Optimal frequency sweep method in multi-rate circuit simulation
  Purpose -- RF circuits often possess a multi-rate behavior. Slow changing baseband signals and fast oscillating carrier signals often occur in the same circuit. Frequency modulated signals pose a particular challenge. Design/methodology/approach -- The ordinary circuit differential equations (ODEs) are first rewritten by a system of (multi-rate) partial differential equations (MPDEs) in order to decouple the different time scales. For an efficient simulation we need an optimal choice of a frequency dependent parameter. This is achieved by an additional smoothness condition. Finding -- By incorporating the smoothness condition into the discretization, we obtain a nonlinear system of equations complemented by a minimization constraint. This problem is solved by a modified Newton method, which needs only little extra computational effort. The method is tested on a Phase Locked Loop with a frequency modulated input signal.   Originality/value -- A new optimal frequency sweep method was introduced, which will permit a very efficient simulation of multi-rate circuits. 
Kai Bittner, Hans Georg Brachtendorf
math.NA