Turns out my pi-filter simulation from the previous post does not tell the full story, as with a power filter it's best to first look at the step response before looking at the frequency response. With that said, here are the updated simulations which now include two decoupling capacitors at the load (both ceramic, one 100nF and other 10μF)

## Chosen Pi-Filter Configuration

Here is the step and frequency response of the chosen pi-filter configuration. If you want to know how I came to this conclusion then see the following sections

Comparing no filter to pi-filter, note how there is no drastic phase shift and the attenuation is grater, with the -3dB point starting at 70kHz instead of 170kHz

## Pi-Filter Step Response

For the step response I am using a current load configured with a **pulse function**, with the step/pulse looking something like this:

To help with comparison, below is what the step response looks like without any filter present

**NOTE:** This plot is a bit deceptive as it looks like the circuit is able to respond well to transients, HOWEVER if you also look at the frequency response (see next section) you will see that we can do better

Here is the initial pi-filter configuration I have chosen, a 10μF electrolytic capacitor, a 33Ω (@100MHz) ferrite bead, and a 10μF ceramic capacitor

**NOTE:** This is not my final configuration, if you have a look at the last section you will see that lowering the ferrite bead impedance drastically helps with step response

And here are some configurations that did not did not make the cut. Again, it's a bit harder to see why if you just look at the step response; if you also see the frequency response (see next section) you will note that some configurations have sharp phase shifts that lead to a "peaky" attenuation

**NOTE:** I realise that ELEC/CER & CER/CER configurations have a similar step response (with CER/CER actually having a better frequency response). However I am fairly certain that in the real world ELEC/CER will give better performance due to the relatively large ESR of the electrolytic capacitor, as with low ESR capacitors it's much easier to introduce oscillations/ringing with fast transients

## Pi-Filter Frequency Response

Same order as before, first we have no filter (to help with comparison). Note how we have a tolerable attenuation up to 10GHz where he see a drastic phase shift and the peak that comes with it (though I suspect we don't really care what happens after the 1GHz mark)

Here is how things look if we implement the chosen filter from the previous section. Note how there is no drastic phase shift and the attenuation is grater, with the -3dB point starting at 90kHz instead of 170kHz

And for completion, here are the frequency responses of the configurations that did not make the cut. The -3dB point for these (in order) is 230kHz, 170kHz, & 65kHz

## Pi-Filter Step Response vs Ferrite Bead Impedance

From here on out I am trying to see what impact the ferrite bead impedance has on the filter performance, the results will shock you ;^)

As before, to make comparison easier here is the step response without any filter present

And here are our candidates. Note how drastic the difference is between the 8Ω (@100MHz) & 120Ω (@100MHz) ferrite beads. As you might guess, am leaning towards the 8Ω ferrite bead for the pi-filter

## Pi-Filter Frequency Response vs Ferrite Bead Impedance

Again, to make comparison easier here is the frequency response without any filter present

And here are our candidates, the -3dB point for these (in order) is 70kHz, 90kHz, & 70kHz. Note how the 120Ω ferrite gives +2dB amplification (not attenuation) around 40kHz

## Tips For Power Filter Simulation

Here are some things to keep in mind when simulating a power filter:

- Make sure to include parasitic elements in your simulation. This would be the parasitic resistance/inductance/capacitance of cables, connectors, tracks, planes, decoupling capacitors, relays...
- Include a series resistance in your AC/noise source when doing a frequency response. With my simulation is set it at 10mΩ. If you forget this element (or set it to 0Ω) then your simulation would show amplification before you see the roll-off, while in the real world you would not see a response like this as the source would have a finite series resistance (which I guess is a parasitic resistance)
- Know what a typical current transient you are bound to run into looks like for your circuit. For example, if you are switching a relay and you know the could current is 10A then you can better understand what sort of filter response you need
- In addition to above, see if you can figure out the constant current consumption of your circuit. Again knowing this will give a more authentic simulation
- It's useful to know the input/output impedance of the filter, as with this information you can figure out what filter topology will be best. For example, a pi-filter is designed to "match" a high input impedance with a high output impedance, whereas a T-filter is the opposite, a CL filter is high/low, and a CL filter is low/high

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