Frequency Compensation Methods:

Phase-Lag and Phase-Lead Compensation – Lag compensation and lead compensation are two Frequency Compensation Methods often employed to stabilize op-amp circuits. The phase-lag network in Fig. 15-7(a) introduces additional phase lag at some low frequency where the op-amp phase shift is still so small that additional phase lag has no effect. It can be shown that at frequencies where X_C1 ≫ R₂, the voltage v₂ lags v₁ by as much as 90°. At higher frequencies where X_C1 ≪ R₂ no significant phase lag occurs, and the lag network merely introduces some attenuation. The effect of this attenuation is that the A_v/f graph is moved to the left, as illustrated in Fig. 15-7(b). Thus, the frequency (f_x1) at which A_vB = 1 [for a given closed-loop gain (A_CL)] is moved to a lower frequency (f_x2), as shown. Because f_x2 is less than f_x1, the phase shift at f_x2 is less than that at f_x1, and the circuit is likely to be stable.

The network in Fig 15-7(c) introduces a phase lead. In this network, when X_C1 ≫ R₁, the voltage v₂ leads v₁. This phase lead cancels some of the unwanted phase lag in the operational amplifier θ/f graph, [see Fig. 15-7(d)], thus rendering the circuit more stable. Phase-lag and phase-lead networks are both used internally to Frequency Compensation Methods op-amp circuits. Both types of circuit can also be used externally.

Manufacturer’s Recommended Compensation:

Most currently-available operational amplifiers contain internal compensating components, and do not require additional external components. Some have internal compensating resistors, and need only a capacitor connected externally to complete a compensating network. For those that require Frequency Compensation Methods, IC manufacturers list recommended component values and connection methods on the op-amp data sheet. An example of this is illustrated in Fig. 15-8 for the LMI08.

When selecting standard value compensating capacitors the next larger values should be used. This is termed over-compensation and it results in better amplifier stability, but, it also produces a smaller circuit bandwidth.

Miller Effect Compensation:

Miller effect involves connecting a capacitor between the output and input terminals of an inverting amplifier. Miller-effect compensation of an op-amp circuit is very simple, and it is often the only external method available for stabilizing a circuit where the op-amp is internally compensated. A capacitor (C_f) is connected across the feedback resistor, as shown in Fig. 15-10(a) and (b). The capacitor value is calculated to have an impedance equal the feedback resistor value at the desired signal cutoff frequency (f₂).

This reduces the closed-loop by 3 dB at the selected frequency. So long as the op-amp is stable at this frequency, the circuit will not oscillate. The op-amp used should have an upper cutoff frequency much higher than f₂.