1 Solving Op Amp Stability Issues Presented by Marek Lis Sr Application Engineer Texas Instruments - Tucson Prepared by Collin Wells HPA Linear Applications.

1

Solving Op Amp Stability Issues

Presented by

Marek Lis

Sr Application Engineer

Texas Instruments - Tucson

Prepared by Collin Wells

HPA Linear Applications

2

The Culprits!!!Capacitive Loads!

High Input Network Impedance!

Transimpedance Amplifiers!

Reference Buffers! Cable/Shield Drive! MOSFET Gate Drive!

High-Source Impedance or Low-Power Circuits!

-

+

IOP2

R3 499kR4 499k

+

VG2

Cin 25p Vout

-

+

OPA

Cin 1u

C1 1u

C2 1u

VIN 5Vin

Temp

GND

Vout

Trim

U1 REF5025

C3 10u

ADC_VREF

C4 100n

-

+

OPA

RL 250

Rf 20kRg 1k

+

Vin

-

+

OPA

C_Cable 10nVout

VREF 2.5

VREF

Shielded Cable

-

+

OPA

VRef 2.5

R1 20k

R2 20k

Vin 10

VReg

Q1

RL 200

Vo

Rf 1M

Rd 4.99G Cd 10p-

+

OPA

Id

Photodiode Model

Attenuators!

V+

-

+

OPA

Rf 49kRg 4.99M

Cd 200p Vout

+Vin

D1

D2TVS

3

Just Plain Trouble!!Inverting Input Filter??

Output Filter??

-

+

OPA

VoutV1 5R1 10k

R2 49kC1 10u C5 100n

-

+

OPA

Rf 100kRg 10k

Cin 1u

Vout

+

Vin

Oscillator

OscillatorT

Time (s)

1.95m 2.23m 2.50m

VG1

0.00

10.00m

Vfb

-37.08m

62.12m

Vo

-1.00

1.16

T

Time (s)

1.95m 2.23m 2.50m

VG1

0.00

10.00m

Vfb

-37.08m

62.12m

Vo

-1.00

1.16

4

Recognize Amplifier Stability Issues on the Bench

• Required Tools:– Oscilloscope

– Step Generator

• Other Useful Tools:– Gain / Phase Analyzer

– Network / Spectrum Analyzer

5

Recognize Amplifier Stability Issues• Oscilloscope - Transient Domain Analysis:

– Oscillations or Ringing

– Overshoots

– Unstable DC Voltages

– High Distortion

T

Time (s)

1.75m 2.25m 2.75m

Vo

ltag

e (

V)

0.00

18.53m

T

Time (s)

1.75m 50.88m 100.00m

Ou

tpu

t

-14.83

0.00

15.00T

Time (s)

1.75m 2.25m 2.75m

Vo

ltag

e (

V)

0.00

21.88m

6

Recognize Amplifier Stability Issues• Gain / Phase Analyzer - Frequency Domain: Peaking, Unexpected

Gains, Rapid Phase Shifts

T

Ga

in (

dB

)

-60.00

-40.00

-20.00

0.00

20.00

40.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

-360.00

-180.00

0.00

7

What causes amplifier stability issues???

8

Poles and Bode Plots

+90

-90

+45

+-45

10 100 1k 10k 100k 1M 10M

Frequency(Hz)

0

(d

egre

es)

-45o @ fP

-45o/Decade

-90o

0o

0

20

40

60

80

100

10M1M100k10k1k100101

Frequency (Hz)

A (

dB)

-20dB/Decade-6dB/Octave

fPG

0.707G = -3dB

ActualFunction

Straight-Line Approximation

R

CVIN

VOUT

A = VOUT/VIN

Single Pole Circuit Equivalent

X100,000

Pole Location = fP

Magnitude = -20dB/Decade Slope

Slope begins at fP and continues down as frequency increases

Actual Function = -3dB down @ fP

Phase = -45°/Decade Slope through fP

Decade Above fP Phase = -84.3°

Decade Below fP Phase = -5.7°

9

Zeros and Bode Plots

+90

-90

+45

+-45

10 100 1k 10k 100k 1M 10M

Frequency(Hz)

0

(d

egre

es)

+90o

0o

+45o/Decade

+45o @ fZ

0

20

40

60

80

100

10M1M100k10k1k100101

Frequency (Hz)

