Page 208 - Analog and Digital Filter Design

20
Bandstop Filters

The first branch has a value X= 1.000, and could be a series arm or a shunt
arm. Taking the shunt arm case first (series resonant) gives:

[fi -FLl.X
CShr,,,, = = 2.4 x 10'/3.2169 x 10" = 74.6pF
2n. FL FL .R
R
L5,!,,,!r = =50/15,079.65 = 3.3157mH
2Tc.[F, -FL].x
The second branch has a value X= 2,000. Since the first arm was chosen to be
a shunt arm, this arm must be series. Calculating the values gives:

The third branch has the same prototype element values as the kst branch. The
filter is symmetrical, so the first and third branch component values will be the
same. Symmetry is useful because if components have the same value, the cost
of manufacturing is sometimes lower.

Differences between the results just obtained and those presented in Figure 7.5
are due to round-off errors, both in the tables of normalized values and during
the calculations. The calculations were done by hand using a calculator.
Floating-point arithmetic in a computer program achieves more accurate results.

To obtain the circuit given in Figure 7.6, it is necessary to calculate the series
arm first. This will use a value of X= 1.000.
1
=
CSlr*l.r = 11753,982.2 = 1.32629pF
2~.[fi - FLIRX
[FL - FL].RX
L,,,,,'. = = 12 x 10J/6.43389x 10" = 186.51nH
2x4 .FL
A shunt arm must be calculated next, using X= 2.0, Readers are invited to do
the calculations themselves and compare their results with the values given ir,
Figure 7.6. Because of symmetry, the final arm's component values are identi-
cal to those calculated above.

Passive Cauer and Inverse Chebyshev Bandstop Filters

The method for designing all-pole bandstop filters has been explained. However,
unlike all-pole filters, Cauer and Inverse Chebyshev responses produce zeroes in
the S-plane that are not at the center of the stopband. Odd-order filters have
one zero at the center of the stopband. All the other zeroes are in the stopband,