Some Practical Applications of Discretely Tunable Couplers’ Matrix Model

Abstract

The findings of a research of the practical application of a previously developed model of a decametric waves discrete coupler are presented. Due to the high accuracy achieved in describing the transforming properties of Coupler in the operating frequency range, together with the apparatus of the theory of complex variables, in particular with the method of conformal maps of fractional linear functions, it was possible to solve a number of applied problems. A method for calculating the area of consistent loads of discretely tunable power circuits of arbitrary structure has been developed. For completeness of the result, the case of matching a generator with a complex value of internal resistance with a given quality (with an acceptable value of the traveling wave coefficient) has been considered. The proposed approach to matching assumes that for any possible antenna load there must be appropriate combinations of discretely tunable elements of the Coupler power circuit that ensure matching with a given quality. The design ratio for images of arbitrary circles and straight lines conformally mapped by a matching quadrilateral to a given complex domain (i.e., expressions for calculating the coordinates of the circle center and its radius, as well as coefficients of the equation of straight lines) has been obtained. Studies of the matching properties of various circuits implemented on discrete elements have been carried out. The results of this study are important when choosing the structural design of the Coupler power circuit. Calculation formulas are obtained that allow us to estimate the relative losses of active power in the Coupler power circuit. This contributes to the reasonable choice of the best configuration option from several, similar in quality matching, thereby avoiding complicated temperature settings of the circuit elements. An exhaustive search method of tuning the discrete contour of the Coupler has been proposed, which is extremely simple and does not require heavy calculations with matrices and complex numbers.