How to find the component values of a Butterworth low pass f

[joe]

Sorry about asking silly questions. I am a programmer writing assembly
programs for MCU. But I am interested in some electronics circuits recently.

I looked at some website. I knew that the poles of a Butterworth filter are
all on the unit circit separated in equal angles (Sorry, there may be
specific terms, but I just can think of it this way). And I knew the magic
equation of something like [1+(w/wc)^2n].
My question is, how to find out the values of the components, so that the
circuit have poles on the unit circle, and also match the magic equation?
Are there any equations to find them out?
Also there are the Chebyshev filters. They look the same as the Butterworth
one. What are the difference between them? Just some component values
different? Or is the magic equation? Or is there a concept behind?

Regards,
joe

 

[Steve K.]

joe wrote:

Sorry about asking silly questions. I am a programmer writing assembly
programs for MCU. But I am interested in some electronics circuits recently.

I looked at some website. I knew that the poles of a Butterworth filter are
all on the unit circit separated in equal angles (Sorry, there may be
specific terms, but I just can think of it this way). And I knew the magic
equation of something like [1+(w/wc)^2n].
My question is, how to find out the values of the components, so that the
circuit have poles on the unit circle, and also match the magic equation?
Are there any equations to find them out?
Also there are the Chebyshev filters. They look the same as the Butterworth
one. What are the difference between them? Just some component values
different? Or is the magic equation? Or is there a concept behind?

Theoretically, once you've derived your butterworth polynomial, you
physically realize your filter by partial fraction expansion or
continued fraction expansion. But in practice, no one does that, they
simply work from the normalized tables that are widely published in many
texts, and scale to impedance and frequency.

Zverev's text probably was most comprehensive for published tables. But
for cheaper and likely sufficient, you could simply get Winder's book.

If you want to get down to the derivations (and synthesis via
expansion), then Aram Budek, Kendall Su, and Earnst A. Guillemin (sp?)
books can get you there.

http://www.amazon.com/exec/obidos/ASIN/1402070330/
http://www.amazon.com/exec/obidos/tg/detail/-/0881336254/

The Budak book is probably the best for the money. The Guillemin book
is particularly gnarly. I can't find a used one...

http://www.ee.sun.ac.za/Noteworthy/FamousScientists/OttoBrune%20Guillemin%20tribute.pdf

 

[Steve K.]

"Steve K." wrote:

The Budak book is probably the best for the money. The Guillemin book
is particularly gnarly. I can't find a used one...

too fast

http://www.amazon.com/exec/obidos/tg/detail/-/0882754815/

 

[Jim Thompson]

On Fri, 06 May 2005 00:59:09 GMT, "Steve K." <never@here.net> wrote:

"Steve K." wrote:

The Budak book is probably the best for the money. The Guillemin book
is particularly gnarly. I can't find a used one...

too fast

http://www.amazon.com/exec/obidos/tg/detail/-/0882754815/

I was lucky... the 6B students (EE honors), in 1959, didn't have to
take passive circuit theory from Guillemin, we had H.B. Lee instead...
marvelous instructor... and we got real values, not just 1H, 1 ohm and
1F ;-)

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice480)460-2350 | |
| E-mail Address at Website Fax480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

 

[Jens Tingleff]

In article <427AC15C.C06588D4@here.net>, Steve K. says...

"Steve K." wrote:

The Budak book is probably the best for the money. The Guillemin book
is particularly gnarly. I can't find a used one...

too fast

http://www.amazon.com/exec/obidos/tg/detail/-/0882754815/

Or a gratuitous plug for where I got my copy

http://dogbert.abebooks.com/servlet/SearchResults?an=Guillemin&y=16&tn=synthesis&x=39

A recent book which has Butterworth and Chebyshev tables is R W Rhea "HF filter
design and computer simulation" McGraw Hill

Best Regards

Jens


--
Key ID 0x09723C12, jensting@tingleff.org
Analogue filtering / 5GHz RLAN / Mdk Linux / odds and ends
http://www.tingleff.org/jensting/ +44 1223 211 585
"Never drive a car when you're dead!" Tom Waits

 

[gwhite]

Jens Tingleff wrote:

In article <427AC15C.C06588D4@here.net>, Steve K. says...

"Steve K." wrote:

The Budak book is probably the best for the money. The Guillemin book
is particularly gnarly. I can't find a used one...

too fast

http://www.amazon.com/exec/obidos/tg/detail/-/0882754815/

Or a gratuitous plug for where I got my copy

http://dogbert.abebooks.com/servlet/SearchResults?an=Guillemin&y=16&tn=synthesis&x=39

I buy thru abe too. $22.50 is great for the Guillemin text.

 

[Ben Bradley]

On Fri, 06 May 2005 00:59:09 GMT, "Steve K." <never@here.net> wrote:

"Steve K." wrote:

The Budak book is probably the best for the money. The Guillemin book
is particularly gnarly. I can't find a used one...

too fast

http://www.amazon.com/exec/obidos/tg/detail/-/0882754815/

Look on http://www.bookfinder.com - there are five copies, starting
at 1/10th the price.
-----
http://mindspring.com/~benbradley

 

[joe]

Thanks for you answer! =)

"Jens Tingleff" <jensting@tingleff.org> źśźgŠóślĽóˇsťD
:d5fqvo0130r@drn.newsguy.com...

In article <427AC15C.C06588D4@here.net>, Steve K. says...

