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

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.

Thanks

• David - one comment to the referenced online tutorial: In this tutorial (at the beginning) it is mentioned that an AC analysis would show that the circuit works in a stable mode; however, the stability margin could not be found. This statement is NOT correct! Make the following test: Exchange the input terminals and connect the feedback path to the non-inverting input node. You will get the same gain response as before. That means: We know the circuit is NOT stable (and cannot work) - however, the AC analysis tells us that everything would be OK. Only a TRAN analysis can reveal the problem. – LvW Dec 2 '16 at 10:12
• to continue: To avoid misunderstandings- my comment above concerns the closed-loop analyses only. Hence: An ac closed-loop analysis cannot show if the circuit works in a stable mode. A possible oscillation or saturation can be revealed only with a simulation in the time domain. But - of course - the loop gain analyses must be performed in the ftrequency domain (ac analyses). – LvW Dec 2 '16 at 10:28

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).

• Thanks a lot. I am familiar with loop gain (denoted as L in my textbooks), I just didn't realize the tutorial was referring to "loop gain" when it said "open loop gain". – DavidG25 Dec 1 '16 at 21:02
• @zx485, thanks for editing; however - why did you remove the examples? Something wrong? I am surprised that somebody else takes the freedom for removing/shortening a contribution. – LvW Dec 2 '16 at 8:53
• Just had a look at the edit history. I can't remember removing the examples, and also I've never removed examples before. Must have been a mistake, I apologize for that and am glad that you've noticed and fixed it. (This comment can be removed if you accept my apology). – zx485 Dec 2 '16 at 16:42
• Sorry - perhaps a misunderstanding. As you have noticed, I have included the examples again. – LvW Dec 2 '16 at 17:03

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.

• Thanks. Nyquist stability criterion is a little over my head. I've done all my stability analysis with gain/phase margin and bode plots. But I do understand the importance of loop gain in stability. – DavidG25 Dec 1 '16 at 21:06