Equivalent Circuit Modeling of Millimeter-Wave On-Chip Transformers

This work presents a wideband extraction methodology for Equivalent Circuit Models (ECM) of millimeter-wave on-chip transformers. The flow is based on multiple modal excitations of a device through suitable n-port transformations (i.e. Y/H/Z-parameters) of the original S-parameters representation extracted by the electromagnetic simulation of said device. In addition to the many extraction methods described in the literature, we include the significant influence of the guard ring surrounding the device in our model. The different excitations are aimed at isolating specific branches of a physics-based ECM that is devised for the interpretation of the n-port data. Responses to the stimuli are computed and visually interpreted in the frequency domain through Bode plots to validate and, if necessary, augment the ECM; successively, circuit parameters for an isolated branch are extracted via a combination of analytical expressions and gradient-based numerical optimization. Finally, numerical optimization is exploited on the whole ECM to maximize overall accuracy after a representation change of basis that is functional to the use case of the device.