Switch-mode power converter compensation made … · • Compensation examples ... 2016/17 Power Supply Design Seminar Type II error amplifier ... 2016/17 Power Supply Design Seminar

Texas Instruments – 2016/17 Power Supply Design Seminar

Louis DianaRobert Sheehan

Switch-mode power converter compensation made easy


Agenda

• Compensation design and objectives• Explanation of poles and zeros• Power stage characteristics• Error amplifier and transconductance amplifier• Isolated feedback with optocoupler• Compensation examples• Circuit limitations and other issues

3-2


Compensation design and objectives

• Feedback is needed to regulate the output voltage

• The bandwidth of the control loop determines the response time

Why do we need feedback and why do we need compensation?

3-3


Control loop response

• Response is under-damped causing oscillatory behavior

• Response is well damped with good settling behavior

• Maximize crossover frequency for fastest transient response

• Adjust compensation for best settling behavior

Good transient responseObjectivePoor transient response

VOUT

IOUT

VOUT

IOUT

3-4


Phase margin and gain margin

• Sufficient phase margin is needed to prevent oscillation (45º min.)

• Gain margin goal 10 dB min.• Slope of –20 dB/decade when passing

through 0 dB• Bandwidth rule of thumb is 1/5 to 1/10

of switching frequency

Phase margin and stability

-90

-45

0

45

90

135

-40

-20

0

20

40

60

100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

Control loop – frequency response

Phase margin

Gain margin

3-5


Poles and zerosZeroPole

P

ssH

1

1)(

1

1)( Z

s

sH

-135

-90

-45

0

45

-60

-40

-20

0

20

10 100 1,000 10,000 100,000 1,000,000PH

ASE

(°)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

-45

0

45

90

135

-20

0

20

40

60

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)FREQUENCY (Hz)

3-6


Inverted and right-half-plane zerosRight-half-plane zeroInverted zero

1

1)( ssH

Z

1

1)( Z

s

sH

-135

-90

-45

0

45

-20

0

20

40

60

10 100 1,000 10,000 100,000 1,000,000PH

ASE

(°)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

-135

-90

-45

0

45

-20

0

20

40

60

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)FREQUENCY (Hz)

3-7


Complex conjugate pole and ESR zeroWith ESR zeroComplex conjugate pole

2

2

1

1)(

OOO

sQs

sH

2

2

1

1)(

OOO

Z

sQs

s

sH

-180

-135

-90

-45

0

45

-80

-60

-40

-20

0

20

10 100 1,000 10,000 100,000 1,000,000PH

ASE

(°)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

-180

-135

-90

-45

0

45

-80

-60

-40

-20

0

20

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)FREQUENCY (Hz)

Gain

Phase

Q = 2Q = 1Q = 0.5Q = 0.25

3-8


Control methods and operating modes

• Voltage-mode control

• Current-mode control

Switching frequency and period

Control methods

Operating modes

SWfT 1

• Fixed frequency

• Continuous conduction-mode (CCM)

• Switching frequency – fSW

• Switching period – T

3-9


Buck, boost and buck-boost derived topologies• Forward• Two switch forward • Active clamp forward• Half bridge

