Two Methods for Amplifier Stability Analysis Using SPICE

“When engineers design op amps, they often use SPICE simulation to check the stability of the designed circuit. SPICE simulation is especially common in high-speed amplifier applications, where tiny capacitances and inductances can easily affect circuit stability.

“

Author: JACOB FREET

When engineers design op amps, they often use SPICE simulation to check the stability of the designed circuit. SPICE simulation is especially common in high-speed amplifier applications, where tiny capacitances and inductances can easily affect circuit stability.

A typical approach to stability analysis is to insert AC breakpoints in the feedback loop so that the loop gain (Aol × β) response can be measured using AC analysis, which is applicable to almost all SPICE simulators. However, the exact location where the feedback network inserts the breakpoint may have a greater impact on the accuracy of the simulation.

This article will use the OPA607 op amp to illustrate the pros and cons of two of the most common insertion positions engineers use in feedback networks.

Method 1: Break the loop at the output

In this stability analysis method, the feedback loop at the output of the amplifier is disconnected. This is a fairly simple and popular method. Figure 1 shows a typical example of this approach.

Figure 1: The stability simulation circuit breaks the loop at the output.Source of this article: Texas Instruments

Op amps very effectively demonstrate the difference between the two approaches; let’s explore why. In the circuit of Figure 1, the loop is broken using a 1TH Inductor at the output. It is important to use a very large inductor to break the loop, rather than just disconnect it completely, so that the simulation can still calculate the DC operating point for the analysis, but it appears to be an open circuit for the AC simulation. Without the inductor, the simulation may not be able to find the operating point for the simulation, or it will find an inaccurate operating point due to the loop being broken at the output, while the input is connected to the output of the feedback network, from the input source The transfer function to the amplifier output will be equal to the feedback factor (β) multiplied by the amplifier’s open-loop gain (Aol), commonly referred to as the loop gain. Then, to get the phase margin, you can run an AC simulation and evaluate the loop gain phase for amplitudes above 0dB. Figure 2 shows the simulation results for stability from 10MHz to 100MHz, with a phase margin of approximately 82 degrees.

Figure 2: Stability simulation results obtained using method one.

Method 2: Disconnect the loop at the inverting node

Another logical place to disconnect the feedback network out of the output is the inverting input of the amplifier. Figure 3 shows an example circuit for stability simulation similar to Figure 1, but where the loop is broken at the input of the amplifier, not the output.

Figure 3: The stability simulation circuit breaks the loop at the input.

In the circuit of Figure 3, notice the two extra capacitors (Ccm and Cdiff) added to the circuit’s feedback loop. These capacitors represent the common-mode and differential input capacitances of the amplifier, respectively. With method two, they must be added back into the feedback loop as discrete components, because breaking the loop at the input disconnects the Model’s input capacitance from the feedback network, which can significantly affect response accuracy.

Amplifier input capacitance values ​​are listed on most amplifier data sheets. For the OPA607, the common mode capacitance is 5.5pF and the differential capacitance is 11.5pF. The differential capacitor is usually connected to the non-inverting input, but since the non-inverting input is grounded in this example, the Cdiff capacitor is also grounded.

By analyzing the circuit shown in Figure 3, you can see that the transfer function between the input and output labeled “Loop Gain” is actually the same as that of the circuit in Figure 1, where Loop Gain = Aol × β . The inductor also acts to break the AC loop, while also providing the proper DC operating point.

Figure 4 shows the loop gain simulated response of the circuit in Figure 3, with a phase margin of approximately 91 degrees. The attentive reader will quickly notice that this phase margin is nearly 10 degrees higher than that obtained using method one in Figure 2. What is the root cause of the different simulation results? How do you get equivalent results from two simulations?

Figure 4: Stability simulation results obtained using method two.

How can I make the results of the two methods equivalent?

To obtain equivalent results from either method, it is important to understand the differences between the two circuits that may cause the simulated responses to differ. The fundamental difference between the two circuits is how the loading of the amplifier differs between the two approaches. In method two, the amplifier is loaded by the feedback network; any effect this has on the amplifier response will show up in the loop gain simulation. However, method one completely separates the feedback network from the loading of the amplifier output because of the loop break at the output.

This may not be a problem for an amplifier whose response is not affected by the amplifier load, but this assumption cannot always be made. The OPA607 is an example of this phenomenon, as the loading of the amplifier directly affects the response and thus the stability of the circuit.

Fortunately, you can work around the feedback network loading problem of method one by adding a separate load at the output of the amplifier to represent the load that the feedback network typically presents. Figure 5 shows the modified circuit with an equivalent 700 Ω load on the output of the OPA607 to account for the normal loading of the feedback network. In this case, the load is a simple 700 Ω, but a more complex feedback network (such as that of an active filter) requires all components of the feedback network to be included in the equivalent load.

Figure 5: Modified circuit diagram considering output load in Method 1.

Figure 6 shows the new results for the improved circuit using method one, with a measured phase margin of approximately 91 degrees, a difference of 0.14dB from the result from method two. For functional model SPICE simulations, this small difference is within an acceptable margin of error.

Figure 6: Loop gain simulation results obtained using the modified circuit of method one.

Which method should be chosen?

After the above discussion, knowing that you can achieve similar results using either method, which method should you choose for your simulation? The answer really comes down to which method you prefer.

In Method 1, there is no need to figure out the input capacitance of the amplifier, but an additional equivalent load needs to be added to the amplifier output.

Method 2 requires knowledge of the amplifier’s input capacitance, but couples the output to the feedback network. Method two can reduce the complexity of circuits with complex feedback networks, but for circuits with more complex input networks (such as differential amplifiers), it can be confusing how to set it up correctly.

In conclusion, both methods have their advantages and disadvantages. The most important conclusion of this analysis is not to say that one method is better than the other, but to always ensure that the amplifier and feedback network have an equivalent load impedance to the closed-loop circuit wherever the loop is broken.