Effect of Differential Loss on Approximate Solutions to the Coupled Line Equations

Consider t h e coupled line equations / · ' ( * ) = - IVo(z) +jc(z)h(z) /,'(«) = jc(z)I0(z) - TMz). (1) (2) These equations are useful in describing the effects of coupling between a signal mode, represented by a complex wave amplitude I o , and a single spurious mode, represented by I i , caused by geometric imperfections in a multimode transmission line. These equations m a y be derived in two ways from basic principles. The coupled line 1 or generalized telegrapher's equations 2 , 3 m a y be derived directly, or the geometric imperfections m a y be considered discrete; the case of continuous imperfections can then be considered as a limiting form of the discrete case. 4 Exact solutions for these equations are known in only a few special cases, so considerable attention has been given to approximate solutions. 4,5 A second-order approximate solution is difficult to examine in general; however, Rowe and Warters 4 , 5 have given a very thorough investigation for the case of equal attenuation for the two modes or zero 2787