P

SINOUT N

NDVV

• Push-pull• Full bridge• Phase-shifted full

bridge DVV INOUT

P

SINOUT N

NDVV 2

Buck-boost, SEPIC, flyback

Buck, forward,

push-pull, bridge

DVV INOUT

1

• Boost topology

DDVV INOUT

• Buck-boost derived topologies

• SEPIC• Cuk

Boost

• Flyback

P

SINOUT N

NDDVV

On-time duty cycle:D

Off-time duty cycle:D′ = 1 - D

3-10


Voltage-mode buck power stage

OUTO CL

1

OUTESRZ CR

1

2

2

1

1

ˆˆ

OOO

ZVC

C

OUT

sQs

s

Avv

OUT

OUTO

CLRQ

-180

-135

-90

-45

0

45

-60

-40

-20

0

20

40

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

VCA

2O

2Z

RAMP

INVC V

VA

3-11


Current-mode buck power stage

OUTESRZ CR

1

OUTOUTP RC

1LRK im

L

SLOPE

INm V

VK i

OUTVC R

RA

LP

ZVC

C

OUT

ss

s

Avv

11

1

ˆˆ

VIN

COUT

RESR

ROUT

LVOUT

+ +

VC+- VSLOPEPWM

A

LogicRS

-180

-135

-90

-45

0

45

-60

-40

-20

0

20

40

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

VCA

2P

2Z

2L

at D = 0.5

Si RAR

3-12


Current-mode boost power stage

OUTESRZ CR

1

OUTOUTP RC

2

LRK im

L

SLOPE

OUTm V

VK

i

OUTVC R

DRA

2

LP

ZRVC

C

OUT

ss

ss

Avv

11

11

ˆˆ

LDROUT

R

2

-180

-135

-90

-45

0

45

-60

-40

-20

0

20

40

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

VCA

2P

2R

2L

2Z

at D = 0.5

Si RAR

3-13


Current-mode buck-boost power stage

OUTESRZ CR

1

OUTOUTP RC

D

1

LRK im

L

SLOPE

OUTINm V

VVK

i

OUTVC RD

DRA

1

LP

ZRVC

C

OUT

ss

ss

Avv

11

11

ˆˆ

DLDROUT

R

2

at D = 0.5

-180

-135

-90

-45

0

45

-60

-40

-20

0

20

40

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

VCA

2P

2R

2L

2Z

Si RAR

3-14


Current-mode forward power stage

OUTESRZ CR

1

OUTOUTP RC

12

P

SimL N

NLRK

SLOPE

INm V

VK S

P

i

OUTVC N

NRRA

LP

ZVC

C

OUT

ss

s

Avv

11

1

ˆˆ

-180

-135

-90

-45

0

45

-60

-40

-20

0

20

40

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

VCA

2P

2Z

2L

at D = 0.5

Si RAR

3-15

CIN

Q1

D1VIN

VSLOPE

+

+-

PWM

VC

Logic

T1NP : NS

D2

L

RS

A

COUT

RESR

ROUT

VOUT


Current-mode flyback power stage

OUTESRZ CR

1

OUTOUTP RC

D

1

P

imL L

RK

SLOPE

S

POUTIN

m VNNVV

K

S

P

i

OUTVC N

NRDDRA

1

LP

ZRVC

C

OUT

ss

ss

Avv

11

11

ˆˆ

22

S

P

P

OUTR N

NDLDR

at D = 0.5

-180

-135

-90

-45

0

45

-60

-40

-20

0

20

40

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

VCA

2P

2R

2L

2Z

Si RAR

3-16

+


Type I error amplifier

COMPFBTEA CR

1

svv EA

OUT

C

ˆˆ

-90

-45

0

45

90

135

-40

-20

0

20

40

60

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

2EA

3-17


Type II error amplifier

COMPCOMPZEA CR

1

HFCOMP CC HFCOMP

HF CR

1

FBT

COMPVM R

RA -45

0

45

90

135

180

-20

0

20

40

60

80

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

2ZEA

VMA

2HF

HF

ZEA

VMOUT

C

ssA

vv

1

1

ˆˆ

HF

ZEAZEAVM

s

s

sA

1

1

Assumption:

3-18


Type II transconductance amplifier

COMPCOMPZEA CR

1

COMPEAHFCOMP RRCC &

COMPmFBVM RgKA

HFCOMPHF CR

1

FBTFBB

FBBFB RR

RK

EAmOL RgA

HF

ZEAZEAVM

s

s

sA

1

1

HF

ZEA

VMOUT

C

ssA

vv

1

1

ˆˆ

Assumptions:

-45

0

45

90

135

180

-20

0

20

40

60

80

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

2ZEA

VMA

2HF

3-19


Type III error amplifier

COMPCOMPZEA CR

1

FFFBTFZ CR

1

FFFFFP CR

1HFCOMP

HF CR

1

FBT

COMPVM R

RA

HFFP

FZ

ZEA

VMOUT

C

ss

ss

Avv

11

11

ˆˆ

FFFBTHFCOMP RRCC &

0

45

90

135

180

225

270

-40

-20

0

20

40

60

80

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

2ZEA

VMA 2HF

2FZ

2FP

HFFP

FZZEAZEAVM

ss

ss

sA

11

11

Assumptions:

