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Wilhelm Cauer His Life and the Reception of his Work

Wolfgang Mathis* and Emil Cauer** *Electromagnetic Theory Group University of Hannover ** Hofstätten-Dhaun

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Content

1. Cauer’s Problem of Network Synthesis

2. Life of Wilhelm Cauer

3. Cauer’s Projects

4. Reception of Cauer’s Work 5. Conclusions

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1. Cauer’s Problem of Network Synthesis

After the first world war: Electrical filter circuits : FDMA was a focus problem in Electrical Engineering

(e.g. lack of telephone copper cables)

Modulator Demod./Filter

frequency

frequency

frequency

frequency

frequency frequency

Filter design approach (before 1926): network analysis and suitable choice

In Cauer’s dissertation (1926) a new filter design theory was presented: network synthesis based on prescribed filter properties

The first systematic design concept in electrical engineering

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Modernelectrical circuits and ICs

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Lieben vacuum tube

Meissner, 1913

F. Pichler’s presentation

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Circuit

Modeling

Network Model

Electrical Networks = Models of Electrical Circuits

Partitioning b

b

Network Analysis:

Network Properties

Inverse Problem:Network Synthesis

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b

b

Mathematical Description of Elektrical Networks:

1 1,..., ; ,.( , ..) : ,( )bb

bbi ii uu u Z := R R

Space of Currents and Voltages

O

( , ) ( , ) 0, : ;b b b b kR Ri u F i u F k b O := R R R R R

Description of resistive NW-Elements: Ohmian Space

K

Description of Connections: Kirchhoff Space

( , ) 0 0, ( , ) exaktb bi u Ai B u A B K := R R

Basics of Network Analysis

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KO

S :=K OState spaceof networks

Remark: O must be not smooth

S

Dynamic network elements (capacitors and inductors) generate a flow on

A geometric picture of networks:

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Filter synthesis process:(Cauer, 1928)

• Approximation

• Equivalence

• RealizationLCR filters

R. Pauli’s presentation

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2. Life of Wilhelm Cauer

Minna Cauer

Wilhelm Cauer (born June 24, 1900)was a son of a distinguished Berlin family:

• his father was a professor at the TH Berlin-Charlottenburg(railway engineering)

• his first grammar school was founded by his grandfather• Minna Cauer was engaged in women’s liberation movement• since many generations had been academically trained• many sculptors in the Cauer family

Sundial at the Cauer basic school, Berlin- Charlottenburg, fall 1997

Wilhelm Cauer’s education:

• matura at June 30, 1917• eastern 1918 Cauer started at the

TH Berlin-Charlottenburg• first examination (‘Vorprüfung’)

at Mai 12, 1919• he studied theoretical physics and

mathematics at the Universities of Berlin and Bonn (summer 1921)

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• February 2, 1923: Cauer started with his dissertation in physics under his supervisor Prof. Max von Laue (C. met him in 1922)

• theme: Relativity theory • first paper on relativity theory in “Physikalische Zeitschrift”• difficulties with von Laue, Cauer left the University of Berlin

and changed to the TH Berlin-Charlottenburg

• assistant of Prof. Reißner• his first examination was accepted

(in essential)• March 24, 1924: Diploma in “Technical Physics” • August 1, 1924 - November 1925:

Mix & Genest Company• Cauer married Karoline Cauer (a relative of Wilhelm)• Cauer became the first research assistant of Prof. G. Hamel

Max von Laue

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Around 1924 Cauer got knowledge about Foster’s Theorem for LC circuits(maybe at Mix & Genest: then a branch of Bell Telephone Company)

Telephone conversations between Foster and Darlington in 1983

Cauer’s famous dissertation (July 7, 1926): “The Realization of Impedances of Specified Frequency Dependence” Referent: G. Hamel, Koreferent: K.W. Wagner

V. Belevitch (1962): The starting point of systematic design of one-ports (see R. Pauli’s presentation)

• Cauer had difficulties with his Habilitation thesis at the TH Berlin-Charlottenburg(thesis is ready at the beginning of 1928)

