Lead Compensation

Sometimes lead compensation is forced on the circuit designer because of the parasitic capacitance associated with packaging and wiring op amps. Figure 7–13 shows the circuit for lead compensation; notice the capacitor in parallel with RF. That capacitor is often made by parasitic wiring and the ground plane, and high frequency circuit designers go to great lengths to minimize or eliminate it. What is good in one sense is bad in another, because adding the parallel capacitor is a good way to stabilize the op amp and reduce noise. Let us analyze the stability first, and then we will analyze the closed-loop performance.

Figure 7–13. Lead-Compensation Circuit

The loop equation for the lead-compensation circuit is given by Equation 7–12.

The compensation capacitor introduces a pole and zero into the loop equation. The zero always occurs before the pole because RF >RF||RG. When the zero is properly placed it cancels out the τ2 pole along with its associated phase shift. The original transfer function is shown in Figure 7–14 drawn in solid lines. When the RFC zero is placed at ω = 1/τ2, it cancels out the τ2 pole causing the bode plot to continue on a slope of –20 dB/decade.

When the frequency gets to ω = 1/(RF||RG)C, this pole changes the slope to –40 dB/decade. Properly placed, the capacitor aids stability, but what does it do to the closed-loop transfer function? The equation for the inverting op amp closed-loop gain is repeated below.

Figure 7–14. Lead-Compensation Bode Plot

When a approaches infinity, Equation 7–13 reduces to Equation 7–14.

Substituting RF||C for ZF and RG for ZG in Equation 7–14 yields Equation 7–15, which is the ideal closed-loop gain equation for the lead compensation circuit.

The forward gain for the inverting amplifier is given by Equation 7–16. Compare Equation 7–13 with Equation 6–5 to determine A.

The op amp gain (a), the forward gain (A), and the ideal closed-loop gain are plotted in Figure 7–15. The op amp gain is plotted for reference only. The forward gain for the inverting op amp is not the op amp gain. Notice that the forward gain is reduced by the factor RF/(RG +RF), and it contains a high frequency pole. The ideal closed-loop gain follows the ideal curve until the 1/RFC breakpoint (same location as 1/τ2 breakpoint), and then it slopes down at –20 dB/decade. Lead compensation sacrifices the bandwidth between the 1/RFC breakpoint and the forward gain curve. The location of the 1/RFC pole determines the bandwidth sacrifice, and it can be much greater than shown here. The pole caused by RF, RG, and C does not appear until the op amp’s gain has crossed the 0-dB axis, thus it does not affect the ideal closed-loop transfer function.

Figure 7–15. Inverting Op Amp With Lead Compensation

The forward gain for the noninverting op amp is a; compare Equation 6–11 to Equation 6–5. The ideal closed-loop gain is given by Equation 7–17.

The plot of the noninverting op amp with lead compensation is shown in Figure 7–16. There is only one plot for both the op amp gain (a) and the forward gain (A), because they are identical in the noninverting circuit configuration. The ideal starts out as a flat line, but it slopes down because its closed-loop gain contains a pole and a zero. The pole always occurs closer to the low frequency axis because RF > RF||RG. The zero flattens the ideal closed-loop gain curve, but it never does any good because it cannot fall on the pole. The pole causes a loss in the closed-loop bandwidth by the amount separating the closed-loop and forward gain curves.

Figure 7–16. Noninverting Op Amp With Lead Compensation

Although the forward gain is different in the inverting and noninverting circuits, the closed loop transfer functions take very similar shapes. This becomes truer as the closed-loop gain increases because the noninverting forward gain approaches the op amp gain. This relationship cannot be relied on in every situation, and each circuit must be checked to determine the closed-loop effects of the compensation scheme.