Capacitor Inductor Low Pass Passive Filter – Passive Pi Low Pass Filter LC

capacitorinductorlow passpassive-filter

I'm trying to use a simple pi low pass filter using two capacitors and one inductor.
Schematic Pi LC low pass filter

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

Best Answer

The impedance magnitude of a capacitor is:

    ZC = 1 / ωC

The impedance magnitude of a inductor is:

    ZL = ωL

The rolloff frequency of a LC filter is when these two are equal. Set the two equations above equal to each other, and solve for ω. Then remember that ω = 2Πf, where f is the frequency in Hz.