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• Cauer contacted (June-July 1927, July 1928) Courant (Univ. Göttingen), Ossanna (TH München), V. Bush (MIT), C.L. Hull (Univ. Wisconsin), A. Matthies (TH Berlin) with respect to “Computing Machines capable to solve systems of linear equations“

• Suggestion of R. Courant (with respect to Cauer’s Habilitation thesis):“Changing to the University of Göttingen”(he changed at April 1, 1928 to Göttingen)

• Cauer became (in April 1928) research assistant in Courant’s Mathematical Institute

• Cauer presented his first lectures in Göttingen

• Cauer presented his Habilitation thesis in Göttingen (June 1928): “Studies of a problem that related 3 positive definite quadratic forms with an algebraic complex”

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Cauer’s visit in USA 1930/31 (11 months)

• February 10, 1930: Rockefeller Foundation an Courant: visit accepted: 200$ for Cauer

• February 10, 1930: Letter to V. Bush• March 19, 1930: Letter from the Rockefeller Foundation to Cauer: Details of the visit• July 2, 1930: Letter from V. Bush: scientific details of Cauer’s visit• February 18, 1931: V. Bush asked Baily (Univ. Michigan) for lectures of

Cauer (answer April 13, 1931)• Februar 18, 1931: Wiener asked Hillebrand for lectures of Cauer• March 13, 1931: Veblen invited Cauer to a talk at Havard;

met E. Hopf and Tamarkin• May 5, 1931 (in a letter to Courant): met Campbell, Zobel, Foster (N.Y.)

and V. Bush, Guillemin, Wiener and Brune at MIT• June 29, 1931: Departure of Cauer’s wife Karoline; Cauer worked at

“Wired Radio Company” • August 26, 1931: Departure with ‘Europa’ (letter to Courant) • August 31, 1931: Arrival in Southhampton (with ‘Europa’)

and to Germany with the ‘Berlin’ at September 5, 1931

February 10, 1930 July 2, 1930 March 13, 1931 June 29, 1931 September 5, 1931

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Cauer’s search for an Employment

• February 9, 1932: Walther to Cauer “no professorship in Darmstadt”

• Summer 1934: professorship at a university impossible (ministry)

• August 6, 1934: Philips (Eindhoven) (rejected by van der Pol; Aug. 11)• August 31, 1934: Siemens “directors have no interests w.r.t. a cooperation”• September 28, 1934: asked K.W. Wagner for employment

at the “Reichspostzentralamt”• Oktober 27, 1934: Telefunken rejected his application• March 6, 1935: “Deutsche Versuchsanstalt für Luftfahrt” rejected his application• April 11, 1935: Telefunken rejected his application• April 16, 1935: Henschel aircraft rejected his application• April 29, 1935: Junkers aircraft rejected his application• March 20, 1935: Cauer visited Donnier (Friedrichshafen)• May 7, 1935: Donnier aircraft rejected his application • July 19, 1935: Cauer was employed at Fieseler aircraft company

• 1936-1945: Cauer became a director of a laboratory at Mix & Genest

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Cauer’s Calculation Machine:• September 7, 1928: Cauer received the receipt for a patent

“Device for Solving Systems of linear Equations”• September 22, 1928: Cauer should apply for support from the

“Notgemeinschaft” (Hamel, Rothe)• Contacts to Engineer Hamann (Berlin-Babelsberg)• Cauer in USA (1930/31)• June-July: Applied for

3500.- DM from the “Notgemeinschaft”

• Received 1346,35 RM for the “Notgemeinschaft”

• Final paper in 1935

(see paper of H. Petzold,Deutsches Museum)

3. Cauer’s Projects

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Cauer’s “Siebschaltungen”: (finished during his USA visit)

• In a letter from January 28, 1930 to Barlett: Mrs. Dr. Mary Taylor helped with numerical calculations

