Ken Kundert
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Each of the methods you describe can be fooled. Generally, if any indicates instability, then your circuit is unstable. But each may indicate stability on a circuit that is not stable.
Stb and PZ are fooled by circuits that are small-signal stable but large-signal unstable. And a circuit may not oscillate in transient if you do not excite the instability.
Stb also requires that you accurately identify the loop by proper placement of the probe element, and it only works for circuits with a single loop.
-Ken
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