Opamp Stability Compensation Reduced

Opamp Stability and Compensation

BITS PilaniPilani Campus Anu Gupta

Compensationp p

Stability issues

Without feedbackWithout feedbackAll poles are negative

With feedbackAll poles negative but negative feedback canAll poles negative but negative feedback can

cause stability issues

BITS Pilani, Pilani Campus

Feedback mode

Single pole response-----always stableg p p y

Two pole response freq compensation isTwo pole response------freq compensation is required

3 pole response-----nested miller compensation is required


inresultsaxis)realnegative(on the-satpoleathen0,Suppose

infinitytogoeswhicht)exp(formtheofresponse transientain results axis) real positive (on the s pole a hand,other On the

0. todecays eventually which t),exp(- form theof response transienttheinresultsaxis)realnegative(on thesat polea then 0, Suppose

infinity.togoeswhich t),exp(form theof response

constanttimethecallediswhere ),exp(-t/ form in the written are terms transientexponetial analysis,circuit In

.1/ isconstant time the,-sat pole aFor constant.timethecalled is where

Transient response in terms of pole location From the Circuit Analysis , the mathematical form of the transient response is

l t d t th l ti f th l i th l d i

pole location

related to the location of the poles in the complex domain.

0todecayseventuallywhicht)exp(-formtheofresponsetransientthein results axis) real negative (on the -sat pole a then 0, Suppose

infinity. togoes which t),exp( form theof response transientain results axis) real positive (on the s pole a hand,other On the

0.todecayseventuallywhich t),exp(-formtheofresponse transientthe

Obviously, we do not want to have poles on the positive real axis, because the

transient response eventually drives the amplifier into voltage limits, resulting in

nonlinear distortion.

),exp(-t/ form in the written are terms transientexponetial analysis,circuit In


.1/ isconstant time the,-sat pole aFor constant.time thecalled is where

Approximately within 5 time constant theApproximately within 5 time constant, the

amplitude of exp terms decays to negligible

value compared to initial amplitude.

The greater the distance of the pole from the

origin, the faster the transient response decays


Transient response in terms of pole locationpole location

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

Frequent response in terms of pole locationpole location

Complex polesComplex poles

with much

less than

display a sharpdisplay a sharp

gain peak


Desired pole location

aforgainconstantnearlyhave torequired are amplifiers Often,

C id if ihi hat off roll torequired isgain

theandfrequency of rangegiven afor gain constant nearly have

of in terms responsefrequency and responseient both trans

gConsiderin s.frequenciehigher

axis. real negative theof 45with are amplifiersmost for locations

poledesired thelocations, pole

o

noshowing responsefrequency andfaster decaying response transientgivesregion in this Poles


peaks.gain excessivegpq y

BITS PilaniBITS PilaniPilani Campus

Single dominant pole responseSingle dominant pole responseSingle stage diff amplifier, Telescopic opamp, Folded cascode

amplifier

Feedback mode

open-loop gain of real amplifiers is a function of frequency.

Magnitude response drops off and phase shift increases at high

frequencies.

When feedback is applied to the open-loop amplifier, undesirable

frequency response (also transient response) can result.

Considering frequency dependence, the closed-loop gain of a

feedback amplifier should be re-formatted as function of Laplace

variable S as follows: )()( sAA


)()(1)()(

ssAsA f

Effects of feedback on pole: one pole system

Negative feedback has dramatic effects on pole locations of

pole system

amplifiers (OpAmp), which in turn affects transient responseand frequency response of the amplifiers

First, considering a one-pole (or dominant pole) amplifier, theopen loop gain is of the form

,)( 0AsA

.

,2/1

)(

0 frequencycornerloopopenisfandgainloopopenisAwhere

fssA


. 0 frequencycornerloopopenisfandgainloopopenisAwhere

With f db k i thi lifi th thWith f db k i thi lifi th th With feedback in this amplifier, then the With feedback in this amplifier, then the closedclosed--loop gain loop gain

constant. is assuming ,))2/(1/(1

))2/(1/()()(1

)()(0

0

fsAfsA

ssAsAsAf

frequencybreakorcornerandgaindcloop-closedwhere,)(

)(

))2/(1/(1)()(1

0

0

sAsA

fsAssA

ff

frequencybreak or corner andgain dcloopclosed where,)2/(1

)(

0

A

fssA

ff

lififiifiihifdb d id hihihi

)1( ,1

be will 00

00

fAfA

AffA

AA ff


needs.design obandwith t andgain thechangecan we,different Using

amplifier.an for ion specificatais thisoften,producebandwidth -gain theis this,00

fAfA ff

how the pole would change as feedback ratio changes?