• March 1930: Glowatzki (Rostock) was able to calculate for Cauer• June 18, 1930: Cauer received 2000.- RM from the “Elektrotechnischer

Verein” for the “Siebschaltungen”• February 14, 1931: Cauer in a letter to the VDI Publisher

“no honorary but 25 instead of 15 free copies”• June 21, 1931: Glowatzki to Cauer (Newark): “Siebschaltungen” not ready• December 2, 1931: Letter from E.A. Guillemin

“... Had occasion to study more thoroughly your publication‘Siebschaltungen’ and (I) am delighted with your method to to attack on this problem. ... Your method is the first whichelegantly solves this very important problem.”“... I find that the mathematical methods involved in the Tschebyscheff approximation processes are in general too involved for the average student mind.”“... I in no wish to take from you any of the credit which will be coming to you for having contributed this new design process.”

(in his 1953 article Guillemin didn’t mentioned the name of Cauer!)

E.A. Guillemin

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Cauer’s “Wechselstromschaltungen”:

• January 4, 1934: Cauer asked the president of the University of Göttingen for a sabbatical semester

“reason: he will write a book”• December 18, 1935: Cauer presented his book to the Teubner-Publisher• January 10, 1936: Cauer presented his book to the Springer-Publisher• July 15, 1938: Teubner-Publisher rejected the book project• November 12, 1939: Cauer presented his book to the Akademische

Verlagsgesellschaft • February 1, 1940: Cauer accepted the contract with the Akademische

Verlagsgesellschaft • April 21, 1940: Akademische Verlagsgesellschaft informed about the end

of the press• 1941: “Theorie der Wechselstromschaltungen” was available• 1942/43 and 1945: The 2. Volume was destroyed

• Positive Buchbesprechungen (1942): Hameister, Piloty

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4. Reception of Cauer’s WorkWe have to distinguish (before the 2nd World War)

Germany Foreign Countries(e.g. USA, France, Great Britain)

personalcontacts

• Wiener (since 1927 & 1930/31)• V. Bush (1930/31)• Campbell (1930/31)• Foster (1930/31) • Bode (1930/31?)• Darlington (1930/31, last letter 1939)• Guillemin (1930/31)• Veblen (1930/31)• Tamarkin (1930/31)• Bailey (1931)• Bartlett (1931)• Julia (1932)• van der Pol (1934)?• Belevitch (1940)

personalcontacts

Mathematicians:• Courant (1927)? • Schur (1928)• Pick (1929) • Herglotz (1928-1944)• Caratheodory (1928)

60 pages paper (193132)

70 pages paper (1935)

Electrical Engineers:• Hamel (1925)• Busch (1931)• Wagner (1925) • Piloty (1932)?• Küpfmüller (1932)? • Barkhausen (1934)• Jaumann/Siemens (1932)• Feldtkeller*

contacts

S. Darlington

(*didn’t mentioned Cauer’s work in his review articles in “Die Physik”)

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Cauer with colleagues at the Mathematiker Konferenz in Zürich (1932)

Feldtkeller: didn’t mentioned Cauer’s work in his review articles in “Die Physik”

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5. Conclusions

• Cauer was a pioneer in the area of systematic systems design

• Cauer published fundamental results in this area

• Cauer never got a professorship (for several reasons)

• Therefore: Cauer worked for Mix & Genest (1936-1944)(during the 2nd World War on arming arrangements)

• Finally Cauer died during the last days of war in Berlinat April 22, 1945 together with the manuscript of volume 2 of his “Wechselstromschaltungen”)

• After the 2nd World War many people forgot Cauer’s achievements (which are essential for systems synthesis processes in general)

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Cauer was educated as physicist, had a Habilitation in mathematics,and worked in electrical engineering

but he was “too involved in applied sciences”for mathematicians,

and another that his contributions “include too much mathematics” for electrical engineers

and eventually he worked in a time with dangerous aspects

1921 1944