Page 256 - Op Amps Design, Applications, and Troubleshooting

238 ACTIVE FILTERS

tially raises the impedance offered by C 3 and R 3 at a particular frequency. There-
fore, they don't attenuate the off-resonance signals as much, which has the effect
of narrowing the bandwidth or, we could say, increasing the Q.
Resistor £4 is to compensate for the voltage drops caused by the op amp bias
current flowing through Rj and R 2. It is generally equal in value to the sum of RI
and R 2.

5.5.2 Numerical Analysis
The component values for the twin-T circuit normally have the following ratios:

L R j = R 2
2. R! = 2R 3
3. q=C 2
4. C 3 = 2Q
5. 0<R 4 <(R 1 + R 2)

Under these conditions, let us compute the following circuit characteristics:

1. Center frequency
2, Input impedance

Center Frequency. The center frequency for the twin-T filter is the frequency
that causes the reactance of C 3 to equal the resistance of JR 3. At this same frequency,
XQ = X a = RI = R 2. The equation for the center frequency, then, is simply a trans-
posed version of the basic capacitive reactance equation:

Since, at the center frequency, XQ = RI/ we can substitute RI for X c in the preced-
ing equation to yield our equation for the center frequency of the twin-T filter:

In the case of the circuit shown in Figure 5.17, we can compute the center fre-
quency as follows: