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
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Greig Scott
Prepolarized Magnetic Resonance Imaging Lab,
Department of Electrical Engineering, Stanford University
PMRIL Stanford Electrical Engineering
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
I*R: 25 Volts
Voltage rail: 1500V
250A
L~1mH
R~0.1W
1300 Volts
25 Volts
PMRIL Stanford Electrical Engineering
x20 (single) x40 (master/slave)
Techron
+
8607

R1
magnet
+

RC damp
x1/20
i
R2
current
transducer
Master/Slave: ~200V, 100 A linear gradient amplifier
PMRIL Stanford Electrical Engineering
OP27 1.8 Million
NE5532 0.2 Million
LT1007 20 Million
OPA227 100 Million
GBW~8 MHz, SR 2.38 V/us
Higher DC gain minimizes gradient 1/f noise and drift
PMRIL Stanford Electrical Engineering
a
c
Linear or PWM H arm.
Isolated transformer
Can boost supply
Can place in series.
Techron placed 2 in series.
+

b
d
a
c
+

d
b
PMRIL Stanford Electrical Engineering
PMRIL Stanford Electrical Engineering
PMRIL Stanford Electrical Engineering
N
750
10
W
Ideal transformer to DC
Danfysik Ultrastab 866
PMRIL Stanford Electrical Engineering
PMRIL Stanford Electrical Engineering
18 bit, 500ksps (eg AD767x ADC) ENOB~ 17 bits
LEM Hall device
18 bit ADC floor
For 4V reference, 18uV rms noise
For 500 ksps, ~35nV/rtHz floor or ~4uA/rtHz.
Primary current noise uA/rt(Hz)
Ultrastab fluxgate
High speed high resolution ADC noise floor can now digitize current sensor.
+
e
x
u
S
A
B
S
S
S

y
n
n
n
3
1
2
C
S
S
n
n
4
5
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
(s+1/RaCa)
LG
1+LG
ghR2
LG~
I/V =
R2
s
L(s+R/L)
R1
Loop Gain+
Loop gain
g
x

R
R1
Co
Transfer function:
L
Ca
Ra
i
R2
h
y
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
Set RaCa = L/R @ crossover frequency
Bandwidth
Co
Co kills high freq. gain
Ra
Ca

Higher bandwidth allows more low freq loop gain & more noise reduction.
R2
+
PMRIL Stanford Electrical Engineering
Ideal Current source with scaled RCC network
+
g
x

R
R1
Co
Z
Cp
Cs
Ca
Ra
i
R2
h
Cp =Co*R2/gh
Cs = Ca*R2/gh
R = Ra*gh/R2
y
v=hi
Zout
PMRIL Stanford Electrical Engineering
Feedforward
+
+
+
G
+

R
L
Feedback
x1/20
H
Set:
then
Integrator gives infinite gain & 0 loop error at DC. Feedforward does not change feedback dynamics
PMRIL Stanford Electrical Engineering
Feedforward voltage boost PWM
Vm
PWM
+


+
+
Linear

Vsb
Rsense
+
magnet
agnd

+

PWM
Linear feedbackcontrol

+
PWM
Vsa
Isolated Linear or PWM bridges can be placed in series
PMRIL Stanford Electrical Engineering
Majority carrier device
On voltage drop 10100V at high (~600A) current.
Higher switch frequency
Easy to parallel
IGBT
Minority carrier device
Superior conduction. Vce sat 23 volts at 600A.
Higher breakdown V
Double current density
New devices +ve Tc so parallel connections possible.
MOSFET vs IGBTPMRIL Stanford Electrical Engineering
Powerex CM600HA24H: 1200V, 600A.
Vcesat: 2.12.4V for 600A
30kHz hard, 6070kHz soft
PMRIL Stanford Electrical Engineering
Apex Microtechnology SA03 hybrid PWM: 22.5kHz, 30A
PMRIL Stanford Electrical Engineering
PMRIL Stanford Electrical Engineering
Va
Isolated supplies
Linear amplifier
coil
Mueller, Park IEEE APEC 1994?
Vb
PMRIL Stanford Electrical Engineering
Inductor current imbalance
coil
IGBTs: 1200V/300A, 20 kHz, driven in 90 degree phase steps
Ripple current: [email protected]
Takano et al. IEEE IECON’99 p785.
PMRIL Stanford Electrical Engineering
31 kHz
62.5 KHz
600V IGBT
1200V IGBT
PWM mode for <400V
400V
400V
400800V variable supply
Steigerwald, IEEE PESC 2000 p643
PMRIL Stanford Electrical Engineering
4parallel bridge
filter
+
20kHz, 17bit PWM
+
+
_
_
Voltage control
10 bit A/D
coil
Current loop control
18 bit A/D
Current transducer
PMRIL Stanford Electrical Engineering
Ldi/dt
IR
200V, 62.5kHz
+
+
+

720MHz DSP & FPGA
700V, 31.25kHz
18bit
Sabate IEEE PESC 2004,p261
PMRIL Stanford Electrical Engineering
load
Implements ZeroVoltage Switching (ZVS) using TQRCP. Switching losses reduced.
Fukuda et al, IEEE Conf. Industrial Automation & Control 1995
PMRIL Stanford Electrical Engineering
a
a
b
b
Crown Balanced Current Amplifier 1998
Ripple frequency double that of standard bridge
Load excitation
PMRIL Stanford Electrical Engineering
load
Ripple frequency double that of standard H bridge
Crown Balanced Current Amplifier 1998
PMRIL Stanford Electrical Engineering
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
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
PMRIL Stanford Electrical Engineering
PMRIL Stanford Electrical Engineering
PMRIL Stanford Electrical Engineering
6 Turns
10 ohm R
Noise floor:
20 nV/rt Hz
1.6 pA/rt Hz
0.2uA/rt Hz
PMRIL Stanford Electrical Engineering
Ldi/dt control
g
x
g
x
R1
Ya
Z
R1
Ya
Yb
Z
i
R2
Yb
h
R2
i
y
h
v=hi
y
v=hi
Voltage boost control is feedforward, so dynamics is same.
PMRIL Stanford Electrical Engineering