4 R_O, R_ISO, and Capacitive Load Drive

The output impedance, also referred to as output resistance, can be modeled as a series resistor at the output of the amplifier.

Figure 4-1 Op Amp Output Resistance Internal Model

The load capacitance (C_LOAD) interacts with the output impedance of the amplifier (R_O), producing an additional pole in the amplifier’s A_OL curve, as shown in Figure 4-2. This additional pole (f_p2) causes the A_OL to decrease an additional 20 dB/decade resulting in a total of 40dB/decade rate of closure with 1/β. The rate of closure (ROC) is defined by the difference in slopes of the A_OL and 1/β curves at the frequency in which the two curves intersect. A stable circuit exhibits a rate of closure of approximately 20 dB/decade.

Figure 4-2 Effects of Capacitive Load on Amplifier Open-Loop Gain

Considering the rate of closure between A_OL and 1/β, stability issues arise when f_p2 occurs at a frequency less than the bandwidth of the amplifier. For amplifiers with comparable bandwidth, an amplifier with lower open-loop output impedance is capable of driving larger capacitive loads, while maintaining stability.

When R_ISO is implemented in the circuit, the isolation resistance interacts with the load capacitance to produce a zero in the A_OL curve. This zero (f_z1) causes the A_OL curve to increase by 20 dB/decade, canceling out the effect of f_p2, and restoring the rate of closure to 20 dB per decade.

Equation 4. $f_{z1}=\frac{1}{2\pi \bullet R_{ISO}\bullet C_{LOAD}}$

Figure 4-3 Op Amp Output Resistance with R_ISO and Capacitive Load

R_ISO also causes a shift in the pole frequency from f_p2 to f_p2* as defined in Equation 5.

Figure 4-4 Effects of R_ISO on Amplifier Open-Loop Gain with Capacitive Load

R_ISO is designed to be as small as tolerable while maintaining closed-loop stability. A larger isolation resistor increases the phase margin, but at the cost of voltage error and settling time. If the load has a resistive element, R_ISO creates a resistor divider between the output of the amplifier and the load resistance, resulting in a voltage error. If the load resistance is much greater than R_ISO, this voltage error can be negligible. Figure 4-5 shows two amplifiers driving complex loads with a resistive element of 10 kΩ and 5 nF of capacitance. The voltage error caused by the 20 Ω isolation resistor can be tolerable for the application, whereas the 200 Ω isolation resistor produces an unacceptable error. For DC applications, if the R_ISO required to stabilize the amplifier is too large, the dual feedback method can be used. For AC applications, choose an op amp with a low output impedance to minimize the isolation resistance required for stability.

Figure 4-5 R_ISO Voltage Divider with Resistive-Capacitive Load