFRs used for
monitoring
In-‐flight Calibra*on Analysis Complete Data Set at highest resolu*on and quality
February 2001 – April 2012
91
Calibra*on Team: Leah-‐nani Alconcel, Patrick Brown (TM), Peter Fox, Chris Carr (PI), Tim Oddy, Barry Whiteside
92
Spacecraft Magnetic Cleanliness: Cluster
• Cluster had a very rigorous (and expensive) magnetic cleanliness programme
• A residual magnetic field of <0.25nT is atypical
• Rosetta ~50nT
• Solar Orbiter ~20nT
93
Mod.dip. field
Obs. field
Real ambient field
Dual Magnetometer Method for Determining Spacecraft Field
• Used in cases where S/C field is variable and contaminates measurement
• IB and OB sensor used as a gradiometer
• Ambient field same at both IB & OB
• S/C field NOT same at IB & OB
• Two sensors limit model to a dipole of fixed posi*on
• Example missions: Double Star, Venus Express
Figure courtesy M. Delva
94
Example: Double Star magnetometer • OB sensor 5m, IB sensor 3.5m from satellite centre • Spin synchronised disturbance due to unbalanced solar array current • Amplitude varies with power demand • Data cleaned using gradiometer mode • Resul*ng data set is spin averaged resolu*on (0.25Hz) compared to 11Hz on-‐board
Un-cleaned data and shunting modes Un-cleaned and cleaned data
Carr (2005)
