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 MCM substrate. This paper models the inductor from on-wafer high frequency measurement by utilizing the S parameter formulation and exponential gradient method. The S parameter formulation enables us to understand the phase shifting effects within the model while the exponential gradient learning algorithm provides us with a more robust and better fitting technique than the gradient descent algorithm. Both the magnitudes and phases of all S parameters fit well for all the inductors we constructed. It is shown that the phase shifting of the distributed effects should not be neglected even in MCM-D technology. The resulting experimental model provides measurement-verified solid ground for circuit design and numerical characterization