# 2nd Order Pi Filter Cutoff Frequency Calculation

#### engineergc

Joined Oct 21, 2016
5
Dear All;
I will use 2nd order pi filter in my design. But I can not find any information about how I can calculate cut off frequency of 2nd order p filter? Could you help me please?

#### Bordodynov

Joined May 20, 2015
3,025
See

#### MrChips

Joined Oct 2, 2009
27,702
What you have shown using CLC is a 3rd-order filter.
Use CRC for a 2nd-order pi filter.

#### engineergc

Joined Oct 21, 2016
5
I will use CLC filter but I want to add 2 CLC filter as cascade.

#### Bordodynov

Joined May 20, 2015
3,025
See

#### Bordodynov

Joined May 20, 2015
3,025
What you have shown using CLC is a 3rd-order filter.
Use CRC for a 2nd-order pi filter.
I agree with you. I forgot about the impedance of the source of the signal. With a zero resistance of the signal source, a second order filter is obtained.

#### engineergc

Joined Oct 21, 2016
5
Hi Bordodynov,
Thank you for your interest. But I can not understand how you write formula that I attached to post this formula and how you calculated values of capacitor and inductor? ı know f=1/(2*pi*R*C) but I can not understand that formula? Could you explain me? Thank you.

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#### Bordodynov

Joined May 20, 2015
3,025
R=50
For a matched filter:
R=|Zc|=|ZL|
|ZL|=2*pi*Freq*L
|Zc|=1/(2*pi*Freq*C)

Last edited:

#### engineergc

Joined Oct 21, 2016
5
I calculated value of inductors and capacitors by using online calculators and document that I attached to post. I want to obtain 17 kHz cut off frequency. According to document and online calculator value of capacitors and inductor are given below. Since I have restriction in component heights in my PCB, I used these values L1 and L2 4.7uH, C1 and C3 4.7uF and C2 is 22 uF. According to these values I am getting 17Khz cut off frequency in LTSpice. According to document values that I used in LTSpice is not correct, but I get correct cut offf frequency. If cut off freqeuncy of filter depends on formulas how I can get correct cut off freqeuncy in LTSpice with wrong component values? Regards.

*I am using Butterworth Filter.

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#### MrAl

Joined Jun 17, 2014
9,633
Hello there,

I dont know where you are getting this "2nd Order" thing from, but when you use two inductors and three capacitors you could have a filter order as high as fifth. In fact, even with two caps and one inductor you could have as high as a third order filter.

I think what you mean is a "2 stage" filter where you connect two stages together to form one filter. That is very different from a "2nd order" filter which could be just one cap and one inductor for example.

If you draw a schematic that would clear this up, as usual. Once we have that we can double check that you have the right values for what you need.

#### MrAl

Joined Jun 17, 2014
9,633
Hello again,

In addition to the above, what load and source impedances are you using? This changes the response by a huge amount and in other ways too that demand knowing these two values.

For example, with the input source set to 50 ohms and output load set to 50 ohms (typical) i get the following -3db points (all in Hertz):
202.7817965718546
33542.24217255076
34223.46261723706
40191.2114262766
40669.65007693585

As you can see from the above, we have one lone point near 200Hz that represents a low pass response, then we have two pairs that represent two bandpass responses, one near 34KHz and one near 40.3KHz.

If we had lower R values however we would get a low pass response up near 20KHz, which is very, very different.

So you need to specify the source and load impedances too or else there is no one single answer.

Also, did you maybe mean 2.2uf for C2 instead of 22uf?