A (

dB)

fZ

+20dB/Decade+6dB/Octave

Straight-Line Approximation

G

1.414G = +3dB(1/0.707)G = +3dB Actual

Function

R

C

VOUT

A = VOUT/VIN

Single Zero Circuit Equivalent

X100,000

Zero Location = fZ

Magnitude = +20dB/Decade Slope

Slope begins at fZ and continues up as frequency increases

Actual Function = +3dB up @ fZ

Phase = +45°/Decade Slope through fZ

Decade Above fZ Phase = +84.3°

Decade Below fZ Phase = 5.7°

10

Capacitor Intuitive Model

frequencycontrolled

resistor

OPEN SHORT

DC XCHi-f XCDC < XC < Hi-f

XC = 1/(2fC)

11

Inductor Intuitive Model

frequencycontrolled

resistor

SHORT OPEN

DC XLHi-f XLDC < XL < Hi-f

XL = 2fL

12

Op-Amp Intuitive Model

K(f)Ro

Rin

Vo

Vout

Vdiff+

-

IN+

IN-

x1

13

Op-Amp Loop Gain Model

+

-

RF

RI

VIN

+

-

network

Aol+

-

VOUTVIN

VFB

VOUT

VFB

RF

RI

=VFB/VOUT

VOUT

network

VOUT/VIN = Acl = Aol/(1+Aolβ)

If Aol >> 1 then Acl ≈ 1/β

Aol: Open Loop Gain

β: Feedback Factor

Acl: Closed Loop Gain

14

Amplifier Stability CriteriaVOUT/VIN = Aol / (1+ Aolβ)

If: Aolβ = -1

Then: VOUT/VIN = Aol / 0 ∞

If VOUT/VIN = ∞ Unbounded Gain

Any small changes in VIN will result in large changes in VOUT which will feed back to VIN

and result in even larger changes in VOUT OSCILLATIONS INSTABILITY !!

Aolβ: Loop Gain

Aolβ = -1 Phase shift of +180°, Magnitude of 1 (0dB)

fcl: frequency where Aolβ = 1 (0dB)

Stability Criteria:

At fcl, where Aolβ = 1 (0dB), Phase Shift < +180°

Desired Phase Margin (distance from +180° Phase Shift) > 45°

15

T

Time (s)

1.95m 2.08m 2.20m

Vo

-15.00

0.00

15.00

Vfb

-2.25

0.00

2.25

VG1

0.00

10.00m

ab

Fundamental Cause of Amplifier Stability Issues

• Too much delay in the feedback network

-

+BUF

BUF BUF

R1 100kR2 100k+ VG1

Vfb

Vo

DELAY

DELAY

16

T

Time (s)

1.95m 2.23m 2.50m

VG1

0.00

10.00m

Vfb

-37.08m

62.12m

Vo

-1.00

1.16

Cause of Amplifier Stability Issues• Example circuit with too much delay in the feedback network

-

+BUF

BUF BUF

R1 100kR2 100k+

VG1

Vfb

Vo

R3 10

C1 10uC2 20p

17

Cause of Amplifier Stability Issues• Real circuit translation of too much delay in the feedback network

-

+BUF

BUF BUF

R1 100kR2 100k

+

VG1

Vfb

VoRo 10

Cin 4pCstray 16p

Cload 10u

18

Cause of Amplifier Stability Issues• Same results as the example circuit

-

+BUF

BUF BUF

R1 100kR2 100k

+

VG1

Vfb

VoRo 10

Cin 4pCstray 16p

Cload 10u

T

Time (s)

1.95m 2.23m 2.50m

VG1

0.00

10.00m

Vfb

-37.08m

62.12m

Vo

-1.00

1.16

19

How do we determine if our system has too

much delay??

20

Phase Margin• Phase Margin is a measure of the “delay” in the loop

V+

V-

+

VG1 353.901124n+

-

+

U2 OPA627E

VF1

Open-Loop

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (

degr

ees)

Frequency (Hz)

100

Phase Margin

AOL

AOLPhase

Unity-Gain f(cl)

21

Small-Signal Overshoot vs. Phase Margin

From: Dorf, Richard C. Modern Control Systems. Addison-Wesley Publishing Company. Reading, Massachusetts. Third Edition, 1981.

