# Designing a Pi filter as input of dc dc converter

#### Dagoni

Joined Jan 6, 2023
8
Hi,

I need to filter the input of a dc dc converter because of the conductive voltage emissions. With a Pi filter (as shown below).

I am really confused about selecting components because some sources say that C1 and L are the main filter components and other sources say that it's C2 and L that do the job (and C1 should have a really low ESR). C3 and R are used to damp the filter.

Is there a guide, a course or something that explains the pi filter in a complete way and without ambiguity ?

I followed this guide https://fscdn.rohm.com/en/products/...ower/input-filter-for-dcdc-converter_an-e.pdf but I'm not sure that what I calculated is correct. So,

Vin = 24V
The switching frequency (fs) of the converter is 330kHz
(The input current of the converter is 160mA at full load)
(The maximum ripple voltage of the converter is 60mVpp)

The capacitor should have a voltage that is at least twice the input voltage, so it should be 50V.

First, C1 is chosen for its low ESR (to not heat). I found a 33uF / 50V ceramic capacitor that has an ESR of 0.02 ohm at the frequency of 300kHz (near the resonance).
Next for C2, with L = 10uH (starting point, more or less arbitrary), we have the equation
$fc = \frac{1}{2\pi\cdot\sqrt{L\cdot C_{2}}}$
And to reduce the noise, the filter frequency should be a tenth of the converter switching frequency.
So we have :
$C_{2}=\frac{1}{(2\pi\cdot0.1\cdot fs)^2\cdot L}$
$C_{2}=\frac{1}{(2\pi\cdot0.1\cdot 330\cdot10^3)^2\cdot 10\cdot10^{-6}}\cong2.32\mu F \to 2.7\mu F$

For the damping resistor/capa, we have :
$R=\sqrt\frac{L}{C_{1}}$
$R=\sqrt\frac{10\cdot10^{-6}}{2.7\cdot10\cdot10^{-6}}\cong3.7\Omega \to 3.3\Omega$
And $5\cdot C_{1} < C_{3} < 10\cdot C{1}$
The minimum value of C3 would be 180uF but it seems impossible with a low ESR.

I would have C1 = 33uF/50V, C2 = 2.7uF/50V, C3 = 180uF/50V (electrolytic ?), L = 10uH / 192mA (at least + 20% of input converter current), R = 3.3 ohm

What do you think of this ? Is a 0.02 ohm ESR (C1) good ? How could I have a more precise idea of its impact ? Is it $I_{C2}=\frac{U_{ripple_{rms}}}{ESR}$ which would be 1A ?

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#### Dagoni

Joined Jan 6, 2023
8
R would be 0.33 ohm, wrong capacitor in the numeral equation
And last is IC1 not IC2

#### Papabravo

Joined Feb 24, 2006
19,850
IMHO the pi filter is a poor choice for this application. A cascade of a common mode choke and a differential mode choke would be superior.

#### Ian0

Joined Aug 7, 2020
7,008
What frequencies are you trying to filter out?
what are the self resonant frequencies of your inductor and capacitors?

#### Dagoni

Joined Jan 6, 2023
8
IMHO the pi filter is a poor choice for this application. A cascade of a common mode choke and a differential mode choke would be superior.
Thank you, do you know where I could look to learn to do that ?

#### Dagoni

Joined Jan 6, 2023
8
What frequencies are you trying to filter out?
what are the self resonant frequencies of your inductor and capacitors?
I actually only know the switching frequency of the converter... So I guess the filtering design should be done after the measurement of the converter (without any filter) ?
The self resonance frequency of C1 would be close to the switching frequency (330kHz). I didn't check for the others, is it important for L and C2 ? Should it be the same ?

#### Papabravo

Joined Feb 24, 2006
19,850
Thank you, do you know where I could look to learn to do that ?
This video is where I learned of this technique used in spacecraft.

#### Ian0

Joined Aug 7, 2020
7,008
I actually only know the switching frequency of the converter... So I guess the filtering design should be done after the measurement of the converter (without any filter) ?
The self resonance frequency of C1 would be close to the switching frequency (330kHz). I didn't check for the others, is it important for L and C2 ? Should it be the same ?
It's very important, above its self resonant frequency, a capacitor is no use as a capacitor, it looks more like an inductor.
Above its self-resonant frequency, and inductor looks capacitive. That means that the self-resonant frequency is of much more importance than the value of capacitance, because above that frequency all your calculations are pretty much useless.

#### MisterBill2

Joined Jan 23, 2018
14,244
IMHO the pi filter is a poor choice for this application. A cascade of a common mode choke and a differential mode choke would be superior.
I agree that a PI section filter may not be the best choice for blocking noise transmission via the power input. Consider that many RF transmitters use a PI section filter to couple efficiently to an antenna. In this application efficient coupling is not the goal. So providing a maximum impedance to the ripple frequency will be the best choice. Of course I also understand that the cost of any inductor increases as the inductance increases. So there is always a trade off.
so one question is about the common side: Is the input negative common with the output negative? If so, then a common-mode choke is not applicable, as I see it.
Looking at the proposed circuit, it appears that the return side is indeed common with the load return side, so that a common mode choke is not applicable for this one.
My choice would be a second inductance at the noise generating end of the filter, because blocking a signal is less demanding than shunting it to common.

