Page 121 - Op Amps Design, Applications, and Troubleshooting

104 AMPLIFIERS

Bandwidth. Bandwidth can be defined as that range of frequencies that pass
through a circuit with a voltage amplitude of at least 70.7 percent of the maximum
output voltage—in other words/ the range of frequencies between the two half-
power points. These two frequencies can be readily determined in at least three
ways;

1. Numerical analyses involving higher mathematics
2. Computer-aided analysis
3. Direct measurements in the lab

You may be able to employ all three of these methods. However, none of them
are suitable for use in this reference book, so we will examine yet another, less
direct approach. Let us begin by making some observations. First, since the op
amp has a frequency response that extends all the way to DC, the lower cutoff
frequency will be unaffected by the op amp. That is, the input and output RC
circuits will determine the lower cutoff frequency. Second, in a practical circuit,
the upper cutoff frequency will be determined by the op amp itself. The RC cir-
cuits act as high-pass filters and will not restrict the gain at the higher input fre-
quencies.
Calculation of the upper cutoff frequency was discussed in previous sec-
tions. We estimate it with Equation (2.40).

In the case of Figure 2.27(a), our ideal upper cutoff frequency is computed as

U) MH*x 27*0
J
68 Jfcft + 27 kQ.

Next we calculate the lower cutoff frequency, which is determined by the input
and output RC networks. The cutoff frequency of each individual RC network is
determined with the following equation:

The lower cutoff frequency for the entire circuit is determined by the ratio of the
cutoff frequencies for the RC circuits.
Let us now compute the lower cutoff frequency for the circuit in Figure
2.27(a). First we compute the individual cutoff frequencies for the two RC net-
works. The input circuit calculations, as in Equation (2.41), are