Wilhelm Cauer | |
|---|---|
 | |
| Born | (1900-06-24)24 June 1900 |
| Died | 22 April 1945(1945-04-22) (aged 44) Berlin-Marienfelde, Germany |
| Nationality | German |
| Alma mater | Technische Universität Berlin |
| Scientific career | |
| Fields | Mathematics |
| Doctoral advisor | Georg Hamel |
| Doctoral students | Vitold Belevitch |
Wilhelm Cauer (24 June 1900 – 22 April 1945[1]) was a Germanmathematician andscientist. He is most noted for his work on the analysis and synthesis of electricalfilters and his work marked the beginning of the field ofnetwork synthesis. Prior to his work, electronic filter design used techniques which accurately predicted filter behaviour only under unrealistic conditions. This required a certain amount of experience on the part of the designer to choose suitablesections to include in the design. Cauer placed the field on a firmmathematical footing, providing tools that could produce exact solutions to a given specification for the design of an electronic filter.
Cauer initially specialised ingeneral relativity but soon switched toelectrical engineering. His work for a German subsidiary of theBell Telephone Company brought him into contact with leading American engineers in the field of filters. This proved useful when Cauer was unable to feed his children during theGerman economic crisis of the 1920s and he moved to theUS. He studied early computer techniques in the US prior to returning to Germany. According to Wilhelm Cauer's son Emil the rise ofNazism in Germany stifled Cauer's career[2] because he had a remoteJewish ancestor. Cauer was murdered during thefall of Berlin bySoviet soldiers.
The manuscripts for some of Cauer's most important unpublished works were destroyed duringthe war. However, his family succeeded in reconstructing much of this from his notes and volume II ofTheorie der linearen Wechselstromschaltungen was published after his death. Cauer's legacy continues today, with network synthesis being the method of choice for network design.
Wilhelm Adolf Eduard Cauer was born inBerlin, Germany, on 24 June 1900. He came from a long line of academics. His early grammar school (gymnasium) was theKaiserin Augusta Gymnasium, an institution founded by his great-grandfather, Ludwig Cauer. This school was located on Cauerstrasse, named after Ludwig, in theCharlottenburg district of Berlin.[3] The building still exists, but is now a primary school, the Ludwig Cauer Grundschule.[4] He later attended the Mommsen Gymnasium, Berlin. His father, also Wilhelm Cauer, was aPrivy Councillor and a professor of railway engineering at theTechnische Hochschule in Charlottenburg (nowTechnische Universität Berlin). Cauer became interested in mathematics at the age of thirteen and continued to demonstrate that he was academically inclined as he grew.[5]
Briefly, Cauer served in the German army in the final stages ofWorld War I. He married Karoline Cauer (a relation)[6] in 1925 and eventually fathered six children.[5][7]
Cauer started off in a field completely unrelated to filters; from 1922 he worked withMax von Laue ongeneral relativity, and his first publication (1923) was in this field. For reasons that are not clear, he changed his field after this toelectrical engineering. He graduated in applied physics in 1924 from theTechnische Hochschule in Charlottenburg (nowTechnische Universität Berlin).[5]
He then spent a period working forMix & Genest, a branch of theBell Telephone Company, applying probability theory to telephone switching. He also worked on timer relays. He had two telecommunications-related publications during this period on "Telephone switching systems" and "Losses of real inductors".[5]
The relationship of Mix & Genest with Bell gave Cauer an easy path to collaboration withAT&T's engineers atBell Labs in the US which must have been of enormous help when Cauer embarked on a study of filter design. Bell were at the forefront of filter design at this time with the likes ofGeorge Campbell in Boston andOtto Zobel in New York making major contributions.[8] However, it was withRonald M. Foster that Cauer had much correspondence and it was his work that Cauer recognised as being of such importance. His paper,A reactance theorem,[9] is a milestone in filter theory and inspired Cauer to generalise this approach into what has now become the field ofnetwork synthesis.[5]
In June 1926 Cauer presented his thesis paper,The realisation of impedances of specified frequency dependence[a], at the Institute of Applied Mathematics and Mechanics of the Technische Hochschule Charlottenburg.[5] This paper is the beginning of modern network synthesis.[10]
In 1927 Cauer went to work as a research assistant atRichard Courant's Institute of Mathematics at theUniversity of Göttingen. In 1928 he obtained hishabilitation and became an external university lecturer.[5]
Cauer found that he could not support his family during theeconomic crisis of the 1920s and in 1930 took his family to the USA where he had obtained a scholarship (aRockefeller fellowship) to study atMIT andHarvard University. He worked withVannevar Bush who was building machines for the solution of mathematical problems. Essentially, these were what we would now callanalogue computers: Cauer was interested in using them to solve linear systems to aid in filter designs. His work onFilter circuits[b] was completed in 1931 while still in the US.[5]
Cauer met, and had strong contacts with, many of the key researchers in the field of filter design at Bell Labs. These includedHendrik Bode,George Campbell,Sidney Darlington,Foster andOtto Zobel.[11]
For a short while, Cauer worked for theWired Radio Company in Newark, New Jersey but then returned to Göttingen with the intention of building a fast analogue computer there. However, he was unable to obtain funding due to the depression.[5]
Cauer seems to have got on very poorly with his German colleagues. According to Rainer Pauli, his correspondence with them was usually brief and business-like, rarely, if ever, discussing issues in depth. By contrast, his correspondence with his American and European acquaintances was warm, technically deep and often included personal family news and greetings.[12] This correspondence went beyond his American contacts and includedA.C. Bartlett of theGeneral Electric Company in Wembley,Roger Julia ofLignes Télégraphiques et Téléphoniques in Paris, mathematiciansGustav Herglotz,Georg Pick and Hungarian graph theoristDénes Kőnig.[11]
After leaving the Technical Institute for Mix & Genest, Cauer sought to become active in theVerband Deutscher Elektrotechniker (VDE, the German Electrical Engineers Society). He left the VDE, however, in 1942 after a serious falling out withWagner, previously his PhD supervisor and ally.[12]
In November 1933 Cauer signed theVow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State.
