Orchid XP v8 wrote:
> Invisible wrote:
> 
>> A Chebyshev low-pass filter arranges poles in a semicircle. The 
>> resonance comes from deforming this circle to make it elliptical. As 
>> you do so, the poles get nearer to the line, and the "ripples" you see 
>> are actually the edges of the peak surrounding each pole. I'll draw 
>> you a graph if you like... ;-)
> 
> ...and what *is* the most advanced graphing tool known?
> 
> Yeah, that's right! ;-)
> 
> The first image shows a plot of the transfer function for a 3-pole 
> Butterworth filter. (I.e., a lowpass filter with 0% ripple.) You can't 
> see it terribly well from this angle, but those three mountain peaks 
> (poles) are arraned in a semicircle.
> 
> The second image is the same thing, but I've cut a slice through the 
> graph along the critical line to reveal the filter's frequency response 
> (red). As you can see, it's flat in the middle, and tapers down at 
> either side. (The X-axis is frequency, with 0 Hz in the middle and 
> negative/positive frequencies on each side.) Normally you'd look at the 
> s-domain the other way round, but in 3D you can't see the cut very well, 
> so I've rotated it.
> 
> The third image is the same as the second, except that I've made the 
> semicircle elliptical. (You can't see this very much with this camera 
> angle. Feel free to change it...) Notice how the frequency response now 
> has "ripples" - corresponding to the edges of the peaks.
> 
> The radius of the circle is the cutoff frequency, and the 
> ellipticallness is the ripple (and cutoff slope). The parts to fiddle 
> with are the lines that #define the R1-R3 and I1-I3 variables. Set the 
> radius of both equal for a Butterworth filter, and then decrease R# only 
> for Chebyshev.
> 

Gotta love POV-Ray for visualizing a surface. I'm guessing then what the 
Q parameter (to the resonant filter) then was adjust the elipticalness 
of the surface, then ...

-- 
~Mike

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