Why does the LTspice op amp stability tutorial recommend open loop analysis?

Question

I have performed a hand analysis on an amplifier circuit that I am suspicious of, and I am still suspicious, so I want to validate my hand analysis with LTspice.

I found this tutorial online: http://www.linear.com/solutions/4449

It recommends to find the "open loop gain and phase response" to analyze the phase margin. It discredits the "closed loop response" from having the necessary information to analyze amplifier stability.

I can't post my exact circuit, but that shouldn't matter. Here's an example circuit, modified as instructed by the tutorial:

My prior understanding was that the open loop response of an op amp was just the op amp by itself with no feedback circuit, and that the closed loop response contained all the information needed to analyze an amplifier with its feedback circuit.

Can someone please explain what the LTspice tutorial is talking about?

Thanks

Answer 1

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).

Answer 2

The stability of the closed loop system can be found by analyzing the open loop system.

This is a result of Nyquist's stability criterion which is often used in a simplified form where only phase margin and gain margin are considered.

Analyzing the open loop system is done by breaking the feedback loop. The transfer function of the opamp and (!) the transfer function of the feedback network are considered since the loop is only opened but no element is removed.

When analyzing the loop gain it is important to do this in a way such that all important properties of the original circuit are preserved. Just opening the circuit at an arbitrary point could remove the loading from some crucial node and result in a completely different response.