Brushing up on theory: Butterworth LCR filter design?

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

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, 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.

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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
Reply to
Richard Rasker
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Have you looked at this?

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Reply to
Charles

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

Reply to
John Larkin

It's actually not at all a trivial "connection" -- you sit down and figure out the transfer function of your circuit, and then equate the component values with the coefficients in your transfer function... which is also not completely trivial due to the "mixing" of component values within each coefficient. However, there are some simplifications/generalizations available due to the regular "ladder" structure of the circuit.

This difficulty is why the vast majority of people designing LC filters start with 1Hz prototypes and component values taken from a table (e.g.,

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or
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and then transform them to the frequency and response they need. :-) (There is software out there that will directly synthesize a circuit from an arbitrary transfer function, although there's no guarantee that this can be done with only L's and C's and a source/termination R in the general case... hence even if you have a somewhat oddball transfer function, many people still start with a table-based design that's somewhat close and then just let an optimizer mess around with component values to tweak the design as needed.)

If you want to delve into the theory behind where the "magic numbers" in the tables came from, most of the "hard core" filter synthesis books have a section on it. I took a quick look at "Design of Analog Filters" by Schaumann and Van Valkenburg and it does (chapter 13, "LC Ladder Filters").

---Joel

Reply to
Joel Koltner

That's way too difficult. ;-) If you want to easily make active filters that work, check this out:

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I've built several using this software and they all worked great.

Reply to
Anthony Fremont

If you like software simulations then you can download LTSpice form LinearTech web site... and build your own filters and simulated them.

Joe

Reply to
Joe G (Home)

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I'm with you here. I have a copy of Huelsman and Allen with the tables, as well as Zverev.

Reply to
miso

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

Reply to
John Larkin

The butterworthiness is in the geometry of the filter and the component ratios, which become reflected in the ratios of the coefficients of the transfer function.

The transfer function can be derived by analyzing Vo/Vi for the circuit. As the text indicates, this is done by substituting L*s for inductors and 1/(C*s) for the capacitors, and writing and solving the circuit equations. Then the magnitude at any frequency is found by plugging in j*2pi*f in place of s. I can show you how to get the transfer function from the circuit, if you want. Going back the other way is another thing.

Anyway, if you look at the caption for the first schematic, it shows a set of component values for wc = 1 rad / sec, or 0.159 Hz. Both inductance and capacitance get smaller for the same impedance as frequency increases, so if you want a filter with fc = 1 kHz, divide the indicated values by (2pi * 1 kHz) = 6283. Then you will have C2 =

212 uF, L1 = 238.5 uH, L2 = 79.5 uH, the values for a 1 kHz filter.
--
John
Reply to
John O'Flaherty

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
Reply to
Richard Rasker

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These are very good, thanks for pointing out!

It sort of feels like I grasp two domains: the math domain with the imaginary plane, poles and polynomials on the one hand, and the practical topology (but without values) required for a particular function on the other hand. It's the number crunching in between which eluded me -- and which isn't all that easy, I know. There's a good reason why people rely on tables and design software to come up with practical solutions.

Anyway, thanks once again; I think I can find my own way from here :-)

Richard Rasker

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

I already found that at 1kHz, either the capacitors or the inductors end up having rather unwieldy values ... so I'm afraid the actual filter will be active after all. But thanks for the explanation all the same (also to all the others I didn't personally thank); I will certainly dig deeper into this, until I (hope)fully understand!

Richard Rasker

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

And you ?:-)

...Jim Thompson

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| James E.Thompson, P.E.                           |    mens     |
| Analog Innovations, Inc.                         |     et      |
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Reply to
Jim Thompson

Huelsman was one of my first victims. (Probably is/was a leftist weenie.)

Presented a seminar at Motorola SPD around 1962-1963 glorifying a gyrator configuration that he claimed had less component sensitivity than designs by others.

When I stood up and pointed out that he had simply moved sensitivity from one set of components to another, my boss at the time (Jan Narud of ECL fame *) almost rolled in the floor with laughter.

(*) Narud, Seelbach, Miller, Cappon (sp?), and me, the new analog guy, later joined by Jim Solomon and Tom Frederiksen.

...Jim Thompson

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| James E.Thompson, P.E.                           |    mens     |
| Analog Innovations, Inc.                         |     et      |
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Reply to
Jim Thompson

H(s)

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

Reply to
John Larkin

I

H(s)

values.

some

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with

Nice! How does the guy stay in business/

...Jim Thompson

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| James E.Thompson, P.E.                           |    mens     |
| Analog Innovations, Inc.                         |     et      |
 Click to see the full signature
Reply to
Jim Thompson

and I

H(s)

values.

some

nothing

here,

with

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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Reply to
Don Lancaster

bandpass

connecting

and I

H(s)

values.

some

nothing

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with

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

Reply to
John Larkin

bandpass

connecting

and I

H(s)

values.

some

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here,

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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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Reply to
Jim Thompson

"Jim Thompson" wrote in message news: snipped-for-privacy@4ax.com...

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

Reply to
Joel Koltner

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