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Date: Sun, 29 Apr 2007 03:58:10 +0000 (GMT)
From: "Alexander S. Yurkov" <fitec@omskcity.com>
To: rsgb_lf_group@blacksheep.org
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Subject: Re: LF: RE: Filter expert needed - Mystery of the lost real zero.
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Dear Jim and group,

On Sat, 28 Apr 2007, James Moritz wrote:
> One classic way of designing a bandpass filter with a symmetrical response 
> is to start with a low-pass ladder filter (i.e. series inductors, shunt 
> capacitors) response with the desired bandwidth, ripple, etc., then to 
> perform "lowpass to bandpass transformation", which results in 
> each shunt C being replaced with a parallel LC with the original value
> of C, and  each series L being replaced by a series LC with the original
> value of L. The other component in each LC has a value such that each LC is 
> resonant at the desired centre frequency. This gives a response with 
> the same bandwidth and shape as the original low-pass, but with perfect 
> geometrical symmetry about the centre frequency, i.e. if centre 
> frequency = fo, the response at k*fo is the same as at fo/k . 

IMHO this is true for narrow bandpass filters only. If bandpass is not
narrow in comparison with central frequency then one can do LPF to BPF
transformation also. But it is more complex and yelds not symmetrical
response of BPF about central frequency. But all poles and zerros of
prototype LPF are present anyway.

For narrow band BPF impedance of sieries LC near \omega_0 is approximatly
(!)  Z=j*L'(\omega-\omega_0) which corresponds to Z=j*L*\omega of
L in prototype LPF. Similary Z of paralel LC is aproximatly (!)
Z=1/j*C'*(\omega-\omega_0) which corresponds to Z=1/j*C*\omega
of C in prototype LPF. But this is only narrow band approximation.  
I can not easy remember general (without narrow band approximation) form
of LPF to BPF transformation but shure it is posible and yelds
some asymmetry in BPF response.

73 de RA9MB/Alex
http://www.qsl.net/ra9mb