Page 219 - Analog and Digital Filter Design

2 1 6 Analog and Digital Filter Design

R3 R3
These become, R1= - and R2 = for the bandstop filter.
2 ~ 4Q2 -2

Denormalization of Bandstop Design Using MFBP Section

Consider one pole found earlier for the fourth-order Butterworth 50Hz notch
filter. For this polef, = 48.58493Hz or 305.26812rad/s, having Q = 5.361447.

R3
R1= - = 2795 Q
2
R2=-- R3 - 49.47158 Q
4Q2 -2
In practice, obtaining resistor values close to those calculated may be difficult.
Individual component selection may be needed in order to achieve a notch filter
design with the desired amount of stopband loss.

Bandstop Using Dual Amplifier Bandpass (DABP) Section

A bandstop filter section can be made using a dual amplifier bandpass (DABP)
design. This is achieved by using a summing amplifier to subtract the bandpass
response from the input signal. The DABP topology is more complicated than
using the MFBP structure, but it has the advantage that much higher Q factors
can be achieved; Q factors of up to 150 are possible. The DABP is an all-pole
response bandpass ater section and has been described in Chapter 6. The band-
pass response can be subtracted from the input signal by a summing circuit to
create a bandstop response. The DABP filter has a noninverting output with a
gain of two at the resonant frequency, so a slightly different summing circuit to
the MFBP filter is required. In Figure 7.14, the input signal is applied to the
noninverting input of the summing amplifier. The output from the bandpass
section is applied to a resistor in series with the inverting input. The feedback
resistor from the summing amplifier’s output forms a potential divider to signals
from the bandpass section. The bandpass section output will be at ground
potential when no bandpass signals are present (outside the stopband). There-
fore the summing amplifier forms a noninverting amplifier with a gain of two.
The circuit diagram for a DABP filter is given in Figure 7.14.