Electronic – Stability from Bode Plot

amplifierbode plotstabilitytransfer function

I am studying analog design, and my instructor told me that you could determine whether or an amplifier is stable without knowing the transfer function, or the circuit diagram, just by examining the Bode plot. Below is an example of an unstable system. He claimed that it is unstable because there is non zero gain at the 180 degree phase shift point. My understand is that this only unstable if there is feedback, which we don't necessarily know.

My question is this: How do we know if the system is stable from just the Bode plot?

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Best Answer

The open loop Bode plot provides relative stability information on the closed loop system.

If an open loop can provide unity gain (or 0dB gain) in response to a sinusoid at a particular frequency where it also provides a -180deg phase shift then it can use the output sinusoid to replace the input sinusoid (the negative f/b provides the necessary additional -180deg phase shift). This is critical stability. Oscillation is self-sustaining. The loop does not see any difference between the externally applied sinusoid, and the one that it has created itself at the output terminal.

An open loop gain greater than 0dB at the frequency where the phase is -180deg will, clearly, give an unstable closed loop. And an open loop gain less than 0dB at that particular frequency will mean that the sinusoid gradually reduces in amplitude as it travels around the closed loop. That's a stable system.