Pro c. 16th Eur. Meeting on Cyb ernetics and Systems Research EMCSR, Vienna, April 2 { 5, 2002,
vol. 2, pp. 934-939 = Cyb ernetics and Systems, R. Trappl, ed., Austrian So c. for Cyb ernetics Studies.
The Scienti c Work of Wilhelm Cauer and its Key Position at the
Transition from Electrical Telegraph Techniques to
Linear Systems Theory
Rainer Pauli
Munich UniversityofTechnology
D { 80290 Munich
Germany
email: [email protected]
Abstract together with their mutual relations which are de ned
by the frequency-indep endent holonomic constraints
The pap er sketches a line of historical con-
imp osed byinterconnection rules. Therefore, network
tinuity ranging from telegraph pioneers and
theory ab initio was set up as a purely mathemati-
early submarine cable technology of the 19th
cal discipline. Most notably, under the standard as-
century to some asp ects of mo dern systems
sumptions of linearity and time-invariance, the the-
and control theory. Sp ecial emphasis is laid
ory of passive networks is equivalent to the theory of
on the intermediary role of the scienti c work
dissipative mechanical systems that p erform small os-
of Wilhelm Cauer 1900-1945 on the synthe-
cillations around a stable equilibrium. Esp ecially in
sis of linear networks.
[ ]
his early pap ers on network synthesis Cauer, 1926 ,
[ ]
Cauer, 1931b Cauer's mathematical starting p ointis
this relation to classical analytical mechanics. Nev-
1 Intro duction
ertheless, it is fair to recall that the motivation and
While it is almost commonplace that mo dern metho ds
detailed structure of the problem was rmly ro oted
of data compaction, co ding and encryption in to day's
in electrical telegraph techniques of the 19th century,
communications all have their ro ots in the techniques
esp ecially in submarine cable transmission problems;
[ ]
of the telegraph pioneers Beauchamp, 2001 , analo-
[ ] [ ] [
see Belevitch, 1962 , Darlington, 1984 and Wunsch,
gous facts concerning the evolution of classical net-
]
1985 . In order to keep the numb er of citations un-
work and systems theory seem to fall into oblivion.
der control, we refer the reader to these references for
This is partly due to the dichotomy of the historical
more details ab out the historical asp ects sketched in
ro ots of mo dern system and control theory into ana-
the subsequent section.
lytical mechanics and into classical network theory in
the style of Bo de, Cauer, Darlington, Foster, Youla,
2 Before Network Synthesis
and many others combined with a widespread un-
2.1 Electrical Telegraph Techniques in
willingness to lo ok b eyond the b orders of one's own
the 19th Century
eld of research. Additionally, in recent decades there
has b een a dramatic decline of knowledge ab out clas- Although network analysis has emerged as a near-
sical network theory that has resulted in the expulsion mathematical discipline in the mid of the 19th century,
of the basic academic and educational asp ects of net- the development of submarine telegraph cables had a
work mo dels from electrical engineering curricula and very imp ortant in uence on the progress of network
a progressive fading out of network theory as an inde- theory, the main reasons b eing i the extremely com-
[ ]
p endent scienti c discipline Rohrer, 1990 . plicated dynamical b ehavior of transmission cables as
Long b efore the advent of general electromagnetic compared to the ubiquitous RLC -circuits of mo dest
theory rst formulated in 1873 by Maxwell in his complexity and ii the b oiling hot economic interest
celebrated Treatise the theory of electrical networks in the advancement of electrical telegraph technology
emerged as an indep endent discipline with original | comparable only to the Internet euphoria of to day.
concepts and metho ds. These rst achievements were For a vivid p opular account on the remarkable paral-
Ohm's law 1827, Kirchhoff's laws 1845 and the lels in the history of the electrical telegraph and the
p ertaining top ological rules 1847, as well as the revolution in communications due to the Internet, see
[ ]
sup erp osition principle and the so-called Thevenin- Standage, 1998 though from a decidedly american
equivalent circuits credited to Helmholtz 1853. viewp oint.
Typically,aphysical device such as a resistor made of The rst working electrical telegraph had b een con-
metallic wire or carb on is considered a black box de- structed in 1833 by Gau and Weber in Gottingen
ned by a linear relation v = Ri between the external using de ected needle technology, followed in 1837 by
electrical variables v and i . This abstraction turned Steinheil's recording telegraph in Munichaswell as
the analysis of realistic physical devices into the study by similar exp eriments in the same year by Wheat-
of sets or \systems" of well-de ned idealized ob jects stone in England and Morse in the USA. The rst
protagonists Breisig, Campbell, Franke, Haus- cable to cross the English Channel was laid in 1851,
rath, Kennelly, Strecker, to mention just a few. so on followed by the rst deep-sea cable b etween Sar-
Many new circuits and devices such as arti cial lines, dinia and Tunisia in 1854. When the celebrated
attenuators, hybrid coils, balancing networks, T - and transatlantic cable connecting Europ e and America
-equivalent circuits for two-p orts, lters, and allpass went on-line in 1858 misconceptions and the lackof
lattice sections and equalizers were designed. electrical mo dels for understanding transmission line
op eration p osed serious practical diculties due to an
At the same time complex calculus vulgarized in
excessive spread of transmitted pulses. Telegraph en-
electrical p ower engineering by Steinmetz b ecame
gineering at that time was crude empiricism. Not even
ubiquitous; rational functions and p oles and zeros
Ohm's law had found its way to many of the early ex-
gradually entered into engineering pap ers and the no-
p erimentalists.
tion of a multip ort and its various matrix descriptions
emerged. LaCour 1903 seems to have b een the
Various steps towards network mo delling of trans-
rst to write down the equations for a symmetric two-
mission lines had b een undertaken by Lord Kelvin
p ort in chain matrix form that is also the solution to
since 1855, but his mo dels were not well suited to ex-
eqn.1
plain most of the practical diculties. After Bell's
" invention of the \sp eaking telegraph" in 1876 pre-
cosh g Z sinh g
ceeded ab out 15 years by Reis these de ciencies b e-
U U
1 2
= ; 2
1
sinh g cosh g came even more evident when engineers tried to trans-
I I
1 2
Z
mit sp eech signals over long aerial or mo dest subma-
rine distances. In the early 1880's there were ab out
while the general black box concept of a two-p ort was
150 000 kilometers of submarine telegraph cables op er-
formulated by Breisig in 1921. Campbell and Fos-
ating byhookorby cro ok when Heaviside prop osed
ter established the theory of the ideal transformer as
his celebrated analysis of transmission lines in terms
a new network element and gave a complete enumera-
of his telegraphist's equations
tion of all realizations of lossless four-p orts comp osed
[ ]
of ideal transformers Campb ell, 1937, pp. 119-168 .
@i @u
The rst breakthrough towards a systematic syn-
= Ri + L ;
@x @t
thesis of lters was achieved in 1924 by Foster in his
@i @u
[ ]
pap er Areactance theorem Foster, 1924 . The im-