A Novel Reformulation of LRRM Calibration Algorithm Using the Pseudo Cascading Relationship

In this paper, by combining the error network mapping model with the pseudo cascading relationship, the line-reflect-reflect-match (LRRM) calibration of a vector network analyzer (VNA) is reformulated in a novel and simple way. Based on the error network mapping model in the hybrid parameter representation, the raw measured waves are mapped to the equivalent voltages and currents at the test ports. To describe the mapping relationship, the hybrid parameter matrix is constructed by measurement of the thru standard, and only three calibration coefficients, namely x, y, and z, are required to be solved for the VNA calibration. Meanwhile, when measuring the double one-port standard, the pseudo cascading relationship is defined and used to establish the calibration equation in the form of matrix multiplication. By this means, an eigenvalue problem similar to that in thru-reflect-line (TRL) calibration is derived after a series of simple matrix operations. Solving the eigenvalue problem enables the calibration coefficients x and y to be calculated in a convenient manner. Then, by utilizing the lumped models of partial calibration standards, the last calibration coefficient z is determined. Once all three calibration coefficients are obtained, the LRRM calibration is completed. Finally, on-wafer experiments are performed to verify the formulated LRRM calibration.