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Belevitch's Theorem
Belevitch's theorem is a theorem in electrical network analysis due to the Russo-Belgian mathematician Vitold Belevitch (1921–1999). The theorem provides a test for a given S-matrix to determine whether or not it can be constructed as a lossless rational two-port network. Lossless implies that the network contains only inductances and capacitances – no resistances. Rational (meaning the driving point impedance ''Z''(''p'') is a rational function of ''p'') implies that the network consists solely of discrete elements (inductors and capacitors only – no distributed elements). The theorem For a given S-matrix \mathbf S(p) of degree d; : \mathbf S(p) = \begin s_ & s_ \\ s_ & s_ \end :where, :''p'' is the complex frequency variable and may be replaced by i \omega in the case of steady state sine wave A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vitold Belevitch
Vitold Belevitch (2 March 1921 – 26 December 1999) was a Belgian mathematician and electrical engineer of Russian origin who produced some important work in the field of electrical network theory. Born to parents fleeing the Bolsheviks, he settled in Belgium where he worked on early computer construction projects. Belevitch is responsible for a number of circuit theorems and introduced the now well-known scattering parameters. Belevitch had an interest in languages and found a mathematical derivation of Zipf's law. He also published on machine languages. Another field of interest was transmission lines, where he published on line coupling. He worked on telephone conferencing and introduced the mathematical construct of the conference matrix. Early life Belevitch was born 2 March 1921 in Terijoki, Karelia, now incorporated into Russia, but at the time part of Finland. Belevitch's parents were Russian and his mother was an ethnic Pole. They were attempting to flee fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
