This is the SourceLink article Frank was referring to. My book has even more ways of measuring loop gain ("The Designers Guide to Spice and Spectre").
-KenFrom
SpectreNews Issue #7, 4 July 1993.
Loop Gain (Revisited)In Issue #3 of SpectreNews, we presented a method for measuring the loop gain of an amplifier that did not require opening the loop. That method had two drawbacks, it required a separate AC analysis and was inaccurate if the input impedance of the amplifier was not much larger than the output impedance of the feedback network. We now present a more direct approach that avoids the weaknesses of the previous approach. It also allows you to measure all four important quantities of a feedback amplifier with a single AC analysis. For the series-shunt feedback amplifier shown below:
Series-Shunt Configuration:
A = Vo / Vp -- closed-loop gain
a = Vo / (Vp-Vn) -- open-loop gain
T = Vn / (Vp-Vn) -- loop gain
f = Vn / Vo -- feedback factor
By substituting the appropriate current for the voltages given in the above equations, they can apply to the other three feedback configurations:
Series-Series Configuration:
A = Io / Vp -- closed-loop gain
a = Io / (Vp-Vn) -- open-loop gain
T = Vn / (Vp-Vn) -- loop gain
f = Vn / Io -- feedback factor
Shunt-Series Configuration:
A = Io / Ip -- closed-loop gain
a = Io / (Ip-In) -- open-loop gain
T = In / (Ip-In) -- loop gain
f = In / Io -- feedback factor
Shunt-Shunt Configuration:
A = Vo / Ip -- closed-loop gain
a = Vo / (Ip-In) -- open-loop gain
T = In / (Ip-In) -- loop gain
f = In / Vo -- feedback factor
The desirable features of this approach include:
1. No changes to the circuit are required.
2. All four measurements can be made from the results of a single AC analysis.
3. The loading on the various sections of the circuit does not change, as will occur if the loop is broken in any fashion.
4. The DC operating point remains unchanged.
This approach to measuring loop gain is superior to several other possible approaches. For example, the most obvious approach to measuring the loop gain is to open the loop. However, opening the loop changes the loading on the feedback circuit and often changes the operating point. The effect of either of these changes could invalidate the results.
A more refined approach is to open the loop in such a way that the DC operating point is not changed. Some simulators provide a resistor that takes different values in the DC and AC analyses. To measure loop gain, the resistor would be placed in series with the feedback loop and takes the value of 0 Ohms in the DC analysis (so the loop is closed when computing the DC operating point) and takes the value of infinity Ohms in the AC analysis (so the loop is open when measuring the loop gain). While this avoids a possible shift in the operating point, the loading still changes when the loop is opened during the AC analysis. This results in the computed value of loop gain being in error, particularly at high frequencies where the capacitive loading of the input on the output could be significant.
Thanks go to Max Hauser for bringing this approach to our attention.
--- Editor.