Abstract
The problem of classical electrical network synthesis (flourished between 1920-1970) is subjected to scientific critique. Conclusions: the first attacks on the problem were frustrated and eventually defeated by a naive over-reliance on engineering/physical intuition and shoving the mathematical issues whenever possible under the rug; now, by concentrating on essential mathematics, much of it known since the 19th century, research will be revived with spectacular prospects of scientific progress.
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References
Apéry, F., Jouanolou, J.-P.: Élimination: le cas d’une variable, Hermann (2006)
Bott, R., Duffin, R.J.: Impedance synthesis without use of transformers. J. Applied Physics 20, 816 (1940)
Brune, O.: Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency. J. of Mathematical Physics 10, 191–236 (1931)
Foster, R.M.: A reactance theorem. Bell System Technical J. 3, 259–267 (1924)
Foster, R.M.: Academic and theoretical aspects of circuit theory. Proceedings IRE 50, 866–871 (1962)
Freygang, W.H., Trautwein, W.: The structural implications of the linear electrical properties of cardiac Purkinje strands. J. General Physiology 55, 524–547 (1970)
Gel’fand, I.M., Kapranov, M.M., Zelevinsky, A.V.: Discriminants, Resultants and Multidimensional Determinants. Birkhäuser (1994)
Guillemin, E.A.: Synthesis of Passive Neworks. Wiley (1957)
Kalman, R.: Discovery and invention: the Newtonian revolution in systems technology. J. Guidance, Control, and Dynamics 26, 833–837 (2003)
Ladenheim, E.L.: A synthesis of biquadratic impedances, M.S. thesis, supervised by R. M. Foster, Polytechnic Institute of Brooklyn (May 1948)
Lipschitz, S.P.: On RIAA equalization networks. J. Audio Engineering Society 27, 458–491 (1979)
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Kalman, R. (2010). Old and New Directions of Research in System Theory. In: Willems, J.C., Hara, S., Ohta, Y., Fujioka, H. (eds) Perspectives in Mathematical System Theory, Control, and Signal Processing. Lecture Notes in Control and Information Sciences, vol 398. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93918-4_1
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DOI: https://doi.org/10.1007/978-3-540-93918-4_1
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