Evolutionary/ Intelligent
Design of Gradient
Amplifiers
Greig Scott
Prepolarized Magnetic Resonance Imaging Lab,
Department of Electrical Engineering, Stanford University
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
PMRIL
Stanford Electrical Engineering
Gradient Driver Problem
di
V  IR  L
dt
h=8500A/T/m: 3G/cm is 250A
200ms rise time to 3 G/cm
is SR 150 (150T/m/s)
400 kVAR Amp
Ldi/dt: 1275 Volts
250A
L~1mH
coil
Voltage
rail:
1500V
I*R: 25 Volts
R~0.1W
1300 Volts
25 Volts
PMRIL
Stanford Electrical Engineering
Techron 8607
Techron
x20 (single) x40
(master/slave)
+
8607
magnet
R1

-
R-C damp
R2
x1/20
i
current
transducer
Master/Slave: ~200V, 100 A linear gradient amplifier
PMRIL
Stanford Electrical Engineering
OPAMP DC GAIN
OP27 1.8 Million
NE5532 0.2 Million
LT1007 20 Million
OPA227 100 Million
GBW~8 MHz, SR 2.3-8 V/us
Higher DC gain minimizes gradient 1/f noise and drift
PMRIL
Stanford Electrical Engineering
Basic Bridge Power Stage
a
c
Linear or PWM H arm.

b
d
Isolated transformer
Can boost supply
a

-
Can place in series.
c
Techron placed 2 in series.
d
PMRIL
b
Stanford Electrical Engineering
Power Stage Freq. Response
Power Amp Frequency Response
Power Stage Phase Response
45
200
40
150
100
30
Phase [degrees]
Voltage Gain
35
25
20
15
10
0
-50
-100
0.5ohm
10ohm
5
0 1
10
50
-150
2
10
10
3
4
10
5
10
10
6
-200 1
10
Frequency [Hz]
2
10
10
3
4
10
5
10
10
6
Frequency [Hz]
PMRIL
Stanford Electrical Engineering
Power Stage Noise
Power Amp Current Noise 0.5 Ohm Load
-2
10
-3
Irms
10
-4
10
-5
10
-6
10
1
10
2
10
10
3
Frequency [Hz]
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Stanford Electrical Engineering
Fluxgate Current
Transducers
N
750
10W
Ideal transformer to DC
Danfysik Ultrastab 866
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Stanford Electrical Engineering
Danfysik 866 Freq. Response
Current Transducer Response
-1
10
Current Transducer Phase Response
200
100
Phase [degrees]
Current Ratio
150
-2
10
50
0
-50
-100
-3
10
4
10
5
10
10
6
10
-150
7
Frequency [Hz]
-200 4
10
5
10
10
6
10
7
Frequency [Hz]
PMRIL
Stanford Electrical Engineering
Primary current noise uA/rt(Hz)
LEM Hall device
18 bit ADC floor
Ultrastab fluxgate
18 bit, 500ksps
(eg AD767x ADC)
ENOB~ 17 bits
For 4V reference,
18uV rms noise
For 500 ksps,
~35nV/rtHz floor
or ~4uA/rtHz.
High speed high
resolution ADC
noise floor can
now digitize
current sensor.
Feedback Loop Noise
x
+
S
e
- y
S
S
A
B
S
C
u
n3
n2
n1
S
S
n4
n5
U/X = AB/(1+ABC)
transconductance
U/n3 = 1/(1+ABC) -> 0
power noise
U/n4 = ABC/(1+ABC) ~ 1 sensor noise
High loop gain ABC minimizes noise to sensor level
PMRIL
Stanford Electrical Engineering
Loop Gain

g x
R1
Co
Ca
R2
h
y
R
Ra
L
i
Loop gain
ghRa (s+1/RaCa)
LG~
R2 s L(s+R/L)
Transfer function:
I/V = -ghR2 LG
R1 1+LG
v=hi
Gradient coil adds up to –90 degrees. Opamp integrator at –90
Degrees. Ra and Ca cancel coil phase shift at high frequency.
PMRIL
Stanford Electrical Engineering
Compensation Network
Set RaCa = L/R @
crossover frequency
Bandwidth
ghRa
f 
2LR2
Co
Ra
Ca
-
R2
PMRIL

Co kills high freq. gain
Higher bandwidth allows
more low freq loop gain &
more noise reduction.
Stanford Electrical Engineering
Output Impedance
Ideal Current source with scaled RC-C network

g x
-
R
R1
Co
Ca
R2
y
Z
Ra
Cp
Cs
i
h
Cp =Co*R2/gh
v=hi
Cs = Ca*R2/gh
Zout
PMRIL
R = Ra*gh/R2
Stanford Electrical Engineering
Proportional Integral Control
Ra
Ca
Ra 1 / sC a
GR2
R2
-
R2

K I  -1 / R2Ca
K p  - Ra / R2
K p s (t )
K I  s (t ) dt
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+
KI
Kp 
s
Stanford Electrical Engineering
Feedforward & Feedback System
LdI / dt
K p s (t )
+
K I  s (t ) dt
-
Feedforward
+
+ G +
Feedback
Set:
Kp
R