3-20


Isolated feedback with optocoupler

-45

0

45

90

135

180

-20

0

20

40

60

80

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

2ZEA

VMA

2HF

D

PVM R

RCTRA

COMPFBTZEA CR

1

PPHF CR

1

F

C

IICTR

HF

ZEA

VMOUT

C

ssA

vv

1

1

ˆˆ

HF

ZEAZEAVM

s

s

sA

1

1

3-21


Voltage-mode buck

Output filter

Error amplifier

Modulator

IN

OUT

VVD

IN

OUTIN

VVVD

3-22


Voltage-mode buck compensation strategy• Choose a value for RFBT based on bias current and power

dissipation• Pick target bandwidth, typically fSW/10:

ωC = 2·π·fC• Find the mid-band gain AVM to achieve target bandwidth• Set ωZEA and ωFZ equal to the output filter complex conjugate

pole ωO:ωZEA = ωFZ = ωO

• Set ωFP equal to the output filter zero ωZ:ωFP = ωZ

• Set ωHF equal to half the switching frequency: ωHF = 2·π·fSW/2

FBTFZFF RC

1

FFFPFF CR

1

OVC

CVM ωA

ωA

FBTVMCOMP RAR

COMPZEACOMP RC

1

COMPHFHF RC

1

3-23


Control loop

Error amplifier

Power stage

Voltage-mode buck compensation results

OUT

C

C

OUT

OUT

OUT

vv

vv

vv

ˆˆ

ˆˆ

ˆˆ

HFFP

FZ

ZEA

VMOUT

C

ss

ss

Avv

11

11

ˆˆ

2

2

1

1

ˆˆ

OOO

ZVC

C

OUT

sQs

s

Avv

-180-135-90-45045

-60-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

VCA

2O

2Z

4590135180225270

-40-20

0204060

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

2&

2FZZEA

VMA

2HF

2FP

-90-4504590135

-40-20

0204060

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

2C

3-24


Output filter

Error amplifier

Modulator

Isolated current-mode flyback

OUTP

SIN

OUT

VNNV

VD

S

POUTIN

IN

NNVV

VD

+3-25


Current-mode flyback compensation strategy

(mod)m

OUTCVM G

CA

S

P

im N

NRDG

(mod)

22

S

P

P

OUTR N

NDLDR

• Choose a value for RFBT based on bias current and power dissipation

• Find the modulator transconductance in A/V• Find the RHPZ frequency at minimum input voltage and

maximum load current• Set the target bandwidth to 1/4 of the RHPZ frequency:

ωC = 2·π·fC = ωR/4• Find the mid-band gain AVM to achieve target bandwidth

Adjust RD, RP and COUT as required• Set ωZEA equal to 1/10 the target crossover frequency:

ωZEA = ωC/10• Set ωHF equal to the lower of the RHP or ESR zero

frequency:ωHF = ωR or ωZ

VMAP

DRCTRR

ZEAFBTCOMP RC

1

HFPP RC

1

3-26


Control loop

Error amplifier

Power stage

Current-mode flyback compensation results

LP

ZRVC

C

OUT

ss

ss

Avv

11

11

ˆˆ

HF

ZEA

VMOUT

C

ssA

vv

1

1

ˆˆ

OUT

C

C

OUT

OUT

OUT

vv

vv

vv

ˆˆ

ˆˆ

ˆˆ

-180-135-90-45045

-60-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

4590135180225270

-60-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

-90-4504590135

-40-20

0204060

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

VCA

2C

2P

2Z

2ZEA

VMA

2HF

2R

2L

3-27


Bandwidth vs. transient responseCurrent-mode transient responseCurrent-mode bandwidth

-90-4504590135

-40-20

0204060

100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (Hz)

vPtP

∆I

With no ESR, slew rate or duty cycle limiting:

Current-mode single pole approximation:

Current-mode critically damped:

Voltage-mode:

fC

CP ft

41 s

kHztP 25

1041

OUTCP Cf

IV

8

OUTCP Cf

IV

2

OUTCP Cfe

IV

mV

FkHzeAVP 130

440105

mVFkHz

AVP 180440102

5

mVFkHz

AVP 140440108

5

shown above

3-28


Switching regulator with poor compensation

4590135180225270

-40-20

0204060

0.1 1 10 100 1000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (kHz)

Error amplifier

-180

-135

-90

-45

0

45

-60

-40

-20

0

20

40

0.1 1 10 100 1000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (kHz)

