John Jardine wrote:
Diego Stutzer wrote in message
m...
Hi,
Every one knows, that e.g. a simple RC-parallel circuit has a
frequency-dependent impedance-characteristic (Absolute Value) - the
impedance (Abs) raises as the Frequency approaches zero. As a
formula: Zin = 1/(1/R + i w C) , where i ist the imaginary number
and w the frequency.

Now the hard part. How does one create an Impedance, which decreases
"slower", for frequencies close to zero but then decreases "faster"
for higher frequencies, than the simple parallel RC-Circuit?
Is there some kind of procedure like the one for syntesizeing
LC-Filters (Butterworth, Chebychev,..)?


You need to graph out the required frequency-impedance slope then
approximate the required roll off rates using a segmented breakpoint
scheme consisting of a number of CR series sections in parallel.
Essentially it's a straight line approximation to the required Z-F
curve. The CR's adding zeroes as the frequency goes up.

Estimating the individual time constants can be irksome as each has
effect outside it's area of interest. Use a 'least-squares
approximation' to obtain a best curve fit for the number of sections
involved.

It's an interesting subject but I've come across nothing out there
that's of use.

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created by Andy´s ASCII-Circuit v1.24.140803 Beta www.tech-chat.de
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This does exactly what you want, in the beginning the slope is less than
3dB/oct. and at 10kHz it goes to 6dB/oct.
This is how to produce a pink noise that rolls off faster at the end of
range, or to make some weighted filters (dBA) etc.

ciao Ban