Engineers often use SPICE simulations for operational amplifiers to look at the stability of a proposed circuit. SPICE simulations are particularly frequent for high-speed amplifier applications where small capacitances and inductances can easily affect circuit stability.
The typical approach to stability analysis, which works in almost all SPICE simulators, is to insert an AC break in the feedback loop in order to measure the loop-gain (Aol × β) response using AC analysis. However, the location where you insert the break into the feedback network can potentially affect the accuracy of the simulation.
This article will outline the pros and cons of the two most common locations where engineers break the feedback network.
First method: Break the loop at output
The first method of stability analysis breaks the feedback loop at the amplifier output. This is a fairly straightforward and popular method. Figure 1 shows a typical example of this method using the OPA607 operational amplifier.
Figure 1 Stability simulation circuit breaks the loop at the output. Source: Texas Instruments
The op-amp very effectively demonstrates the differences between the two methods; let’s explore why. In Figure 1’s circuit, the loop is broken at the output using a 1TH inductor. It is important to use a very large inductor to break the loop instead of just removing the connection entirely so that the simulation can still calculate a DC operating point for the analysis, but will appear to have an open circuit to the AC simulation. Without the inductor, the simulation would likely fail to find an operating point for the simulation, or it would find an inaccurate operating point that would not properly represent the behavior of the actual circuit.
With the loop broken at the output and the input connected to the output side of the feedback network, the transfer function measured from the input source to the output of the amplifier will yield the feedback factor (β) times the open-loop gain (Aol) of the amplifier, often called the loop gain. You can then run an AC simulation and evaluate the phase of the loop gain when the magnitude crosses 0 dB in order to obtain the phase margin. Figure 2 shows the resulting stability simulation from 10 MHz to 100 MHz, with a phase margin of approximately 82 degrees.
Figure 2 Stability simulation results use the first method with OPA607 op-amp. Source: Texas Instruments
This method is presented in TI’s Precisions Labs – Op Amps: Stability – SPICE Simulation training module.
Second method: Break the loop at inverting node
The other logical place to break the feedback network instead of the output is at the inverting input of the amplifier. Figure 3 shows a stability simulation example circuit similar to Figure 1, but instead breaks the loop at the input side of the amplifier instead of the output.
Figure 3 Stability simulation circuit breaks the loop at the input. Source: Texas Instruments
In Figure 3’s circuit, notice the two additional capacitors (Ccm and Cdiff) added to the feedback loop of the circuit. These capacitors represent the common-mode and differential input capacitances of the amplifier, respectively. They must be added back to the feedback loop as discrete components when using the second method because breaking the loop at the input disconnects the input capacitance of the model from the feedback network, which can significantly affect the response accuracy.
Most amplifier datasheets include the values for amplifier input capacitance. In the case of the OPA607, the common-mode capacitance is 5.5 pF and the differential capacitance is 11.5 pF. The differential capacitance would typically connect to the non-inverting input, but since the non-inverting input connects to ground in this example, the Cdiff capacitor also connects to ground.
By analyzing the circuit shown in Figure 3, you can see that the transfer function between the input and output labeled “Loop Gain” is effectively the same as the transfer function of the circuit in Figure 1, where Loop Gain = Aol × β. The inductor again serves the same purpose of breaking the AC loop while also providing a proper DC operation point.
Figure 4 shows the loop-gain simulation response for the circuit in Figure 3 with a phase margin of approximately 91 degrees. Attentive readers will be quick to notice that this phase margin is almost 10 degrees higher than the one shown in Figure 2, which was obtained using the first method. What are the underlying reasons for the simulation results to differ? And how can you obtain equivalent results from both simulations?
Figure 4 Stability simulation results use the second method with OPA607 op-amp. Source: Texas Instruments
Making results of both methods equivalent
To obtain equivalent results from either method, it’s important to understand what differs between the two circuits that could be contributing to a different response from the simulation. The fundamental difference between the two circuits is how the amplifier’s load differs between the methods. In the second method, the amplifier is loaded by the feedback network; any effect this has on the amplifier response will show in the loop-gain simulation. The first method, however, entirely decouples the feedback network from loading the output of the amplifier because of the break in the loop at the output.
This may not be a problem for amplifiers with responses that are not affected by the loading of the amplifier, but it’s not possible to always make that assumption. The OPA607 is an example of this phenomena, as the loading of the amplifier directly affects the response and therefore the stability of the circuit.
Fortunately, you can solve the feedback network loading issue of the first method by adding in a separate load to the output of the amplifier to represent the load normally presented by the feedback network. 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 was a simple 700 Ω, but more complex feedback networks—such as those for active filters—would need to include all of the components of the feedback network in the equivalent load.
Figure 5 Modified circuit of the first method can be used to account for output loading. Source: Texas Instruments
Figure 6 shows the new results of the modified circuit using the first method with a measured phase margin of approximately 91 degrees, and with a difference of 0.14 dB from the results of the second method. This small difference is within an acceptable margin of error for a functional model SPICE simulation.
Figure 6 Loop-gain simulation results use the modified circuit of the first method. Source: Texas Instruments
Which method should you choose?
Knowing that you can obtain similar results with either method, which one should you choose for simulations? The answer really comes down to what you prefer. The first method does not require finding the input capacitance of the amplifier, but it does require adding additional equivalent loads to the amplifier output.
The second method requires knowledge of the amplifier’s input capacitance, but leaves the output coupled to the feedback network. The second method may reduce complexity for circuits with complex feedback networks, but can become confusing to set up properly for circuits with more complex input networks, such as difference amplifiers.
Overall, the most significant conclusion from this analysis is not that one method is superior to the other, but that you should always make sure that the amplifier and feedback network have equivalent load impedances to the closed-loop circuit wherever the loop is broken.
Jacob Freet, applications manager at Texas Instruments (TI), is author of Signal Chain Basics blog # 171 for Planet Analog.
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