Diego:
You cannot do *exactly* what you propose, but you can get arbitrarily
close to it.
The "closeness" being a function of the cost you are prepared to pay.
The closer you want to get to the desired function [curve] of impedance
versus
frequency, the more the cost [cost = total number of R-L-C elements in the
design].
Basically what you are trying to doe is very well known in the network
synthesis
literature as driving point impedance [DPI] synthesis. [e.g. Darlington's
method and other similar techniques. Darlngton's technique approaches
the problem of DPI as the synthesis of a lossless two port terminated
in an appropriate single resistance.]
Network synthesis was widely researched, studied and taught back in the
1940 - 1970 era but... today it is seldom seen, used, or taught. There are
however lots of older textbooks which cover this field in great depth.
I'll post a few such references here below for your reference.
Before you can actually perform the DPI synthesis you will first have to
find an appropriate rational polynomial function, to form the basis for your
synthesis, which approximates the impedance function [curve] you desire to
match. To obtain such a rational polynomial you will have to solve an
appropriate approximation problem.
Approximation theory and the techniques for doing this with rational
polynomial
are a whole 'nother problem, and other than a few simple graphical straight
line
segment tricks, will usually require the use of a computer with an
appropriate
algorithm, such as Remez second method, which you may have to write
yourself!
Unless you can find consultant to help you... :-)
Check out the following classic texts on network synthesis for a complete
run down on what you need to do to accomplish your objective:
1.) Ernst A. Guillemin, "Synthesis of Passive Networks", John Wiley & Sons,
NY, 1957. [LC# 57-8886. On technical library shelves at LCShelf
Call # TK3226.G84. See Chapters 3, 4, 9, 10 which cover the DPI synthesis
in detail, and Chapter 14 which covers the approximation problem.]
2.) Norman Balabanian, "Network Syntheis" Prentice-Hall, Englewood
Cliffs, NJ 1958. [LC# 58-11650. On technical library shelves at LCC
Shelf Call # TK3226.B26. See Chapters 2 & 3 for DPI and Chapter
9 for the approximation problem.]
3.) Louis Weinberg, "Network Analysis and Synthesis", McGraw-Hill,
New York, 1962. [LC# 61-16969. On technical library shelves at
LC Shelf Call # TK3226.W395. See Chapter's 9 & 10 for DPI
synthesis and Chapter 11 for the approximation problem]
One does not have to realize such designs with purely passive RLC
networks and, in appropriate frequency ranges, they can often be
synthesized with active RC networks [R, C and Op-Amps] by
appropriate transformations of the passive synthesis results.
See for instance...
4.) Adel S. Sedra and Peter O. Brackett, "Filter Theory and Design:
Active and Passive", Matrix Publishers, Portland, OR, 1978. [LC #
76-39745. On technical library shelves at LCC Shelf Call #
TK7872.F5S42.]
Also, and I have done this myself a couple of times for special low
frequency
applications, one can match the analog driving point impedance through
an appropriate Op-Amp reflectometer circuit to a combination analog
to digital A/D and digital to analog converter D/A and perform/emulate
the DPI synthesis in real time using digital signal procssing [DSP]
techniques. Basically to use the A/D - D/A digital technique to emulate
the desired DPI you will have to solve the same synthesis and approximation
problems mentioned above but under a suitable *warping* of the real
frequency
axis.
Hope that all helps... and good luck
:-)
--
Peter K1PO
Consultant - Signal Processing and Analog Electronics
Indialantic By-the-Sea, FL
"Diego Stutzer" wrote in message
om...
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,..)?
Simply increasing C does not really help, because this equals a factoring
of
the frequency.
Increasing R does not help as well, as it seems.
I hope one of you cracks can help me out.
So far, thanks for reading.
Diego Stutzer
"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,..)?
Simply increasing C does not really help, because this equals a factoring
of
the frequency.
Increasing R does not help as well, as it seems.
I hope one of you cracks can help me out.
So far, thanks for reading.
Diego Stutzer
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