Evolutionary/ Intelligent Design of Gradient Amplifiers Greig Scott Prepolarized Magnetic Resonance Imaging Lab, Department of Electrical Engineering,

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


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


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


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


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


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


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


Fluxgate Current Transducers

Danfysik Ultrastab 866

10

N 750

Ideal transformer to DC


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.


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


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


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


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


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


PWM Basics


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


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.


Powerex CM600HA-24H: 1200V, 600A.

Vce-sat: 2.1-2.4V for 600A

30kHz hard, 60-70kHz soft

Insulated Gate Bipolar Transistor


Motor Torque Control

Apex Microtechnology SA-03 hybrid PWM: 22.5kHz, 30A


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.


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?


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


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


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


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.


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


Opposed Current Interleaved Amplifier (OCIA)

Ripple frequency double that of standard bridge

Crown Balanced Current Amplifier 1998

a

b

a

b

Load excitation


Opposed Current Interleaved Amplifier (OCIA)

load

Ripple frequency double that of standard H bridge

Crown Balanced Current Amplifier 1998


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


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


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.


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.


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


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

Documents

Evolutionary/ Intelligent Design of Gradient Amplifiers Greig Scott Prepolarized Magnetic Resonance Imaging Lab, Department of Electrical Engineering,