In the circuit below we have a positive potential VDD=3.3V and ground potential VSS=0V which are supplying the digital part of an integrated circuit. Digital part of circuit is operating at frequency f=12MHz and can therefore cause some disturbances. Same integrated circuit also has analog part which needs more stable potentials VDDA=3.3V and VSSA=0V derived from previously mentioned potentials by using LC filters.

But this are not ordinary filters because there are always 3 electronic elements added. I haven't found any calculus for example like this that would show, how to derive size of L2 and L3. Does anyone have idea how to derive the equation for L2 and L3 or could at least recommend a good book on the subject?

I tried simulating it with some random values for L2, L3 & L1, but it won't kill the 12MHz frequency entirely so I am lost without theory. I don't know if this is even the response I need to look for…

After applying some changes like @The Photon suggested in the comments I really get better response and frequency is almost flattened out entirely. Not quite there yet, but it is better now. But it looks like it keeps on ringing…

Here is the clocking of my integrated circuit as user @analogsystemsrf requested in the comments:

## Best Answer

You need some dampening. Use Rdampen = sqrt(L/C).

For 0.1uf and 0.1uH, R = sqrt(1/1) = 1 OHM. Add 1 OHM in each ringing path.

Or place that 1 Ohm in parallel with each inductor.

The formula sqrt(L/C) produces a couple dB overshoot in a frequency response.

Here is a PI filter: 100nH from digital-section (10cm wire) into the PI of 10uF as Cpi1, into series R+L, into Cpi2 of 1uF. This provides 40+db filtering.

The series Resistor is crucial. Otherwise, lots of ringing as you see in your own simulations.

^{simulate this circuit – Schematic created using CircuitLab}