What is the transfer function of this filter? Does this filter have a name?

 

Originally posted by paultwang@Apr 1 2006, 09:55 PM
What is the transfer function of this filter? Does this filter have a name?

[post=15713]Quoted post[/post]​

It is called a pi-filter because it has a vague resemblance to the greek letter pi.
Depending on the transfer function and the location of the poles it may have other characteristics. I would expect it to have a lowpass characteristic.

 

Originally posted by paultwang@Apr 1 2006, 08:55 PM
What is the transfer function of this filter? Does this filter have a name?

[post=15713]Quoted post[/post]​

Greeting paultwang,

See attached PDF for the results of my analysis of your pi-network.

I took great pains to micro-step through the derivation to insure that the movement from equation n to n+1 was clear.

Hopefully someone will vet my effort and let me know if I missed the mark.

hgmjr

 

Originally posted by hgmjr@Apr 7 2006, 05:50 AM
Here is the results of my analysis of your pi-network.

[post=15936]Quoted post[/post]​

Thank you so much. I didn't expect it to become this complicated.

 

Originally posted by paultwang@Apr 7 2006, 09:48 AM
Thank you so much. I didn't expect it to become this complicated.

[post=15945]Quoted post[/post]​

You are very welcome.

Transfer function calculations can be challenging but this one was was fairly manageable. It probably appears more complicated than it is because I tried not to take too large a leap between the intermediate equations so as not to throw the reader off.

I was hoping someone would check my results to make sure that I did not drop a stitch in one of the many equations that I used to show my work.

hgmjr

 

Plotted using your equation.

 

I like it. Great Job......

The plot looks just as I expected. It is a third order low pass filter just as papabravo had stated at the outset.

The plot shows the -6 dB attenuation that you would expect when the two resistors are set equal.

Can you expand the plot to show the slope at the point it takes a dive?

hgmjr

 

Couldn't upload png files.. Forum glitch.. blank page. Worked around.

 

hgmjr,

Here's a plot from 1k to 1M,

 

Drew straight lines and found the corner frequency:



Mathematically solved the -3dB and -6dB frequencies:

 

check following:

fcutoff = 1/ (2*pi*sqrt(C*(L/2)))
damping factor varies with input/output resistance.

Electromagnetic compatibility handbook

By Kenneth L. Kaiser