Need to understand how LC-filter works, help please
Here is a PI filter:







simulate this circuit &ndash; Schematic created using CircuitLab

When the frequency is very low, the capacitors are almost open circuit and the inductor is almost a short circuit.

As the frequency increases, the capacitors become a lower reactance (thus sinking some of the input signal to ground) and the inductor increases its reactance, limiting the flow of current to the output.

The reactance of a capacitor is \$ \frac {1} {2 \pi fC}\$ and therefore decreases with increasing frequency. The reactance of an inductor is \$2 \pi fL\$ and therefore increases with increasing frequency.

So the capacitors and the inductor are achieving the same thing (they form a low pass filter); a series inductor and a parallel capacitor can both form a low pass filter on their own in conjunction with a resistor.

The cutoff frequency assuming C1 and C2 are equal (they normally are but not always) is:

\$Fc = \frac {1} {2\pi \sqrt LC}\$

You can derive this:

The cutoff frequency is when \$ \frac {1} {2 \pi fc} = 2 \pi fl\$ and is fairly simple algebra to simplify.