# Pi-Filter for EMC

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First let's define what a "Pi filter" is:

The name comes from the inductor and two caps forming the shape of the Greek letter Π.

These filters are used for EMC compliance because they attenuate high frequencies. At minimum there is a L-C filter, which attenuates by 12 dB/octave above the rolloff frequency.

The special point of a Pi filter is that they work both ways. The power line would typically be on one side, and a device that consumes power on the other. For EMC compliance, the high frequencies caused by the device are attenuated before getting dumped onto the power line. In the other direction, it protect the device from nasty high frequencies that might be on the power line for whatever reason.

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What would be the main considerations to use Pi-filters for EMC?

**Using the filter correctly and understanding its limitations**

EMC or EMI (electromagnetic interference) is noted for its high frequency energy content. Applying a $\pi$ filter like the one below can significantly attenuate those unwanted high frequencies: -

The regulations dealing with EMC and EMI are largely interested in the prevention (or significant reduction) of high frequencies and the $\pi$ filter achieves this because it is a low-pass filter; it allows low frequencies to pass unhindered (such as AC mains power voltages and current) but attenuates the higher frequencies progressively.

However, to use a $\pi$ filter on it's own or connected to a load that has high impedance is asking for trouble because, at the resonant point of the circuit, it can seriously amplify interference: -

As you can see, if the loading is too light, the resonance of the inductor with load-side capacitor causes significant problems.

What would be the main considerations to use Pi-filters for EMC?

How you use and load the $\pi$ filter is certainly one main consideration.

**Inductor self-resonance**

Another consideration is where the attenuating slope of the filter's response begins. The one above begins at this frequency: -

$$F_C = \dfrac{1}{2\pi\sqrt{LC}} = \text{734 kHz}$$

Ideally, you would want $F_C$ to be as low as possible but there are constraints on how low you can go. For instance, to drop from 734 kHz to 73.4 kHz requires that L1 increases to 47 uH and C2 increases to 100 nF. This is a potential cost and size constraint placed on any "volume-product". To get an inductor of 47 uH also comes with another hidden cost and that is self resonance.

In the examples below I've constrained the load resistance to be fixed at 20 ohms for reasons of simplicity. In other words, I don't want to overload the images with too many responses because it might confuse things.

Initially I've considered the self-resonant frequency of a practical inductor. This self-resonance is due to internal parasitic capacitance. So, if I make L1 into 47 uH and added 100 pF of parasitic capacitance, I would get this AC response: -

The parasitic (aka self) resonance of the inductor occurs at just over 2 MHz and although this is produces impressive attenuation (a big "notch") there is a down-side.

With L1 at 47 uH and C2 at 100 nF, the point where $F_C$ occurs is now at 73.4 kHz but, from about 3 MHz, we get no deeper attenuation. We are still getting 60 dB attenuation above 3 MHz but, sometimes, we need more.

What would be the main considerations to use Pi-filters for EMC?

Inductor self-resonance is certainly a consideration

**Capacitor self-resonance**

There is also self-resonance for capacitor C2 to consider. Capacitors are usually at least an order of magnitude better than inductors for filter applications but, they are still prone to problems and can resonate with leakage inductance significantly: -

Hopefully you can see that just a few nano henries of self inductance for C2 makes a big potential problem around 20 MHz or 30 MHz and, above 100 MHz we might as well not have this $\pi$ filter at all. You realistically can't rely on a $\pi$ filter to deliver the goods across more than 2 decades of spectrum.

What would be the main considerations to use Pi-filters for EMC?

Capacitor self-resonance is certainly a consideration

In other words, we can only go so far with the physical realities of a single $\pi$ filter stage. We may, in some awkward designs, need to use two cascaded $\pi$ filters and apply a broadband assault on interference. We may need to do a lot more.

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