# Passive Pi Low Pass Filter LC

I'm trying to use a simple pi low pass filter using two capacitors and one inductor. I've found the formula to calculate the value of the capacitance and of the inductance using the cut off frequency, but I would like to know where this formula comes from, I can't find any explanation on the internet. These are the formulas :

L     =     Zo / (2pi x Fc) Henries

C     =     1 / (Zo x 2pi x Fc) Farads

Fc     =    1 / (2pi x square root ( L x C) Hz

For example with a RC low pass filter I just use the voltage divider formula and from that, using the impedances, I find the transfer function of the filter. Then from the transfer function I'm able to find the cutoff frequency. Could be done like this also for the pi LC l.p.f? Thank you

• can you post the formula? Oct 3, 2017 at 10:22
• What is important also is the schematic and the source resistance/impedance driving this filter. A small sketch would be helpful. Oct 3, 2017 at 10:49
• I've posted the formula. I'm not interested in this specific case, but I would like to understand the demonstration of the formula Oct 3, 2017 at 11:26
• You've missed a "2" from your formula. Oct 3, 2017 at 11:34
• Note: The formulas above assume the capacitors are equal. Sep 2, 2021 at 20:21