evolutionary/ intelligent design of gradient amplifiers greig scott prepolarized magnetic resonance...
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Evolutionary/ Intelligent Design of Gradient
Amplifiers
Greig Scott
Prepolarized Magnetic Resonance Imaging Lab,
Department of Electrical Engineering, Stanford University
PMRIL Stanford Electrical Engineering
Goals
• Gradient Amplifier Problem Statement• The venerable Techron 8607• Feedback Control and Compensation• PWM design evolution & digital control.• Advanced topologies for ripple
reduction.• Gradient coil inductance ramifications
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Gradient Driver Problem
dt
diLIRV
coil
L~1mH
R~0.1
Voltage rail:
1500V
250A
=8500A/Tm: 3G/cm is 250A
200s rise time to 3 G/cm is SR 150 (150T/m/s)
Ldi/dt: 1275 Volts
I*R: 25 Volts
400 kVAR Amp
25 Volts
1300 Volts
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Techron 8607
-
+
R1
R2 i
mag
net
currenttransducer
R-C damp
Techron
8607
x1/20
x20 (single) x40 (master/slave)
Master/Slave: ~200V, 100 A linear gradient amplifier
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OPAMP DC GAIN
OP27 1.8 Million
NE5532 0.2 Million
LT1007 20 Million
OPA227 100 Million
Higher DC gain minimizes gradient 1/f noise and drift
GBW~8 MHz, SR 2.3-8 V/us
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Basic Bridge Power Stage
Linear or PWM H arm.
Isolated transformer
Can boost supply
Can place in series.
Techron placed 2 in series.
a
b
c
d
a
c
b
d
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Power Stage Freq. Response
101
102
103
104
105
106
-200
-150
-100
-50
0
50
100
150
200Power Stage Phase Response
Frequency [Hz]
Pha
se [d
egre
es]
101
102
103
104
105
106
0
5
10
15
20
25
30
35
40
45Power Amp Frequency Response
Frequency [Hz]
Vol
tage
Gai
n
0.5ohm10ohm
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Power Stage Noise
101
102
103
10-6
10-5
10-4
10-3
10-2
Power Amp Current Noise 0.5 Ohm Load
Frequency [Hz]
Irm
s
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Fluxgate Current Transducers
Danfysik Ultrastab 866
10
N 750
Ideal transformer to DC
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Danfysik 866 Freq. Response
104
105
106
107
10-3
10-2
10-1
Current Transducer Response
Frequency [Hz]
Cur
rent
Rat
io
104
105
106
107
-200
-150
-100
-50
0
50
100
150
200Current Transducer Phase Response
Frequency [Hz]
Pha
se [d
egre
es]
Pri
ma
ry c
urre
nt n
ois
e u
A/r
t(H
z)
Ultrastab fluxgate
LEM Hall device
18 bit, 500ksps (eg AD767x ADC) ENOB~ 17 bits
For 4V reference, 18uV rms noise
For 500 ksps, ~35nV/rtHz floor or ~4uA/rtHz.
18 bit ADC floor
High speed high resolution ADC noise floor can now digitize current sensor.
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Feedback Loop Noise
U/X = AB/(1+ABC) transconductance
U/n3 = 1/(1+ABC) -> 0 power noise
U/n4 = ABC/(1+ABC) ~ 1 sensor noise
+
-
A B
C
n1 n2 n3
n4n5
x
y
ue
High loop gain ABC minimizes noise to sensor level
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Loop Gain
LG1+LG
-ghR2R1
I/V =
LG~ (s+1/RaCa)
s L(s+R/L)
ghRaR2
Gradient coil adds up to –90 degrees. Opamp integrator at –90
Degrees. Ra and Ca cancel coil phase shift at high frequency.
Transfer function:
Loop gain
R
L
R1
R2
g
h
v=hi
i
x
y
Co
Ca Ra
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Compensation Network
Set RaCa = L/R @ crossover frequency
CaRa
CoCo kills high freq. gain
Higher bandwidth allows more low freq loop gain & more noise reduction.
Bandwidth
R2
22 LR
ghRf a
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Output Impedance
Cp =Co*R2/gh
Cs = Ca*R2/gh
R = Ra*gh/R2
Ideal Current source with scaled RC-C network
Zout
CpCs
R
R1
R2
g
h
Z
v=hi
i
x
y
Co
Ca Ra
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Proportional Integral Control
22
/1
R
sC
R
RG aa
CaRa
R2
2/ RRK ap aI CRK 2/1
s
KK Ip
dttsK I )(
)(tsK p
+
L
R
K
K
I
p
x1/20
dttsK I )(
)(tsK p
+ G
H
+
+-
+
R
L
L
GHKf p
2
dtLdI /
Set: then
Feedforward
Feedforward & Feedback System
Feedback
Integrator gives infinite gain & 0 loop error at DC. Feedforward does not change feedback dynamics
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PWM Basics
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Series Bridges
Isolated Linear or PWM bridges can be placed in series
Linear feedbackcontrol
Feedforward voltage boost PWM
PWM
Linear
PWM
PWM
agnd
Vm
Rsense
mag
net
Vsa
Vsb
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MOSFET vs IGBT
• MOSFET• Majority carrier device• On voltage drop 10-
100V at high (~600A) current.
