This article showcases the advantages of an op amp loop-stability analysis method that I use myself and recommend to others. This method looks at the behavior and rate of closure of the open-loop gain (Aol) and inverse feedback factor (1/β) curves in addition to the loop-gain (Aol β) phase margin. This method applies to general control systems but was championed for op amp circuit analysis by Jerald Graeme and later taught to me by my mentors when I joined Texas Instruments.
The strength of this method lies in the ability to visually identify the cause of the stability issue in the circuit feedback network or output network. Once you’ve identified the root cause of the stability issue, you can implement an appropriate compensation scheme.
Let’s use the two circuits in Figure 1 to demonstrate this stability analysis method. The circuits share the same component arrangement, but the component values selected in the two circuits have led to the two most common stability issues I see designers accidentally create in op amp circuits.
The transient responses for these two circuits in Figure 2 show that they are both unstable, with significant overshoot and ringing. Using these circuits as MUX buffers, reference buffers, analog-to-digital converter (ADC) input drivers or other applications where transient settling time is important would result in poor circuit performance because of the unpredictable transient responses. The differences in transient-response behavior between the two circuits are based on the locations and pairing of poles and zeros in the transfer function, which goes beyond the scope of this article.
Standard loop-stability analysis focuses on the loop-gain magnitude and phase. The difference between the circuit phase shift and 180 degrees when Aol crosses 0dB is where the recognizable “phase-margin” stability measurement comes from. However, analyzing the loop gains of the two circuits in Figure 3 shows that they have nearly identical loop-gain magnitude and phase responses, with crossover frequencies of roughly 875kHz and phase margins of less than 9 degrees. I’ve already hinted that the circuits have two different stability issues, but by only looking at the loop-gain responses, there isn’t any indication of how to tailor the compensation scheme based on the cause of the issues for each circuit.
Plotting the Aol and 1/β curves along with loop gain enables you to identify if the stability issues are coming from the feedback network or output network. In Figure 4, Circuit 1 results show that the Aol response is standard but that the 1/β response has an unwanted zero, which decreases the loop-gain phase. Circuit 2 results show a flat 1/β but the Aol has an additional pole, which decreases the loop-gain phase. Both circuits have a 40dB/decade rate of closure between the Aol and 1/β responses, which is a first-order indication that the circuit will have stability issues. Issues in 1/β originate from interactions between the components in the feedback network; compensation schemes should address these interactions. Issues in Aol arise from interactions with the amplifier output impedance and the circuit loads, most commonly capacitive loads.
The results in Figure 4 enable you to determine that adding a capacitor in parallel with the feedback resistor will compensate Circuit 1. You could also have stabilized Circuit 1 by decreasing the value of the feedback resistors or by selecting a lower bandwidth amplifier. Increasing the resistance between the output and load capacitance will compensate Circuit 2. Decreasing the load capacitance or selecting an amplifier with lower open-loop output impedance, and therefore better capacitive load drive, would have also solved the stability challenges in Circuit 2. The compensated circuits are shown in Figure 5. The compensation used in this example was not necessarily optimized for a particular goal (bandwidth, noise, etc.), other than to be stable. To learn more about the selection and design of compensation methods, see the TI Precision Labs Op Amps videos on stability.
The loop-stability analysis for the two updated circuits in Figure 6 shows that the zero in 1/β in Circuit 1 has been canceled with a pole and the pole in Aol in Circuit 2 has been compensated with an added zero. Both circuits now have high phase margins, confirming that compensation was successful.
Figure 7 shows the transient responses for the two compensated circuits. The compensated circuits both have transient responses free from large overshoots and ringing.
I hope that showing how two circuits can have two different stability issues, but identical loop-gain responses emphasize the advantages of performing Aol and 1/β rate-of-closure stability analysis to determine the cause of the stability issue. My next Signal Chain Basics article will cover more details on the simulation method used to generate these curves and how it produces results that match the results from other stability simulation methods I often see recommended.
Jerald Graeme books: