1. Op amp Stability Analysis and Compensation
Analog Electronics
Lecture 6
Op amp Stability Analysis and Compensation
Muhammad Amir Yousaf

2. Stability analysis and compensation of op-amps
Lecture:
Stability analysis and compensation of op-amps
Op-amps
Three gains:
Open Loop Gain Aol
Closed Loop Gain Acl
Loop Gain AolB
Un-Stability
Compensation
Op-amp Circuits

3. 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,

4. Negative Feedback
Negative feedback is used to control the gain

5. Closed loop gain Acl Op-amp feedback systems
Non-inverting amplifier
Non-inverting amplifier

6. Closed loop gain Acl Op-amp feedback systems
Inverting amplifier

7. Loop Gain for Op-amp feedback systemsRf Ri V

8. 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.

9. Loop Gain and Stability analysis
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:
It could lock to maximum supply rails.
It could oscillate.

10. Loop gain plots are key to understanding Stability:
AolB

11. Bode plots and stability analysis.
Bode plots of loop gain is a tool to understand Stability:
Stability is determined by the loop gain,
when AolB = -1 = |1| ∠180o 
instability or oscillation occurs

12. Loop gain plot is a tool to understand Stability:f1 f2
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.
A two-pole system can accumulate 180° phase shift, therefore a transfer function with a two or greater poles is capable of oscillation.

13. 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. f1 f2
The amplifier will oscillate if it has a loop-gain of one at this frequency.

14. Phase Margin, Gain Margin
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. f1
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) f2
Safe Margin

15. Phase Margin, Gain Margin
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. f1 f2
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

16. Compensation Techniques:
Dominant Pole Compensation (Frequency Compensation)
Gain Compensation
Lead Compensation

17. 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.

18. Dominant Pole Compensation (Frequency Compensation)
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.

19. Gain Compensation
As loop gain is a product of open loop gain, Aol and feed back factor B, it can be manipulated by varying feedback factor.
Feedback factor B is equal to inverse of
Closed loop gain Acl so technique is called Gain compensation.
As long as the application can stand the higher gain, gain
compensation is the best type of compensation to use.

20. Gain Compensation

21. 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.

22. Lead Compensation

23. 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