An op-amp will in general have a small resistive output impedance from the push-pull output stage. We will model the open-loop output impedance by adding a series resistor to the output of an ideal op-amp as shown in figure 6.28.

**Figure 6.28:** Real, current-limiting operational
amplifier partially modeled by an ideal amplifier and an output
resistor.

Assuming no current into the input terminals (unloaded), and hence no current through , we have . Using the open-loop transfer function we obtain

Shorting a wire across the output gives and hence

Using the standard definition for the impedance gives

If than , which is small as required by our infinite open-loop gain approximation.

We can now draw the impedance outside the feedback loop and use

to obtain

The circuit can now be modeled by a resistor in series with an inductor all in parallel with another resistor (three passive components) as shown in figure 6.29. Students should convince themselves of this.

**Figure 6.29:** An equivalent circuit for a 741-type operational
amplifier.

If the op-amp is used to drive a capacitive load, the inductive component in the output impedance could set up an LCR resonant circuit which would result in a slight peaking of the transfer function near the corner frequency as shown in figure 6.30

**Figure 6.30:** The overall transfer function when the amplifier
drives a capacitive load.

Tue Jul 13 16:55:15 EDT 1999