Nonsymmetrical Three-Line Microstrip Couplers

Abstract

The Green's function matrix facilitates the study of multiconductor transmission lines, including nonsynmetrical three-line microstrip couplers, since the effect of terminating impedances upon the input immittances as well as voltage and current ratios can be incorporated. Hence scattering parameters can be computed in an efficient manner. THEORYThere is a vast literature discussing general properties of multiconductor transmission lines and the paper by Marx [1] dealing with lossless lines surrounded by inhomogeneous dielectrics is particularly relevant to microstrip applications.In addition, a large number of papers concerned with the transmission of power has been published and, while not directly applicable, some are of indirect interest. Apart from topological differences, in power applications multiconductor transmission lines are in general lossy and surrounded by a homogeneous dielectric as distinct from lossless conductors in inhomogeneous dielectric media, of concern to the designer of microstrip circuitry. Referring to coupled microstrip lines, Tripathl [2,31, Pavlidis and Hartnagel [41, Azizi [51 as well as Rigg and Carroll [61 describe special cases of interest, viz. a nonsymmetrical pair of microstrip lines [21 as well as symmetrical three-line couplers [3,4,5]. The determination of the scattering parameters of symmetrical three-line couplers has been discussed by Pavlidis and Hartnagel [4], Collier and El-Deeb [71 as well as Tripathi [ 81.Finally, a quite recent paper by Chang [9] dealing with the computer aided characterisatlon of coupled TEM lines, illustrated with reference to a three-line symmetrlcal microstrip coupler, should be mentioned.In all cases the theory is based on the classical telegrapher's equations whlch are known to hold exactly for uniform lossless lines. Their solution and hence the determination of the individual voltages and currents leads to an eigenvalue problem. Thus dI -Y 1 1 IS