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Simultaneous canonic synthesis of two dual impedances
Author(s) -
Belevitch V.
Publication year - 1975
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490030310
Subject(s) - lossless compression , reciprocal , realization (probability) , cascade , transformer , electrical impedance , mathematics , topology (electrical circuits) , port (circuit theory) , ideal (ethics) , control theory (sociology) , physics , computer science , combinatorics , electrical engineering , algorithm , engineering , voltage , quantum mechanics , philosophy , linguistics , statistics , control (management) , chemical engineering , artificial intelligence , epistemology , data compression
It is proved that two dual passive impedances Z and R 2 / Z (R real constant) each of degree m are simultaneously realizable by a lossless reciprocal 4‐port of degree 2 m closed on two constant resistances. Moreover, the lossless reciprocal 4‐port is itself realizable as a cascade of such 4‐ports of degrees 2 and 4. These are extensions of the Bott–Duffin and Fialkow‐Gerst bridges but generally contain ideal transformers. As in Fialkow‐Gerst synthesis, the only algebraic equation to be solved is Z(p) + Z(–p) = 0 but, in contrast with Fialkow‐Gerst, the realization is minimal.