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词条 Otto Brune
释义

  1. Works

  2. Background

  3. Notes

  4. References

{{Use dmy dates|date=November 2013}}{{Use South African English|date=November 2013}}Otto Walter Heinrich Oscar Brune (10 January 1901 – 1982) undertook some key investigations into network synthesis at the Massachusetts Institute of Technology (MIT) where he graduated in 1929[1] while working for General Electric USA{{Citation needed|date=March 2019}}. His doctoral thesis was supervised by Wilhelm Cauer and Ernst Guillemin),[1] who ascribed to Brune the laying of "the mathematical foundation for modern realization theory".[2]

Works

In 1933, Brune was working on his doctoral thesis entitled, Synthesis of Passive Networks and Cauer suggested that he provide a proof of the necessary and sufficient conditions for the realisability of multi-port impedances. Cauer himself had found a necessary condition but had failed to prove it to be sufficient. The goal for researchers then was "to remove the restrictions implicit in the Foster-Cauer realisations and find conditions on Z equivalent to realisability by a network composed of arbitrary interconnections of positive-valued R, C and L."[3] There was a race to solve the problem and Brune won it.

Brune coined the term "positive-real" (PR) for that class of analytic functions that are realisable as an electrical network using passive components.[4] He did not only introduce the mathematical characterization of this function in one complex variable but also demonstrated "the necessity and sufficiency for the realization of driving point functions of lumped, linear, finite, passive, time-invariant and bilateral network.[5] Brune also showed that if the case is limited to scalar PR functions then there was no other theoretical reason that required ideal transformers in the realisation (transformers limit the practical usefulness of the theory), but was unable to show (as others later did) that transformers can always be avoided. The eponymous "Brune cycle" continued fractions were invented by Brune to facilitate this proof.[6]

The so-called Brune theorem is:

a. The impedance Z(s) of any electric network composed of passive components is positive real.
b. If Z(s) is positive real it is realisable by a network having as components passive (positive) R, C, L as well as ideal transformers T.[3]
Brune is also responsible for the Brune test for determining the permissibility of interconnecting two-port networks. For his work, Brune is recognized as one of those who laid the foundation of network analysis by means of mathematics. For instance, American computer scientist Ernst Guillemin dedicated his book Synthesis of Passive Network to Brune, describing him with these words: "In my opinion the one primarily responsible for establishing a very broad and mathematically rigorous basis for realization theory generally was Otto Brune."[7]

Background

Brune was born in Kimberley, South Africa in 1901 and returned there in 1935.[8] He became Principal Research Officer at the National Research Laboratories, Pretoria.[9] Brune was married to Grace Brune, they had one child, Jennifer Brune (Grosskopf).{{Cn|date=March 2019}}

Notes

1. ^Karl L. Wildes, Nilo A. Lindgren, A century of electrical engineering and computer science at MIT, 1882-1982, p157, MIT Press 1985 {{ISBN|0-262-23119-0}}.
2. ^{{Cite book|title=A Century of Electrical Engineering and Computer Science at MIT, 1882-1982|last=Wildes|first=Karl L.|last2=Lindgren|first2=Nilo A.|date=1986|publisher=MIT Press|isbn=9780262231190|location=Cambridge, MA|pages=157|language=en}}
3. ^1 {{Cite book|title=Perspectives in Mathematical System Theory, Control, and Signal Processing|last=Willems|first=Jan|last2=Hara|first2=Shinji|last3=Ohta|first3=Yoshito|last4=Fujioka|first4=Hisaya|publisher=Springer|year=2010|isbn=9783540939177|location=Berlin|pages=6}}
4. ^Brune, 1931
5. ^{{Cite book|title=Multidimensional Signals, Circuits and Systems|last=Galkowski|first=Krzysztof|last2=Wood|first2=Jeff David|date=2004-02-03|publisher=Taylor & Francis|year=2001|isbn=0415253632|location=London|pages=5-6|language=en}}
6. ^Cauer et al., pp 7–8
7. ^{{Cite book|title=The Fuzzification of Systems: The Genesis of Fuzzy Set Theory and its Initial Applications - Developments up to the 1970s|last=Seising|first=Rudolf|publisher=Springer|year=2007|isbn=9783540717942|location=Berlin|pages=28}}
8. ^1 Seising, p19
9. ^Wai-Kai Chen, Active Filters: Theory and Implementation, p. 23, Wiley, 1986 {{ISBN|047182352X}}.

References

{{refbegin}}
  • E. Cauer, W. Mathis, and R. Pauli, "Life and Work of Wilhelm Cauer (1900–1945)", Proceedings of the Fourteenth International Symposium of Mathematical Theory of Networks and Systems (MTNS2000), Perpignan, June, 2000. Retrieved online 19 September 2008.
  • O. Brune, "Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency", Doctoral thesis, MIT, 1931. Retrieved online 22 March 2010.
  • O. Brune, "Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency", MIT Journal of Mathematics and Physics, vol 10, pp 191–236, 1931.
  • O. Brune, "Equivalent Electrical Networks", Phys. Rev., vol 38, pp 1783–1783, 1931.
  • Seising, Rudolf, Die Fuzzifizierung der Systeme, Franz Steiner Verlag, 2005
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4 : South African mathematicians|1901 births|1982 deaths|20th-century South African mathematicians
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