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"Diego Stutzer" in m...
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,..)? What you are asking about is a form of what's traditionally called the network synthesis problem (creating a network of components to realize a prescribed signal response) and specifically the synthesis of a one-port, or impedance. At one time (when phone companies ruled the earth and computers had conquered few signals and DSP was reserved for BIG things like the US Perimeter Acquisition Radar at Concrete, North Dakota -- affectionately the "PAR"), this was a popular subject in engineering schools at the advanced-undergrad or graduate level. It is still extremely important sometimes, especially with the sophisticated signal processing used today on continuous-time signals in consumer products. A host of applied-mathematical techniques (Foster and Cauer synthesis, Brune's impedance-synthesis lemma, etc.) apply even to one-ports. Some of them are highly counterintuitive. Not, in other words, a subject perfectly matched to the contraints of brief advice on newsgroups. (Note also that Butterworth and Chebyshev approximants are mathematical methods to approach one group of curves out of things that naturally give you a different type of characteristic -- "Butterworth and Chebyshev" have nothing to do with specific circuit topologies or components). If you want to pursue it further I could suggest investigating "network synthesis." Temes and LaPatra had a reasonable modern (1970s) book about it. Karl Willy Wagner started it all in 1915 by inventing filters. Richard Clark suggested also investigating the small op-amp "biquad" networks for designable frequency response (actually you can turn them into one-ports, the so-called shunt-filter class, but again a bit of a subject for a brief response). Note that technically a "bi-quad" is any network giving a biquadratic transfer function (2nd-order numerator and denominator) though in RC-active filters it's often applied to the closely related Ã…kerberg-Mossberg and Tow-Thomas configurations. For practical info see van Valkenberg's excellent general introductory book on filters from the 1980s. For an accessible modern example of these small op-amp-based "biquad" networks, look up the LTC1562 from Linear Technology, a commercial chip with four trimmed "biquad" networks, programmable by outboard components for applications from a few kHz to a few hundred kHz. |