Power stage

-90

-45

0

45

90

135

-40

-20

0

20

40

60

0.1 1 10 100 1000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (kHz)

Control loop

• Power stage: phase at –180°indicates high internal slope compensation

• Error amplifier: zero appears high and mid-band gain is 3 dB

• Control loop: fC is 95 kHz with only 20° phase margin

VOUT

IOUT

Transient response

U1

VIN

GND

EN

SS/TR RT/CLK

BOOTPH

VSENSE

COMP

VIN

0.1 μF

10 nF 100 kΩ

3.3 μH

31.6 kΩ

10 kΩ

5 kΩ

1 nF

47 μF

VOUT

15 μF

22 μF effective

capacitance

TPS54620

3-29


Switching regulator with revised compensation

4590135180225270

-40-20

0204060

0.1 1 10 100 1000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (kHz)

Error amplifier

-180

-135

-90

-45

0

45

-60

-40

-20

0

20

40

0.1 1 10 100 1000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (kHz)

Power stage

-90

-45

0

45

90

135

-40

-20

0

20

40

60

0.1 1 10 100 1000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

FREQUENCY (kHz)

Control loop

• Power stage: cannot change slope compensation

• Error amplifier: decrease RCOMP and rescale CCOMP

• Control loop: now fC is 30 kHz with 67° phase margin

VOUT

IOUT

Transient response

U1

VIN

GND

EN

SS/TR RT/CLK

BOOTPH

VSENSE

COMP

VIN

0.1 μF

10 nF 100 kΩ

3.3 μH

31.6 kΩ

10 kΩ

1 kΩ

10 nF

47 μF

VOUT

15 μF

22 μF effective

capacitance

TPS54620

3-30


Practical limitations

• Error amp BW can limit maximum fC

• Wider BW op amp needed for voltage-mode due to Type III compensation

• Resistance seen by output transistor forms a pole in kHz range

• More of an issue for forward topologies at higher fC

• Maximum fC is a fraction of fSW

• Rule of thumb is 1/5 to 1/10 of fSW

3-31


DCM vs. CCM characteristics

• Discontinuous conduction-mode (DCM) occurs when the inductor current dwells at zero before the end of the switching cycle

• This causes a reduction in the bandwidth• Generally, if the loop is stable in CCM, it will be stable in DCM

• Buck

• Boost

• Buck-boost

DCM duty cycle

IN

OUTOUTSW

VVIfL

D

2

IN

INOUTOUTSW

VVVIfL

D

2

OUTININ

OUTOUTSW

VVVVIfLD

2

3-32


Filter considerations

• Capacitors: make COUT1 smaller than COUT2• Inductors: make L2 smaller than L1• Resonance: make second stage filter

resonance 3 times fC• Damping: make second stage filter damped

to a Q of 1

• Characteristic impedance• Damping factor

Second stage filtersInput filter stability

For stability: Filter ZOUT << Converter ZIN

IN

INS C

LZ

IN

S

S

CL

ZZ

ZRR

21

3-33


Summary

• Identify poles and zeros of the power stage• Cancel with zeros and poles in the error amp• Adjust the gain for best performance

3-34


Resources and references• “Closing the Feedback Loop” by Lloyd Dixon, SEM300

• “Current-Mode Control of Switching Power Supplies” by Lloyd Dixon, SEM400

• “The Right-Half-Plane Zero -- A Simplified Explanation” by Lloyd Dixon, SEM500

• “Isolating the Control Loop” by Robert Mammano, SEM700

• “Control Loop Design” by Lloyd Dixon, SEM800

• “Control Loop Cookbook” by Lloyd Dixon, SEM1100

• “A More Accurate Current-Mode Control Model” by Ray Ridley, SEM1300

• “Designing Stable Control Loops” by Dan Mitchell and Bob Mammano, SEM1400

• “Current-Mode Modeling – Reference Guide” by Robert Sheehan, SNVA542

• “Understanding and Applying Current-Mode Control Theory” by Robert Sheehan, SNVA555

• “Frequency Compensation and Power Stage Design for Buck Converters to Meet Load Transient Specifications” by S. Bag, R. Sheehan, et al., APEC 2014

3-35


Appendix

• Current-mode buck compensation• Current-mode boost compensation• Current-mode buck-boost compensation• Isolated compensation techniques• Isolated forward converter compensation