Phase Margin Overshoot

90° 0

80° 2%

70° 5%

60° 10%

50° 16%

40° 25%

30° 37%

20° 53%

10° 73%

22

Damping Ratio vs. Phase Margin


23

AC Peaking vs. Damping Ratio


Phase Margin AC Peaking @Wn

90° -7dB

80° -5dB

70° -4dB

60° -1dB

50° +1dB

40° +3dB

30° +6dB

20° +9dB

10° +14dB

24

T

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00120

80

60

40

20

0

-20

-40

Gai

n (d

B)

100

1 10 100 1k 10k 100k 1M 10M 100MFrequency (Hz)

AOL

AOL*B

1/Beta

Rate of Closure= 20dB/decade

Rate of ClosureRate of Closure: Rate at which 1/Beta and AOL intersect

ROC = Slope(1/Beta) – Slope(AOL)

ROC = 0dB/decade – (-20dB/decade) = 20dB/decade

25

T

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00120

80

60

40

20

0

-20

-40

Gai

n (d

B)

100


AOL

1/Beta

Rate of Closure and Phase MarginSo a pole in AOL or a zero in 1/Beta inside the loop will decrease AOL*B Phase!!

40dB/decade

40dB/decade

AOL pole

1/B zero

26

Rate of Closure and Phase MarginRelationship between the AOL and 1/Beta rate of closure and Loop-Gain (AOL*B) phase margin

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[d

eg

]

0.00

45.00

90.00

135.00

180.00

a120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (d

egre

es)

Frequency (Hz)

100

Phase Margin≥ 45 degrees!

Rate of Closure= 20dB/decade

AOL

1/B

AOL*BPhase

AOL*B

27

Rate of Closure and Phase Margin

AOL Pole

1/Beta Zero

28

Testing for Rate of Closure in SPICE

V+

V-

+

VG1 0

+

-

+

U2 OPA627E

VF1

R1 1k R2 1k

V+

V-

+

-

+

U1 OPA627E

Vo

R3 1k R4 1k

L1 1T

C1 1T

+

VG2

Vfb

VinShort out the input source

Break the loop with L1 at the inverting input

Inject an AC stimulus through C1

• Break the feedback loop and inject a small AC signal

29

Breaking the Loop

DC AC

V-

V+

+

-

+U1 OPA627E

Vo

Rf 1k

Rg 1k

+

VG2 Vfb

Vin

L1

C1V-

V+

+

-

+U1 OPA627E

Vo

Rf 1kRg 1k+

VG1

Vfb

VinL1

C1

30

Plotting AOL, 1/Beta, and Loop GainAOL = Vo/Vin

1/Beta = Vo/Vfb

AOL*B = Vfb/Vin

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 14.14k 200.00M

Ph

ase

[d

eg

]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (d

egre

es)

Frequency (Hz)

100

Phase Margin= 82degrees

AOL*B

1/B

AOL*BPhase

AOLV+

V-

+

-

+

U1 OPA627E

Vo

+

VG1 0

L1 1T

C1 1T

Vin

Rg 1k Rf 1k

Vfb

31

Noise Gain• Understanding Noise Gain vs. Signal Gain

Inverting Gain, G = -1 Non-Inverting Gain, G = 2

Both circuits have a NOISE GAIN (NG) of 2.

NG = 1 + ΙGΙ = 2 NG = G = 2

V+

V-

V+

V-

+

VG1

+

-

+

U1 OPA627E

Vo

R1 1k R2 1k

+

VG1

+

-

+

U1 OPA627E

Vo

R1 1k R2 1k

32

Noise Gain• Noise Gain vs. Signal Gain

Gain of -0.1V/V, Is it Stable?

Inverting Gain, G = -0.1

If it’s unity-gain stable then it’s stable as an inverting attenuator!!!

