We determine the primary transmission parameters (capacitance and impedance per unit length) of a line consisting of a thin horizontal strip of finite or infinite width, and of a thin return wire situated above the centre ofthe strip. In the analysis of the lateral skinand proximity-effects, the cross-section ofthe strip offinite width is assumed to be a thin ellipse.

AbstractThe optimal double side‐band converter, a novel circuit briefly presented in a previous paper,' is a rectifier bridge operating between selective terminations and containing an infinite number of resonant circuits. the circuit performance was justified by considering a finite number of resonant circuits and then letting that number become infinite. This limit process was erroneously handled, and is now corrected, so that the results for the infinite circuit (which were correct) are rigorously validated.

AbstractIt is proved that an n‐port composed of ideal transformers, gyrators and ideal rectifiers has a unique solution for the port variables when it is excited by generators in series with strictly positive resistances. the multiplicity of solutions for the internal variables is discussed. Connections are established with the theory of linear inequalities and with the coloured branch theorem of graph theory.

AbstractThe Brune and Darlington syntheses for one‐ports have been extended to n‐ports by several authors. the synthesis algorithms are well established and are not discussed in this paper, which is essentially concerned with the minimal realizations (in the total number of elements, including ideal transformers) of the 2n‐ports occurring as building‐blocks in the synthesis. A unified view of that subject is presented, including many new results and a critical survey of the literature. an appendix dealing with the contragradient reduction of a pair of rectangular matrices is of independent algebraic interest.

Minor criticisms, improvements and additions are brought to the passivity conditions discussed by Kuh and Rohrer [1].

The anti-sidetone telephone circuit is a frequency-independent passive reciprocal 3-port whose scattering matrix between three prescribed resistive terminations (transmitter, receiver, line) meets a certain specification. In their 1920 paper, Campbell and Foster (CF) showed that the prescribed 3-port can be realized as a lossless 4-port consisting in two 3-winding transformers closed on one resistance (the balancing network). If one (two) relations are imposed between the terminating resistances of the 4-port, realizations involving a single 3-winding (2-winding) transformer are available, and the resulting 136 (38) distinct realizations have been listed by CF. In this paper, we reestablish the CF-results (which were stated almost without proof in their paper and have never been rediscussed in the literature) and present a genetic classification of their 136 + 38 circuits. Recently, a realization of the anti-sidetone 3-port containing more than one internal resistance (in addition to the balancing network, a light-emitting diode serves to illuminate the dial) has been described by D. R. Means; in this paper, we present a complete characterization of that wider class of circuits.

The classical treatment of the Laplace equation by separation of variables in toroidal coordinates is used to obtain analytical expressions and numerical results for the solution of various electrostatic problems pertaining to a perfectly conducting torus: charged torus in freespace, torus in a uniform axial or transverse electric field. Two quasi-stationary electromagnetic problems for a perfectly conducting torus are also solved: (i) current resulting from a uniform alternating potential difference applied over a cut at a meridian cross-section, (ii) current induced by a uniform axial , alternating magnetic field; in both cases, the torus inductance is computed and the high-frequency resistance of an imperfectly conducting torus is deduced. For a tight torus, that is, a torus without central hole, a suitable rescaling reduces the conformal representation defining the toroidal coordinates to Kelvin's inversion. Solutions of the mentioned problems for the tight torus are obtained directly by inversion and also as limits of the solutions for the general torus; approximations to the solutions for the case of an almost tight torus are discussed as well. 1. Introduetion

After some methodological remarks on the theory of Stieltjes transforms, a systematic classification of transforms involving Γ \Gamma -functions is presented As a consequence, many new transforms are established and much simpler proofs for a few known transforms are obtained.

AbstractThe hypergeometric function p−1F(1, b; c; −p−2) is a positive real function of p for all real values of the parameters satisfying c ≧ b ≧ 0. The corresponding impedance is realizable as an LC‐ladder beginning with a unit shunt capacitance. The behavior on the j‐axis of this class of impedances is analysed.

AbstractThe field of validity in the frequency‐power relations is discussed, mainly in connection with the early work of Groszkowski in oscillator theory. Several new applications are treated. Integral relations for non‐periodic states are established and applied to noise spectrum conversion.

AbstractIt is proved that two dual passive impedances Z and R2/Z (R real constant) each of degree m are simultaneously realizable by a lossless reciprocal 4‐port of degree 2m 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.