Cauer filters?

[theChris]

ok, i'm really new to audio, nor new to analog, but i've never really had enough money or time to "put everything together" so to say. in any case, i recently saw:

http://www.fortunecity.com/marina/pontoon/3/audio/elliptic/elliptic.html

in any case, it looks promising for the car audio setup i plan to do. since i listen to a lot of music in my car, i figured that this crossover may be a good plan.

however, i don't know exactly how to design it, or much like that, and i definately haven't heard any implementations of it. CDT audio does make an elliptic filter for their high end "eurosport" speakers, and these speakers have been reviewed highly.

the question mainly is to find more opinions and information on this type of filter.

 

[Christer]

I don't know how much it helps you, but my old textbook onlysays
that a Cauer filter is a Chebychev filter with added zeroes on
the jw axis. As far as I can see it should be possible to add such zeroes freely, but I guess they are supposed to be placed in
some kind of relationship to the poles. I have no idea what
the purpose of these zeroes is. Maybe it is possible to reduce
the ripple this way.

Time for the experts to fill in the details now, I think.

 

[Jocko Homo]

A Cauer, or elliptical, filter adds a suckout at the edge of the passband. Usually needed where additional filtering is needed, as when there might be some interference that needs to be reduced more than is nominal outside the passband.

Basically, it is done by placing an inductor/capacitor across a capacitor/inductor already in the series arm of a filter to create a resonant circuit to present a high impedance in the forward transfer.

Jocko

 

[Christer]

A Cauer, or elliptical, filter adds a suckout at the edge of the passband. Usually needed where additional filtering is needed, as when there might be some interference that needs to be reduced more than is nominal outside the passband.

Just for the record, since there is a risk for misunderstandings,
a Cauer filter is an elliptical filter, but an
elliptical filter need not be a Cauer filter. The most well known
elliptical filter is probably the Chebychev filter.

Now back to the technicalities. I am not sure what you mean
by "suckout" but I understand you as saying that a Cauer
filter is even sharper than a Chebychev. Intuitively I don't
quite see how adding zeroes to a Chebychev could do that,
but I haven't sat down with pen and paper doing any serious
thinking about it.

PS, I just realized that both this and my previous post was a
bit unclear, since it made the assumption that we are talking
about a lowpass filter without saying so. Appropriate changes
must be made for other filters.

 

[Christer]

Sorry Jocko,

after having a closer look in my book I seem to have been wrong.
It actually does say that elliptical filters and Cauer filters are
the same thing. This is IMHO somewhat confusing, however,
since both Chebychev and Cauer filters have their poles placed
on a semi-elipse and are both just as worthy candidates to
the name.

Anyway, I found some info in my book about what the added
zeroes do. The Cauer filter has an even sharper transition
between passband and blockband (what is it called in english?)
than the Chebychev filter, but it has less damping than the
Chebychev and it has ripple also in the blockband. I found no
info, however, on how to place the zeroes (except that they
should be on the jw axis). If you do want to use these filters,
I am sure there are books that tell you how to synthesize them.

 

[Jocko Homo]

Yes, the Cauer will have sharper response right outside of the passband, but this is due to effect of the "suckout" that exists, not because of bassband ripple, as the Chebychev does.

Cauer filters were used a lot in frequency-division multiplex gear to knock down signals from the adjacent band. You tune the Cauer section, as it is called, to remove the offending out-of-band signal. I don't think we ever worried about where it was on the "jay-omega" axis. They are almost always tuned in the frequency domain.

Jocko

 

[phase_accurate]

There is one famous book dealing with Cauer filters (amongst other types):

Rudolf Saal: "Handbuch zum Filterntwurf", AEG Telefunken Berlin, 1979

Regards

Charles

 

[theChris]

"blockband (what is it called in english?)"
-in the book i have it is called "stopband", but blockband makes sense as well.

the book i have lists:
chebycheff - ripple in passband
inverse chebycheff - ripple in stopband
elliptic - ripple in both
papoulis - a monotonic filter, not flat though.

in any case, most times i look at filter design, no one seems to suggest chebycheff for audio because of phase response. i was wondering if this also applies to the other types of filters.

 

[jackinnj]

What does a filter response look like?

see an example at the most current issue of EDN:
http://www.e-insite.net/ednmag/index.asp?layout=article&articleid=CA302235&pubdate=6/12/2003

 

[theChris]

hmm. interesting that it seems like filters with a higher change in slope also have a higher change in group-delay. i don't think i particularly like that idea. since in my design, the tweeter will be located near the midwoofer, i may just use a 4th order filter like everyone else.

 

[Christer]

"blockband (what is it called in english?)"
-in the book i have it is called "stopband", but blockband makes sense as well.

Ah, that's it, thanks. I do remember now having seen the
term stopband before.

in any case, most times i look at filter design, no one seems to suggest chebycheff for audio because of phase response. i was wondering if this also applies to the other types of filters.

I suppose they are best avoided unless a very steep response
is necessary. They were used, though, in earlier CD players.
My old player from 1986 used a 16-bit non-oversampling DAC
followed by a 7- or 9-pole (can't remember which) Chebychev
filter.

 

[jackinnj]

here's a picture

couldn't manipulate it on the laptop I was using last night:

 

[rick57]

Practical & measured Cauers

Metal cones, tweeters pushed low ..

http://www.htguide.com/forum/showthread.php4?t=12083&highlight=Cauer

 

[rayfutrell]

If you want to learn about elliptical filters go to The Handbook of Filter Synthesis by Anatol I. Zverev. It is one of the few filter books that discusses the theory of elliptical filters starting with the double periodic elliptic functions. Warning! Very mathematical. It also contains over 100 pages of design tables for people simply looking for a cookbook approach to filter design.

I believe the book is out of print, but any good engineering library should have a copy of this classic.
Regards,
Ray

 

[jackinnj]

If you want to learn about elliptical filters go to The Handbook of Filter Synthesis by Anatol I. Zverev. It is one of the few filter books that discusses the theory of elliptical filters starting with the double periodic elliptic functions. Warning! Very mathematical. It also contains over 100 pages of design tables for people simply looking for a cookbook approach to filter design.

I believe the book is out of print, but any good engineering library should have a copy of this classic.
Regards,
Ray

you can get a copy for $140 on Amazon !

 

[LineSource]

I need a 2 opamp Cauer filter design for both 80Hz hi-pass and lo-pass. My textbooks do not contain elliptic filters.

Hope someone has a filter design package that includes the Cauer varient of elliptic filter. Getting both the opamp block diagram and the filter equations would be a great help.

My goal is to determine if using 2 buffers in a 80Hz steeper slope Cauer (48db) Xover with some ripple will sound better than a 24db LR4.

Thanks for any help.

 

[Spasticteapot]

Any news on this?

 

[consort_ee_um]

Try this:
HTGuide Forum - Active Cauer-Elliptic filter design in 20 minutes

My blog:
Consort3′s Blog