V+

V-

+

VG1

+

-

+

U1 OPA627E

Vo

R1 10k R2 1k

V+

V-

+

VG1

+

-

+

U1 OPA627E

Vo

R1 10k R2 1k

Noise Gain, NG = 1.1

33

Capacitive Loads

34

Capacitive LoadsUnity Gain Buffer Circuits Circuits with Gain

V+

V-

+

-

+

U1 OPA627E

VF1

R2 100kR3 249

+

VG1 0 CLoad 1uV+

V-

+

Vin

+

-

+

U1 OPA627E

Vo

CLoad 1uF

0 150u 300uTime (seconds)

80m

0

Vo (V)

T

Time (s)

0.00 150.00u 300.00u

VF1

-40.00m

-10.00m

20.00m

50.00m

80.00m

VG1

0.00

20.00m

Vin (V)

20m

-40m20m

10m

T

Time (s)

0.00 150.00u 300.00u

V1

0.00

20.00m

40.00m

VG1

0.00

1.00m


40m

0

Vo (V)

Vin (V)

20m

01m

35

Capacitive Loads – Unity Gain Buffers - ResultsDetermine the issue:

Pole in AOL!!

ROC = 40dB/decade!!

Phase Margin 0!!

NG = 1V/V = 0dB

V+

V-

+

-

+

U1 OPA627E

Vo

CLoad 1u+

VG1 0

L1 1T

C1

1T

Vin

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (

degr

ees)

Frequency (Hz)

100

T

Vo

ltag

e (

V)

-40

-20

0

20

40

60

80

100

120

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Vo

ltag

e (

V)

0.00

45.00

90.00

135.00

180.00

Phase Margin= 0.2degrees!

Rate of Closure= 40dB/decade!

AOL + AOL*B

1/B

AOL*BPhase

Pole in AOL

36

Capacitive Loads – Unity Gain Buffers - Theory

V+

V-

+

-

+

U1 OPA627E

Vo

CLoad 1u+

VG1

L1 1T

C4

1T

Vin

Loaded AOLRo 54

CLoad 1u

L1

+

VG1

-

+

-

+

AOL 1M

C1

+

AOL

Ro 54

CLoad 1u

Loaded AOL

37


Transfer function:

W(s)=1

1+RoCload

s

T

Ga

in (

dB

)

-80.00

-60.00

-40.00

-20.00

0.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

-90.00

-45.00

0.00

0

-20

-40

-60

-80

0

-45

-901 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (

degr

ees)

Frequency (Hz)

Loaded AOLPole

CLoadRoFPOLE

2

1

+

Vin

Ro 54

CLoad 1u

Loaded AOL

38


X

=

T

Ga

in (

dB

)

-80.00

-60.00

-40.00

-20.00

0.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[d

eg

]

-90.00

-45.00

0.00

0

-20

-40

-60

-80

0

-45

-901 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)Ph

ase

(deg

rees

)

Frequency (Hz)

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[d

eg

]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)Ph

ase

(deg

rees

)

Frequency (Hz)

100

T

Vo

lta

ge

(V

)

-40

-20

0

20

40

60

80

100

120

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Vo

lta

ge

(V

)

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gain

(dB)

Phas

e (de

gree

s)

Frequency (Hz)

100

AOL AOL Load

Loaded AOL

39

Stabilize Capacitive Loads – Unity Gain Buffers

40

Unity-Gain circuits can only be stabilized by modifying the AOL load

T

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00120

80

60

40

20

0

-20

-40

Gai

n (d

B)

100


Stability Options

41

Method 1: Riso

V+

V-

+

-

+

U1 OPA627E CLoad 1u

Riso 6+

VG1

Vo

VLoad

42

Method 1: Riso - ResultsTheory: Adds a zero to the Loaded AOL response to cancel the pole

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (

dB)

Pha

se (

degr

ees)

Frequency (Hz)

100

Phase Margin = 87.5degrees!

Rate of Closure = 20dB/decade

AOL + AOL*B

Pole in AOL1/B

AOL*BPhase

Zero in AOL

V+

V-

+

-

+

U1 OPA627E CLoad 1u

Riso 6

+

VG1

Vo

VLoad

43

Method 1: Riso - ResultsWhen to use: Works well when DC accuracy is not important, or when loads are very light

Vo (V)

Vload (V)

Vin (V)

T

Time (s)

