Novel Formulation of Mixed-Mode S-Parameters

In this paper, we present a new formulation for the conversion of mixed-mode S-parameters from single-ended S-parameter results. The formulation can be used to improve the accuracy of the characterization of mixed-mode S-parameters including the measurement of differential insertion loss S-parameters (S
_DD21
) for transmission lines. The formulation can also be used to reduce the length of test structures or coupons with an acceptable rate of accuracy. The formulation is an explicit expression, which is also useful as a basis for other derivations and applications. For example, the single-ended transmission to differential insertion loss (SET2DIL) formula can be simply derived from the S
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term. The applications to coupled microstrips and striplines are illustrated. The method is compared to time-domain methods for S
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characterization. Simulation and measurement results are shown to validate the method.