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From: The Technical Manager
Subject: Re: Asymmetrical frequency response of lumped element bandpass filters
Date: Fri, 18 Oct 2002 08:28:08 +0100
Organization: Microwave Department
References: <3DAAF2B0.FA01AC9F@niobiumfive.co.uk> <firstname.lastname@example.org> <3DAD4EE6.E32D1AC0@niobiumfive.co.uk> <3DAECAEC.email@example.com>
NNTP-Posting-Date: 18 Oct 2002 07:28:09 GMT
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Fred Bloggs wrote:
> Peter O. Brackett wrote:
> > Techman:
> > Lumped element band pass filters designed using the standard low pass to
> > band pass transformation [a.k.a. reactance transformation] will always
> > have equal numbers of loss poles [a.k.a. transmission zeros, the zeros of
> > the polynomial P(s)] in the upper and lower stopbands. Hence sucn
> > transformed low pass filters will always have an asymmetrical frequency
> > response with higher rates of cutoff on the lower stop band side than on the
> > upper stop band side.
> I don't think such an exotic explanation is necessary. Anyone can see
> from the reactance transformation A*(Wc^2-W^2)/W-->Wlp that the
> resulting bandpass function maps W1=K*Wc and W2=Wc/K to the same point
> on the prototype low-pass attenuation characteristic. These two radian
> coordinates are both displaced by Log(K) from Wc and hence the geometric
> symmetry. The reactance transformation also destroys any linearity and
> so is useless for linear phase filters as well.
So what I was thinking was right after all.
It makes me wonder why I have seen so many textbooks and journal articles that
use lumped element filters as benchmarks to compare distributed element filters
with. A distributed element Chebyshev filter and its lumped element prototype
even have their passband ripples in slightly different places. Some engineers
might think `what the heck' but times exist when a real world filter must have a
response which faithfully follows its insertion loss function response vs
frequency as closely as possible.
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