0.00 125.00u 250.00u

V1

0.00

20.37m

V2

0.00

20.00m

VG1

0.00

20.00m

V+

V-

+

-

+

U1 OPA627E CLoad 1u

Riso 6

+

VG1

Vo

VLoad

44

Method 1: Riso - Theory

V+

V-

+

-

+

U1 OPA627E CLoad 1u

L1 1T

C1 1T

Vin

Riso 5

+

VG1

Vo

Ro 54

CLoad 1u

+

VG1

-

+

-

+

AOL 1M

Riso 5

Loaded AOL

C1

Ro 54

Riso 5

Loaded AOL

CLoad 1u

+

AOL

45


Zero Equation:

f(zero)=1

2piRisoCLoad

s

Pole Equation:

f(pole)=1

2pi(Ro+Riso)CLoad

s

Transfer function:

Loaded AOL(s)=1+CLoad

Risos

1+(Ro+Riso)CLoad

s

Ro 54Ohm

Riso 5Ohm

Loaded AOL

CLoad 1uF

+

Vin

T

Ga

in (

dB

)-40.00

-20.00

0.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

-90.00

-45.00

0.00

0

-20

-40

0

-45

-901 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (

degr

ees)

Frequency (Hz)

46


X

=

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[d

eg

]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)Ph

ase

(deg

rees

)

Frequency (Hz)

100T

Ga

in (

dB

)

-40.00

-20.00

0.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[d

eg

]

-90.00

-45.00

0.00

0

-20

-40

0

-45

-901 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)Ph

ase

(deg

rees

)

Frequency (Hz)

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[d

eg

]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gain

(dB)

Phas

e (d

egre

es)

Frequency (Hz)

100

47

Method 1: Riso - DesignEnsure Good Phase Margin:

1.) Find: fcl and f(AOL = 20dB)2.) Set Riso to create AOL zero: Good: f(zero) = Fcl for PM ≈ 45 degrees. Better: f(zero) = F(AOL = 20dB) will yield slightly less than 90 degrees phase margin

fcl = 222.74kHz

f(AOL = 20dB) = 70.41kHz

T

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

f(AOL = 20dB)

fcl

120

80

60

40

20

0

-20

-40

Gai

n (

dB)100


48

Method 1: Riso - Design

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (

degr

ees)

Frequency (Hz)

100

F(zero) = 70.41kHz

PM = 84°

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (

dB)

Pha

se (

degr

ees)

Frequency (Hz)

100

F(zero) = 222.74kHz

PM = 52°

f(AOL = 20dB) = 70.41kHz

→ Riso = 2.26Ohms

fcl = 222.74kHz

→ Riso = 0.715Ohms

Zero Equation:

f(zero)=1

2piRisoCLoad

s

Pole Equation:

f(pole)=1

2pi(Ro+Riso)CLoad

s

Transfer function:

Loaded AOL(s)=1+CLoad

Risos

1+(Ro+Riso)CLoad

s

2.26R

V+

V-

+

-

+

U1 OPA627E

CLoad 1u

L1 1T

C1 1T

Vin

Riso 714m

+

VG1

Vo

1uF

0.715R

V+

V-

+

-

+

U1 OPA627E

CLoad 1u

L1 1T

C1 1T

Vin

Riso 714m

+

VG1

Vo

1uF

Ensure Good Phase Margin: Test

49

Method 1: Riso - Design

T

Ga

in (

dB)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Ga

in (

dB

)P

ha

se (

de

gre

es)

Frequency (Hz)

100

PM_min = 35°

F(zero) = 26.5kHzF(pole) =

2.65kHz

T

Gai

n (d

B)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Pha

se [d

eg]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Ga

in (

dB

)P

ha

se (

de

gre

es)

Frequency (Hz)

100

PM_min = 20°

F(zero) = 100.2kHz

F(pole) = 2.86kHz

Riso = Ro/9 Riso = Ro/34

Prevent Phase Dip:

Place the zero less than 1 decade from the pole, no more than 1.5 decades away Marginal: 1.5 Decades: F(zero) ≤ 35*F(pole) → Riso ≥ Ro/34 → 70° Phase Shift Desirable: 1 Decade: F(zero) ≤ 10*F(pole) → Riso ≥ Ro/9 → 55° Phase Shift

50

Method 1: Riso – Design Summary

6R

V+

V-

+

-

+

U1 OPA627E

CLoad 1u

L1 1T

C1 1T

Vin

Riso 714m

+

VG1

Vo

1uF

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (

degr

ees)

