Stability analysis of cross-coupled amplifier in Cadence

Question

I am trying to implement a cross coupled amplifier with OP-AMP feedback. I am not able to get it stable for a square wave however. The circuit looks as follows: The OP AMP is ideal from Cadence, all parameters can be tuned. The circuit is unloaded. The open loop gain, i.e without feedback, Vout/Vin looks as follows:

As it can be seen the gain is negative, which is correct.

Now the closed loop gain from AC analysis with the feedback opamp i.e Vout/Vin* looks as follows: Looking at the closed loop gain there appears to be a zero at ~10 MHz. I have no idea why, because the open loop gain does not introduce any zeroes.

And the loop gain which is calculated using 'stb analysis' where the loop is broken at 'iprobe' and the loop gain is calculated between the terminals of iprobe. The loop gain also shows that the phase has been shifted to negative, compared to the phase at DC. Hence the entire amplifier is not stable.

The time domain response looks as follows: For a sinusoidal input: For a square wave input:

Now my questions based on the observations above:

1. Where does the zero come from?
2. If the closed loop gain and loop gain shows unstable behavior at 10 MHz then the amplifier should oscillate unconditionally, because of negative phase margin. But it does not for a sinusoidal wave and does so for a square wave. Why?
3. I know some compensation caps need to be added, but where should I add them? Basically how do I go about to make the circuit stable?

Any help will be appreciated.

Answer 1

1. Where does the zero come from?

Do a ""small signal analysis" on the circuit to find the poles and zeros. So start drawing the small signal equivalent model of the circuit and perform some simple network calculations. This is all done by hand on a piece of paper. You could confirm your findings using a simulator. You could even build the small signal equivalent model and simulate with it.

2. If the closed loop gain ... for a square wave. Why?

Applying a sinewave and/or squarewave as an input signal to do stability analysis is "silly", you want to see if the circuit generates its own signals (oscillates) so why apply a signal??? The proper way that all experienced EEs use is 1) the small signal stability analysis and to confirm and double check 2) do a transient (time) simulation but with a pulse or a step as the input signal. Then look at the step response of the circuit. Much has been written about stability of systems and their step response (the two are strongly related).

3. I know some compensation caps need to be added, but where should I add them? Basically how do I go about to make the circuit stable?

When you have the small signal equivalent model it becomes more evident where the poles and zeros are and what can be done to make the system stable. Many books have been written about making unstable systems stable, there is no need to repeat all that here.