Op-amp input filtering can cause instability without proper compensation

When applying an input signal to an operational amplifier (op amp) that is far beyond its bandwidth, you would expect that the op amp would reject or attenuate the input signal. For example, if you’re applying a 600-MHz input signal to an op amp with a 10-MHz bandwidth, you would expect the 600-MHz signal to have significant attenuation. Both SPICE and general amplifier theory will predict this expected output.

Unfortunately, the high-frequency noise will not be rejected, and will actually cause a shift in the op amp’s input offset voltage (V_OS). In addition to the shift in offset, some of the high-frequency noise will simply pass through the op amp.

Some op amps are better at rejecting this high-frequency signal than others: The ability of an op amp to reject radio-frequency signals is called the electromagnetic interference rejection ratio (EMIRR). See the application report, “EMI Rejection Ratio of Operational Amplifiers” with OPA333 and OPA333-Q1 op amps as a design example.

Amplifiers with good EMIRR often have a simple internal filter on the input pins of the op amp. Amplifiers with this feature are called EMI-hardened. The input filter is a simple RC filter where the amplifier inputs have small resistors and capacitors placed both in common mode and differentially across the inputs (Figure 1). The input resistors generate noise, and the differential capacitor can degrade amplifier stability, so there are limits to how effective this filter can be.

Figure 1 Here is how EMI-hardened op-amp works using input filtering. Source: Texas Instruments

To improve the EMI rejection, many engineers choose to add an external filter capacitor across the input pins of the op amp. This can be an effective solution, but the op amp generally needs additional components to maintain stability. Stability in this context is the ability of an op amp to properly amplify a signal without oscillating.

Op amps can become unstable when connecting a capacitive load to the output pin or when capacitance connects to the inverting node. For the EMI filter, the concern is the capacitance on the inverting node because the filter capacitor is connected between the inverting and noninverting nodes.

It’s possible to use a transient small-signal step on the input or a transient load step on the output of an op amp to test stability. The amount of overshoot to the step directly relates to the circuit phase margin, which is a measurement of stability. A circuit is considered to be stable with an overshoot of less than 23%, which corresponds to a phase margin of greater than 45 degrees.

For a circuit with a filter on the input pins, test the stability with an output load step rather than an input step. An input step does not work for this circuit because the edges on the input step will be filtered by differential capacitance.

Figure 2 shows the transient response stability test for the uncompensated amplifier to a ±1 mA load step. The circuit in this example is a difference amplifier with a 1-nF filter capacitance between the inputs. For the load-step stability test, the initial output transient spike is the step size, and the following spike is the overshoot.

Figure 2 A transient output load stability test shows instability. Source: Texas Instruments

The percentage overshoot for Figure 2 is 68.2% (see Equation 1):

The Analog Engineer’s Calculator can convert the percentage overshoot to a phase margin of 13.8 degrees (Figure 3). The circuit is unstable, since a phase margin of greater than 45 degrees is required for stability.

Figure 3 Analog Engineer’s Calculator is used to convert overshoot to phase margin. Source: Texas Instruments

Understanding why the input capacitor causes instability requires some background in stability theory. Figure 4 shows the standard open-loop test circuit applied to the same circuit that underwent the transient stability test.

Figure 4 Here is a view of open-loop test circuit for op-amp stability. Source: Texas Instruments

The open loop is the most accurate way to test stability; it provides curves for open-loop gain (A_OL), loop gain (A_OL×β), 1/β, and phase margin (Figure 5). Stability is tested at the point where 1/β intersects A_OL. The phase margin is the phase shift where A_OL intersects 1/β.

Figure 5 Open-loop stability results show instability. Source: Texas Instruments

The phase margin for the open-loop circuit is 17.5 degrees, whereas the phase margin from the transient step test was 13.8 degrees. Technically the two numbers should match exactly, but there are some differences because the transient test assumes that the system is a second-order system. Nevertheless, the results are reasonably close, and both results indicate instability.

The open-loop test has an additional benefit in that it provides insight into what is causing the stability problem and how to stabilize the circuit. One way to understand the source of the stability issue is to use the rate-of-closure (ROC) rules. The ROC looks at the difference in slopes where the A_OL and 1/β curve intersect.

If the difference in slopes is greater than 40 dB/decade, then the circuit is unstable. In Figure 5, the slope of A_OL is –20 dB/decade, and the slope of 1/β is +20dB/decade. The difference between these two slopes is 40 dB/decade, so the circuit is unstable (Equation 2):

To correct the stability issue, you need to adjust the ROC to 20 dB/decade. The problem in this example is that 1/β has a zero at approximately 87.5 kHz, which causes the gain to increase by 20 dB/decade (Equation 3):

Adding a pole at the same frequency cancels this zero. The zero frequency is set by C_IN and 2 × R_G, and C_F and R_F set the pole frequency. To set the pole frequency the same as the zero frequency, choose C_F so that R_F × C_F = R_IN × C_IN. In this example, setting C_F = 100 pF will cancel the zero (Equation 4):

Setting C_F = 200 pF yields the open-loop response shown in Figure 6. Note that the 1/β curve is completely flat because the pole and zero cancel each other (Equation 5 and Equation 6). Since the ROC is now 20 dB/decade and the phase margin is 81 degrees, the circuit is stable.

Figure 6 Stable open-loop response is shown with C_F = 100 pF. Source: Texas Instruments

The compensated transient response, shown in Figure 7, also shows minimal overshoot and no ringing, indicating good stability.

Figure 7 Stable transient response is shown with C_F = 200 pF. Source: Texas Instruments

Setting the pole and zero in 1/β equal provides good stability and also improves noise, since the noise-gain peaking is minimized. It’s possible to stabilize the circuit and increase the bandwidth using a smaller value of C_F, however. Equation 7 gives the minimum value of C_F that will stabilize the circuit, and Equation 8 applies the example values.

Figure 8 shows the open-loop and transient response for the minimum C_F value (C_{F_MIN} = 47pF). The phase margin is lower for the minimum value of C_F compared to the case where the pole and zero cancel, but the circuit is still very stable (phase margin = 62 degrees).

Figure 8 Open-loop and transient response is shown for minimum C_F compensation. Source: Texas Instruments

Figure 9 compares the bandwidth and noise for the two compensation options.

Figure 9 Here is a comparison between bandwidth and noise for two different C_F compensations. Source: Texas Instruments

Stabilize the circuit

When using a capacitive filter across the input pins of an op amp, it’s important to use feedback capacitors to stabilize the circuit. The theory presented in this article is useful for understanding the root cause, but not necessary to compensate the circuit. Ultimately, you can stabilize the circuit by choosing the feedback capacitors according to Equation 3.

The feedback capacitor can also be helpful in reducing noise and stabilizing circuits with capacitive load. In general, it’s a good idea to include a placeholder for the feedback capacitors in most op-amp circuits because it can often be helpful in resolving stability and noise issues.

Art Kay is application engineer at Texas Instruments.

Op-amp input filtering can cause instability without proper compensation

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