In another thread Brian Neunaber wrote:
> 1. IIR filters can be easily designed such that they have an analog
> counterpart, with which the user is familiar.
That got me thinking, especially when someone commented that it might
have been true 20-30 years ago. That matches when I last dealt with
anything similar in real world.
I know how my my filter sections would be realized (including component
values) if I were to physically build them. They would be of form
0-----z1-----*----0
|
r2
|
0------------*----0
For a "bandpass" element, z1 would be series resonant RLC.
For a "bandstop" element, z1 would be parallel resonant RLC.
To pass/stop multiple bands these sections would interconnected with
ideal unity gain summing amps - difficult in analog but trivial digitally.
I *EXPLICITLY* want the amplitude and phase response from that topology.
How should I go about this?
Are there appropriate Google search terms?
Digitally mimicing an RLC filter section
Started by ●April 7, 2006
Reply by ●April 7, 20062006-04-07
Richard Owlett wrote:> In another thread Brian Neunaber wrote: > > > 1. IIR filters can be easily designed such that they have an analog > > counterpart, with which the user is familiar.Only approximately. The approximation is good well below the sampling frequency, and falls apart badly as Fs/2 is approached.> That got me thinking, especially when someone commented that it might > have been true 20-30 years ago. That matches when I last dealt with > anything similar in real world. > > I know how my my filter sections would be realized (including component > values) if I were to physically build them. They would be of form > 0-----z1-----*----0 > | > r2 > | > 0------------*----0 > > For a "bandpass" element, z1 would be series resonant RLC. > For a "bandstop" element, z1 would be parallel resonant RLC. > To pass/stop multiple bands these sections would interconnected with > ideal unity gain summing amps - difficult in analog but trivial digitally. > > I *EXPLICITLY* want the amplitude and phase response from that topology.Tough.> How should I go about this?Read about impulse-invariant and biquadratic (biquad) responses for IIRs in Rick's book on the shelf behind you. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 7, 20062006-04-07
Jerry Avins wrote:> Richard Owlett wrote: > >> In another thread Brian Neunaber wrote: >> >> > 1. IIR filters can be easily designed such that they have an analog >> > counterpart, with which the user is familiar. > > > Only approximately. The approximation is good well below the sampling > frequency, and falls apart badly as Fs/2 is approached.For my initial experiments I can stay below Fs/3 or Fs/4.> >> That got me thinking, especially when someone commented that it might >> have been true 20-30 years ago. That matches when I last dealt with >> anything similar in real world. >> >> I know how my my filter sections would be realized (including >> component values) if I were to physically build them. They would be of >> form >> 0-----z1-----*----0 >> | >> r2 >> | >> 0------------*----0 >> >> For a "bandpass" element, z1 would be series resonant RLC. >> For a "bandstop" element, z1 would be parallel resonant RLC. >> To pass/stop multiple bands these sections would interconnected with >> ideal unity gain summing amps - difficult in analog but trivial >> digitally. >> >> I *EXPLICITLY* want the amplitude and phase response from that topology. > > > Tough.I'll assume a ;)> >> How should I go about this? > > > Read about impulse-invariant and biquadratic (biquad) responses for IIRs > in Rick's book on the shelf behind you. >Part of my problem it's no longer there. But until I find it, I'll Google the above. Thanks.> Jerry
Reply by ●April 7, 20062006-04-07
Richard Owlett wrote: ...> I'll assume a ;)Good assumption.> Part of my problem it's no longer there. > But until I find it, I'll Google the above. > Thanks.You're welcome. Try http://www.dspguide.com/ch19.pdf and http://www.bores.com/courses/intro/iir/index.htm. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 7, 20062006-04-07
Richard Owlett wrote:> Jerry Avins wrote: > > Richard Owlett wrote: > > > >> In another thread Brian Neunaber wrote: > >> > >> > 1. IIR filters can be easily designed such that they have an analog > >> > counterpart, with which the user is familiar. > > > > > > Only approximately. The approximation is good well below the sampling > > frequency, and falls apart badly as Fs/2 is approached. > > For my initial experiments I can stay below Fs/3 or Fs/4. > > > > >> That got me thinking, especially when someone commented that it might > >> have been true 20-30 years ago. That matches when I last dealt with > >> anything similar in real world. > >> > >> I know how my my filter sections would be realized (including > >> component values) if I were to physically build them. They would be of > >> form > >> 0-----z1-----*----0 > >> | > >> r2 > >> | > >> 0------------*----0 > >> > >> For a "bandpass" element, z1 would be series resonant RLC. > >> For a "bandstop" element, z1 would be parallel resonant RLC. > >> To pass/stop multiple bands these sections would interconnected with > >> ideal unity gain summing amps - difficult in analog but trivial > >> digitally. > >> > >> I *EXPLICITLY* want the amplitude and phase response from that topology. > > > > > > Tough. > > I'll assume a ;) > > > > >> How should I go about this? > > > > > > Read about impulse-invariant and biquadratic (biquad) responses for IIRs > > in Rick's book on the shelf behind you. > > > > Part of my problem it's no longer there. > But until I find it, I'll Google the above.ya know Richard, the 2nd order bandpass and bandstop is directly modeled (to the extent possible with the same order digital filter and the bilinear transform) in: http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt it's a small enough problem that, for a good while, it's been solved many times by many people and multiple ways. given a few trig identities and a harmonization of multiple definitions of spec, the results all agree. for the low frequencies you've mentioned, you won't know the difference between that and the RLC. r b-j
Reply by ●April 7, 20062006-04-07
robert bristow-johnson wrote:> Richard Owlett wrote: > >>Jerry Avins wrote: >> >>>Richard Owlett wrote: >>> >>> >>>>In another thread Brian Neunaber wrote: >>>> >>>> > 1. IIR filters can be easily designed such that they have an analog >>>> > counterpart, with which the user is familiar. >>> >>> >>>Only approximately. The approximation is good well below the sampling >>>frequency, and falls apart badly as Fs/2 is approached. >> >>For my initial experiments I can stay below Fs/3 or Fs/4. >> >> >>>>That got me thinking, especially when someone commented that it might >>>>have been true 20-30 years ago. That matches when I last dealt with >>>>anything similar in real world. >>>> >>>>I know how my my filter sections would be realized (including >>>>component values) if I were to physically build them. They would be of >>>>form >>>>0-----z1-----*----0 >>>> | >>>> r2 >>>> | >>>>0------------*----0 >>>> >>>>For a "bandpass" element, z1 would be series resonant RLC. >>>>For a "bandstop" element, z1 would be parallel resonant RLC. >>>>To pass/stop multiple bands these sections would interconnected with >>>>ideal unity gain summing amps - difficult in analog but trivial >>>>digitally. >>>> >>>>I *EXPLICITLY* want the amplitude and phase response from that topology. >>> >>> >>>Tough. >> >>I'll assume a ;) >> >> >>>>How should I go about this? >>> >>> >>>Read about impulse-invariant and biquadratic (biquad) responses for IIRs >>>in Rick's book on the shelf behind you. >>> >> >>Part of my problem it's no longer there. >>But until I find it, I'll Google the above. > > > ya know Richard, the 2nd order bandpass and bandstop is directly > modeled (to the extent possible with the same order digital filter and > the bilinear transform) in: > > http://www.musicdsp.org/files/Audio-EQ-Cookbook.txtYou are ubiquitous ;/ [ LOL !!!! ;] While following up on Jerry's post I was directed to YOUR site ;] That search also showed me that I had no idea of what either Chebyshev or Butterworth meant. None of my EE texts from "mid/late 60's/early 70's" had index reference to either. CAVEAT LECTORS b prepared fo plaint askin 2 b reffed to r'medial sites ;] [Do y'all recognize I'm beginning to realize how little I know]> > it's a small enough problem that, for a good while, it's been solved > many times by many people and multiple ways. given a few trig > identities and a harmonization of multiple definitions of spec, the > results all agree. for the low frequencies you've mentioned, you won't > know the difference between that and the RLC. > > r b-j >
Reply by ●April 8, 20062006-04-08
Richard Owlett skrev:> In another thread Brian Neunaber wrote: > > > 1. IIR filters can be easily designed such that they have an analog > > counterpart, with which the user is familiar. > > That got me thinking, especially when someone commented that it might > have been true 20-30 years ago. That matches when I last dealt with > anything similar in real world. > > I know how my my filter sections would be realized (including component > values) if I were to physically build them. They would be of form > 0-----z1-----*----0 > | > r2 > | > 0------------*----0 > > For a "bandpass" element, z1 would be series resonant RLC. > For a "bandstop" element, z1 would be parallel resonant RLC. > To pass/stop multiple bands these sections would interconnected with > ideal unity gain summing amps - difficult in analog but trivial digitally. > > I *EXPLICITLY* want the amplitude and phase response from that topology. > > How should I go about this?At the risk of revealing my ignorance, the term "Laplace tranform" springs to mind. If you can get an "s-domain" expression for the tranfer function, you ought to be able to get a discrete-time realization by applying the BLT. BTW, you might find the book van Valkenburg: Analog Filter Design, 1982 interesting. It started out with transfer functions and designed filters all the way down to selecting realizations and components. Most of the filters seemed to be active (i.e. they included OpAmps), but there were some really nifty tricks in there. One section dealt with a ~30-component filter (including 3 OpAmps) where gain, bandwidth and center frequency culd be adjusted independently. It seems the book may be hard to find these days, though. Rune
