[sdiy] Cauer Filter Design (was : new to the list...)

[Robert Pietrusko]

Hi Mangus and everyone on the list,

After a much appreciated (though not necessarily
deserved) week long break I am back to work which also
means back to emailing. :)
I hope everyone's new year is off to a good start!

Now then, the Elliptic Filter and its related
frustration. 

During my hiatus I did some Matlab simulations and
such and created a *.pdf with the transfer functions
for each of the second order sections, I also included
the plots of their magnitude vs. frequency.  It seemed
like a good way for us to reference it. 
anyway, it is at
http://www.enfason.com/10thOrderCauer.pdf 


> The result is a high-pass notch. I'm fairly certain
>I
> can't get this response out of a Sallen-Key design.

>Sallen-Key is nice for "clean" responces in the
>traditional sense, but Cauer
>stuff is not as straigh on. Sallen-Key is not my
>choice for large-pole stuff
>that you are looking at anyway.


Agreed. That's why I went looking for a circuit that
could do high pass notch responses,  such as the
Boctor circuit.  Sallen-Key seems better suited for
Butterworth designs and the like.  Before this design
it was my "go to."  

Looking at the figures for the different stages'
magnitudes, the first stage is the only one without
additional gain at the cutoff frequency,  likewise it
is the only transfer function that doesn't break the
Gioffi equations, so I am going to assume that's where
the problem is-- that the boctor circuit can't give me
this peak.  

I agree with your idea that I should have a toolbox
(of sorts) of filter layouts to use as needed, and I
think the Boctor works good for this first stage.


>I would however consider doing a ortonormal leapfrog
>ladder. It is really a
>good choice since you both have a low sensitivity to
>individual components and
>good dynamic properties. When doing a 10th order
>filter I think you should pay
>attention to those details.

>From my small knowledge of leapfrog ladders, I know
that they are used for resonant circuits, which seems
consistent with the gain around the center frequency. 
The only thing that worries me about this idea however
is the number op-amps needed per section.  A single
Op-amp (per section) solution is ideal but I
understand that it might not be possible.  It's not a
cost concern but a space concern as this is a 10th
order filter and the design calls for two of them.  If
you had any luck digging up that paper though, I'd
love to take a look at it. 

Now, with the universal filter (SVF) I know I can get
a couple of stages of those on a single IC, from some
place like Maxim and that helps with the space
requirements. Unfortunately, I've had no experience
designing for these and I'm wondering if now, after
seeing the response of the stages (highpass notch with
a resonance), do you think SVFs will do the trick for
the remaining 4 stages.  If so, I've got a ton
information on designing them but I'd like to avoid
spending a lot of time on them only to find out in 2
weeks that I won't be able to get this response. :)

I guess that is the big question now -  is the SVF the
layout for me? and if so, would cascading a number of
those maxim universal filter ICs do the trick? 
(something like the max266).


Thanks for the input on this; your suggestions have
very helpful.  


take care, 
Bobby.









---------------------------------------------------

> I guess another more practical question is,  if most
> people are not familiar with this approach and I am
> having a hard time finding material, am I barking up
> the wrong tree?

I would consider doing either a multiple
state-variable filter design,
with 2-pole/2-zero per section. It is very easy to
design and the dimensioing
formulas is really a childsplay relative to what you
are looking at.

I would however consider doing a ortonormal leapfrog
ladder. It is really a
good choice since you both have a low sensitivity to
individual components and
good dynamic properties. When doing a 10th order
filter I think you should pay
attention to those details. I have the relevant
ortonormal leapfrog ladder
paper lying around here somewhere. As I recall it (it
is after all some 10
years ago I read it), it was not that horrifying to
dimension once you've
read it. Basically any leapfrog filter contains
multiple feedback loops and it
takes some experience to make fault analysis on it. It
does become good filters
in the end.

> What is a more "standard" method of realizing
> Cauer/Elliptic filters using opamps? or even, a more
> standard method of realizing high-pass notch
functions
> that are peaky at the cutoff frequency?

State-variable filters isn't a bad selection many
times, but if you want to
press the most cream out of it, you should have a
large selection of filter
layouts and choose depending on each requirement. The
above mentioned methods
is fairly good and would probably do the trick for you
most of the times, when
doing FIXED filters.

> as is  always the case for me, it's not the filter
> design, but its analog implementation that is
causing
> the trouble. :) ugh!

Start of in the SVF-field then. It is farily easy,
well known and really quite
straight-forward. They also have a theoretic beutty to
them, but then are not
as good as you can do it if you make more specific
choices, but may very well
do the trick for you.

> I'd be happy to message in more detail off list to
> spare the inboxes of other list members.

Feel free! ;O)

However, I know for a fact that there is several
lurkers out there that tend to
read threads like this in the quite and just sucking
up knowledge even if it is
over their heads. I've got comments from some of these
that they read ALL of my
posts! Lately my production of quality comments have
been low though, but you
got me going on one of my favorite topics, so... ;O)

Cheers,
Magnus - a.k.a. Captain Signaltheory - your
continous-time superhero!