Frequency (Hz)

100

PM_min = 35°

PM = 87.5°

Final Circuit

Summary:

Ensure stability by placing Fzero ≤ 10* Fpole

51

Method 1: Riso - Disadvantage

6R

1uFV+

V-

+

-

+U1 OPA627E

CLoad 1u

Riso 6

+

VG1

Vo

Vload

RLoad 25

25R

+ -

T

Time (s)

0.00 125.00u 250.00u

Vol

tage

(V)

0.00

20.09m20.19m

0

0 125u 250u

Vo

ltag

e (

V)

Time (seconds)

Riso Voltage Drop

Vo

VLoad

Disadvantage:

Voltage drop across Riso may not be acceptable

52

Method 2: Riso + Dual Feedback

V+

V-

+

-

+

U1 OPA627E CLoad 1u

Riso 6

+

VG1

VLoad

Rf 49k

Cf 100n

Vo

53

Method 2: Riso + Dual FeedbackTheory: Features a low-frequency feedback, Rf, to cancel the Riso drop and a high-frequency feedback, Cf, to create the AOL pole and zero.

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (

degr

ees)

Frequency (Hz)

100



AOL + AOL*B

Pole in AOL1/B

AOL*BPhase

Zero in AOL

V+

V-

+

-

+

U1 OPA627E CLoad 1u

+

VG1

Rf 49k

Cf 100n

VoL1 1T

C1 1T

Vfb

Vin

Riso 6

54

Method 2: Riso + Dual FeedbackWhen to Use: Only practical solution for very large capacitive loads ≥ 10uF

When DC accuracy must be preserved across different current loads

T

Time (s)

0.00 150.00u 300.00u

V1

0.00

20.27m

V2

0.00

20.00m

VG1

0.00

20.00m


20.3m

0

VLoad(V)

020m

20m0

Vo(V)

Vin(V)

V+

V-

+

-

+

U1 OPA627E CLoad 1u

Riso 5

+

VG1

Vload

R2 49k

C1 100n

Vo

55

Capacitive Loads – Circuits with Gain

56

Capacitive Loads – Circuits with Gain

V+

V-

+

-

+

U1 OPA627E

Vo

Rf 100kRg 4.99k

+

VG1 0 CLoad 100n


40m

0

Volta

ge (V

)

30m

20m

10m

T

Time (s)

0.00 150.00u 300.00u

Vo

lta

ge

(V

)

0.00

10.00m

20.00m

30.00m

40.00m

57

Capacitive Loads – Circuits With Gain - ResultsSame Issues as Unity Gain Circuit

Pole in AOL!!

ROC = 40dB/decade!!

Phase Margin = 10°!!T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Ga

in (

dB

)P

has

e (

deg

rees

)

Frequency (Hz)

100

PM = 10.5°

AOL

1/B

AOL*BPhase

Pole in AOL

AOL*B

ROC = 40dB/decade

V+

V-

+

-

+

U1 OPA627E

Vo

Rg 100kRf 4.99k

CLoad 100n

+

VG1

L1 1T

C1 1T

Vin

Vfb

58

Stabilize Capacitive Loads – Circuits with Gain

59

T

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00120

80

60

40

20

0

-20

-40

Gai

n (d

B)

100


AOL

1/Beta

Stability Options – Circuits with GainCircuits with gain can be stabilized by modifying the AOL load and by modifying 1/Beta

60

Method 1 + Method 2

Method 1: Riso

Method 2: Riso+Dual Feedback

Methods 1 and 2 work on circuits with gain as well!

V+

V-

+

-

+U1 OPA627E

Rf 100kRg 4.99k

+

VG1CLoad 100n

Riso 10VLoad

Vo


25m

0

VLoad(V)

025m

1m

0

T

Time (s)

0.00 150.00u 300.00u

V1

0.00

12.50m

25.00m

V2

0.00

12.50m

25.00m

VG1

0.00

1.00m

Vo(V)

Vin(V)

V+

V-

+

-

+

U1 OPA627E CLoad 100n

Riso 10VLoad

Rf 100k

Cf 100p

Vo

Rg 4.99k

+

VG1

T

Time (s)

0.00 150.00u 300.00u

V1

0.00

10.00m

20.00m

V2

0.00

10.00m

20.00m

VG1

0.00

1.00m


25m

0

VLoad(V)

025m

1m

0

Vo(V)

Vin(V)

61

Method 3: Cf

V-

V+

+

-

+U1 OPA627E CLoad 100n

Vo

Rf 100kRg 4.99k

C1 27p

+

VG1

62

Method 3: Cf - ResultsTheory: 1/Beta compensation. Cf feedback capacitor causes 1/Beta to decrease at -20dB/decade and if placed correctly will cause the ROC to be 20dB/decade.