Reply by ●April 8, 20062006-04-08
Rune Allnor wrote:> Richard Owlett skrev: > >>In another thread Brian Neunaber wrote: >> >> > 1. IIR filters can be easily designed such that they have an analog >> > counterpart, with which the user is familiar. >> >>That got me thinking, especially when someone commented that it might >>have been true 20-30 years ago. That matches when I last dealt with >>anything similar in real world. >> >>I know how my my filter sections would be realized (including component >>values) if I were to physically build them. They would be of form >>0-----z1-----*----0 >> | >> r2 >> | >>0------------*----0 >> >>For a "bandpass" element, z1 would be series resonant RLC. >>For a "bandstop" element, z1 would be parallel resonant RLC. >>To pass/stop multiple bands these sections would interconnected with >>ideal unity gain summing amps - difficult in analog but trivial digitally. >> >>I *EXPLICITLY* want the amplitude and phase response from that topology. >> >>How should I go about this? > > > At the risk of revealing my ignorance, the term "Laplace tranform" > springs to mind. If you can get an "s-domain" expression for the > tranfer function, you ought to be able to get a discrete-time > realization by applying the BLT. > > BTW, you might find the book > > van Valkenburg: Analog Filter Design, 1982I'll see if I can get a copy through interlibrary loan. I've a copy of his _Network Analysis_ which I may have to dig into. I even has chapter on Laplace.> > interesting. It started out with transfer functions and designed > filters all the way down to selecting realizations and components. > Most of the filters seemed to be active (i.e. they included OpAmps), > but there were some really nifty tricks in there. One section dealt > with a ~30-component filter (including 3 OpAmps) where gain, > bandwidth and center frequency culd be adjusted independently. > > It seems the book may be hard to find these days, though. > > Rune >
Reply by ●April 8, 20062006-04-08
Richard Owlett wrote:> Rune Allnor wrote:> > > > At the risk of revealing my ignorance, the term "Laplace tranform" > > springs to mind. If you can get an "s-domain" expression for the > > tranfer function, you ought to be able to get a discrete-time > > realization by applying the BLT.i can't imagine what ignorance is revealed in that, Rune.> > BTW, you might find the book > > > > van Valkenburg: Analog Filter Design, 1982 > > I'll see if I can get a copy through interlibrary loan. > I've a copy of his _Network Analysis_ which I may have to dig into. > I even has chapter on Laplace.boy, *that* takes me back! that is the book we used for "Linear Electric Circuits", the two semesters that EEs took after the very first EE Fundamentals course that all engineering students have to take. this 2nd and 3rd semester course (with the vanValkenburg book) was the sorta counterpart to today's "Signals and Systems" or "Linear System Theory" that they should have had back in my day. it was EE's formal introduction to Laplace, Fourier, and such transforms (in continuous-time, no Z-Transform). we got a lot of cool circuit stuff like Tellegen's Theorem and 2-port circuit stuff that i don't think EE students get now. r b-j
Reply by ●April 9, 20062006-04-09
robert bristow-johnson wrote:> Richard Owlett wrote: > >>Rune Allnor wrote: > > >>>At the risk of revealing my ignorance, the term "Laplace tranform" >>>springs to mind. If you can get an "s-domain" expression for the >>>tranfer function, you ought to be able to get a discrete-time >>>realization by applying the BLT. > > > i can't imagine what ignorance is revealed in that, Rune. > > >>>BTW, you might find the book >>> >>>van Valkenburg: Analog Filter Design, 1982 >> >>I'll see if I can get a copy through interlibrary loan. >>I've a copy of his _Network Analysis_ which I may have to dig into. >>I even has chapter on Laplace. > > > boy, *that* takes me back! that is the book we used for "Linear > Electric Circuits", the two semesters that EEs took after the very > first EE Fundamentals course that all engineering students have to > take. this 2nd and 3rd semester course (with the vanValkenburg book) > was the sorta counterpart to today's "Signals and Systems" or "Linear > System Theory" that they should have had back in my day. it was EE's > formal introduction to Laplace, Fourier, and such transforms (in > continuous-time, no Z-Transform). we got a lot of cool circuit stuff > like Tellegen's Theorem and 2-port circuit stuff that i don't think EE > students get now.You would go ape over Guilliman! Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
