Generalized Analytical Formulation for De-Embedding of Multiport Devices Based on Known Fixtures

The de-embedding is a technique used in radio frequency and signal integrity measurements to extract the scattering (S)-parameters of the device under test (DUT) from the measured data of a global assembly and based on known S-parameters of the left and right test fixtures; thus, it removes the impact of the text fixtures used for the connection of the DUT to the instrumentation. Once the S-parameters are measured, the de-embedding is performed by a multistep approach involving the bidirectional transformation of the S-parameters into the corresponding transfer scattering (T)-parameters. The latter approach is well established for two and 4-port networks and has been recently expanded to the multiport case. This work proposes an alternative analytical formulation to de-embed a multiport device, knowing in advance only the S-parameters of the global multiport assembly and those of the test fixtures. The proposed method does not involve the S-to-T conversion and it requires only the algebraic manipulation of the S-parameter matrix elements; its practical implementation is very well fitted especially for multiport cases, and it is very fast in calculating the de-embedded DUT S-parameters for large port numbers. The results of the proposed formulation, applied to the case of a multipin high-speed connector, are compared with those obtained by measurement and simulations. Their accuracy is shown and discussed to demonstrate the validity of the proposed approach.