3-36


Current-mode buck

Output filter

Error amplifier

Modulator

IN

OUT

VVD

IN

OUTIN

VVVD

3-37


FBTVMCOMP RAR

Current-mode buck compensation strategy

FBm

VMCOMP Kg

AR

COMPHFHF RωC

1

COMPZEACOMP RωC

1

(mod)m

OUTCVM G

CA

im RG 1(mod) • Choose a value for RFBT based on bias current and power

dissipation• Find the modulator transconductance in A/V• Pick target bandwidth, typically fSW/10:

ωC = 2·π·fC• Find the mid-band gain AVM to achieve target bandwidth• Set ωZEA equal to 1/10 the target crossover frequency:

ωZEA = ωC/10• Set ωHF equal to the ESR zero frequency:

ωHF = ωZ

(op amp)

(gm amp)

3-38


Control loop

Error amplifier

Power stage

Current-mode buck compensation results

LP

ZVC

C

OUT

ss

s

Avv

11

1

ˆˆ

HF

ZEA

VMOUT

C

ssA

vv

1

1

ˆˆ

OUT

C

C

OUT

OUT

OUT

vv

vv

vv

ˆˆ

ˆˆ

ˆˆ

-90-4504590

-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

4590135180225

-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

-90-4504590135

-40-20

0204060

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

VCA

2C

2P

2Z

2ZEA

VMA 2HF

2L

3-39


Current-mode boost

Output filter

Error amplifier

Modulator

OUT

INOUT

VVVD

OUT

IN

VVD

VIN

CIN

RCOMP

CCOMP

COUT

RESRROUT

L

RFBT

RFBB

VOUT

VREF

+ +

VFBVC

Logic VSLOPE

Peak current-mode boostOptimal VSLOPE = (VOUT - VIN)·Ri·T/L

CHF

gm+-

PWM+-

Ri

3-40


FBTVMCOMP RAR

Current-mode boost compensation strategy

FBm

VMCOMP Kg

AR

COMPHFHF RωC

1COMPZEA

COMP RωC

1

(mod)m

OUTCVM G

CA

im R

DG

(mod)• Choose a value for RFBT based on bias current and power dissipation

• Find the modulator transconductance in A/V

• Find the RHPZ frequency at minimum input voltage and maximum load current

• Set the target bandwidth to 1/4 of the RHPZ frequency:ωC = 2·π·fC = ωR/4

• Find the mid-band gain AVM to achieve target bandwidth

• Set ωZEA equal to 1/10 the target crossover frequency:ωZEA = ωC/10

• Set ωHF equal to the lower of the RHP or ESR zero frequency:ωHF = ωR or ωZ

LDROUT

R

2

(op amp)

(gm amp)

3-41


Control loop

Error amplifier

Power stage

Current-mode boost compensation results

LP

ZRVC

C

OUT

ss

ss

Avv

11

11

ˆˆ

HF

ZEA

VMOUT

C

ssA

vv

1

1

ˆˆ

OUT

C

C

OUT

OUT

OUT

vv

vv

vv

ˆˆ

ˆˆ

ˆˆ

-180-135-90-45045

-60-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

4590135180225270

-60-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

-90-4504590135

-40-20

0204060

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

VCA

2C

2P

2Z

2ZEA

VMA

2HF

2R

2L

3-42


Current-mode buck-boost

Output filter

Error amplifier

Modulator

OUTIN

OUT

VVVD

OUTIN

IN

VVVD

3-43


FBTVMCOMP RAR

Current-mode buck-boost compensation strategy

FBm

VMCOMP Kg

AR

COMPHFHF RωC

1COMPZEA

COMP RωC

1

(mod)m

OUTCVM G

CA

im R

DG

(mod)• Choose a value for RFBT based on bias current and power dissipation

• Find the modulator transconductance in A/V

• Find the RHPZ frequency at minimum input voltage and maximum load current

• Set the target bandwidth to 1/4 of the RHPZ frequency:ωC = 2·π·fC = ωR/4

• Find the mid-band gain AVM to achieve target bandwidth

• Set ωZEA equal to 1/10 the target crossover frequency:ωZEA = ωC/10

• Set ωHF equal to the lower of the RHP or ESR zero frequency:ωHF = ωR or ωZ

DLDROUT

R

2

(op amp)

