A theory for combined differential and commonmode normalized power waves is developed in terms of even and odd mode impedances and propagation constants for a microwave coupled line system. These are related to even and odd-mode terminal currents and voltages. Generalized s-parameters of a two-port are developed for waves propagating in several coupled modes. The two-port s-parameters form a 4-by-4 matrix containing differential-mode, common-mode, and cross-mode sparameters. A special case of the theory allows the use of uncoupled transmission lines to measure the coupled-mode waves. Simulations verify the concept of these mixed-mode s-parameters, and demonstrate conversion from mode to mode for asymmetric microwave structures.
A practical measurement system is introduced for measurement of combined differential and common-mode (mixed-mode) scattering parameters, and its operation is discussed. A pure-mode system measures network parameters of a differential circuit in the fundamental modes of operation, and has improved accuracy over a traditional network analyzer for the measurement of such circuits. The system is suitable for onwafer measurements of differential circuits. The transformation between standard s s s-parameters and mixed-mode s s s-parameters is developed. Example microwave differential structures are measured with the pure-mode vector-network analyzer (PMVNA), and the corrected data is presented. These structures are simulated, and the simulated mixed-mode s s s-parameters correlate well with the measured data.
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