S parameter-based experimental modeling of high Q MCM inductor with exponential gradient learning algorithm

Lumped inductors are very desirable passive components in wireless/RF circuits integrated on multichip module (MCM) substrates. This paper models the inductor by using on-wafer high frequency measurement, S parameter formulation and exponential gradient optimization method. A new equivalent circuit model including both lumped and distributed effects is proposed. Both the magnitudes and phases of all S parameters fit well for all the inductors we built. It is shown that the most effective way to increase the quality factor is to use a high resistivity substrate. The resulting experimental model provides a solid measurement-verified ground for circuit design and numerical characterization.