Multimode TRL Calibration Technique for Characterization of Differential Devices

In this paper, a new comprehensive analytical derivation and discussion of the multimode thru-relfect-line (TRL) calibration based on the new generalized reverse cascade matrices is presented. The advantage of the presented formulation is that it can account for certain symmetries in the measurement setup and reflect them in the symmetry of the derived relationships. The focus is on the two-mode case since this covers the majority of the practical applications. To demonstrate the effectiveness of the new formulation, the practical use of the multimode TRL calibration technique for de-embedding purposes is discussed. The common de-embedding assumptions such as reciprocity and symmetry are analyzed and their consequences on the multimode TRL calibration are discussed. It is shown that these assumptions applied to the embedding networks can reduce the requirements on the reflect standard. The use of the multimode TRL calibration technique for un-terminating purposes is discussed. It is demonstrated that in the special de-embedding case it is possible to completely characterize the partially leaky embedding networks. The problems of interpretation and re-normalization of the measured scattering parameters are also discussed. Finally, the on-wafer measurement results are presented that verify the multimode TRL approach for four-port vector network analyzer calibration and de-embedding of differential devices.