Multi-port de-embedding methodology based on exponential mapping

This paper proposes a methodology that, starting from a set of calibration measurements picked up at the external ports, allows the de-embbeding of a multi-port transition and the determination of its representative matrix. With this methodology the coupling between internal versus external ports are supposed symmetrical. This hypothesis together with the use of exponential mapping and Baker-Campbell-Hausdorff allows the use of only three standards for the characterization of the multi-port transition. The proposed methodology is applied to the identification of the QFN16 package.

I. Introduction

Due to the higher frequency of operation of modern integrated circuits (ICs), accurate de-embedding techniques are even more important in every phase of the IC design, starting from the device characterization to the package modeling. The device characterization requires deembedding techniques both for on-die and on-package measurements. This techniques are generally developed for a reduced number of ports, typically four-port structure. In [1] a four-port calibration technique has been developed, for “on-wafer” measurements, using admittance matrices. A de-embedding methodology for on-wafer multi-port device characterization, based on the trasmission-line theory and the use of shield-based test structures, has been proposed in [2]. In [3] a circuit based four-port de-embedding technique is set up to model the parasitic effects of the package in power MOSFETs, used in RF applications.