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Design >> Analog Design >> 4th order bandpass filter design
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Message started by Visjnoe on Jun 29^th, 2009, 7:10am

Title: 4th order bandpass filter design
Post by Visjnoe on Jun 29^th, 2009, 7:10am

Dear all,

in the design of a (complex) 4th order bandpass filter, I would tend to use a cascade of 2 biquads. However, one could also use a cascade of 4
1st order stages which each realize 1 complex pole.

Are there certain (dis)advantages for either of these approaches?

Kind Regards

Peter

Title: Re: 4th order bandpass filter design
Post by boe on Jun 29^th, 2009, 8:10am

Peter,
1 Biquad = complex pole pair + (optional) complex zero pair
Note that a 1st order band pass has a complex pole pair, i.e. requires one biquad, so 2 biquads result in 2nd order band pass (or 4th order low [or high] pass).
BOE

Title: Re: 4th order bandpass filter design
Post by ACWWong on Jun 29^th, 2009, 10:00am

boe wrote on Jun 29^th, 2009, 8:10am:

The complex bandpass filter does not have conjugate pole pairs. It is a low-pass which is linearly shifted rather than undergoing a usual real low-pass to bandpass bilinear transform.

So to get a 1st order complex bandpass, you need a single complex pole. To do this you need a complex signal (i.e. I & Q paths).

As to which is approach is better... I have often used the single pole cascades in I and Q with cross coupling on each section to get the linear shift. It allows one to choose the pole ordering better and minimises amplifier performance (in lieu of potentially more amplifiers) since you can control/limit Q easier. BiQuads would inheritly require better opamps (more GBWP) or more linear OTAs.

cheers
aw

Title: Re: 4th order bandpass filter design
Post by buddypoor on Jun 29^th, 2009, 11:27am

I am afraid that perhaps there is a misunderstanding.

Hi, Peter . Please tell us if you only need a 4th order BP, because the phrase "complex" could puzzle us.

Besides this point, I would like to point to the fact, that there is no BP of first order. It is a common agreement that the degree of the numerator determines the degree of the function. And the simplest BP - as a result of a transformation of a 1st order LP - is a 2nd order BP.
Regards.

Correction: Read "denumerator" instead of "numerator". Sorry.

Title: Re: 4th order bandpass filter design
Post by ACWWong on Jun 29^th, 2009, 2:14pm

buddypoor wrote on Jun 29^th, 2009, 11:27am:

Besides this point, I would like to point to the fact, that there is no BP of first order. It is a common agreement that the degree of the numerator determines the degree of the function. And the simplest BP - as a result of a transformation of a 1st order LP - is a 2nd order BP.

This is not true for a complex filter, which is a filter which is NOT symmetrical in the freq=0 domain. As such it can have a "bandpass response" in either the positive OR negative frequency domain whilst only having a single complex pole, and so order =1.
Your statement is only true of real filters which have been created by bilinear transformation of a lowpass (and are symmetrical around freq=0 for +/ve&-ve frequencies).

Ref: Gingel M.J for the classic paper "A symmetric polyphase filter". 1968
or
"Complex analog bandpass filters designed by linearly shifting real low-pass prototypes" Sedra, A. S., Snelgrove, W. M. and Allen, R 1985.

Title: Re: 4th order bandpass filter design
Post by buddypoor on Jun 29^th, 2009, 11:25pm

Hi ACWWong,

yes, you are right. And exactly this was the reason I have asked PETER to clarify if he really wants a "complex" filter. I doubt.

Title: Re: 4th order bandpass filter design
Post by Visjnoe on Jun 29^th, 2009, 11:59pm

Dear all,

thank you for all your inputs. Sorry for the confusion, I indeed meant a complex, polyphase 4th order bandpas filter (I/Q complex signal path).

Kind Regards

Peter