Brushing up on theory: Butterworth LCR filter design?

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Hi all,

I want to design a passive 3rd or 5th order lowpass filter with an fc of
500Hz or 1kHz, preferably a Butterworth configuration for a flat bandpass
response. So I dusted off ye 'ole filter design theory, set out to
calculate polynomials ... and realized that I somehow miss the connecting
step to real-world components -- at least, as far as the LCLR ladder
configuration is concerned:

       L1    L2    L3
    .--mmm---mmm---mmm--.
    |      |     |      |
 Ri| |  C1=== C2===    | | Ro
   | |     |     |     | |
    |      |     |      |
    `-------------------'

I know how to calculate active filters in a Sallen-Key configuration, and I
looked up things like http://en.wikipedia.org/wiki/Butterworth_filter ,
but I somehow fail to make the connection between the transfer function H(s)
and the first schematic shown, with actual component placements and values.

Can anyone enlighten me in this respect? For active filters, there are some
quite good step-by-step explanations out there (e.g.
http://www.maxim-ic.com/appnotes.cfm/an_pk/1795 ) but so far I found nothing
for the humble LCR stuff. And I'm afraid step-by-step is what I need here,
as I seem to have all necessary information without knowing what to do with
it ...

Thanks already,

Richard Rasker
--
http://www.linetec.nl

Re: Brushing up on theory: Butterworth LCR filter design?

Have you looked at this?

http://www.bessernet.com/articles/lowpfilt/bwfiltstep00.html



Re: Brushing up on theory: Butterworth LCR filter design?

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It's certainly interesting, and it may certainly help me to regain a grip on
the theory -- as it combines a real-world calculator function with some
explanation of the underlying math. But I'm still looking for an example
which actually shows the step-by-step number crunching required to come up
with the values in the third step.

But now I at least partially see where my problem is, in comparison to the
less complicated active filters: the input/output impedance. I intended to
use this filter to block severe intereference caused by very powerful PWM
inverters (600V@8kHz) from entering A/D converter inputs. I prefer a
passive solution, because that could simply be inserted into the existing
signal path, without the need for yet another box with supply and the
likes. But at the desired frequency, I see that the component values aren't
exactly practical -- either the inductors must be around 1H, or the
capacitors range in the dozens of microfarads.
So perhaps it's back to the old Sallen-Key filter after all -- but I still
want to get a better grip on the theory :-)

Anyway, thanks for your reply.

Richard Rasker
--
http://www.linetec.nl

Re: Brushing up on theory: Butterworth LCR filter design?
On Fri, 16 Jan 2009 23:17:31 +0100, Richard Rasker

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Normally one looks up a prototype filter in tables in a book (Williams
and Taylor is excellent) and normalizes it for impedance and
frequency. Chapter 1 of Williams discusses filter synthesis; it can
get "laborious."


John



Re: Brushing up on theory: Butterworth LCR filter design?
On Jan 16, 3:10A0%pm, John Larkin
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I'm with you here. I have a copy of Huelsman and Allen with the
tables, as well as Zverev.

Re: Brushing up on theory: Butterworth LCR filter design?
On Fri, 16 Jan 2009 20:26:19 -0800 (PST), " snipped-for-privacy@sushi.com"

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We bought the Nuhertz passive-filter design software, and it's
amazing. It will design gorgeous filters using finite-Q,
standard-value parts. Trying to do that by normalizing textbook
filters can drive you crazy.

The guy who does this is very smart and very, very crabby.

John




Re: Brushing up on theory: Butterworth LCR filter design?
On Fri, 16 Jan 2009 21:20:34 -0800, John Larkin

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And you ?:-)

                                        ...Jim Thompson
--
| James E.Thompson, P.E.                           |    mens     |
| Analog Innovations, Inc.                         |     et      |
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Re: Brushing up on theory: Butterworth LCR filter design?
On Sat, 17 Jan 2009 08:24:10 -0700, Jim Thompson

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H(s)
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I'm not as smart as he is, but I'm a lot more cheerful. And I don't
send obnoxious, insulting emails to my customers.

John


Re: Brushing up on theory: Butterworth LCR filter design?
On Sat, 17 Jan 2009 08:06:12 -0800, John Larkin

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Nice!  How does the guy stay in business/

                                        ...Jim Thompson
--
| James E.Thompson, P.E.                           |    mens     |
| Analog Innovations, Inc.                         |     et      |
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Re: Brushing up on theory: Butterworth LCR filter design?
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and I
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There's an ugly rumor going around that an "active filter cookbook" exists.



--
Many thanks,

Don Lancaster                          voice phone: (928)428-4073
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Re: Brushing up on theory: Butterworth LCR filter design?

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bandpass
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connecting
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I have a couple of copies. It's the first one I grab when I need a
basic S-K or something. And you have *never* sent me an insulting
email.

