# Electrical – A question about loop gain, feedback and stability of an op amp circuit

loop-gainoperational-amplifierstability

The article describes the relationship between open loop gain, closed loop gain, loop gain and some oscillation effects for the following non-inverting op amp:

Here is the bode plot I plot for the gains:

Here is the summary of what I understood so far:

Basically the gain of the circuit G = Vout/Vin is actually dependent on the open loop gain Ao. G is approximated to Vout/Vin = 1/β for low frequencies, however the general form from the feedback equation is Vout/Vin = Ao/(1+βAo). Ao shows single pole LPF behaviour and decreases in such fashion as in the plot. Since Ao decreases with frequency and since the circuit gain Vout/Vin is directly related to Ao, one can obtain the blue plot in LTspice as Vout/Vin. And open loop gain Ao as in the green plot can be plotted by the ratio Ao = Vout/Vdiff. Another point the article mentions is that when the freq. increases Ao decreases and the circuit fights with this change and tries to keep the Vout same. Since Vout=Vdiff*Ao and when Ao decreases Vdiff increases by feedback.

My question is about interpreting the following plot and seeing the weirdness when the β*Ao=-1 in time domain. The article continues as:

Ao = Vout/Vdiff

β = Vn/Vout (Vn is the inverting input)

β*Ao = Vout/Vdiff * Vn/Vout = Vn/Vdiff

Since βAo = Vn/Vdiff, and I am looking for the frequency where βAo = -1; here is the bode plot for β*Ao = Vn/Vdiff. (I plot Vn/Vdiff in LTspice):

How can I interpret the above plot for βAo? I mean is there a point in this plot where there βAo=-1 (unity gain with 180 degree shift)? If not, does that mean this circuit is never unstable?

And is it possible to see this β*Ao=-1 effect on LTspice time domain?

EDIT:

I followed the user analogsystemsrf's suggestion and added a 10u capacitor at the output. Below the plot of β*Ao.

Here is the new Bode plot of Vout.

Below is the plot of Vout in linear scale:

And below I sweep the 10mV AC input upto 4kHz

Here are my questions:

1-) If you look at the βAo plot, 0dB and 180 degree never crosses. When 180 degree phase shift the dB is -40dB and when 0dB the phase shift is 178 degree.
So it means its never β
Ao=-1. But still one can see some peculiarity on the plot. Why is that so? I mean for oscillation is this a must there must be a point exactly where β*Ao=-1 ?

2-) If you see my plot Vout in linear scale you notice that it makes a peak at around 1.7kHz. But when I sweep in time domain the peak I observe is at around 3.4kHz(the last plot above). Why is Bode and time domain shows this twice different way?