Page 258 - Op Amps Design, Applications, and Troubleshooting

240 ACTIVE FILTERS

The minimum practical value for the capacitors is affected by several things,
including the op amp used and the required degree of stability. A workable goal,
however, is to design the circuit such that all capacitor values are greater than 100
picofarads.
Let us initially choose a value of 22 kilohms for R 3. If the computed values
for the capacitors are found to be too small, or there are no reasonably close stan-
dard values, then we will have to select a different value for R$ and recompute.

Determine the Value for C T. First we compute the ideal value for Q; then we
will select the nearest standard value. We can compute the required value of
capacitance by applying Equation (5.26).

For the present design, we compute the value for Q as follows:

Q = 1 — = 658 pF
1
4 x 3.14 x 5.5 kHz x 22 fcQ ^
Let us choose the nearest standard value of 680 picofarads for Q.

Compute the Exact Value for R 3. Now that a standard value for Q has been
selected, we can determine the exact value required for R 3. It should be noted that
the performance of the twin-T filter design relies heavily on accurate selection and
matching of component values. Therefore, "ballpark" values are usually inappro-
priate. The exact value needed for R 3 can now be computed by applying a trans-
posed version of Equation (5.26).

We can obtain this value by combining fixed resistances (e.g., 27 kQ in parallel
with 100 kO) or by using a fixed resistance and a variable resistor in series (e.g., 18-
kilohm fixed resistor in series with a 5-kilohm variable resistor). In either case,
however, every effort should be made to obtain the correct value.

Compute €2 and €3. Capacitor C 2 is always the same value as Q. That is,