I'm trying to understand the stability against oscillations for op-amps in a feedback circuit. A common argument I've seen on many sites goes as follows: The closed-loop gain is given as

   Acl = A0/(1 + B*A0),      (Eq. 1)

where A0 is the open-loop gain of the op-amp, and B is the fraction fed back to the negative input. Clearly, if the loop gain B*A0 becomes -1, then Acl diverges; this is taken to mean that the output is oscillating (A finite output with zero input).

This leads to what appears to be called the "Barkhausen criterion," that an op-amp circuit will oscillate if the magnitude of the loop gain equals 1 when the phase is -180°.

However, it is just as often stated that an circuit will oscillate if, at the frequency at which the phase = -180°, the loop gain is greater than or equal to 1. How is this reconciled with Equation 1? If I let BxA0 equal, say, 3.0 with phase shift of -180° (or really, any combination of |B*A0| > 1 and phase < -180°), Equation 1 has a perfectly well-behaved solution. Is this equation not really the whole picture?

I looked at the data sheets for a number of uncompensated op-amps (so that the phase would reach 180° while the gain was still > 1). Their Bode plots look nothing like the textbooks, and none of them had a magical frequency at which the loop gain was 1 and the phase was -180°.

I'm trying to understand the stability against oscillations for op-amps in a feedback circuit. A common argument I've seen on many sites goes as follows: The closed-loop gain is given as

$$A_{\text{cl}} = \frac{A_0}{1 + BA_0}\tag{1}$$

where \$A_0\$ is the open-loop gain of the op-amp, and \$B\$ is the fraction fed back to the negative input. Clearly, if the loop gain \$BA_0\$ becomes \$-1\$, then \$A_{\text{cl}}\$ diverges; this is taken to mean that the output is oscillating (a finite output with zero input).

This leads to what appears to be called the "Barkhausen criterion," that an op-amp circuit will oscillate if the magnitude of the loop gain equals 1 when the phase is -180°.

However, it is just as often stated that an circuit will oscillate if, at the frequency at which the phase = -180°, the loop gain is greater than or equal to 1. How is this reconciled with Equation 1? If I let \$BA_0\$ equal, say, 3.0 with phase shift of -180° (or really, any combination of \$|B_A0| > 1\$ and phase < -180°), Equation 1 has a perfectly well-behaved solution. Is this equation not really the whole picture?

I looked at the data sheets for a number of uncompensated op-amps (so that the phase would reach 180° while the gain was still > 1). Their Bode plots look nothing like the textbooks, and none of them had a magical frequency at which the loop gain was 1 and the phase was -180°.