Filter specifications, conversion between them

[cubeleg]

In filters usually you can find two different specifications: number of poles and dB/octave.
I know that the poles gives you the transfer functions using this equation for a low pass filter
$$H(f)=1/\sqrt{1+(f/f_{C})^{2P}}$$
Where P is the number of poles of the filter. But how can I translate this into the dB/octave. I suppose that there is a rule of thumb but I cannot find it. Can anybody indicate to me this rule or give a reference where I could find it?
Thanks in advance

 

[berkeman]

You can derive it or reason it out. For a single pole lowpass filter, calculate the gain at some frequency that is a couple octaves above the cutoff freq. Then double the frequency -- what does the gain do? The gain is _____ with frequency when you're above the cutoff frequency...

 

[cubeleg]

Ok, thanks for the answer. I have done like that and seems that 6 correspond with 1 pole, 12 with 2 poles, beyond that I haven't obtained any correlations.

 

[berkeman]

Ok, thanks for the answer. I have done like that and seems that 6 correspond with 1 pole, 12 with 2 poles, beyond that I haven't obtained any correlations.

Correct. For one LPF pole, every time you double the frequency, you get half the amplitude. For two poles, you get one quarter the amplitude, etc.

 

[dsprao]

Interesting, berk, i guess this is invoking another question, is the radius of pole shows some similar relation with the magnitude response?