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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 |
On Sun, 22 Feb 2004 22:34:02 GMT, "Peter O. Brackett"
wrote: [snip] 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. [snip] 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.] [snip] Gawwwwd! You list makes me feel really old. Not only do I recognize all your references, I knew "Ernie" personally... but I had Harry B. Lee as my instructor, since I was in VI-B. ...Jim Thompson -- | James E.Thompson, P.E. | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona Voice:(480)460-2350 | | | E-mail Address at Website Fax:(480)460-2142 | Brass Rat | | http://www.analog-innovations.com | 1962 | I love to cook with wine. Sometimes I even put it in the food. |
Jim:
[snip] Gawwwwd! You list makes me feel really old. Not only do I recognize all your references, I knew "Ernie" personally... but I had Harry B. Lee as my instructor, since I was in VI-B. ...Jim Thompson [snip] Heh, heh... No one could "splain" driving point synthesis like "Ernie". But... Time moves on... Y. W. Lee, I have met, Harry B. Lee? I never had the pleasure. Best Regards, -- Peter K1PO Consultant - Signal Processing and Analog Electronics Indialantic By-the-Sea, FL. "Jim Thompson" wrote in message ... On Sun, 22 Feb 2004 22:34:02 GMT, "Peter O. Brackett" wrote: [snip] 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. [snip] 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.] [snip] -- | James E.Thompson, P.E. | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona Voice:(480)460-2350 | | | E-mail Address at Website Fax:(480)460-2142 | Brass Rat | | http://www.analog-innovations.com | 1962 | I love to cook with wine. Sometimes I even put it in the food. |
On Sun, 22 Feb 2004 23:55:08 GMT, "Peter O. Brackett"
wrote: Jim: [snip] Y. W. Lee, I have met, Harry B. Lee? I never had the pleasure. Think War of Independence, this guy was a descendent of "Light-Horse" Harry Lee ;-) Harry B. Lee was, IMNSHO, better than Ernie. Everything Ernie did was 1H, 1F and 1 ohm... Harry was a realist, and I still have my notes... I don't think anyone could have taught nodal and loop analysis better; which is why I attack IC design in that fashion. ...Jim Thompson -- | James E.Thompson, P.E. | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona Voice:(480)460-2350 | | | E-mail Address at Website Fax:(480)460-2142 | Brass Rat | | http://www.analog-innovations.com | 1962 | I love to cook with wine. Sometimes I even put it in the food. |
Jim:
[snip] Harry B. Lee was, IMNSHO, better than Ernie. Everything Ernie did was 1H, 1F and 1 ohm... [snip] And of course... "pliers" and "soldering iron"... [snip] Harry was a realist, and I still have my notes... [snip] As I said, I never had the pleasure, but I'm sure he was a grea teacher... [snip] I don't think anyone could have taught nodal and loop analysis better; which is why I attack IC design in that fashion. [snip] Hmmm... how about the "Method of False Assumption"? :-) -- Peter |
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