KI L
then
x1/20
f 
R
L
H
GHK p
2L
Integrator gives infinite gain & 0 loop error at DC.
Feedforward does not change feedback dynamics
PWM Basics
PMRIL
Stanford Electrical Engineering
Series Bridges
Vm

-
PWM

-
Feedforward
voltage boost
PWM
magnet

-
Linear 
Rsense
agnd
Vsb

-
PWM

Vsa
PWM
Linear
feedback
control
Isolated Linear or PWM bridges can be placed in series
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Stanford Electrical Engineering
MOSFET vs IGBT
• MOSFET
•
• Majority carrier device
•
• On voltage drop 10-100V•
at high (~600A) current.
• Higher switch frequency •
• Easy to parallel
•
•
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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.
Stanford Electrical Engineering
Insulated Gate Bipolar
Transistor
Powerex CM600HA-24H:
1200V, 600A.
Vce-sat: 2.1-2.4V for 600A
30kHzPMRIL
hard, 60-70kHz soft
Stanford Electrical Engineering
Motor Torque Control
Apex Microtechnology SA-03 hybrid PWM: 22.5kHz, 30A
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Stanford Electrical Engineering
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.
PMRIL
Stanford Electrical Engineering
Quasi-linear
Va
Isolated
supplies
coil
Linear
amplifier
• Va, Vb add discrete
voltage steps of +/300, +/-900V
• Linear: +/- 150V
• Total V: +/-1350V
• Current feedback
control of linear
amplifier only.
Mueller, Park IEEE APEC 1994?
Vb
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Stanford Electrical Engineering
Paralleled Bridge Configuration
Inductor
current
imbalance
coil
IGBTs: 1200V/300A, 20 kHz, driven in 90 degree phase steps
Ripple current: 250mA@80kHz
Takano et al. IEEE IECON’99 p785.
PMRIL
Stanford Electrical Engineering
Bi-modal PWM Supply
31 kHz
62.5 KHz
600V
IGBT
400V
400V
400-800V
variable
supply
1200V
IGBT
PWM
• V>400: variable
mode for supplies switch.
<400V • Phase shifted so
2x62.5=125kHz
switch rate.
• V<400: PWM
switches
• Amplifier is dual
gain depending
on PWM stage.
Steigerwald, IEEE PESC 2000 p643
PMRIL
Stanford Electrical Engineering
Digital Control of 4 Parallel
Bridge PWM
di
V  IR  L
dt

+
_
4-parallel
bridge filter
+
20kHz, 17bit
PWM
+
_
10 bit
A/D
coil
Voltage control
Current loop control
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18 bit
A/D
Current
transducer
Stanford Electrical Engineering
700V,
31.25kHz
Ldi/dt
IR
+-

+
+
200V,
62.5kHz
720MHz DSP
& FPGA
700V,
31.25kHz
18bit
Sabate IEEE PESC 2004,p261
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.
PMRIL
Stanford Electrical Engineering
Transformer Assisted QuasiResonant Commutated Pole
load
Implements Zero-Voltage Switching (ZVS) using TQRCP.
Switching losses reduced.
Fukuda et al, IEEE Conf. Industrial Automation & Control 1995
PMRIL
Stanford Electrical Engineering
Opposed Current Interleaved
Amplifier (OCIA)
a
a
b
b
Crown Balanced Current Amplifier 1998
Ripple frequency double that of
standard bridge
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Load excitation
Stanford Electrical Engineering
Opposed Current Interleaved
Amplifier (OCIA)
load
Ripple frequency double that of standard H bridge
Crown Balanced Current Amplifier 1998
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Stanford Electrical Engineering
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
PMRIL
Stanford Electrical Engineering
Gradient Coil Inductance:
Impact on Amplifier Design
N turn gradient,
inductance L,
resistance R,
N/2 turn gradient, Split N turn gradient,
inductance L/4,
inductance ~L/2,
resistance R/4,
resistance R/2 each,
-> V, I.
-> V/2, 2I.
-> V/2 per coil, same I.
Gradient L can allow substantial change in device voltage
PMRIL
Stanford Electrical Engineering
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.
PMRIL
Stanford Electrical Engineering
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.
PMRIL
Stanford Electrical Engineering
Danfysik 866 Noise
Current Transducer Noise
-6
10
short cct primary
-7
nV/rt(Hz)
10
-8
10
0.5 ohm
primary
open cct
AD797 floor
-9
10
-10
10
1
10
10
2
3
10
4
10
10
5
Frequency [Hz]
6 Turns
10 ohm R
Noise floor:
20 nV/rt Hz
1.6 pA/rt Hz
0.2uA/rt Hz
PMRIL
Stanford Electrical Engineering
Feedforward Ldi/dt Control
Ldi/dt control
g x
g x
R1
Ya
Yb
R2
y
h
Z
R1
Ya
i
Yb
R2
h
v=hi
y
Z
i
v=hi
Voltage boost control is feedforward, so dynamics is same.
PMRIL
Stanford Electrical Engineering