Beyond GHz operation frequency and Gb/s transfer rate bring a big challenge to high speed package interconnect designs. To make sure the product meets the specifications, signal integrity analysis has to be done carefully for critical signals before tape out for manufacturing. In order to obtain an accurate signal integrity modeling, the package interconnect must be accurately modeled. Frequency domain S-parameter has been widely used to replace the traditional package lumped model characterized by the fixed values of R, L, and C, which is no longer accurate. To facilitate the time domain analysis, equivalent circuits or behavioral macro models can be established based on the frequency domain S-parameter. In order to obtain a stable, casual and accurate time domain response, the S-parameter should be accurate in the full frequency band from DC to the interested maximum frequency. Usually full wave electromagnetic simulators are used to obtain the package S-parameter. The obtained S-parameter is very accurate in high frequency band, but unfortunately poor in low frequency band which is usually an extrapolation of the high frequency results. Improper use of such EM tools will result in wrong S-parameter, which may sometimes bring instability to the final results in a time-domain simulator based on direct convolution. The equivalent circuit synthesized from the high frequency S-parameter may also generate poor result due to lack of accurate information in the low frequency band. In this paper, we first address the theoretic al reason for the inaccurate low frequency result from the full wave electromagnetic simulators. Then we introduce a new process to generate accurate S-parameter in the full interested frequency band. In the process, the frequency band is divided into three parts, the low frequency range, middle frequency range, and the high frequency range. Skin effect phenomenon is found to be the physical explanation for the frequency band division. It is found that properly choosing EM tools in the proper frequency band is the key to get accurate full band S-parameters.
Analytical Modeling of Metamaterial Differential Transmission Line Using Corrugated Ground Planes in High-Speed Printed Circuit Boards
