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Optimal frequency sweep method in multi-rate circuit simulation

Kai Bittner (University of Applied Sciences Upper Austria, Hagenberg, Austria)
Hans Georg Brachtendorf (University of Applied Sciences Upper Austria, Hagenberg, Austria)



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.


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.


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.


A new optimal frequency sweep method was introduced, which will permit a very efficient simulation of multi-rate circuits.



This work was funded partly by the Austrian Science Fund (FWF): P22549-N18, and the project ARTEMOS No. 270683-2, by the FFG Austria and the ENIAC Joint Undertaking.


Bittner, K. and Georg Brachtendorf, H. (2014), "Optimal frequency sweep method in multi-rate circuit simulation", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 33 No. 4, pp. 1189-1197.



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