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Analog Electronics

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Analog Electronics

Lecture 6

Op amp Stability Analysis and Compensation

Muhammad Amir Yousaf

Lecture:

- Stability analysis and compensation of op-amps

- Op-amps
- Three gains:
- Open Loop Gain Aol
- Closed Loop Gain Acl
- Loop Gain AolB

- Op-amp Circuits

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,

Negative Feedback

Negative feedback is used to control the gain

Closed loop gain Acl Op-amp feedback systems

Non-inverting amplifier

Non-inverting amplifier

Closed loop gain Acl Op-amp feedback systems

Inverting amplifier

Loop Gain for Op-amp feedback systems

V

Rf

Ri

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:
- It could lock to maximum supply rails.
- It could oscillate.

Loop gain plots are key to understanding Stability:

AolB

Bode plots and stability analysis.

Bode plots of loop gainis a tool to understand Stability:

Stability is determined by the loop gain,

when AolB = -1 = |1| ∠180o

instability or oscillation occurs

Loop gain plot is a tool to understand Stability:

f1

f2

- Noticethat a singlepole can only accumulate 90° phase shift, so when a transfer function passes through 0 dB with a one pole, it cannot oscillate.
- A two-polesystem can accumulate 180° phase shift, therefore a transfer function with a two or greater poles is capable of oscillation.

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.

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

- 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

- 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.

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

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

’Feedback amplifiersanalysistool’ by TI

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

Modified by Muhammad Amir Yousaf