IEEE Circuits and Systems Magazine - Q4 2022 - 62

Pioneers in CAS
Wilhelm Cauer
W
ilhelm Cauer belonged to a very respected
family in the German capital of Berlin. His
father was a professor railway engineering at
the Technical University of Berlin and several other family
members were scientists or artists. Cauer's research
interests were initially focused on theoretical physics,
but with his contributions to the mathematical foundations
of filter synthesis he became one of the founders
of the new engineering discipline of network theory. Unfortunately,
Cauer was killed in Berlin in the last days of
World War II and therefore did not witness the later success
of insertion loss filter design which is associated
with his name, as well as with Edward Norton, G. Cocci,
Hans Piloty and Sidney Darlington.
Wilhelm Cauer was born on June 24, 1900 in Berlin.
His early high school was the Kaiserin-Augusta-Gymnasium
in Cauerstrasse, founded by his great-grandfather
Ludwig Cauer. From 1919 he studied electrical engineering
at the TH Berlin. After his preliminary exams, he
studied mathematics and physics at the universities of
Bonn and Berlin and completed his diploma studies in
1924 at the TH Berlin in the subject of " Technical Physics " .
Cauer then moved to Mix & Genest, a Berlin-based
company involved in the development of telephone and
telegraph equipment, and began publishing articles in
the field. However, he was probably inspired to work
on the design of electrical filters, which play a key role
in carrier-frequency telephone systems. Cauer realized
that filter design can be treated as an inverse problem,
as it was already known in mechanics, and after leaving
Mix & Genest due to lack of work, he went to Georg
Hamel at the Institute for Applied Mathematics and
Mechanics at TH Berlin. Cauer's estate contains an exchange
of letters with Ronald M. Foster from 1926, which
shows that he followed up on Foster's seminal publication
" A reactance theorem " from 1924, which quickly inspired
Wilhelm Cauer to begin his research of network
synthesis filters which put the design of filters on a firm
mathematical footing. He was awarded a doctorate degree
for his thesis " Die Verwirklichung von Wechselstromwiderständen
vorgeschriebener Frequenzabhängigkeit "
(The realization of impedances of specified
Digital Object Identifier 10.1109/MCAS.2022.3214584
Date of current version: 13 January 2023
62
IEEE CIRCUITS AND SYSTEMS MAGAZINE
frequency dependence) in July 1926 [1]. This work was
later considered to be the beginning of modern network
synthesis, meaning synthesis in the sense of chemistry
as inverse analysis. In electrical network theory, synthesis
was first used in Otto Brune's dissertation instead of
realization, it being Cauer " who suggested the subject
of this research " (Brune's acknowledgement). In 1927,
Cauer became a research assistant at Richard Courant's
Institute of Mathematics at the University of Göttingen.
In 1928, Cauer submitted his habilitation thesis " Untersuchungen
über ein Problem, das drei positiv definite
quadratische Formen mit Streckenkomplexen in Beziehung
setzt " (On a problem where three positive definite
quadratic forms are related to one-dimensional complexes)
[2]. Among other things, he showed that the external
behavior characterized by an impedance Z is an
invariant function of this triple of quadratic forms and
a set of real affine transformations which became the
starting point for further group theoretical studies on
electrical networks.
It quickly became clear that the realization of filter
circuits involved lengthy mathematical calculations,
and soon Cauer came up with the idea of constructing
an electronic calculator for linear equations with 10 variables
to support the filter design. He then contacted several
calculator experts around 1927-28 and this put him
in touch with Vannevar Bush of MIT in Boston who, along
with Richard Courant, helped him get a scholarship by
the Rockefeller Foundation. In September 1930 he sailed
from Bremen to New York with his wife Karoline, and arrived
10 days later. Before they travelled to Boston, Cauer
first visited Otto Julius Zobel and Ronald M. Foster at
Bell Laboratories. At MIT, Cauer presented several lectures
and met colleagues such as Norbert Wiener and
Ernst Guillemin, visited Oswald Veblen, Eberhard Hopf
and Jacob David Tamarkin at Harvard University, and
visited also the General Electric's laboratories in Schenectady,
New York. One of the most important contributions
of Cauer's visit to MIT was suggesting the topic of
Otto Brune for his doctoral research, which became one
of the most important findings in filter design theory. In
his acknowledgements of his thesis, Brune wrote that
he " is also indebted to Dr. W. Cauer of the University of
Göttingen, who is at present in Cambridge, Massachusetts
as an International Research Fellow supported by
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