A New Characterization and Calibration Method for 3-dB-Coupled On-Wafer Measurements

A two-port vector network analyzer (VNA) can be used for measuring the differential-mode (or common-mode) ${ S}$ -parameters of an integrated circuit by combining on-wafer probes with 3-dB-coupling baluns (or power splitters). In such a measurement setup, the error networks from each port of the VNA to the device-under-test are three-port rather than the conventional two-port. This paper proposes a new set of an impedance standards and algorithm that can efficiently extract the full nine mixed-mode ${ S}$-parameters of the three-port error network. For differential-mode measurements, the four differential-mode ${ S}$-parameters are used for the calibration and the remaining five common- and cross-mode ${ S}$-parameters are used for evaluating their associated measurement errors. By a minor variation, the proposed method can be used for characterizing the full nine mixed-mode ${ S}$-parameters of the 3-dB-coupler embedded probe itself, providing a valuable tool in its development stage. The proposed method uses a pseudoinverse of an overdetermined matrix, by which it becomes tolerant to errors that occur when measuring the impedance standards.