Extraction of accurate package models from VNA measurements

To successfully design high-speed computers and networking equipment, it is necessary to model the interconnects (e.g. package, connector, etc.) and control signal integrity over a wide frequency range. The literature showed that lumped models were often extracted from measurements of both "open" and "short" test structures (Young and Sparkman, 1996), but there are several drawbacks. Not all test structures could be easily built. Capacitance, for example, was often measured without properly grounding the other signal conductors. A lumped model is also "narrow-band", in that it cannot easily account for the frequency dependent skin effect and dielectric loss. It is futile to derive lumped models at many frequencies because no time-domain circuit simulator can understand them. This paper presents a novel approach to extract accurate interconnect models from vector network analyzer (VNA) S-parameter measurements, using only one short test structure. The model is based on frequency-dependent coupled transmission lines in cascade. A transmission line can be considered to the most general circuit element in that it morphs into a single R, L, G, or C in the limiting case. A customized optimizer was developed to solve the circuit equations and derive RLGC matrices for HSPICE's W-element transmission line model. S11 and S21 values measured by VNA, and optimized BGA package models are presented. It is interesting to see that we can accurately model a complex BGA package's via, trace, and bond wire from DC to >2 GHz by a single section of transmission line.