Has anyone a good reference for lumped filters?

[Detzi]

Good Day,
has anyone a good reference for lumped filterdesign? I am searching something like this:
sloa049b but for a lumped LC or pi-type filter.

[Anders_Wallin]

I guess it’s a balance between theoretical descriptions and more cookbook-style recipes. Try Bowick’s book? https://archive.org/details/RFCircuitDesign

[Detzi]

I dont know if its any good but so far it does look like it. Thank you!

EDIT

Also from Page 69 to 71 in this Document there’s a bit of it and the mention of “A. B. Williams, Electronic Filter Design Handbook, McGraw-Hill, 1981, ISBN: 0-07-070430-9” dont know if its any good either.

[ekoeck]

If you are looking for a practical approach try for example the Design Seminars from Analog (https://www.analog.com/media/en/training-seminars/design-handbooks/Linear-Design-Seminar-1995/Section10.pdf). If you are more interested in the math behind the scenes, I like can recommend “Analog Filter Design” by van Valkenburg. It’s pretty comprehensive but it takes a while to get through it. Apart from that “The Art of Electronics” also has a chapter on filters with it’s usual very comprehensive style and examples.
If you just want to design some small filters try the AADE Filter Design Tool (http://www.ke5fx.com/aadeflt.htm)

[Detzi]

Thank you very much for the ressources i will check them out and see if there is something i can use.

The last thing for me that is unclear is how to scale the filter components when Rs/Rl is anything else than 1 like here:
A

B

I haven’t found a source that explains to me how the transformation from A to B works. All the books so far used tables with conversion factors and didn’t care to explain how it works. If someone knows how it works or can provide literature that does explain it, i’d be very grateful.

[ekoeck]

Either you use the tables (or a suitable software) or you have to deal with the transfer functions. Chapter Two of the Williams has a part about frequency and impedance scaling as all the other books (should) have, too.

Source: Arthur B. Williams, Electronic Filter Design Handbook, 2006, pp. 11-12

[Detzi]

Dope! I’ll check if that works i have no problem with transfer functions

[Detzi]

On the second thought this looks like “just” impedance scaling for linear growing Rs and RL. What i mean to say is it looks like this is meant to keep the ratio between Rs and Rl constant but scale to any given target R. So the result will be a scaled network but still Rs=Rl=R.
Thats not what i meant to do here, i want to scale the impedance for say a Rs=75Ohm and Rl=50Ohm.
You can check that the formulas are off when comparing with the filters A and B iposted, they are exactly the same filter but with unequal RS and RL.

[ekoeck]

Yes, this was just the first example I found and it is for an unloaded circuit. If you are familiar with transfer functions just solve it for your desired Q and cutoff frequency.

[Detzi]

Okay let’s see if i can follow:
Above pictures A and B show a 1rad/s second order butterworth. The (interesting part of the)poles of the transferfunction come out to be:
[MATH]±sqrt(1/2)[/MATH]
As far as my understanding goes they refer to a symmetrical system and summing them up you end up with the values from A in the post above. Further the transfer function its self takes only account for RL which lets me assume that RS is set to ‘1’ but i haven’t found a source that explicitly tells me about Rs(so this is a guess).
Going with above assumption this means if Rs differs from 1 i have to scale RL such that Rs comes out to be one. in the case above showed in B this means that Rs is one when Rl is 0.5Ohm.
Going with that and taking the L as a example, the relation between R,L and Q is fixed by:
[MATH]Q=wL/R[/MATH]
Since Q has to be fixed to meet the Butterworth, and w(omega) is anyways that means that the function of scaling this would be linear since only R and L can change. As you can see in B the values haven’t just scaled with factor 2 or 4…Furthermore if you lookup the scaling factors for these kind of matching you will see that they do not change linear but rather like a e-Function.

Of course it sure is only a matter of the right transfer function but it does not seem that it is easily derived from the “standard” form.

[ekoeck]

Ah ok, now I think I know, what you are looking for.

Your transmission H factor is

with

If we calculate |H|² we get something like this:
|H|² = 1 + a1 * w^2 + a2 * w^4
with
a1 = (C/Rp + L/Rs) ^ 2 - 2 * L * C * K
and
a2 = (L * C * K) ^ 2

To get a Butterworth response set
a0 = 0
and
a1 = 1
and solve for C and L. For a detailed explanation see chapter two in the Handbook of Filter Synthesis by by Anatol Zverev.

[Detzi]

That looks much more like it thank you! I’ll have a closer look at this soon and give you feedback on how it went.
The Book looks good but it is pricey, here in Germany the prices for a used one top the ones for a new copy…its 300€ on ebay and 100€ new

[Rabbit]

Hi Detzi

Here you can some good information for HF design not only filters.

https://www.fritz.dellsperger.net/downloads.html

The last link on the page is the filter handbook.

FILTER%202012.pdf

It is written in German but the formulas are valid for all languages

BR
Rabbit

[Detzi]

Thank you! Looks interesting i’ll work through.