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I learnt that for any amplifier (with some capacitor) if we short/open the capacitor and the polarity of gain changes, it is a sign of RHP zero.

Now, while applying the same analysis I obsevred that for a two stage miller compensated OTA(Cc), the polarity of gain switches if I short/open the miller capacitor. (CIRCUIT 1)

So, in order to stabilize the system we added a nulling resistor in series (with Cc) and expected that the zero has now shifted to the left half plane. I tried doing the same test again with shorting and opening the capacitor and checking the polarity in both cases. (CIRCUIT 2)

When Cc is open the gain is definietly negative but when Cc is short, the gain is 1-gm6Rz, which is "conditonally negative"(1<gm6Rz).

If this is correct, can I say that it has LHP zero but not always, it is "conditional"?

CIRCUIT 1

CIRCUIT 2

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