The infinitely long Yagi array of concentric circular loops

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1976

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Abstract

An analysis of wave propagation on an infinitely long Yagi array of concentric circular loops is presented. A dispersion relation is derived and numerically solved for the phase velocity of the wave. For the first propagating mode, the concentric array of loops is found to possess two distinct passbands separated by a stop band. The first passband corresponds to the near resonance of the outer loop, while the second passband corresponds to the near resonance of the inner loop. The width of each of the pass- and stop- bands is a function of the ratio of radii b2/b^. In the first passband, the outer loop carries a minimum of five times the current on the inner loop; however, in the second passband, the current on the inner loop is at least 1.5 times that of the outer loop. The theoretically determined phase velocities are verified by experimental measurement using the surface-wave resonator method. Also, propagation characteristics are examined in the light of measured near-field at representative frequencies throughout the pass- and stop- bands. It is also shown that the character of wave propagation on a concentric array remains intact under an arbitrary axial displacement of inner loops relative to outer ones. The only change appears as a phase shift in the currents of the displaced loops. This latter property may be used to achieve desired pattern shaping and/or limited beam steering of Yagi antennas. When the outer loop is made extremely large, the concentric array reduces to an isolated array of single loops with one passband per mode. The phase velocities of the propagating waves in the latter case are used to obtain optimum design parameters for the Yagi antenna of circular loops. In the first mode of operation, the Yagi antenna of circular loops radiates mainly in the endfire direction, and in the second mode, the radiation is in a conical shell pattern. This type of antenna is well suited for coarse/ fine tracking applications. Finally, other important and varied applications of the concentric array of circular loops and variations thereof are discussed. Applications as Yagi antennas, surface waveguides, TWT interaction circuits, microwave filters, and open-structure resonators are included.

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