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From: The Technical Manager
Subject: Re: Asymmetrical frequency response of lumped element bandpass filters
Date: Fri, 18 Oct 2002 15:37:55 +0100
Organization: Microwave Department
References: <3DAAF2B0.FA01AC9F@niobiumfive.co.uk> <firstname.lastname@example.org> <3DAD4EE6.E32D1AC0@niobiumfive.co.uk> <3DAECAEC.email@example.com> <3DAFB808.4081B8B0@niobiumfive.co.uk> <3DB001BE.firstname.lastname@example.org>
NNTP-Posting-Date: 18 Oct 2002 14:37:57 GMT
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Fred Bloggs wrote:
> The Technical Manager wrote:
> > Fred Bloggs wrote:
> >>Peter O. Brackett wrote:
> >>>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.
> Well the main strength of the prototype concept is that computation is
> alleviated and the design is reduced to a table look-up.
That advantage may well have been useful 30 or so years ago when many engineers and
virtually all hobbyists had no access to a computer but IMO nowadays is only a small
advantage in a world when computers are cheap and ubiquitous. I consider it to be a
"technicians workbench" method and quite bad design practice to use a standard lumped
element filter response as a benchmark and don't think the deficiencies of this
practice are publicised enough. This is suspicion but I reckon that a lot of books
and papers written on filters using the lumped element prototypes as a benchmark are
written by the older generation who grew up in a world of slide rules, mathematical
approximations and taking pi as 22/7 so old habits die hard.
> As you have
> discovered, it is important to understand the limitations associated
> with this approach, and these should be included with the tabulations
> but usually are not. It sounds like you should try to obtain at least
> one of the filter synthesis CAD programs, and check to be sure that it
> does the synthesis from the kind of specification details important to
> you. Then use a second program like SPICE to independently verify the
> design in the frequency and/or time time-domain.
That is the technique I use to design my own filters.
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