9.2.1.2 Detailed Design Procedure

Figure 47 depicts a unity-gain buffer driving a capacitive load. Equation 1 shows the transfer function for the circuit in Figure 47. Not depicted in Figure 47 is the open-loop output resistance of the op amp, 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. Components R_ISO and C_LOAD determine the frequency of the zero (f_z). A stable system is obtained by selecting R_ISO such that the rate of closure (ROC) between the open-loop gain (A_OL) and 1 / β is 20 dB per decade. Figure 48 shows the concept. Note that the 1 / β curve for a unity-gain buffer is 0 dB.

Figure 48. Unity-Gain Amplifier with R_ISO Compensation

ROC stability analysis is typically 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 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 4 shows the overshoot percentage and ac gain peaking that correspond to phase margins of 45° and 60°. For more details on this design and other alternative devices that can be used in place of the OPA172, refer to the precision design, Capacitive Load Drive Solution using an Isolation Resistor (TIPD128).