Purpose - Radio-frequency 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. The paper aims to discuss these issues. Design/methodology/approach - The ordinary circuit differential equations are first rewritten by a system of (multi-rate) partial differential equations in order to decouple the different time scales. For an efficient simulation the paper needs an optimal choice of a frequency-dependent parameter. This is achieved by an additional smoothness condition. Findings - By incorporating the smoothness condition into the discretization, the paper obtains a non-linear 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.
|Number of pages||9|
|Journal||COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering|
|Publication status||Published - 1 Jul 2014|
- Circuit analysis
- Galerkin Method
- Mathematical methods
- Numerical simulation