Figure 8-1 shows a unity-gain buffer driving a capacitive load. Equation 1 shows the transfer function for the circuit in Figure 8-1. Figure 8-1 does not show the open-loop output resistance of the operational amplifier (R_o).

Equation 1.

The transfer function in Equation 1 has a pole and a zero. The frequency of the pole (f_p) is determined by (R_o + R_ISO) and C_LOAD. The R_ISO and C_LOAD components determine the frequency of the zero (f_z). A stable system is obtained by selecting R_ISO so that the rate of closure (ROC) between the open-loop gain (A_OL) and 1/β is 20 dB per decade. Figure 8-2 shows the concept. The 1/β curve for a unity-gain buffer is 0 dB.

Figure 8-2 Unity-Gain Amplifier With R_ISO Compensation

Typically, ROC stability analysis is simulated. The validity of the analysis depends on multiple factors, especially the accurate modeling of R_o. In addition to simulating the ROC, a robust stability analysis includes a measurement of overshoot percentage and/or AC gain peaking of the circuit using a function generator, oscilloscope, and gain and phase analyzer. Phase margin is then calculated from these measurements. Table 8-1 shows the overshoot percentage and AC gain peaking that correspond to a phase margin of 45°. For more details on this design and other alternative devices that can replace the TLV936x, see the Capacitive Load Drive Solution Using an Isolation Resistor precision design.