Frequency compensation in CMOS operational amplifier:

Frequency compensation is done so that the amplifier is stable for any desired value of the closed loop gain. Compensation technique modifies magnitude and phase plots so that |AB| < 1 when the angle of AB is 180°. That is, compensation techniques reduces the gain of the amplifier at those frequencies for which phase shift is high.

There are three general frequency compensation techniques:

1. Dominant pole or lag compensation: In this method a new pole is introduced in the open loop transfer function at the lower frequency than the existing poles.
2. Lead compensation: In this technique zero is added to the transfer function.
3. Pole-zero or Lag-lead compensation: This technique adds to the pole and zero to the transfer function.

Dominant pole:

When a pole is introduced in the appropriate position in the s-plane, then the modified loop gain to 0 dB with a slope of -20 dB/decade. Consider a three stage amplifier. Each stage produces a capacitive component. Thus there will be many breaks associated with each RC pole pair. For example when there are three stages, it will have three corner frequencies.

A dominant pole can be added by introducing RC network in series with the amplifier as shown in below figure or it can be added by connecting a capacitor C from a suitale high resistance point to ground.   

After adding dominant transfer function pole becomes

for three stage amplifier with dominant pole

Lead compensation:

Lead compensation adds positive feedback (phase) back into loop so as to avoid negative phase in frequency domain due to the delay in time domain.

Lead compensations defined by a lower frequency zero at fZ and a higher frequency pole at fP.