Analog Electronics

© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.

Electronic Devices, 9th editionThomas L. Floyd

Analog Electronics

Lecture 6

Muhammad Amir Yousaf

Op amp Stability Analysis and Compensation



Lecture:

Op-amp Circuits

Stability analysis and compensation of op-amps

Op-ampsThree gains:

Open Loop Gain Aol

Closed Loop Gain Acl

Loop Gain AolBUn-StabilityCompensation



Open Loop Gain

Op-amp’s gain is so high that even a slightest input signal would saturate the output.

In most real op amps the open loop gain starts to decrease before 10 Hz,



Vout

+

–

Vin

Vf

Internal inversion makes Vf

180° out of phase with Vin.

Negativefeedbackcircuit

Negative Feedback

Negative feedback is used to control the gain

Rf

Ri

Vf

Vin

+

–

Feedbackcircuit

Vout

–

+

Rf

Vout

Ri

Vin



Non-inverting amplifier

Closed loop gain Acl Op-amp feedback systems

Rf

Ri

Vf

Vin

+

–

Feedbackcircuit

Vout

Non-inverting amplifier

).(f

Ri

Ri

RVVAV OUTINol.out

fR

iR

iR

A

A

V

V

ol

ol

IN

out

1



Closed loop gain Acl Op-amp feedback systems

Inverting amplifier

–

+

Rf

Vout

Ri

Vin

fR

iR

iR

Vf

Ri

Rf

RVV

VAV

OUTINA

Aol.out

..

fR

iR

iRA

Vf

Ri

Rf

RAV

V

fR

iR

iR

Vf

Ri

Rf

RV

A

V

ol

OUT

ol

INOUT

OUTINol

OUT

..

..

..

)1(.

.

fR

iR

iRA

fR

iR

fRA

V

Vol

ol

IN

OUT

)1( .

.

BAf

Ri

Rf

RA

V

V

ol

ol

IN

OUT



Loop Gain for Op-amp feedback systems

Rf

Ri

fR

iR

iR

VV turn

Re

oltest AVV .

fR

iR

iR

Atest

Vturn

Vol

.

Re

fR

iR

iR

ABA olol

V



Loop Gain

The term AolB is very important in stability analysis and is called ‘Loop Gain’

As the Loop Gain is identical in both inverting and non inverting amplifier circuits, hence the stability analysis is identical.



System output heads to infinity as fast as it can when 1+ AB approaches to zero.

Or |AB| =1 and ∠AB = 180o

If the output were not energy limited the system would explode the world.

System is called unstable under these conditions:o It could lock to maximum supply rails.o It could oscillate.

Loop Gain and Stability analysis



Loop gain plots are key to understanding Stability:

AolB



Bode plots of loop gain is a tool to understand Stability:

Stability is determined by the loop gain, when AolB = -1 = |1| 180∠ o instability or oscillation occurs

Bode plots and stability analysis.



Loop gain plot is a tool to understand Stability:

o Notice that a single pole can only accumulate 90° phase shift, so when a transfer function passes through 0 dB with a one pole, it cannot oscillate.

o A two-pole system can accumulate 180° phase shift, therefore a transfer function with a two or greater poles is capable of oscillation.

f1

f2



Op-amp transfer function

The open loop gain of even the simplest operational amplifiers will have at least two poles.

At some frequency, the phase of the amplifier's output = -180° compared to the phase of its input signal.

The amplifier will oscillate if it has a loop-gain of one at this frequency.

f1

f2



Phase Margin = ΦM

Phase margin is a measure of the difference in the actual phase shift and the theoretical 180° at gain 1 or 0dB crossover point.

Phase Margin, Gain Margin

Gain Margin = AM

The gain margin is a measure of the difference of actual gain (dB) and 0dB at the 180° phase crossover point.

For Stable operation of system:ΦM > 45o or AM > 2 (6dB)

Safe Margin

f1

f2



The phase margin is very small, 20o

So the system is nearly stable

A designer probably doesn’t want a 20° phase margin because the system overshoots and rings badly.

Phase Margin, Gain Margin

Increasing the loop gain to (K+C) shifts the magnitude plot up. If the pole locations are kept constant, the phase margin reduces to zero and the circuit will oscillate.

f1

f2

f1

f2



Dominant Pole Compensation (Frequency Compensation)

Gain Compensation

Lead Compensation

Compensation Techniques:



Dominant Pole Compensation

A pole placed at an appropriate low frequency in the open-loop response reduces the gain of the amplifier to one (0 dB) for a frequency at or just below the location of the next highest frequency pole.



The lowest frequency pole is called the dominant pole because it dominates the effect of all of the higher frequency poles.

Dominant Pole Compensation (Frequency Compensation)

Dominant-pole compensation can be implemented for general purpose operational amplifiers by adding an integrating capacitance.

The result is a phase margin of ≈ 45°, depending on the proximity of still higher poles.



As loop gain is a product of open loop gain, Aol and feed back factor B, it can be manipulated by varying feedback factor.

Gain Compensation

As long as the application can stand the higher gain, gaincompensation is the best type of compensation to use.

fR

iR

iR

ABA olol

Feedback factor B is equal to inverse of Closed loop gain Acl so technique is called Gain compensation.

BAcl

1



Gain Compensation



Lead Compensation

It consists of putting a zero (inverse of a pole) in the loop transfer function to cancel out one of the poles.

The best place to locate the zero is on top of the second pole, since this cancels the negative phase shift caused by the second pole.



Lead Compensation



References

Slides by ‘Pearson Education’ for Electronic Devices by Floyd

‘Op.amp for every one’ by Ron Mancini

’Stability Analysis for volatge feedback op-amps’, Application Notes byTexas Instruments (TI)

’Feedback amplifiers analysis tool’ by TI

‘Feedback, Op Amps and Compensation’ Application Note 9415 by Intersil

Modified by Muhammad Amir Yousaf

Analog Electronics

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