Multimode TRL technique for de-embedding of differential devices

The thru-reflect-line (TRL) is one of the most fundamental and accurate vector network analyzer (VNA) calibration techniques. The multimode TRL calibration method generalizes the standard TRL technique to multimode waveguides. In this paper, the practical use of the multimode TRL calibration technique for de-embedding purposes is discussed. The focus is on the four-port case, since this covers the majority of the practical applications. However, the formulation can be easily extended for networks with higher number of ports. The common de-embedding assumptions such as reciprocity and symmetry are analyzed and their consequences on the multimode TRL algorithm are discussed. It is shown that the reciprocity assumption applied to the embedding networks reduces the requirements on the reflect standard. It is demonstrated that additional assumptions of either identical or symmetrical error networks make it possible to completely resolve the problem related to the reflect standard. Based on the derived formulation, it is shown that the multimode TRL calibration reduces to the traditional TRL de-embedding under reciprocity and symmetry assumptions. The problems of interpretation and re-normalization of the obtained scattering parameters (S-parameters) are also discussed. Finally, the measurement results are presented that verify the multimode TRL approach for de-embedding of four-port differential devices.