Hi!

I am curious if there is a mathematical expression for how much gain the phase shift in a frequency plot will give to the signal. For example, I have a bode plot that says 0db gain, but the feedback signal is shifted by -150 degrees from the input (30 degree phase margin), how much additional gain will the closed loop signal experience because of this?

 

I seems to me that with positive feedback, gain greater than 1 always results in exponential growth and below 1 in exponential decay.

Of course real circuits cannot continue growing exponentially for long.

 

In a fixed circuit (one that cannot change component values during operation) gain and phase are a pair of fixed numbers for a given frequency. Changing the frequency will change both the gain and the phase simultaneously. You appear to expect that gain or phase can be changed independently, but with changes in one affecting the other. This is not the case.

It may be possible to achieve something like this behavior using some sort of AGC (Automatic Gain Control) scheme. At any fixed setting of the AGC, phase, gain, and frequency will be connected in the same way is if the AGC was not there.