Electronic – Op amp circuit stability in linear regulator circuit

Yes - sometimes the terms are somewhat misleading. In general, we have three different gain conventions for feedback circuits:

• Open-loop gain of the amplifier (alone): Aol,
• Closed-loop gain of the amplifier with feedback: Acl,
• Loop gain Aloop, which is the gain of the complete loop (to be measured or simulated after breaking the loop at a suitable point). Hence, the loop gain is the product $$A_{loop}=(-A_{ol}*\beta)$$ with beta = feedback factor
  Note that this definition includes the inverting sign at the opamp input.
• Based on these conventions the closed-loop gain is $$A_{cl}=(A_{ol}*\alpha)/(1-A_{loop})$$with alpha = forward factor, if existent, otherwise unity

Note that stability margins (phase margin, gain margin) are defined for the loop gain Aloop only. For the purpose of determining the margins, the loop must be opened at a suitable point (opamp output or inv. input) for injecting a test signal. I hope this clarifies something.

It is the purpose of the following example to demonstrate the meaning (and the correct sign) of the term"alpha":

Example:

(a) Non-inverting amplifier (R2=feedback resistor): alpha=1, beta=R1/(R1+R2);

(b) Inverting amplifier: alpha=-R2/(R1+R2), beta=R1/(R1+R2).

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.