Stability of amplifier circuits

Feedback of the output signal to the input signal results in a control loop. However, this control loop is not always stable, i.e. feedback does not mean that the output variable only changes as long as there is a differential voltage at the input¹. This becomes clear when the output signal is fed back to the non-inverting input instead of the inverting input. If a voltage difference is now applied to the input and amplified at the output, this output voltage leads to a renewed increase in the voltage difference at the input. The system is therefore not stable. A similar phenomenon can be observed when energy storage devices (capacitors or coils) are used in the amplifier circuit. Such a circuit always has a stability limit, which is reached when the signal fed back to the inverting input has a phase shift of 180\(^{\circ }\). In this case, the negative feedback becomes positive feedback and the circuit becomes unstable. However, this is not the only way in which a circuit can become unstable. The circuit can also start to oscillate if the energy storage devices are not correctly dimensioned. For this reason, stability analyses of the designed circuits are essential.

The following skills are to be acquired in this chapter:

Some of the stability criteria used for stability assessment are described below. Assessing the stability of operational amplifier circuits is an important skill for electrical engineering students, whether they are designing circuits from scratch or troubleshooting existing circuits. This assessment ensures that operational amplifier circuits work reliably and effectively, which is essential for their integration into various electronic systems. The methods used to assess stability are explained below.

Frequency response analysis (experimental/simulative)  

A fundamental technique is frequency response analysis. This method examines how the gain and phase of an operational amplifier circuit change when the frequency of the input signal varies. Tools such as Bode diagrams are often used to visualise this response and help identify potential stability issues such as gain spikes or phase shifts that could lead to instability. An important criterion here is phase margin. Determining this quantity is a quantitative approach to stability assessment. It helps measure the stability margin within a feedback system by considering the phase difference between the actual phase shift at the passband frequency (i.e., 0 dB) and 180\(^{\circ }\). This point is referred to as the „critical point“ because, with a phase shift greater than 180\(^{\circ }\) and a gain greater than 0 dB, the feedback becomes positive feedback. If the phase difference exceeds a certain threshold value, typically around 45\(^{\circ }\), it is assumed that the system is far enough away from the stability limit. This analysis is usually performed graphically based on the Bode diagram.

Analysis of the transfer function (analytical)  

If the transfer function of the operational amplifier circuit is available, a stability analysis can also be performed directly. To do this, the poles of the transfer function (e.g. in the Laplace domain) are analysed. If these are in the left s-half-plane (i.e. all poles are negative), the circuit has stable transfer behaviour. With this approach, as well as with frequency analysis (unless the Bode diagram has been determined experimentally), it must be noted that the transfer function is usually only valid for a certain frequency range, since, for example, the dynamics of the operational amplifier are not usually taken into account in these methods.

Analysis of transient behaviour (experimental/simulation)  

Another important method is the analysis of transient behaviour. In this method, a voltage jump is applied to the amplifier circuit to examine how an operational amplifier circuit reacts to sudden changes in the input signals. By observing the reaction of the circuit, it is possible to determine whether the system is prone to instability. In reality, this test must be carried out very carefully, as components can quickly be destroyed in an unstable circuit. For this reason, such tests are now often carried out purely as simulations. As a rule of thumb, if the circuit tends towards a fixed value after excitation by a unit step and does not oscillate continuously, the transient behaviour can be assumed to be stable.

As explained, stability analysis is a complex topic and will only be touched upon here. No claim is made to completeness at this point. The analysis methods mentioned are part of control engineering and can be found in the relevant literature.