# pole of a low-pass filter

Discussion in 'General Electronics Chat' started by anik321, May 4, 2009.

1. ### anik321 Thread Starter Member

Oct 25, 2008
22
0
In a simple RC low pass filter, the simplified transfer function comes out to:

1/(1+jwRC)

Solving for the root in the denominator, we see a pole exists at S=j/RC

This is also the w3db point where the magnitude of the transfer function starts falling.

Question: How is the w3db point also a pole? When you are making the bode plot, why does the magnitude not blow up at this point?

2. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,397
355
Since s = jω, the pole is at s = -1/RC, not j/RC.

The Bode plot is along the positive imaginary axis, so you don't pass through the pole, which is on the negative real axis.

3. ### anik321 Thread Starter Member

Oct 25, 2008
22
0
Electrician, thank you for the quick response. But i dont think I still understand

How is the bode plot along the positive imaginary axis (specially the magnitude plot)? The 3db point (and all other values on the magnitude plot) is an observable physical quantity - how can it be along the imaginary axis?

I feel as though my fundamental understanding may not be correct.

4. ### steveb Senior Member

Jul 3, 2008
2,433
469
The Fourier Transform is a special case of the Laplace Transform with $s=j\;\omega$. The bode plot is just a representation of the Magnitude and Phase of the Fourier Transform.

5. ### StayatHomeElectronics AAC Fanatic!

Sep 25, 2008
1,022
70
The magnitude does not blow up because the denominator is not going to zero at that point. The three db point is determined by w(3db) = 1/RC. Substitute that back into the equation and you get

1/(1+jw/w(3db))

To get the magnitude plot, you need to take the magnitude of the complex number.

So, at w = w(3db), the denominator is not zero.

6. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,397
355
A Bode plot is simply the magnitude of the transfer function as the jω variable is allowed to vary from some low frequency to some higher frequency.

A typical pole-zero plot is on the complex plane, and the jω axis is vertical. Your pole is on the left horizontal (negative real) axis, and the jω variable never encounters the pole. If your pole were complex with a zero real part, then your plot would have a singularity, but that's not what you have.

The so-called rubber sheet model may help your intuitive understanding.

See these for further information.

http://www.edaboard.com/ftopic108513.html

http://www.electronics-related.com/usenet/basics/show/35473-1.php