Thanks!

John




Re: Brushing up on theory: Butterworth LCR filter design?

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bandpass
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On my bookshelf... if I can remember where ;-)

                                        ...Jim Thompson
--
| James E.Thompson, P.E.                           |    mens     |
| Analog Innovations, Inc.                         |     et      |
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Re: Brushing up on theory: Butterworth LCR filter design?
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Your book is great, Don, but download the Nuhertz demo sometime... you'll be
amazed how powerful it is.

The one time I've spoken to you in person to you were most polite and
friendly. :-)



Re: Brushing up on theory: Butterworth LCR filter design?
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These days Applied Waves Research offers his software as part of Microwave
Office, which I suspect significantly increased his sales.  (AFAICT, this was
largely a move to compete with the filter design software that Eagleware --  
now Agilent -- offered in Genesys... it's also quite good, having benefitted
from Randy Rhea's years of experience designing filters, although these days
Randy isn't directly involved with Genesys anymore whereas Jeff Kahler -- the
Nuhertz guy -- seems to still be actively developing his works.)

I've e-mailed him a couple of times and he was always perfectly pleasant to
deal with... perhaps he was having a bad day when he was talking to John?

Heck, for that matter, I met Randy Rhea once in person and found him to be a
little curt, but maybe he too was having a bad day.

---Joel



Re: Brushing up on theory: Butterworth LCR filter design?
On Sat, 17 Jan 2009 12:18:26 -0700, Jim Thompson

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Yep, me too.  even have the TTL cookbook around.
Don's a fine man..   He's got a few crazy and twisted ideas,
but he's OK in my book (shelf).  It wouldn't be quite as CooL  of an
electronics industry without him.

boB


Re: Brushing up on theory: Butterworth LCR filter design?

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of
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I also have "a few crazy and twisted ideas", but no one cuts me any
slack :-(

                                        ...Jim Thompson
--
| James E.Thompson, P.E.                           |    mens     |
| Analog Innovations, Inc.                         |     et      |
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Re: Brushing up on theory: Butterworth LCR filter design?
On Jan 16, 9:20A0%pm, John Larkin
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To be accurate here, I've only used those tables for SCF leapfrog
designs. Since you can get phase inversion pretty easily in SCF, the
leapfrog design works well. Designing them is really a great exercise
in signal flow graph theory, especially if the filter has transmission
zeros. Daniel Senderowich was consulting at Exar at the time, which is
where I learned the techniques.

One of the funnier lines Dan used was "it is hard to move a ladder."
The translation is ladder filters are very insensitive to component
tolerance. The line he would use is "As I told you once before...".
And yes, he did tell you once before, but I probably didn't get it at
the time.


Re: Brushing up on theory: Butterworth LCR filter design?
"One of the funnier lines Dan used was "it is hard to move a ladder."
The translation is ladder filters are very insensitive to component
tolerance."

Yeah, but they're also challenging to debug if they're of high order, since
everything is all coupled together... one of the things Gabor Temes always
told us was, "Don't use a leapfrog topology for your first post-graduation
filter design assignment in industry."

Of course, he was thinking of the kind you built out of discrete op-amps and
R's and C's like he had done back working for the telephone industry in the
'60s/'70s; these days if it works in SPICE the fab will guarantee it'll work
on-chip, rgiht? :-)



Re: Brushing up on theory: Butterworth LCR filter design?
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There isn't much SCF being done these days, but Switcap was what we
used.Spice doesn't conserve charge.

I really don't see the logic in Temes statement. In SCF, it was an
opamp per pole regardless of topology. If you can design a ladder, so
much the better. The "localized Qs", a term I never liked, are lower
with a ladder. That is, the response at individual nodes is less
peaked in a ladder. This kept the component spread (cap ratio) low. We
also used filtor (sic) out of University of Toronto.

What you were selling in the day was a very tightly controlled filter
shape. The customer put up with THD and clock feedthrough. You had to
have some selling advantage, and repeatability was what you sold.

One of the more annoying things was in the dark ages when Bell 212
filters were being sold for $25 a pop in NMOS technology, the THD plus
noise was more significant than what came through the filter. However,
for marketing purposes, you had to deliver the Bell 212 pole/zeros,
even if you could do better. When we finally integrated the entire
modem, i.e. nobody could see what the filters looked like, I yanked at
least a third of the filters out. It was truly a waste of silicon. The
lower Q meant less group delay compensation, so fewer allpass stages.

Often less is more if you look at the big picture.

Re: Brushing up on theory: Butterworth LCR filter design?
On Sun, 18 Jan 2009 00:46:37 -0800 (PST), " snipped-for-privacy@sushi.com"


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That's a startling concept. Can you elaborate?

John



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