An improved Z-parameter macro model for substrate noise coupling

A new formulation of Z-parameter based macro models for substrate noise coupling is presented. With this new formulation, the variation of the self Z-parameter at small contact separations can be simulated. Instead of calculating the Z-parameters directly by two-contact models, the Z-parameters are calculated as a least-square solution to an overdetermined set of equations. In this way, the interaction between neighboring contacts can be easily accounted for in the Z-parameter calculation. The method can be applied to both the lightly and the heavily doped substrates. Examples for a lightly doped substrate are provided.