Transient and frequency response of feedback amplifiers

feedback ratio changes?

q y p p

are related to the pole location,

F i l l (d i t l ) lifi th it d For single-pole (dominant-pole) amplifier, the magnitude

of pole for the closed-loop gain increases

So, the above pole is still on the negative real axis, but

moves further from the origin as increasesg

Feedback Amplifier is stable, linear settling time is fast


Differential AmplifierActive loadActive load

mpg2BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

EZ C

2

Zero calculation -intuitive

Zero will occur when i2 = i4 i. e no i ( ) i i it di ti

i4i3x

iout (s) i. e. i4 reverses its direction at wz, i. e i4 =i2= i3 at wz

i2i1

e 4 2 3 at z Vx is negative voltage. So i3 is positive

So i1 = i3; vx = - i1 x 1/ gm3 = - i1/ gm3

Current mirror operation at high freq at wCurrent mirror operation at high freq. at wz

431,__ iiifrequencylowat

31

431

)1(

__

sCgiV

f q y

Emx

3

1

]1[gsCg

iVE

m

x

23

1

3

13

3

)(]21[

1)(;2 igi

giV

Cgsat

g

xE

m

m

33 ]21[ ggC mmE

Polarity of Vx changes, Hence i3, i4 changes


its direction

A analysis using A plotWhy? Convenience

Pl f A i f iliPlot of A is familiar to us.Phase of A is similar to phase of A

h A lNo need to draw another A plot.Locate frequency where |A|=1Find phase at the frequency. Estimate phase margin


Method


20 logA plot20 logA plot

|A|=1

1/ lineFor =1

Figure 8.37 Stability analysis using Bode plot of |A|.

Stable system----no signal buildupPhase crossover Gain crossoverPhase crossover , Gain crossover

Gain crossover

phase crossover


Stable system

Gx < PxGx < PxDecrease Gx---easy time constant to be increased by adding capacitor

ororincrease Px---

Difficult circuit modification is reqd.


Telescopic OPAMPpole estimationpole estimation


Fully differential Telescopic Amp.

;1w ;])[||( 0204408066 Lmm

out Crrgrrgw

11

Xw

])[1(3

Xm

Cg

])[(1

4 NoN Cr

w


Impact of wN on wout


Folded cascode opamp


1

stagelastofgainAACCrrgmrrrgm

wcL

___

;])[||)||(

1

0130111102040990

])[||(1

F CCw

])[||( 015014 cF CCrr

1 1])[||(

1

01208 DD Crr

w ])[||1(

1

0128

Cm

C

Crg

w

])[1(

1B

Cw 1

Aw


])[(8

Bm

Cg ])[||( 01309 A

A Crrw


2 pole Amplifiers2 pole Amplifiers

2 stage fully differential OPAMP, 2 stage single ended OPAMP

Considering a two-pole amplifier, the open loop gain transfer function is of the form

at DC gainloopopenisAwherefsfs

AsA ,)2/1)(2/1(

)( 00

values)o be real (assumed tfrequencyeaken-loop brare two opfandfandfsfs

bb

bb

)2/1)(2/1(

21

21

Assume feedback ratio is constant (not a function of frequency) and evaluate the poles of the closed loop transfer function

thenarerootsthe,04)1()22(s0A(s)1equation solve

212

0212

ffAffs bbbb


)1(16)22(21)22(

21-s

t ea eootst e,0)()(s

02122

2121

21021

Affffff

ffffs

bbbbbb

bbbb

For the poles, as increases, the poles move together p , , p g

until they meet at the point in the middle.

Then, further increase causes the poles to become

l i f th l i l th ti lcomplex, moving away from the real axis along the vertical

line across the meeting point.

(the path followed by the poles is called a root locus)


Effects of feedback on pole:

Usually, feedback amplifiers aredesigned so that A is muchdesigned so that Ao is muchlarger than unity, which isusually necessary to achievegain stabilization, impedancecontrol, nonlinear distortionreduction etc.

From the root locus, it can beseen that a too large value ofAomight move the poles outsidemight move the poles outsidethe desirable region of the s-plane (the 45 degree negativeaxis). In that case, undesirable


frequency response peaks andtransient ringing occurs.

Freq. Compensation


2 stage opamp


Compensation


Impact of zero


Removing zero


Removing zeroexpressionexpression


Third pole due to RC compensationcompensation

CERZ


Third poleapprox expressionapprox. expression



EndEnd

Opamp Stability Compensation Reduced

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