(gm amp)

3-44


Control loop

Error amplifier

Power stage

Current-mode buck-boost compensation results

LP

ZRVC

C

OUT

ss

ss

Avv

11

11

ˆˆ

HF

ZEA

VMOUT

C

ssA

vv

1

1

ˆˆ

OUT

C

C

OUT

OUT

OUT

vv

vv

vv

ˆˆ

ˆˆ

ˆˆ

-180-135-90-45045

-60-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

4590135180225270

-60-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

-90-4504590135

-40-20

0204060

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

VCA

2C

2P

2Z

2ZEA

VMA

2HF

2R

2L

3-45


Isolated compensation techniquesSimplest method: Optocoupler with shunt regulator

• CTR – Current transfer ratio

• CP – Includes optoparasitic capacitance. This creates a pole with gain setting resistor RP

• RD – Connected to VOUTcreates a feedback path even when CCOMP rolls off the gain

• TL431 – Cathode cannot pull lower than the reference voltage

PP

FBTCOMP

D

P

OUT

C

RCsRCs

RRCTR

vv

1

11

ˆˆ

3-46


Primary side compensation

-+

VCC

VREF

VC

RE

RI

RF

• Uses primary side inverting amplifier to implement frequency compensation

• Opto emitter is at virtual ground of VREF• This minimizes pole due to opto

parasitic capacitance

Primary side compensation High bandwidth configuration

3-47


Secondary side compensation

• An RC pole to the opto can be used to cancel the output capacitor ESR zero

• Feed-forward across RD adds phase boost for increased bandwidth

• Zener bias for RD eliminates the high frequency feedback path for secondary-side compensation

Zener biasPhase boostESR zero compensation

TL431

CFF

CCOMP

RFF

RFBT

RFBB

RD

V′OUT

TL431

ZS

CCOMP

CHF

RCOMP

RFBT

RFBB

V′OUTRSRD

CCOMP

TL431

CS

RFBT

RFBB

V′OUTRSRD

3-48


+

Isolated current-mode forward

Output filter

Error amplifier

Modulator

S

P

IN

OUT

NN

VVD

IN

S

POUTIN

VNNVV

D

3-49


Current-mode forward compensation strategy

(mod)m

OUTCVM G

CA

S

P

im N

NR

G 1(mod)

• Choose a value for RFBT based on bias current and power dissipation

• Find the modulator transconductance in A/V• Pick target bandwidth, typically fSW/10:

ωC = 2·π·fC• Find the mid-band gain AVM to achieve target bandwidth

Adjust RD, RP and COUT as required• Set ωZEA equal to 1/10 the target crossover frequency:

ωZEA = ωC/10• Set ωHF equal to the ESR zero frequency:

ωHF = ωZ

VMAP

DRCTRR

ZEAFBTCOMP RC

1

HFSS RC

1

3-50


Control loop

Error amplifier

Power stage

Current-mode forward compensation results

LP

ZVC

C

OUT

ss

s

Avv

11

1

ˆˆ

HF

ZEA

VMOUT

C

ssA

vv

1

1

ˆˆ

OUT

C

C

OUT

OUT

OUT

vv

vv

vv

ˆˆ

ˆˆ

ˆˆ

-90-4504590

-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

4590135180225

-40-20

02040

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

-90-4504590135

-40-20

0204060

10 100 1,000 10,000 100,000 1,000,000

PHA

SE (°

)

MA

GN

ITU

DE

(dB

)