• Higher switch frequency• Easy to parallel
• IGBT• Minority carrier device• Superior conduction. Vce
sat 2-3 volts at 600A.• Higher breakdown V• Double current density• New devices +ve Tc so
parallel connections possible.
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Powerex CM600HA-24H: 1200V, 600A.
Vce-sat: 2.1-2.4V for 600A
30kHz hard, 60-70kHz soft
Insulated Gate Bipolar Transistor
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Motor Torque Control
Apex Microtechnology SA-03 hybrid PWM: 22.5kHz, 30A
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Gradient Topologies
• Stack PWM and linear amp in series– High voltage for high inductance coil.
• Parallel PWM amplifiers.– High current for low inductance coil.
• 20kHz to 60kHz switch frequencies• Digital PI control of feedback.
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Quasi-linear
• Va, Vb add discrete voltage steps of +/-300, +/-900V
• Linear: +/- 150V• Total V: +/-1350V• Current feedback
control of linear amplifier only.co
ilLinear
amplifier
Va
Vb
Isolated supplies
Mueller, Park IEEE APEC 1994?
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Paralleled Bridge Configuration
coil
IGBTs: 1200V/300A, 20 kHz, driven in 90 degree phase stepsRipple current: 250mA@80kHz
Takano et al. IEEE IECON’99 p785.
Inductor current imbalance
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Bi-modal PWM Supply
• V>400: variable supplies switch.
• Phase shifted so 2x62.5=125kHz switch rate.
• V<400: PWM switches
• Amplifier is dual gain depending on PWM stage.
400V
400V
600V IGBT
400-800V variable supply
1200V IGBT
PWM mode for <400V
62.5 KHz 31 kHz
Steigerwald, IEEE PESC 2000 p643
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Digital Control of 4 Parallel Bridge PWM
20kHz, 17bit PWM
10 bit A/D
18 bit A/D
dt
diLIRV
_
+_
+
+
Current loop control
Voltage control
4-parallel bridge filter
coil
Current transducer
Ldi/dt
IR
+- +
+
700V, 31.25kHz
700V, 31.25kHz
200V, 62.5kHz
720MHz DSP & FPGA
18bit
Sabate IEEE PESC 2004,p261
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Advanced Methods
• Quasi-resonant low loss switching• Balanced PWM current amplifier• Notch Ripple filters• All target low loss, higher effective
switching frequency and lower ripple.
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Transformer Assisted Quasi-Resonant Commutated Pole
load
Implements Zero-Voltage Switching (ZVS) using TQRCP. Switching losses reduced.
Fukuda et al, IEEE Conf. Industrial Automation & Control 1995
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Opposed Current Interleaved Amplifier (OCIA)
Ripple frequency double that of standard bridge
Crown Balanced Current Amplifier 1998
a
b
a
b
Load excitation
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Opposed Current Interleaved Amplifier (OCIA)
load
Ripple frequency double that of standard H bridge
Crown Balanced Current Amplifier 1998
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Ripple Cancellation Filters
Notch filter action introduces passband zero at ripple frequency
Transformers act to inject equal and opposite ripple currents but not signal currents.
Sabate, IEEE APEC 2004, p792
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Gradient Coil Inductance: Impact on Amplifier Design
N turn gradient, inductance L, resistance R,
-> V, I.
N/2 turn gradient, inductance L/4, resistance R/4,
-> V/2, 2I.
Split N turn gradient, inductance ~L/2, resistance R/2 each,
-> V/2 per coil, same I.
Gradient L can allow substantial change in device voltage
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Summary
• PWM designs now standard.• Full digital control.• Design conflict: How to structure
IGBT stages with finite voltage and current limits, and switch speed.
• Gradient coil inductance choice can impact amplifier topology.
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Summary
• New precision opamps (eg LT1007) improve 1/f noise by ~100 times.
• Current transducer low 1/f drift.• Gradient amplifier is ideal current
source with RC-C shunt network.• Voltage boost designs still have
same basic stability analysis.
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Danfysik 866 Noise
101
102
103
104
105
10-10
10-9
10-8
10-7
10-6
Current Transducer Noise
Frequency [Hz]
nV/r
t(H
z)
short cct primary
AD797 floor
0.5 ohmprimary open cct
6 Turns
10 ohm R
Noise floor:
20 nV/rt Hz
1.6 pA/rt Hz
0.2uA/rt Hz
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Feedforward Ldi/dt Control
Voltage boost control is feedforward, so dynamics is same.
R1
R2
Ya
Yb
g
h
Z
v=hi
i
x
y
R1
R2
Ya
Yb
g
h
Z
v=hi
i
x
y
Ldi/dt control