This paper proposes an automatic resonant frequency tracking scheme for resonant converters. A plant modeling approach is presented based on realistic ramp variation of resonant frequency due to slowly varying environmental conditions. The drift in resonant frequency is detected by observing the phase relationship of an electrical variable pair. A rigorous analysis is carried out to select the most suitable variable pair for phase comparison. The effects of circuit nonidealities on the proposed phase detection technique have been detailed. The proposed control technique has been implemented using low cost analog circuitry and is applied to a parallel LLC tank-based resonant boost dc-dc converter. Experimental results are presented on a 160-W prototype to validate the analytical predictions.
A space-time polar quadrature technique for numerical integration of Green's function interactions in time-domain integral equations is presented. The method transforms 2-D surface space-time integrals associated with vector and scalar potentials to a 1-D integral that is performed using Gauss-Legendre integration. The advantage of the presented technique compared to standard 2-D Gaussian quadrature is that time delays between each section of the source basis function and the observation point are accounted for exactly in an analytic manner. This ensures highly accurate temporal behavior of the Green's function interactions thereby contributing to the stability of the overall time-domain integral equations.
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