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- W2063138220 abstract "It is a classical result, known as Darlington's theorem, that every rational positive-real function z(p) is realizable as the input impedance of a lumped reciprocal reactance two-port tuner Nt closed at the far end on 1 Ω. The theorem is evidently false if the 1 Ω termination is replaced by some prescribed non-constant positive-real impedance z1(p) . Any z(p) synthesizable in this more restrictive manner is said to be compatible with z1(p) and we write z∼z1 to indicate the correspondence. The determination of necessary and sufficient conditions for the validity of z∼z1 is the problem of compatible impedances. Of the four better-known network treatments, only that of Schoeffler IRE Trans. Circuit Theory, CT-8, 131–137 (1961) is completely correct, although severely restricted in scope. In particular, the remaining three contain a common error which appears to have propagated because a constraint on the ratio of even parts ze(p)/z1e(p) derived by Schoeffler is unnecessary if z(p) is not minimum-reactance. The main theorems of Wohlers (IEEE Trans. Circuit Theory, CT-12, 528–535 (1965)) and Satyanaryana and Chen (J. Franklin Inst., 309, 267–280 (1980)) are very similar in structure to our Theorem 3 but considerably more complex and do not provide a sufficiently explicit description of the associated tuner Nt. In fact (Theorem 1), with the exception of a physically irrelevant degeneracy (which is easily detected), Nt, when it exists, must possess an impedance matrix Z(p). Moreover, the latter can be effectively parametrized in terms of z(p), z1(p) and a regular-allpass b(p) found as the solution of a standard interpolation problem of the Nevalinna–Pick type. Three fully worked examples clarify the theory and also illustrate many of the numerical steps. © 1997 by John Wiley & Sons, Ltd." @default.
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- W2063138220 date "1997-11-01" @default.
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- W2063138220 title "A new study of the problem of compatible impedances" @default.
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- W2063138220 doi "https://doi.org/10.1002/(sici)1097-007x(199711/12)25:6<541::aid-cta974>3.0.co;2-w" @default.
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