VCA

2C

2P

2Z

2ZEA

VMA 2HF

2L

3-51

IMPORTANT NOTICE FOR TI DESIGN INFORMATION AND RESOURCES

Texas Instruments Incorporated (‘TI”) technical, application or other design advice, services or information, including, but not limited to,reference designs and materials relating to evaluation modules, (collectively, “TI Resources”) are intended to assist designers who aredeveloping applications that incorporate TI products; by downloading, accessing or using any particular TI Resource in any way, you(individually or, if you are acting on behalf of a company, your company) agree to use it solely for this purpose and subject to the terms ofthis Notice.TI’s provision of TI Resources does not expand or otherwise alter TI’s applicable published warranties or warranty disclaimers for TIproducts, and no additional obligations or liabilities arise from TI providing such TI Resources. TI reserves the right to make corrections,enhancements, improvements and other changes to its TI Resources.You understand and agree that you remain responsible for using your independent analysis, evaluation and judgment in designing yourapplications and that you have full and exclusive responsibility to assure the safety of your applications and compliance of your applications(and of all TI products used in or for your applications) with all applicable regulations, laws and other applicable requirements. Yourepresent that, with respect to your applications, you have all the necessary expertise to create and implement safeguards that (1)anticipate dangerous consequences of failures, (2) monitor failures and their consequences, and (3) lessen the likelihood of failures thatmight cause harm and take appropriate actions. You agree that prior to using or distributing any applications that include TI products, youwill thoroughly test such applications and the functionality of such TI products as used in such applications. TI has not conducted anytesting other than that specifically described in the published documentation for a particular TI Resource.You are authorized to use, copy and modify any individual TI Resource only in connection with the development of applications that includethe TI product(s) identified in such TI Resource. NO OTHER LICENSE, EXPRESS OR IMPLIED, BY ESTOPPEL OR OTHERWISE TOANY OTHER TI INTELLECTUAL PROPERTY RIGHT, AND NO LICENSE TO ANY TECHNOLOGY OR INTELLECTUAL PROPERTYRIGHT OF TI OR ANY THIRD PARTY IS GRANTED HEREIN, including but not limited to any patent right, copyright, mask work right, orother intellectual property right relating to any combination, machine, or process in which TI products or services are used. Informationregarding or referencing third-party products or services does not constitute a license to use such products or services, or a warranty orendorsement thereof. Use of TI Resources may require a license from a third party under the patents or other intellectual property of thethird party, or a license from TI under the patents or other intellectual property of TI.TI RESOURCES ARE PROVIDED “AS IS” AND WITH ALL FAULTS. TI DISCLAIMS ALL OTHER WARRANTIES ORREPRESENTATIONS, EXPRESS OR IMPLIED, REGARDING TI RESOURCES OR USE THEREOF, INCLUDING BUT NOT LIMITED TOACCURACY OR COMPLETENESS, TITLE, ANY EPIDEMIC FAILURE WARRANTY AND ANY IMPLIED WARRANTIES OFMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, AND NON-INFRINGEMENT OF ANY THIRD PARTY INTELLECTUALPROPERTY RIGHTS.TI SHALL NOT BE LIABLE FOR AND SHALL NOT DEFEND OR INDEMNIFY YOU AGAINST ANY CLAIM, INCLUDING BUT NOTLIMITED TO ANY INFRINGEMENT CLAIM THAT RELATES TO OR IS BASED ON ANY COMBINATION OF PRODUCTS EVEN IFDESCRIBED IN TI RESOURCES OR OTHERWISE. IN NO EVENT SHALL TI BE LIABLE FOR ANY ACTUAL, DIRECT, SPECIAL,COLLATERAL, INDIRECT, PUNITIVE, INCIDENTAL, CONSEQUENTIAL OR EXEMPLARY DAMAGES IN CONNECTION WITH ORARISING OUT OF TI RESOURCES OR USE THEREOF, AND REGARDLESS OF WHETHER TI HAS BEEN ADVISED OF THEPOSSIBILITY OF SUCH DAMAGES.You agree to fully indemnify TI and its representatives against any damages, costs, losses, and/or liabilities arising out of your non-compliance with the terms and provisions of this Notice.This Notice applies to TI Resources. Additional terms apply to the use and purchase of certain types of materials, TI products and services.These include; without limitation, TI’s standard terms for semiconductor products http://www.ti.com/sc/docs/stdterms.htm), evaluationmodules, and samples (http://www.ti.com/sc/docs/sampterms.htm).

Mailing Address: Texas Instruments, Post Office Box 655303, Dallas, Texas 75265Copyright © 2017, Texas Instruments Incorporated

http://www.ti.com/sc/docs/stdterms.htm

http://www.ti.com/lit/pdf/SSZZ027

http://www.ti.com/lit/pdf/SSZZ027

http://www.ti.com/sc/docs/sampterms.htm

Documents

Switch-mode power converter compensation made … · • Compensation examples ... 2016/17 Power Supply Design Seminar Type II error amplifier ... 2016/17 Power Supply Design Seminar