T

Gai

n (d

B)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Pha

se [d

eg]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Ga

in (

dB

)P

ha

se (

de

gre

es)

Frequency (Hz)

100

PM = 68°

AOL

1/B

AOL*BPhase

AOL*B

ROC = 20dB/decade

1/B Pole

1/B Zero

AOL Pole

V-

V+

+

-

+U1 OPA627E

CLoad 100n

Vo

Rf 100kRg 4.99k

Cf 27p

+

VG2

L1 1T

C1 1T

Vin

Vfb

63

Method 4: Noise-Gain

V-

V+

+

-

+U1 OPA627E

CLoad 100n

Vo

Rf 100kRg 4.99k

Cn 820n

+

VG1

Rn 75

64

Method 4: Noise Gain - ResultsTheory: 1/Beta compensation. Raise high-frequency 1/Beta so the ROC occurs before the AOL pole causes the AOL slope to change

T

Gai

n (d

B)-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Pha

se [d

eg]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Ga

in (

dB

)P

ha

se

(d

eg

ree

s)

Frequency (Hz)

100

PM = 56°

AOL

1/B

AOL*BPhase

AOL*B

ROC = 20dB/decade

1/B Pole1/B ZeroAOL Pole

65

Circuits with High Input Impedance

66

Circuits with High Input Impedance


1

0

Vo (V)

Vin (V)

0

-110m

T

Time (s)

0.00 150.00u 300.00u

Vout (V)

-1.00

0.00

1.00

VG1

0.00

10.00m

V-

V+

+

-

+U1 OPA627E

Vo

Rf 499kRg 499k

+Vin

Cstray 20p

67

Circuits with High Input ImpedanceDetermine the issue:

Zero in 1/Beta!!

ROC = 40dB/decade!!

Phase Margin 2!!T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (

degr

ees)

Frequency (Hz)

100

PM = 2°

AOL

1/B

AOL*BPhase

AOL*B

ROC = 40dB/decade!

1/B Zero

V-

V+

+

-

+U1 OPA627E

Vo

Rf 499kRg 499k

+

VG1

L1 1T

C1 1T

Vin

Vfb

Cin 27p

68

Stabilize Circuits With High Input Impedance

69

Stability Options – Zero in 1/BetaThe only practical option is to add a pole to cancel the 1/Beta Zero

T

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00120

80

60

40

20

0

-20

-40

Gai

n (d

B)

100


70

Method 3: Cf

V-

V+

+

-

+U1 OPA627E

Rf 499kRg 499k

+

VG1

Cstray 20p

Cf 21p

Vo

71

Method 3: Cf - ResultsTheory: 1/Beta compensation. Cf feedback places a pole in 1/Beta to cancel the zero from the input capacitance.

V-

V+

+

-

+U1 OPA627E

Vo

Rf 499kRg 499k

Cf 21p

+VG1

L1 1T

C1 1T

Vin

Vfb

Cin 27p

T

Vo

ltag

e (

V)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Vo

ltag

e (

V)

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Ga

in (

dB

)P

ha

se (

de

gre

es)

Frequency (Hz)

100

PM = 81°

AOL

1/B

AOL*BPhase

AOL*BROC =

20dB/decade!

1/B Zero 1/B Pole

72

Ro vs. Zo

73

When Ro is really Zo!!

V+

V-

+

-

+

U1 OPA627E

VoVos 80.0432u

IG1V+

V-

-

++

4

3

5

1

2

U1 OPA2376

Vo

Vos -25.3845uV

IG1

74

With Complex Zo, Accurate Macro-Models are key!T

Ga

in (

dB

)

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00MP

ha

se [d

eg

]

-90.00

-45.00

0.00

45.00

90.00

135.00

180.00

120

80

6040

200

-20

140

180

135

90

-901 10 100 1k 10k 100k 1M 10M 100MG

ain

(dB

)P

hase

(de

gree

s)

Frequency (Hz)

100

PM = -77°!!

