The coupling impedance of tape structures

A periodic array of parallel straight tapes is considered. This can propagate a variety of TEM waves, each one corresponding to a different mode of excitation of the tapes. The case in which there is simply a fixed phase-change from one tape to the next is treated in detail. The exact field distribution is determined by using the theory of analytic functions of a complex variable. It is applied to the calculation of the coupling impedances and dispersion curves of tape helices, ladder lines, interdigital lines and meander lines. The calculations show that, with certain provisos, the product of the coupling impedance and the group velocity is the same for all these structures when they have the same tape length, tape width and gap width. The tape length is to be interpreted as the length of one turn in helices and the length of half a turn in meander lines. The provisos are as follows: the phase-change coefficient must be the same in each case; the coupling impedance must be evaluated at the array in helices, averaged over the array in ladder lines and evaluated at the centre lines of the array in interdigital and meander lines; finally, the ladder lines considered must be slightly perturbed easitron structures. Averaging over the array in helices does not alter the coupling impedance. Averaging over the array in interdigital and meander lines reduces the coupling impedance by a factor between 0.5 and 1. In a strongly perturbed easitron structure, the product of the average coupling impedance at the array and the group velocity differs from that in a slightly perturbed easitron structure by a factor for which an approximate formula is given. The use of tape structures in travelling-wave tubes for the millimetre wavebands is discussed briefly.