Lead-Lag Compensation

Lead-lag compensation stabilizes the circuit without sacrificing the closed-loop gain performance. It is often used with uncompensated op amps. This type of compensation provides excellent high-frequency performance. The circuit schematic is shown in Figure 7–20, and the loop gain is given by Equation 7–23.

Figure 7–20. Lead-Lag Compensated Op Amp

Referring to Figure 7–21, a pole is introduced at ω = 1/RC, and this pole reduces the gain 3 dB at the breakpoint. When the zero occurs prior to the first op amp pole it cancels out the phase shift caused by the ω = 1/RC pole. The phase shift is completely canceled before the second op amp pole occurs, and the circuit reacts as if the pole was never introduced. Nevertheless, Aβ is reduced by 3 dB or more, so the loop gain crosses the 0-dB axis at a lower frequency. The beauty of lead lag compensation is that the closed loop ideal gain is not affected as is shown below. The Thevenin equivalent of the input circuit is calculated in Equation 7–24, the circuit gain in terms of Thevenin equivalents is calculated in Equation 7–25, and the ideal closed-loop gain is calculated in Equation 7–26.

Figure 7–21. Bode Plot of Lead-Lag Compensated Op Amp

Equation 7–26 is intuitively obvious because the RC network is placed across a virtual ground. As long as the loop gain, Aβ, is large, the feedback will null out the closed-loop effect of RC, and the circuit will function as if it were not there. The closed-loop log plot of the lead-lag-compensated op amp is given in Figure 7–22. Notice that the pole and zero resulting from the compensation occur and are gone before the first amplifier poles come on the scene. This prevents interaction, but it is not required for stability.

Figure 7–22. Closed-Loop Plot of Lead-Lag Compensated Op Amp