1/B

AOL + AOL*B

ROC = 60dB/decade!

AOL*BPhase

-40

-60

45

0

-45

V+

V-

-

++

4

3

5

1

2

U1 OPA2376

Vo

CLoad 1uF+

Vin

T

Time (s)

0.00 150.00u 300.00u

V1

-40.00m

10.00m

60.00m

VG1

0.00

20.00m


60m

0

Vo (V)

Vin (V)

-40m20m

75

With Complex Zo, Accurate Models are key!

Green-Lis macro-model op amp architecture

V+

V-

-

++

4

3

5

1

2

U1 OPA2376

Vo

Vos -25.3845uV

IG1


100m

1k

10

1

10k

100

Impe

danc

e (O

hms)

T

Frequency (Hz)

100.00m 1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ga

in (

dB

)

1.00

10.00

100.00

1.00k

10.00k

76

Summary of Op Amp Stabilization Methods

77

Method 1: Riso - ResultsTheory: Adds a zero to the Loaded AOL response to cancel the pole

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (

dB)

Pha

se (

degr

ees)

Frequency (Hz)

100



AOL + AOL*B

Pole in AOL1/B

AOL*BPhase

Zero in AOL

V+

V-

+

-

+

U1 OPA627E CLoad 1u

Riso 6

+

VG1

Vo

VLoad

78

Method 2: Riso + Dual FeedbackTheory: Features a low-frequency feedback, Rf, to cancel the Riso drop and a high-frequency feedback, Cf, to create the AOL pole and zero.

T

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Ph

ase

[de

g]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Gai

n (d

B)

Pha

se (

degr

ees)

Frequency (Hz)

100



AOL + AOL*B

Pole in AOL1/B

AOL*BPhase

Zero in AOL

V+

V-

+

-

+

U1 OPA627E CLoad 1u

+

VG1

Rf 49k

Cf 100n

VoL1 1T

C1 1T

Vfb

Vin

Riso 6

79

Method 3: Cf - ResultsTheory: 1/Beta compensation. Cf feedback capacitor causes 1/Beta to decrease at -20dB/decade and if placed correctly will cause the ROC to be 20dB/decade.

T

Gai

n (d

B)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Pha

se [d

eg]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Ga

in (

dB

)P

ha

se (

de

gre

es)

Frequency (Hz)

100

PM = 68°

AOL

1/B

AOL*BPhase

AOL*B

ROC = 20dB/decade

1/B Pole

1/B Zero

AOL Pole

V-

V+

+

-

+U1 OPA627E

CLoad 100n

Vo

Rf 100kRg 4.99k

Cf 27p

+

VG2

L1 1T

C1 1T

Vin

Vfb

80

Method 4: Noise Gain - ResultsTheory: 1/Beta compensation. Raise high-frequency 1/Beta so the ROC occurs before the AOL pole causes the AOL slope to change

T

Gai

n (d

B)-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1.00 10.00 100.00 1.00k 10.00k 100.00k 1.00M 10.00M 100.00M

Pha

se [d

eg]

0.00

45.00

90.00

135.00

180.00

120

80

60

40

200

-20

-40

180

135

90

45

01 10 100 1k 10k 100k 1M 10M 100M

Ga

in (

dB

)P

ha

se

(d

eg

ree

s)

Frequency (Hz)

100

PM = 56°

AOL

1/B

AOL*BPhase

AOL*B

ROC = 20dB/decade

1/B Pole1/B ZeroAOL Pole

81

Questions / Comments?

Thank You

Special thanks to:

Collin Wells

Art Kay

Tim Green

Bruce Trump

PA Apps Team

Comments, Questions, Technical Discussions Welcome:Marek Lis 520-750-2162 [email protected]

1 Solving Op Amp Stability Issues Presented by Marek Lis Sr Application Engineer Texas Instruments - Tucson Prepared by Collin Wells HPA Linear Applications.

Documents

db slide

dbdecade slide

loop gain aol

loop gain aol

signal gain gain

closed loop gain slide

vfbvin slide

oscillator slide