Page 249 - Op Amps Design, Applications, and Troubleshooting

Bondpass Filter 231

Bandwidth. The bandwidth of the filter can be calculated by applying a trans-
posed version of Equation (5.14).

Thus, the range of frequencies that is amplified at least 70.7 percent as much as the
resonant frequency is 204 hertz wide.

Voltage Gain at the Resonant Frequency. The voltage gain at the resonant
frequency can be estimated with Equation (5.17).

In the case of the circuit in Figure 5.12, the voltage gain is computed as

5.4.3 Practical Design Techniques

We are now ready to design a bandpass filter to satisfy a given design require-
ment. Let us design a filter similar to the circuit in Figure 5.12 that will perform
according to the following design goals:

1. Resonant frequency Skilohertz
2. Q 10

3. Voltage gain at f R Unity
4. Bandwidth 800 hertz

The following design is based on the assumption that the circuit provides unity
gain at the resonant frequency. Although common in practice, how to design a fil-
ter to have a voltage gain of greater than unity at the resonant frequency will also
be shown.

Select Cf and C%. Although the selection of these capacitors is somewhat arbi-
trary, our choice of values for Q and C 2 will ultimately determine the values for
the resistors. If our subsequent calculations result in an impractical resistance