Author Topic: Impedance scaling of passive LC filters  (Read 1184 times)

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Offline DetziTopic starter

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Impedance scaling of passive LC filters
« on: January 10, 2020, 12:29:25 pm »
Good Day,
i am trying to understand how impedance scaling in passive LC Filters works. I have read up this references:

[1]https://archive.org/details/RFCircuitDesign/page/n35
[2]https://www.analog.com/media/en/training-seminars/design-handbooks/Basic-Linear-Design/Chapter8.pdf
[3]https://www.am1.us/wp-content/uploads/Documents/U15710_Bartlett_Bisection_Theorem.pdf
[4]https://en.wikipedia.org/wiki/Bartlett%27s_bisection_theorem

i also tried to find something on the "Darlington realization procedure" but couldn't. I have essentially everything calculated in the filter but i just cant figure out how to scale the values of a simple "L" filter on two given unequal target impedances for the output and input.
For example i would like to know how i can transform this second order Butterworth with fc=1rad/s:

to both of these possible solutions:



I tried to use the bisection theorem but i could only match the Inductor L2, from the first solution, using the method described in [3] but none of the other values matched.
I feel like it's something real easy that i am missing here but i cant see the darn thing!
Can someone provide me with a hint or a nice reference online or written book where this is explained and i can read it up? All sources i can find use tables to look up the values but don't give the method on how to calculate or validate these factors. I also don't know if either the bisection or darlington approach is the right(?) one, if any of both.
Actually any information on this topic will be appreciated
Thanks in advance
Detzi
« Last Edit: January 10, 2020, 12:36:52 pm by Detzi »
 

Offline unitedatoms

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Re: Impedance scaling of passive LC filters
« Reply #1 on: January 10, 2020, 04:08:00 pm »
I tried to repeat [3] calculations, it looks the Wikipedia values are off with x10 error.

Or I could be wrong.


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Offline DetziTopic starter

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Re: Impedance scaling of passive LC filters
« Reply #2 on: January 10, 2020, 04:27:06 pm »
On Page 50 in [1] you can find a table with the actual scaling factors. And above most other stuff necessary to calculate the values, that might help to evaluate your results.
 

Offline graybeard

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Re: Impedance scaling of passive LC filters
« Reply #3 on: January 10, 2020, 05:58:24 pm »
I often find this online tool from Japan to be useful for a quick filter design, but will not work for this.

The absolute best book I have ever read on the subject is Passive Filter Synthesis by James Storer.  It is a book I have used repeatedly over the years.  I have two copies for reference, one at home, and one in my office at work.

Offline DetziTopic starter

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Re: Impedance scaling of passive LC filters
« Reply #4 on: January 10, 2020, 07:20:04 pm »
Thanks @greybeard, i've pick up a copy, but it will take a few weeks untill it arrives...
 

Offline T3sl4co1l

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Re: Impedance scaling of passive LC filters
« Reply #5 on: January 10, 2020, 07:40:51 pm »
Afraid I don't remember the transformation procedure myself (or if it has anything to do with, say, the asymmetry of the filter, being 2nd order?).  Fortunately they're tabulated in books like this,
https://archive.org/details/ElectronicFilterDesignHandbook4thEd
so it's not a big deal as far as practical use.

Tim
Seven Transistor Labs, LLC
Electronic design, from concept to prototype.
Bringing a project to life?  Send me a message!
 

Offline DetziTopic starter

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Re: Impedance scaling of passive LC filters
« Reply #6 on: January 10, 2020, 07:50:21 pm »
Thanks for the book Tim, you're right the net i full of these tables, i actually linked one, but i really want to know how these are calculated  ;)
 


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