Impedance scaling of passive LC filters - Page 1
Forum section: electronics / projects

author: Detzi
author_rank: Regular Contributor
timestamp: January 10, 2020, 12:29:25 pm
content: Good Day,i am trying to understand how impedance scaling in passive LC Filters works. I have read up this references:https://archive.org/details/RFCircuitDesign/page/n35https://www.analog.com/media/en/training-seminars/design-handbooks/Basic-Linear-Design/Chapter8.pdfhttps://www.am1.us/wp-content/uploads/Documents/U15710_Bartlett_Bisection_Theorem.pdfhttps://en.wikipedia.org/wiki/Bartlett%27s_bisection_theoremi 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 inbut 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 appreciatedThanks in advanceDetzi

author: unitedatoms
author_rank: Frequent Contributor
timestamp: January 10, 2020, 04:08:00 pm
content: I tried to repeat  calculations, it looks the Wikipedia values are off with x10 error.Or I could be wrong.

author: Detzi
author_rank: Regular Contributor
timestamp: January 10, 2020, 04:27:06 pm
content: On Page 50 in  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.

author: graybeard
author_rank: Frequent Contributor
timestamp: January 10, 2020, 05:58:24 pm
content: I often find thisonline tool from Japan to be usefulfor a quick filter design, but will not work for this.The absolute best book I have ever read on the subject isPassive Filter SynthesisbyJames 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.

author: Detzi
author_rank: Regular Contributor
timestamp: January 10, 2020, 07:20:04 pm
content: Thanks @greybeard, i've pick up a copy, but it will take a few weeks untill it arrives...

author: T3sl4co1l
author_rank: Super Contributor
timestamp: January 10, 2020, 07:40:51 pm
content: 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/ElectronicFilterDesignHandbook4thEdso it's not a big deal as far as practical use.Tim

author: Detzi
author_rank: Regular Contributor
timestamp: January 10, 2020, 07:50:21 pm
content: 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