Analysis of Nonreciprocal Effects in an N-Wire, Ferrite-Loaded Transmission Line

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Abstract
The N-wire rotationally symmetric transmission line surrounding a thin ferrite rod is analyzed here with the aim of determining the feasibility of this low-frequency nonreciprocal device. The structure is assumed to be infinitely long. The transmission line equations are solved in which the effect of mutual inductances and capacitances between wires and the perturbing effect of the ferrite are taken into account An expression for the rotation per unit length of line is obtained as a function of the structure geometry, the magnetic condition of the ferrite, and the operating frequency. The result is valid for thin wires and thin ferrite rods. Two examples are given. The four-wire line (gyrator) is evaluated for a ferrite radius equal to 1/16 the structure radius and the result is a predicted rotation of 0.76°/cm at 1000 mc for a 500 gauss magnetization ferrite. Somewhat larger rotations than this were obtained experimentally by Rowen who worked with larger diameter ferrites where the perturbation theory developed here would not be expected to apply. The eightwire line (circulator) is also evaluated on the basis of the theory and the analysis indicates that rotations of the order of 4°/cm should be obtained at 1000 mc for a 500 gauss ferrite at similar operating conditions.