Thinking Intuitively About Op Amp Stability: Part 2 of 7

In this post, we’ll carry the intuitive thinking from Stability 101 into our LTspice simulations to better understand the plots and measurements. Remember the Stability 101 Whiteboard Series (parts 1, 2, and 5) I told you to watch in the previous blog post? We will use LTspice to separately visualize the open-loop gain (A), feedback factor (β), and loop gain (Aβ), to see why a circuit becomes unstable, not just predict when it will. Whether you're new to the concepts or looking to reinforce what you've learned, this walkthrough gives you a hands-on way to connect the theory to the simulation.

Figure 1: Screenshot of Stability 101 Whiteboard Series, Part 5

Terminology and Theory

Here’s a quick reference of the terms and equations from the Stability 101 Series:

Instability occurs when the denominator of the closed-loop gain equation approaches zero,

V_{out}=V_{in}\ (\frac{A}{1+A\beta})

which occurs when Aβ approaches -1 (or 1∠180°).

Remember the Unstable Example

Let’s recall the example I introduced in the previous blog to illustrate an example that we know will have stability issues.

Figure 2: Transient Simulation of Both Unstable and Stable Examples

Plotting Open-Loop Gain (A) of an Op Amp in LTspice

Let’s use LTspice to plot the ADA4896-2 open-loop gain (A) to better understand this curve.  Click here for a schematic template and more details on plotting the open-loop gain of an op amp.

Figure 3: Open-Loop Gain (A) of the ADA4896

Notice that I am plotting -V(a) to represent the open-loop curve (LTspice is case-insensitive: V(a) is the voltage at the node labeled A).  Plotting V(a) alone will include the inversion of the loop introduced by the inverting input of the op amp; I will plot -V(a) to normalize the curve to ensure the phase is 0° at DC.  This also matches op amp data sheets for open-loop gain plots.

Download the example circuit to follow along:

Split the Circuit - Separate Aol and Beta.asc

This curve shows the ADA4896’s inherent open-loop response.  Rac and Rdc close the loop during DC analysis, allowing LTspice to determine operating voltages and currents, then open the loop during AC analysis to simulate open-loop gain.

Plotting the Feedback Factor (β) in LTspice

To plot the feedback factor (β), we can isolate the feedback network into a separate circuit.  We generally don’t want to break our circuit apart to plot the loop gain, but I am doing so in this example to help build intuition on this curve.

Figure 4: Feedback Factor (β) Curve for a Simple Resistor Divider Feedback Network

This is a simple resistor divider, so the feedback factor curve isn’t very interesting… or is it?

Including Op Amp Parasitics in the Feedback Factor (β) Circuit

When separating the op amp from the feedback network to analyze A and β separately, I left out a critical component of the feedback factor circuit: any non-ideal, parasitic op amp parameters must be included to accurately represent β.

For the ADA4896, the input capacitance is a major influence on the stability (or lack of) of this circuit.  From Table 3 in the data sheet:

Figure 5: Screenshot of Parameter Table from the ADA4896 Data Sheet

Let’s add those capacitances to our isolated feedback factor circuit and rerun the simulation. 

Figure 6: Adding Realistic Input Capacitance of the ADA4896 to Feedback Factor Circuit

We now see that the feedback network Rf and Rg, combined with the input capacitance of the ADA4896 has a frequency response that looks more like a low-pass filter, rather than a simple voltage divider.

Plotting Aβ and Measuring Phase Margin

Using this separated A and β circuit approach, let’s plot the combined Aβ curve for our stable examples where Rf=Rg=250.

To plot Aβ in LTspice, plot the equation -V(a)*V(beta).  We can manually inspect to determine the phase value when the magnitude is 0dB, the phase margin of the circuit. 

Figure 7: Eyeball Inspection of Phase Margin, Rg=Rf=250 Stable Example

For simpler, more accurate measurement, click on the plot title to bring up the measurement cursor.  Move the cursor as close to 0dB magnitude as possible and read the phase from the measurement window.

Figure 8: Using the Cursor to Measure Phase when Magnitude is 0dB

Remember that our circuit is unstable when Aβ approaches 1∠180°.  Looking at this example where Rf=Rg=250, we can identify the phase where the gain is 0dB at approximately 135° below the 0° at DC.  180° - 135° = 45° of phase margin: a stable circuit, which aligns with what we observed in the transient simulation of this example.

Now, compare that to the example where Rf=Rg=5k.

Figure 9: Loop Gain when Rg=Rf=5k and Unstable

This example is clearly unstable, since the phase margin is 180° - 175° = 5°.

Conclusion

The “split the circuit” technique is helpful for building some intuition around the A and β curves, and the elements that contribute to the poles and zeros in those curves.  You can also use this technique to stretch your understanding of how the amplifier's non-ideal behaviors influence the β curve.

The obvious shortcomings of this technique are that you are isolating the amplifier from the feedback network.  It’s easy for errors to creep in because you must perfectly reproduce the op amp parasitics in the feedback network.  I don’t recommend using this technique to analyze stability alone, but it can be used alongside other methods to get insight into what the A and β curves represent.

Stay tuned for my next blog post, where I will introduce the “open-the-loop” (aka BigL/BigC) technique, which allows us to plot loop gain with a single circuit.

Read all the blogs in the LTspice Amplifier Stability series.