Page 115 - Op Amps Design, Applications, and Troubleshooting

98 AMPLIFIERS

the direct-coupled circuit), we simply divide by the net impedance of Rj and Q
(i.e., Z/). You will recall from basic electronics that the net impedance of a series RC
circuit is computed with the following equation:

where X c is the capacitive reactance of C/. We already know that the gain of an op
amp varies with frequency, but now we have introduced an even more obvious
frequency-sensitive factor (X c). Thus, when we speak of voltage gain, we must
refer to a specific frequency in order to have a meaningful discussion. In most
cases, we are interested in the lowest input frequency because this is where the
capacitors will have their greatest effect (i.e., gain will be the lowest).
For the portion of the circuit in Figure 2.27(a) left of Q> we can compute the
voltage gain as shown. First, we need to determine the capacitive reactance with
our basic electronics formula for X c.

For illustrative purposes, we will assume an input frequency of 800 hertz. The first
step, then, is to calculate the reactance of Q at the frequency of interest.

Now we can compute the impedance of R { and Q:

Substituting this into the voltage gain equation, Equation (2,37), we can compute
the gain of the circuit to the left of Q>

Recall mat the minus sign indicates a phase inversion, but in no way implies a
reduction in signal amplitude.