An analytical model is developed to study the electrical properties (electric field and potential distributions, potential energy barrier height and polarization phenomenon) of polycrystalline materials at intrinsic or low doping for detector and solar cell applications by considering an arbitrary amount of grain boundary charge and a finite width of grain boundary region. The general grain boundary model is also applicable to highly doped polycrystalline materials. The electric field and potential distributions are obtained by solving Poisson's equation in both depleted grains and grain boundary regions. The electric field and potential distributions across the detector are analysed under various doping, trapping and applied biases. The electric field collapses, i.e. a nearly zero-average electric field region exists in some part of the biased detector at high trapped charge densities at the grain boundaries. The model explains the conditions of existence of a zero-average field region, i.e. the polarization mechanisms in polycrystalline materials. The potential energy barrier at the grain boundary exists if the electric field changes its sign at the opposite side of the grain boundary. The energy barrier does not exist in all grain boundaries in the low-doped polycrystalline detector and it never exists in intrinsic polycrystalline detectors under applied bias condition provided that there is no charge trapping in the grain.
A model of permanent magnet synchronous machine (PMSM) including the electromagnetically originated torque ripple is presented in this paper. This unique representation of such equivalent circuit is highly critical to understand the torque ripple content and to develop an appropriate mitigation scheme for low torque ripple applications requiring four quadrant operations. This research proposes a method to quantify the various sources of torque ripple and modifies the existing DQ-model to enhance the modeling capabilities for both surface-mount and interior PMSMs. The study also presents the effect of slot/pole combination on torque ripple contents by analytical and finite element modeling. Finite element analysis is used for modeling various PMSMs to verify the lumped circuit model proposed in this research. The theoretical results obtained from analytical and finite element analysis are validated using experimental test.
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