Extended S-Parameter Model of the Power Distribution Network for Rapid Coupling Predictions

Power and return planes are part of the power delivery network of almost all modern high frequency printed circuit boards. These power and return planes can form the basis of unintended radiated emissions from, or radiated coupling to, these boards. Predicting coupling to complex systems is a difficult problem and typically reserved for full wave simulations. Recent works have introduced segmentation approaches that are able to predict coupling to complex printed circuit board designs by using pre-rendered segments and cascading these segments through a circuit solver approach. The extended S-parameter models used by the segmentation approach currently do not include a model for power-plane pairs typical of power distribution networks. This work introduces an extended S-parameter model for the powerplane pair that can easily be integrated into the segmentation approach to quickly estimate radiated coupling to complex power distribution networks including power-plane pairs, IC packages, traces, and more. The characteristics of the power-plane pair are estimated using a cavity model approach. Methods to compensate for radiation loss from the pair are discussed. This approach is then used to capture the relationship between voltages at ports looking into the power-plane pair and with radiated or coupled plane waves using an extended S-parameter model. A comparison between the radiated coupling to a power distribution network is found using the proposed analytical approach and a full wave model. The results are within 1 dB of one another up to 4.8 GHz.