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From: Fred Bloggs
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Subject: Re: Asymmetrical frequency response of lumped element bandpass filters
References: <3DAAF2B0.FA01AC9F@niobiumfive.co.uk> <firstname.lastname@example.org> <3DAD4EE6.E32D1AC0@niobiumfive.co.uk> <3DAECAEC.email@example.com> <3DAFB808.4081B8B0@niobiumfive.co.uk>
Date: Fri, 18 Oct 2002 12:42:59 GMT
NNTP-Posting-Date: Fri, 18 Oct 2002 05:42:59 PDT
Organization: EarthLink Inc. -- http://www.EarthLink.net
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. 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.
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