Sensitivity analysis of interconnect networks based on S-parameter macromodel

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In this paper a simple and efficient approach for time domain sensitivity analysis is presented. Since moments of the Taylor series of a function are derivatives of the function to frequency, the same technique can be used to compute sensitivities. The basic elements in the linear networks are described by their S-parameters and the first derivatives to parameter variations of the S-parameter; which are expressed as Taylor series. A linear network is reduced to an S-parameter based macromodel together with the driving sources and the nodes of interest. The network transfer functions together with their sensitivities with respect to all the parameter variations can be obtained in one pass during the network reduction process. Since the number of external nodes are much less than the total number of nodes in the network, this method is very efficient The method can be extended to compute the second or higher order sensitivities, which are very difficult, if not impossible, for other known methods. Experimental results show that this method is robust and efficient. This method is very useful for performance optimization, especially when the number of design variables and number of specifications are very large.