An inverse method of characteristics for analyzing circuits with widely separated time-scales

Widely separated time-scales occur in many radio-frequency (RF) circuits, making the analysis with standard numerical methods difficult and costly. Low and high frequency signals are often superimposed enforcing very small time-steps over a long time-period in the computation of the numerical solution. Hence, classical numerical techniques result into long runtimes. In this paper we present a general method of embedding the underlying system of ordinary differential-algebraic equations (DAEs) in a system of partial differential equations (PDEs). such that a restriction of the solution of the PDEs onto a suitable path yields the desired solution of the DAEs. This allows to treat contributions with different frequencies separately in different dimensions, each dimension representing a time-scale. Along the coordinates the solution of the PDEs is typically very smooth, making numerical techniques for the solution of PDEs highly efficient. Here, theoretical results as well as new numerical methods are presented.