# Pi filter design for SMPS output ripple

Given a circuit like a buck-converter like the AOZ1284PI in a circuit such as this one: Or push-pull converters such as this one: If one was to design at the output a low-pass PI filter with a cutoff frequency of 10kHz for example (purely hypothetic), how would one proceed?

I don't see much information about the PI filter. Somewhat there is no real voltage Vo/Vi transfer function like a LCR filter, but instead there are design rules like using the line characteristic impedance $$\Z_0\$$ if I stand correct (like here).

I'm not even sure what to put as $$\Z_0\$$ because after all this would be on a PCB so the line impedance must be extremely low? Does it really even matter?

Except, with a SMPS IC it's next to impossible to determine the output resistance of the IC, or the equivalent load impedance $$\Z_L\$$ (imagine you design a PSU, there are tons of loads possible here, and nevertheless if you supply say a MCU you cannot really predict that load because it's variable).

So given all of this, how does one actually implement a PI filter to filter the ripple voltage, given your Q factor must be around 0.707 to avoid making an oscillator in the process? Given for example a max current of 100mA, fc=10kHz, $$\Z_0\$$=no idea (how would you determine it)?

• I think by modifying the output filter you re modifying the transfer function of your system and so the stability... Carefull must be taken when you change the order of your filter to keep your system "reasonably stable" – Jess Feb 12 '20 at 9:20
• @Jess I don't plan placing it inside the control loop though. – Yannick Feb 14 '20 at 1:02
• It may not matter. Adding inductance and capacitance of any sort after the control loop will affect operation. Some SMPS even state "do not use more than this many µF" etc. – rdtsc Jan 26 at 19:43

If one was to design at the output a low-pass PI filter with a cutoff frequency of 10kHz for example (purely hypothetic), how would one proceed?

You would proceed by going backwards and recognizing that you already have capacitance on the output of your current circuit so, all you actually might require is an LC low pass filter to tack on to the output.

there is no real voltage Vo/Vi transfer function like a LCR filter, but instead there are design rules like using the line characteristic impedance Z0

That's correct, because you are looking in the wrong place for what you perceive to be the right solution. The right solution is not a Pi filter; it's a low pass filter using L, C and R. Z0 refers to the characteristic impedance of the system i.e. 50 ohms and this type of filter design is for filtering RF signals that require impedance matching. It's not what you want.

So given all of this, how does one actually implement a PI filter to filter the ripple voltage, given your Q factor must be around 0.707 to avoid making an oscillator in the process?

Adding a filter to an output does not turn anything into an oscillator. The worst that can happen is that transients from the preceding stage (the power converter) can stimulate ringing voltages on the output and so, that is to be avoided by correct selection of damping resistors.

Use a design like this is my recommendation: - Picture from this online calculator.

Just make sure that you position the resonant frequency of the filter significantly down below the switching frequency of the converter but not so low that transient changes in the switching converter's output have ringing effects that are too high or unacceptable.

• I see so the "PI" filter that are used on PSU's are in fact a LC low pass placed just after the filter capacitor placed right at Vout, is that corect? So in fact it somewhat has a PI network (two caps with a L placed between), but is not a "real" PI filter that is used in a transmission line context where Zo and Zi are known. – Yannick Feb 14 '20 at 1:01
• Yes, a nice summary. – Andy aka Feb 14 '20 at 7:13