Elliptic Filter Algorithms for LP Coefficients

[Tzimtzum]

I have used Darlington's Algorithm for generating the Poles and Zeros for Elliptic Filters. Nonetheless, obtaining the LP coefficients from Poles and Zeros for Elliptic filters is another matter entirely. Zverev has a numerical example for N=3 for K²=1 and K²=∞. But to date, this is the only example in the literature (at least, the literature which I have available) that discusses how LP coefficients are determined for filters such as these (many others seem to take the "Then, a miracle occurs," approach). I've looked through Zverev, Murdock, Daniels, Kuo, Saal, and some others, to no avail. True, I could use charts or a filter design program but neither takes me where I want to go--specifically, I want to understand what's under the hood--after working as a EE for 30 years (and now retired), I've been often forced in my working years on account of deadlines to use the cookbook approach to design--we all have; but I should add that I never considered it an elegant road to travel; still, it often was instrumental for getting the job done (so I am not knocking it). I should also add that were I to know the method being used (brute force pole removal by synthetic division or something more elegant) it would be quite helpful. I no longer have access to Matlab. But as I mentioned above, I want to understand the process rather than just arrive at an answer. Thanks in advance.

 

[LvW]

I am afraid that there is no other chance than to search for some original contributions from W. Cauer.
Good luck
LvW

 

[Tzimtzum]

I have copies of the early papers of Foster, Brune, and some others. I do not have, however, any copies of Cauer's. I guess it's off to the university library for me!
Thanks

 

[LvW]

This link leads you to an EDN article and some further references. Perhaps it helps.

**broken link removed**

 

[Tzimtzum]

Thanks, I'll check it out.

 

[Tzimtzum]

Checked out the EDN article. It appears to be more of a sensitivity analysis approach in the design of filters--comparing Elliptic to Chebshev. Good piece however; but not what I'm looking for. Thanks for considering it in any case.

What I did last night was something which I should have done from the beginning. I reviewed my old Van Valkenberg Network Synthesis text (which has multiple years of accumulated dust from non use) as well as Kuo's; took out my Zverev; and between these texts, started to work the problem backwards for the simplest configuration (N=3). Though my approach is not elegant, I believe that it will get me where I want to go. Also, I reviewed Van Valkenberg's Circuit Theory: Foundations and Classical Contributions which also is very helpful.

When I believe that I have arrived, I'll describe my approach here. Of course, one always must acknowledge the possibility of failure, and if I reach a brick wall, I will also post this information here.
Thanks

 

[JoannesPaulus]

I believe you might enjoy T.C. Fry's "The use of continued fractions in the design of electrical networks" a 1929 paper... but I might have misunderstood your request.

 

[Tzimtzum]

I looked at Saal and Ulbrich's paper from the Sep 1958 IRE Transactions today. They have every thing I want detailed in their work. They use the word "tedious" in decribing the necessary calculations. And after looking at their work, a more appropriate adjective might fit, such as "squirly" (never knew if this was a real word or an imaginary one--still, it has a nice ring to it since it is "lightly damped"[just kidding]). Unlike Zverev, S and U include the way in which their tables were calculated--and in detail. Zverev for the most part leaves this step out--I suppose he felt it was not necessary since his book was really meant as more of a design guide rather than a theoretical treatise. So in any case, my search ended sooner than I thought it would. I suppose in matters such as these, I should consider it the exception rather than the rule. By the way, I will look up Fry's paper. I'm not sure if I have it--I might somewhere around here--but the partial fraction expansion approach seems to be made for this type of study.
Thanks again!

 

[Tzimtzum]

One final word on the matter. The December 1958 edition of the IRE Proceedings on Circuit Theory is a treasure house of filter design information (and other subjects too) for anyone wanting more than a cookbook approach on the subject. I was fortunate enough to find a bound copy of all the 1958 through 1959 transactions. The information contained within these pages is quite phenomenal (true, just about every later book or article on filter design quotes someone or something from it but the reader would be so much more enriched if he/she would read the actual paper itself. Moreover, Cauer's writings--as one of the previous posters indicates--is quite a repository of information. Though written in German, if one has a good handle on mathematics (and fortunately, I do), the language is not that much of a barrier. I've found the 1954 edition of his Theorie der linearen Wechselstromschaltungen as well as the postumously published 1960 second volume (containing notes from his later work) and purchased both.
Thanks again to all who commented.