Optimal frequency sweep method in multi-rate circuit simulation
For RF circuit designers, this method enables more efficient simulation of multi-rate circuits like PLLs, but it is an incremental improvement over existing MPDE-based approaches.
The paper introduces an optimal frequency sweep method for multi-rate circuit simulation, using a smoothness condition to efficiently decouple slow and fast time scales. Tested on a Phase Locked Loop with frequency modulated input, the method requires little extra computational effort.
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.