Page 217 - Analog and Digital Filter Design

2 1 4 Analog and Digital Filter Design

and 499Q, respectively. If standard range resistors must be used, two compo-
nents are required for each value, 9.1 kQ + 390 Q and 470 Q + 27 Q, respectively.

The second op-amp can be omitted if the feedback resistors are much lower
than the values of R1, R2, and R3. The node joining the feedback resistors can
be connected directly to the junction of R3 and the shunt capacitor (value = 2C).
This can lead to slight errors in the notch frequency due to an increase in imped-
ance in the shunt path. Omitting the op-amp is probably not worth considering
just to save space or to reduce costs, since dual op-amps are inexpensive and
readily available.

Denormalization of Twin Tee Notch Filter

For this example, consider a 50Hz notch filter, with lOHz between the upper
and lower passband edges. Q = 50/10 = 5. Using values fi = 50Hz or 314.159
rad/s and C = 0.1 pF (hence 2C = 0.2 pF), component values can be found by
substitution into the following equations:

R1
=
R3 = - 2,533 Q
2

Let R = 20 kn. Resistor element kR = 19 kQ and resistor element
(1 - k)R = 1 kQ.

Bandstop Using Multiple Feedback Bandpass Section

One of the simplest bandstop filters suitable for all-pole responses is the
Multiple Feedback Bandpass (MFBP) circuit, described in Chapter 6, followed
by a summing amplifier. The summing amplifier sums the output of the MFBP
section (which is inverting) with the input signal. In frequency spectrum terms,
the circuit is subtracting a passband from a wideband response to create a stop-
band. The circuit is illustrated in Figure 7.13: op-amp A2 and the three resis-
tors labeled R form the summing amplifier.