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

© 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



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.



Negative Feedback

Negative feedback is used to control the gain.

A classic form of feedback equation



Feedback equation:

Closed Loop Gain

o The system gain with feed back is Vout/Vin and is called Closed Loop Gain Acl.

o It is determined by only feedback factor B.

For AolB >> 1



Closed Loop Gain

o The system gain is determined by only feedback factor B.

o Feedback factor is implemented by stable passive components .

o Thus in ideal conditions the closed loop gain is predictable and stable because B is predictable and stable.

Rf

Ri

Vf

Vin

+

–

Feedbackcircuit

Vout

–

+

Rf

Vout

Ri

Vin



Non-inverting amplifier

Feedback equation for Op-amp feedback systems

Rf

Ri

Vf

Vin

+

–

Feedbackcircuit

Vout

Non-inverting amplifier

fR

iR

iR

ABA olol



Inverting amplifier

Feedback equation for Op-amp feedback systems

–

+

Rf

Vout

Ri

Vin

Replace ZF with Rf and ZG with Ri

The factor AolB is identical in both inverting and non inverting amplifier circuits.

fR

iR

iR

ABA olol



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

Loop Gain and Stability analysis



Bode plots of loop gain are key to understanding 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 plots are key to understanding Stability:

o Notice that a one 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



Loop gain plots are key to understanding Stability:

AolB



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 gain of one or more 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 is implemented by modifying the gain and phase characteristics of the amplifier's open loop output or of its feedback network, or both, in such a way as to avoid the conditions leading to oscillation.

This is usually done by the internal or external use of resistance-capacitance networks.


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.

f1 f2



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


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.



The closed-loop gain of an op-amp circuit is related to the loop gain. So the closed-loop gain can be used to stabilize the circuit.

Gain Compensation

Gain compensation works for both inverting and non-inverting op-amp circuits because the loop gain equation contains the closed-loop gain parameters in both cases.

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

fR

iR

iR

ABA olol



Gain Compensation



Lead Compensation

It consists of putting a zero 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

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

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