Pi Matching Network Problem: Find X Reactance for C1, L1, C2, C3

[zak8000]

hi
i need help with some pi matching for the following cct shown below, i would usually approach this problem with X=sqrt(1000*50) where X is the reactance of L1,C2,C3 but since C1 is in this cct then i can't use this equation so could someone please help me solve this problem

 

[yungman]

There is too many combinations that can match from 1000 to 50, you really have to set you requirement first.This is quite hard if you try to do calculation even if you set the low pass cut off frequency. What you have is like a universal low pass filter circuit!

If you assuming C1 is a short circuit at the frequency of interest, then it is a 3 pole low pass filter and you can look up any filter book to get value depend on the characteristic of the low pass you want. You can get Chebychev, Bessel, Butterworth etc. depend on the value and they provide table for source inpedance of 1000 and termination of 50 like in your circuit.

If you just want to match for the hack of matching, using smith chart is another way and you can swing the impedance around and finally go from 1000 to 50 ( 20 to 1 in normalized to 50 ohm).