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