#### kaindub

Joined Oct 28, 2019
114
So whats the problem you are trying to solve?
Did you just read some random internet post saying PI filters are required?
usually SMPS are designed to meet either some standard (so the product can be certified) or there is a system requirement (ie its going into a submarine) With both cases there will be criteria that the conducted emissions have to meet.
When you know the standard you have to meet, you then start a selection and design of an appropriate filter.
If this is just a home project then dont waist your time with a filter.
There are no emission police out there!

#### Dagoni

Joined Jan 6, 2023
8
My choice would be a second inductance at the noise generating end of the filter, because blocking a signal is less demanding than shunting it to common.
Thank you, do you have in mind a schematic like that (Multiple Filter Sections) Input Filter Design for Switching Power Supplies (ti.com) ? Though they take a value of L/4 and I don't know why. And it's placed at the input of the filter.

#### Dagoni

Joined Jan 6, 2023
8
So whats the problem you are trying to solve?
Did you just read some random internet post saying PI filters are required?
usually SMPS are designed to meet either some standard (so the product can be certified) or there is a system requirement (ie its going into a submarine) With both cases there will be criteria that the conducted emissions have to meet.
When you know the standard you have to meet, you then start a selection and design of an appropriate filter.
If this is just a home project then dont waist your time with a filter.
There are no emission police out there!
It's for a board that didn't pass the conductive voltage emissions (certification). I didn't have the result of the test but as I understand the filter should be designed from there, thanks.

#### MisterBill2

Joined Jan 23, 2018
14,244
OK, so now we know that the supply failed to pass a test by not meeting some specification. Those results should provide the information about what band of frequencies need to be blocked, and how much more blocking is required.
For any design effort, it is always handy to know the requirements.
If there is a specific frequency that is the problem, then an additional series inductance at the noise source end of the filter, so as to produce a series-resonant circuit shunting the noise source, could be very effective.
Does the assembly even have any power supply input filter at all??

We do not even know what sort of load it is, and that does matter.

#### Dagoni

Joined Jan 6, 2023
8
If there is a specific frequency that is the problem, then an additional series inductance at the noise source end of the filter, so as to produce a series-resonant circuit shunting the noise source, could be very effective.
Does the assembly even have any power supply input filter at all??

We do not even know what sort of load it is, and that does matter.
So this series inductor would form a RL low-pass filter with the load of the converter, is that right ? And the inductance could be selected when knowing the specific frequency with this equation : fc = (RL2 || RLoad)/2*pi*L2 ? I can't find what is the load (input load) of the converter (TEM3 2411N), could it be measured ?
Finally, the converter has a pi filter integrated (inside) but it was not enough apparently. The board has the footprint for the pi-filter but it was not implemented. I don't know for the power supply.

#### MisterBill2

Joined Jan 23, 2018
14,244
So this series inductor would form a RL low-pass filter with the load of the converter, is that right ? And the inductance could be selected when knowing the specific frequency with this equation : fc = (RL2 || RLoad)/2*pi*L2 ? I can't find what is the load (input load) of the converter (TEM3 2411N), could it be measured ?
Finally, the converter has a pi filter integrated (inside) but it was not enough apparently. The board has the footprint for the pi-filter but it was not implemented. I don't know for the power supply.
NO, the series inductance with the capacitor would form a series resonant circuit as a path for the dominant frequency to be bypassed before it gets to the next section of the filter.
But if the Pi section filter was not implemented then that is a better place to start. And now I am guessing that this is a product and not a hobby project.
and if it already has "a pi filter integrated (inside) " then we should know what that filter is, as well. And we know that since the product failed a conducted emissions test that there exists a standard that was not met. So what the limits are for various frequencies is something that we need to know. Creating a successful design without knowing the requirements is quite difficult.

#### Dagoni

Joined Jan 6, 2023
8
NO, the series inductance with the capacitor would form a series resonant circuit as a path for the dominant frequency to be bypassed before it gets to the next section of the filter.

and if it already has "a pi filter integrated (inside) " then we should know what that filter is, as well.
So L2 should be selected with the LC formula like the previous filter (C2-L1) (but here with C1) ? And how is the converter's input load involved ?
The converter is a component so the pi filter it is said to be inside is unknown unfortunately.

#### Papabravo

Joined Feb 24, 2006
19,850
So L2 should be selected with the LC formula like the previous filter (C2-L1) (but here with C1) ? And how is the converter's input load involved ?
The converter is a component so the pi filter it is said to be inside is unknown unfortunately.
The combination of DM and CM chokes does not care what is downstream. A considerable advantage in the these circumstances.

#### MisterBill2

Joined Jan 23, 2018
14,244
Wow, if that converter is "a product", does that mean that the noise that is escaping on it's power input feed is unknown? In this case we have power flowing in and noise flowing out, so tghere can be confusion about upstream and downstream directions.
And how is it that the details of the emissions test failure are not known?? Normally test failure results are used to determine what corrections need to be made.
So I am taking back my suggestion for a series resonant bypass because the required information is evidently withheld.
At this point I can comment that practical considerations include cost, and that as current increases so does inductive reactance cost increase.