8 Common Problems in Stability Analysis

Often, engineers who are new to stability analysis learn the theory and methods, but when these engineers try to apply the theory, these same individuals have issues and discrepancies that produce unexpected and incorrect results. Fortunately, many of the problems experienced by new engineers are common issues that can easily be explained and avoided. This section covers the common stability analysis discrepancies and the way to avoid these issues.

Stability for an op amp must be tested on the amplifier output, and not at the load. A common mistake is to check the transient response at the load rather than at the amplifier output. Figure 8-1 illustrates how a small-signal step can respond with significant overshoot at the amplifier output, but can have essentially no overshoot at the load. This is because the RC load circuit has a long time constant and filters out the overshoot pulse. This problem is avoided by checking both open and closed-loop stability at the amplifiers output and not at the load.

The most common stability test applies a small signal step to the input of the op amp. This method assumes that the input does not smooth out or filter the amplifiers input signal. The input to all op amps has common mode and differential capacitors in the picofarad range. Depending on the source impedance this input capacitance can create an RC filer that smooths out the input step. If the input step does not have the abrupt square wave rise time, the output does not respond as expected. Figure 8-2 compares an op amp circuit with a large source impedance to one with 0Ω source impedance. Note that the example device (OPA192) has 6.4pF of input capacitance. This input capacitance in conjunction with the 100kΩ source impedance smooths the edges of the input square wave. The output of the circuit with the 100kΩ source impedance does not show any overshoot, whereas, the circuit with the 0Ω source impedance shows 17.5% overshoot. The point is that applying an input step through a source impedance can smooth the edges of the step and product a transient response that implies the circuit is stable when the circuit is not. One way to avoid this issue is to always apply the step directly to the input and bypass any source impedance. Another approach is to check the output load response as in Figure 8-3.

A step in the output load current can be used to test the amplifier stability the same way a small signal input step can be used. For the output step, a load current step of ±1mA is a good starting point for checking stability. Depending on the response, the step can be adjusted to be larger or smaller. The load step produces an initial large transient that corresponds to the step size and a smaller dampened oscillation that corresponds to the overshoot. The example shown in Figure 8-3 has a 21mV step size, and a corresponding 6.7mV overshoot to a ±1mA step. When choosing the load step magnitude, look for a 10mV to 20mV output step response similar to this example. The example compares the output step to an input step. While the two cases have similar results, the cases are not exactly the same. Most amplifiers have a somewhat different input and output step response. This is in part due to the fact that the circuits are not simple second order systems as the step response assumes. Rather, the circuits have complex higher order responses that have path dependencies. Since the input and output step response can be different, checking the circuit according to the expected application can be useful. For example, a SAR ADC generates a load step response, so if the circuit is used to drive a SAR ADC, look at the output step response.

When the terms small-signal and large-signal are used in conjunction with op amps, these terms really describe the difference between linear operation and slew-rate operation. For small-signal operation, the amplifier acts like a linear system. That is, the amplifier has a small input offset voltage and the output is a linear multiple of the input signal. For large-signal operation, the amplifier is slewing so the offset is very large and the output is not a linear multiple of the input. When the amplifier slews, the output is moving at the maximum rate until the output is near the target value and then the amplifier transitions to small signal operation. A small signal step is generally considered to be 100mVpp or less. A large signal step is generally considered to be 1Vpp or more. In reality, the transition point between a large and small signal varies from device to device, so assuming a small signal is 10mVpp or less is best.

When doing stability testing, the amplifier must be in a linear operating condition (small signal). When a large signal step is applied to an op amp, most of the step response is a slew-rate or nonlinear response. At the end of the large signal step, the op amp reverts to a small signal operation. Figure 8-4 shows a ±5V large signal step and a ±10mV small signal step. For most of the large-signal step, the output is slewing, so the amplifier is not in a linear condition. At the end of the large signal step, the amplifier reverts to a small signal operation and there is an overshoot response. However, the overshoot only corresponds to the small signal portion of the step, and the percentage overshoot calculation does not reflect the system stability. In Figure 8-4, the small large-step has a PO of 2%, whereas, the small-signal has a PO of 41.9%.

The typical way a small signal step response is tested is to apply a small-signal repetitive square wave to the amplifier input or load. In simulation, the very first transient response is not necessarily representative of the steady state response. Most SPICE simulators allow for setting initial conditions by calculating operating point, using predefined initial conditions, or using zero initial conditions. Also, a bipolar waveform can start at zero rather than starting at the negative state. Thus, the first transient has many variables that determine the overshoot response. For accurate overshoot calculations, ignore first transient overshoot and subsequent responses. In Figure 8-5, the first transient response is significantly smaller than subsequent responses.

As discussed previously, the open-loop response of an op amp can be simulated by breaking the loop with very large test inductors and capacitors (1TF and 1TH). These large components allow for a valid closed-loop operation a DC and valid open-loop responses from millihertz and above. This method generally works well, but in some cases, there is a mathematical error that happens at low frequency where the A_OL is very high. The reason for this error is basically a numerical truncation or overflow error. For example, subtracting a very small number from a very large number can cause this kind of numerical analysis error due to the finite precision of computer calculations. Figure 8-6 illustrates what this kind of mathematical error looks like in simulation. In reality, this error is normally confined to very low frequencies and at the frequency of interest, the stability simulation is accurate. Nevertheless, minimizing this error by reducing the test inductor and capacitor values from tera to giga or even mega values is possible. At some point, this reduction can limit the simulation accuracy at low frequency. Ultimately, this math error generally does not effect the overall accuracy of the simulation so the error can be ignored.