The rising force ofNazism became a major obstacle to Cauer's work from 1933 onwards. The anti-Jewish hysteria of the time forced many academics to leave their posts, including the director of the Mathematics Institute,Richard Courant. Although Cauer was not Jewish, it became known that he had a Jewish ancestor,Daniel Itzig, who had been a banker toFrederick II ofPrussia. While this revelation was not sufficient to have Cauer removed under therace laws, it stifled his future career. Thus he gained the title of professor but was never given a chair.[7]
By 1935 Cauer had three children whom he was finding increasingly difficult to support, which prompted him to return to industry. In 1936 he temporarily worked for the aircraft manufacturerFieseler at theirFi 156Storch works inKassel and then became director of the laboratory ofMix & Genest inBerlin. Nevertheless, he did continue to lecture at the Technische Hochschule Berlin from 1939.[7]
In 1941, the first volume of his main work,Theory of Linear AC Circuits was published.[e] The original manuscript to the second volume was destroyed as a result of the war. Although Cauer was able to reproduce this work, he was not able to publish it and it too was lost during the war. Some time after his death, however, his family arranged for the publication of some of his papers as the second volume,[f] based on surviving descriptions of the intended contents of volume II.[7]
After taking his children to stay with relatives inWitzenhausen (inHesse) to protect them from the expected fall of Berlin to the Russians, Cauer, against advice, returned to Berlin. His body was located after the end of the war in amass grave of victims of Russian executions. Cauer had been shot dead inBerlin-Marienfelde by Soviet soldiers[13] as a hostage.[1] Soviet intelligence was actively looking for scientists they could use in their own researches and Cauer was on their list of people to find but it would seem that this was unknown to his executioners.[7]
The major part of Cauer's legacy is his contribution to thenetwork synthesis ofpassive networks. He is considered the founder of the field and the publication of his principal work in English was enthusiastically greeted, even though this did not happen until seventeen years later (in 1958).[14][15] Prior to network synthesis, networks, especially filters, were designed using theimage impedance method. The accuracy of predictions of response from such designs depended on accurate impedance matching between sections. This could be achieved with sections entirely internal to the filter but it was not possible to perfectly match to the end terminations. For this reason, image filter designers incorporated end sections in their designs of a different form optimised for an improved match rather than filtering response. The choice of form of such sections was more a matter of designer experience than design calculation. Network synthesis entirely did away with the need for this. It directly predicted the response of the filter and included the terminations in the synthesis.[16]
Cauer treated network synthesis as being the inverse problem ofnetwork analysis. Whereas network analysis asks what is the response of a given network, network synthesis on the other hand asks what are the networks that can produce a given desired response. Cauer solved this problem by comparing electrical quantities and functions to their mechanical equivalents. Then, realising that they were completely analogous, applying the knownLagrangian mechanics to the problem.[17]
According to Cauer, there are three major tasks that network synthesis has to address. The first is the ability to determine whether a giventransfer function is realisable as an impedance network. The second is to find the canonical (minimal) forms of these functions and the relationships (transforms) between different forms representing the same transfer function. Finally, it is not, in general, possible to find an exact finite-element solution to an ideal transfer function - such as zero attenuation at all frequencies below a given cutoff frequency and infinite attenuation above. The third task is therefore to find approximation techniques for achieving the desired responses.[17]
Initially, the work revolved aroundone-port impedances. The transfer function between a voltage and a current amounting to the expression for the impedance itself. A useful network can be produced by breaking open a branch of the network and calling that the output.[10]
Cauer's work was initially ignored because his canonical forms made use of ideal transformers. This made his circuits of less practical use to engineers. However, it was soon realised that Cauer's Tchebyscheff approximation could just as easily be applied to the rather more usefulladder topology and ideal transformers could be dispensed with. From then on network synthesis began to supplant image design as the method of choice.[10]
Most of the above work is contained in Cauer's first[b] and second[e] monographs and is largely a treatment of one-ports. In his habilitation thesis[c] Cauer begins to extend this work by showing that a global canonical form cannot be found in the general case for three-element kind multiports (that is, networks containing all three R, L and C elements) for the generation of realisation solutions, as it can be for the two-element kind case.[23]
Cauer extended the work of Bartlett and Brune on geometrically symmetric2-ports to all symmetric 2-ports, that is 2-ports which are electrically symmetrical but not necessarily topologically symmetrical, finding a number of canonical circuits. He also studiedantimetric 2-ports. He also extendedFoster's theorem to 2-element LC n-ports (1931) and showed that all equivalent LC networks could be derived from each other[d] by linear transformations.[10]
