The Kennelly theorem which is widely used in three phase systems allows for the delta-star and star-delta conversion and simplification of several electronic circuits. In the present work, we propose a generalization based on the theorem of superposition and some results of linear algebra. Our demonstration is inspired from the proof of the classical Kennelly's theorem. The proposed formulas are very clear and simple. This will make it possible to convert polygon-start and star-polygon if the number of impedances is odd, greater than or equals three. The advantage of our proposal is that it could be understood and programmed easily by undergraduate student when compared to other methods based on the graph theory, which focuses mainly on the mesh-star conversion, which is not possible in all configurations in both ways. This result can be applied to reduce the number of nodes in circuit type models of electrical components and electronic circuits. Thus, the simulation time is reduced.
This paper presents a new behavioural electrothermal model of power Silicon Carbide (SiC) Metal Oxide Semiconductor Field Effect Transistor (MOSFET) under SPICE. This model is based on the MOSFET model level 1of SPICE, in which phenomena such as Drain Leakage Current I DSS , On-State Resistance R DSon , gate Threshold voltage V GSth , the transconductance (gfs), I-V Characteristics Body diode, temperature-dependent and self-heating are included and represented using behavioural blocks ABM (Analog Behavioural Models) of Spice library. This ultimately makes this model flexible and easily can be integrated into the various Spice -based simulation softwares. The internal junction temperature of the component is calculated on the basis of the thermal model through the electric power dissipated inside and its thermal impedance in the form of the localized Foster canonical network. The model parameters are extracted from manufacturers' data (curves data sheets) using polynomial interpolation with the method of simulated annealing (S A) and weighted least squares (WLS). This model takes into account the various important phenomena within transistor. The effectiveness of the presented model has been verified by Spice simulation results and as well as by data measurement for SiC MOSFET transistor C2M0025120D CREE (1200V, 90A).
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