Analysis of the equal-delay topology for transformers and hybrid networks

A complete scattering matrix representation for the ideal equal-delay topology for transformers and hybrid networks is presented. It is shown that while the operation of the hybrid as a 180deg power combiner, current balun, or voltage balun is essentially frequency independent, the operation as a 0deg power combiner or splitter is not. Instead, the isolation between the 0deg and 180deg ports is finite and frequency dependent. Moreover, the reflection coefficient at the sum port is nonzero and frequency dependent. These characteristics lead to the conclusion that while the equal-delay 180deg power splitter/combiner is fundamentally frequency independent, its 0deg counterpart is limited to operation well below the fundamental quarter-wave frequency of the constituent transmission lines. Full three-port scattering parameter representations, which are compatible with the calibration and analysis approach given in the CISPR 16-1 specification, are given for the three fundamental transformer and balun types derivable from the equal-delay hybrid: 1 the Guanella voltage balun, 2 the Guanella current balun, and 3 the 180deg power divider or terminated hybrid balun, as specified in the CISPR 16-1 specification