# I want to calculate the cut off frequency and bandwidth of the following circuit. I need it for EMI/EMC testing

I want to calculate the bandwidth and cut off frequency of this circuit for the following inputs:

Supply - 230VAC, 50Hz.

Components used

22E resistor is 5W,
0.1UF is box type.
470mH inductor.

I tried the pi filter calculation, but it seems like it is not applicable here. I failed for this circuit in EMI test from 200 kHz to 2 MHz range.

• Two voltage divider in series - what is the problem? Find the transfer function and compare it with the standard form (using pole data).
– LvW
Commented Oct 20, 2022 at 10:35
• Use a simulator. They are free and most EEs use them now. Commented Oct 20, 2022 at 10:41
• @LvW will you share the example? Or similar to this link Commented Oct 20, 2022 at 12:09
• Show inductor datasheet. Commented Oct 20, 2022 at 17:05
• @BhushanWaghe milli Henry? Commented Nov 11, 2022 at 12:27

You can derive the transfer function of this 3rd-order network using the fast analytical circuits techniques or FACTs as described in my book on the subject. The principle consists of finding the time constants of the circuits when the energy-storing elements are placed in specific states: an open-circuit or a short circuit for a capacitor respectively in dc and high-frequency states. The opposite for an inductor. You then chop the circuit in several intermediate diagrams as shown below:

You obtain a 3rd-oder denominator and you can try to rearrange it in case you want to show some dominant poles and build an approximate expression:

I have then derived a brute-force expression but also captured the circuit in SIMetrix that I imported into Mathcad. All plots are identical:

Here, I have considered the stimulus on the left side and the response acquired across the right-side 100-nF capacitor. If this is an EMI filter, you may want to derive the TF differently, by considering a voltage source affected by a certain output impedance (it would be the noise generated across the bulk capacitor for instance) driving capacitor $$\C_2\$$ and generating a current flowing through $$\R_1\$$. It will slightly change the TF but the principle to reveal it remains similar to what I've shown.

Additional Edit - 22nd of October

I had a little bit of time to add another part to the original answer. As I said, if you plan on using this filter with a switching converter (ac-dc or dc-dc), then the transfer function must be considered in the other direction where the noise source is placed across capacitor $$\C_2\$$ in your drawing and the output voltage is collected across the 50-ohm resistance of the line impedance stabilization network or LISN. I actually looked into this and published an article in EDN in 1997 (the PDF with the pictures is here, from my webpage). The principle is as below:

The converter produces a specific noise signature which depends on its operating mode and the power it delivers. From this signature, you extract the fundamental value (analytically of via simulation and FFT) which will now feed the filter via the filtering capacitor's ESR. This is $$\r_C\$$ of the front-end bulk capacitor in an ac-dc converter for instance. The exercise now consists of finding the transfer function linking the voltage collected across the LISN (usually expressed in dBµV) to the injected current which represents the fundamental of your signature current. The filter will then have to be computed so that enough attenuation at the fundamental is provided to meet the considered CISPR specifications. This is another story however.

Same principle as before, turn the excitation off and determine all the time constants of the circuit:

Assemble all these time constants and compare the expression with the ugly brute-force approach:

The transfer complicates a little bit but nothing insurmountable for the FACTs. I have also run a simulation with SIMetrix and did import the data in Mathcad to check for the integrity:

As a summary, designing an EMI filter first requires to know the value of the noise source fundamental value then the attenuation needed to size the filter, for instance, 55 dB at 150 kHz. You then determine your filter with this response in mind using the transfer function that I derived. In the end, keep in mind that each element constitutive of the filter hosts parasitics which will considerably degrade the final expression. It is then interesting to individually characterize these elements and see how they will affect the response. Once theoretical values are determined, you can use the simulator and compare the response between the original design and the one hosting the parasitics.

• Hi! I´m having some troubles designing a PI filter for EMI rejection, if the frequency of the line is 50hz, my low pass filter cutoff frequency has to be around 60hz? For that, it will be a 220mH choke and two 100uF capacitors? What type of capacitor should I use? Thank you Commented Feb 29 at 14:38
• Hello, if this is a front-end EMI filter for a switching converter, you need to attenuate the frequencies from 150 kHz to 30 MHz for conducted noise. Check the response I gave on SE here which corresponds perhaps to what you need. Commented Feb 29 at 17:10
• Thanks for your answer! I checked it! I´m not sure if that is what I need. Because I´m trying to reject noise from a SCR switching AC voltage ( 50hz, phase control ). My input is a power transformer 220Vac To 10Vac ( the same transformer that SCR is switching, but another secondary winding ), around 150mA peak. When I was searching, the filter that was according to all I said, was a low pass filter ( Pi ). Do you think that's gonna be more easy to make a separate power transformer? Or it´s reliable to make a EMI filter, and use the same transformer? Commented Feb 29 at 20:51