Multi time scale differential equations for simulating frequency modulated signals

Radio-frequency (RF) circuits produce quasiperiodic signals with widely separated time scales. In the case of autonomous time scales, frequency modulation occurs in addition to amplitude modulation. A multidimensional signal model yields an efficient numerical simulation by computations via a multirate partial differential algebraic equation (MPDAE) with periodic boundary conditions. We present a time domain method for these systems, which integrates along characteristic curves and thus is consistent with the inherent information transport. Moreover, we propose a special choice for additional boundary conditions, which are necessary to determine local frequencies. Test results confirm that the constructed techniques compute efficiently frequency modulated quasiperiodic signals in RF applications.