# Op amp Stability Analysis

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Op amp Stability Analysis
Analog Electronics Lecture 6 Op amp Stability Analysis Muhammad Amir Yousaf

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

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

Closed Loop Gain Feedback equation: For AolB >> 1
The system gain with feed back is Vout/Vin and is called Closed Loop Gain Acl. It is determined by only feedback factor B.

Closed Loop Gain The system gain is determined by only feedback factor B. Feedback factor is implemented by stable passive components . Thus in ideal conditions the closed loop gain is predictable and stable because B is predictable and stable.

Feedback equation for Op-amp feedback systems
Non-inverting amplifier Non-inverting amplifier

Feedback equation for Op-amp feedback systems
Inverting amplifier Replace ZF with Rf and ZG with Ri The factor AolB is identical in both inverting and non inverting amplifier circuits.

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.

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

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

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

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. f1 f2 The amplifier will oscillate if it has a gain of one or more at this frequency.

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

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

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

Dominant Pole Compensation (Frequency Compensation)
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. f1 f2  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.

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.

Gain Compensation 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 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, gain compensation is the best type of compensation to use.

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.