"Steve K." wrote:

The Budak book is probably the best for the money. The Guillemin book
is particularly gnarly. I can't find a used one...

too fast

http://www.amazon.com/exec/obidos/tg/detail/-/0882754815/

Or a gratuitous plug for where I got my copy


http://dogbert.abebooks.com/servlet/SearchResults?an=Guillemin&y=16&tn=synth

esis&x=39

A recent book which has Butterworth and Chebyshev tables is R W Rhea "HF
filter
design and computer simulation" McGraw Hill

Best Regards

Jens


--
Key ID 0x09723C12, jensting@tingleff.org
Analogue filtering / 5GHz RLAN / Mdk Linux / odds and ends
http://www.tingleff.org/jensting/ +44 1223 211 585
"Never drive a car when you're dead!" Tom Waits

 

[Tim Wescott]

joe wrote:

Sorry about asking silly questions. I am a programmer writing assembly
programs for MCU. But I am interested in some electronics circuits recently.

I looked at some website. I knew that the poles of a Butterworth filter are
all on the unit circit separated in equal angles (Sorry, there may be
specific terms, but I just can think of it this way). And I knew the magic
equation of something like [1+(w/wc)^2n].

Using the term "unit circle" will get you in trouble with DSP types --
it has a specific meaning in sampled-time filtering that doesn't have
much to do with Butterworth filters.

My question is, how to find out the values of the components, so that the
circuit have poles on the unit circle, and also match the magic equation?

There are a number of different circuits that can realize a Butterworth
low-pass filter, and low-pass filters aren't the only ones that can be
called "Butterworth". Each circuit topology has specific requirements
for component values, and in each case you have to choose to account for
various non-ideal component effects or not.

Are there any equations to find them out?

Yes, but it goes by the individual circuit.

Also there are the Chebyshev filters. They look the same as the Butterworth
one. What are the difference between them? Just some component values
different? Or is the magic equation? Or is there a concept behind?

A Butterworth filter is "maximally flat" in the passband, meaning that

it's amplitude response changes as little as possible, and is
monotonically decreasing toward cutoff. A Chebychev filter has an
amplitude response that rises and falls in the passband, but always
between the same two points -- it is "equiripple". In return for
tolerating the ripple in the passband the Chebychev gives you a steeper
falloff from the passband to the stopband.

Entire books are written about designing and implementing filters, and
they can be highly technical. Your best bet is to go buy a copy of the
ARRL Handbook, which does a pretty good job of explaining this stuff,
and doesn't assume that you have a BS in electrical engineering to start
with.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

 

[Joel Kolstad]

"joe" <hlwongx@netvigator.com> wrote in message
news:d54e0a$9k71@imsp212.netvigator.com...

My question is, how to find out the values of the components, so that the
circuit have poles on the unit circle, and also match the magic equation?

You sit down and build up the equation for the impedance of the circuit and
its derivatives and equate them to that dictated by the "magic equation."
This is considered a homework problem for, say, 2nd and 3rd order
circuits, but for anything much higher than that either you sit down and write
a program to do it... or just use tables or software like most people have
done for decades now.

There are many, many books that have these tables, and I'm sure they're on the
Internet as well. "Analog and Digital Filter Design" by Steve Winder is a
book I like that strikes a good balance between "cookbook" and "theoretical"
(leaning towards the cookbook side, however). For software, for free you can
get AADE's Filter Designer, or try Elsie. Fancier software tends to support
more topologies -- NuHertz Solutions has their Filter Solutions, but it's not
cheap (hundreds of bucks to thousands of dollars); it's probably about the
cheapest package that will let you specify arbitrary poles and zeroes and it
"does the rest" (completely synthesizes a circuit for you).

Are there any equations to find them out?

For Butterworth and Chebyshev I believe you can find closed form expressions
for component values. For fancier filters (elliptical being the prime
example), there are no closed form expressions for the component values in
terms of common functions.

Also there are the Chebyshev filters. They look the same as the Butterworth
one. What are the difference between them?

This is the game you're playing:

-- Higher order filters have faster (steeper) dropoff between the passband and
stopband
-- Accepting ripple in the passband or stopband response lets you obtain more
steepness for a given order filter.
-- The more ripples, the more you gain... although this is a relatively 'slow'
function
-- Accepting finite (rather than infinite) loss in the stopband also buys you
steepness at a given order

Chebyshev has ripple in the passband but still infinite loss.

BTW, for low order filters, in some cases the finite Q (loss) of the inductors
involved tends to smooth out the ripples and make a Chebyshev look a lot like
a Butterworth!

Just some component values
different?

Yes, for Chebyshev. However, as soon as you go for the 'accepting finite
loss' option, you need to add components to add zeroes to the transfer
function (this occurs in Elliptic filters, so-called Inverse Chebyshev, etc.).

Or is the magic equation?

The equations always change. Butterworth comes from making the passband as
flat as possible, Chebyshev comes from constraining the ripple to a specified
amount in the passband, Bessel comes from making group delay as falt as
possible, etc.

Or is there a concept behind?

Nope, the concept behind them is the same. I do think it's useful to keep in
mind that you (yes, you!) can sit down and desgin a filter just by throwing a
few zeroes and poles around the S plane, writing down the transfer function,
and equating it to a bunch of components... All the filters with Big Names
attached to them are that way because they were designed very systematically
and, by now, most filters people actually want designed can be easily
accomdated by these well-known designs. Still, there's a lot of room for
"tweaking" standard filters by tossing in, e.g., another pole to built various
hybrid-type filters.

---Joel Kolstad