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I
InlPJ =In
Pseudobandpass Matching Networks 215
respectively. An expression for the magnitude of the Chebyshev reflection
coefficient was given in (6.53). Thus numerical integration by Romberg
Program B2-3, described in Section 2.3, is not difficult. The proper integrand
for pseudobandpass networks is
in the pass band and
~~~~~-~-~~-~~~
I+K'+.'cos' (n/2)cos-'[(w'-w5)/A]
K'+.2COS2{ (n/2)COs-'[(w'-w5)/A])
(6.102)
In- I - =In
IpIi
1+K'+ .'cosh' (n/2)cosh-I [(w 2 -w5)/A]
K'+ .'cosh'{(n/2)cosh -1[(w 2 _ w5)/A])
(6.103)
in the stopband. The values of constants K and. will be required; they can be
determined as follows.
Assume that the resistance ratio, r= R,/R" and the maximum passband
ripple, L m " in Figure 6.36, are given, where
L m
,,= IOlog lO
(l +K'+.')dB.
Then (6.94) and (6.96) may be equated for w= 0:
where defined constant EC is
(I +r)'
~=I+K'+.2'EC,
,
EC= COSh'(1cosh-I ~ ).
(6.104)
(6.105)
(6.106)
Exponentiating both sides of (6.104) enables its simultaneous solution with
(6.105) for the ripple factor:
The flat-loss factor is now available from (6.104):
(6.107)
K'= IOLm,,/IO_.'_1. (6.108)
The only other issue to be resolved before. numerically integrating (6.102)
and (6.103) is the upper limit of integration. It is well known that the
asymptote for the high-frequency attenuation in Figure 6.36 is 6n dB/octave;
here the octaves are taken as multiples of passband width above "'0' The
reflection coefficient should be essentially I when the attenuation is at least 60
dB. Program B6-4 in Appendix B includes the earlier Romberg integration
routine and makes these calculations, including the upper limit of integration
in line 250.