Legendre polynomial method which describes the structure and incorporates automatically the boundary conditions in constitutive and propagation equations is used to model acoustic wave cylindrical resonators. It is the first time this method is applied to study standing rather than propagative waves. The advantage of this approach is, in a unique formulation, to take into account electric sources. The analytical and numerical resolutions are presented to highlight the potentialities of the Legendre polynomial approach. The vibration characteristics of piezoelectric discs with regard to diameter to thickness D/H ratios are analyzed by the three dimensional modeling approach through both modal and harmonic analyses. Resonance and antiresonance frequencies, electric input impedance, dispersion curves, field profiles and electromechanical coupling coefficient, easily obtained, are presented for PZT5A resonator piezoelectric discs. To validate our approach, the results using our 3D polynomial modelling of acoustic wave resonator are compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the radial modes of all orders.
This original paper deals with a new approach for the study of behavior in nonlinear regime of a new three-phase high voltage power supply for magnetrons, used for the microwave generators in industrial applications. The design of this system is composed of a new three-phase leakage flux transformer supplying by phase a cell, composed of a capacitor and a diode, which multiplies the voltage and stabilizes the current. Each cell. in turn, supplies a single magnetron. An equivalent model of this transformer is developed taking into account the saturation phenomenon and the stabilization process of each magnetron. Each inductance of the model is characterized by a non linear relation between flux and current. This model was tested by EMTP software near the nominal state. The theoretical results were compared to experimental measurements with a good agreement. Relative to the current device, the new systemprovides gains of size, volume, cost of implementation and maintenance which make it more economical.
This article treats the development of one of the equivalent electrical models for a single phase power supply for one magnetron; in particular that of its own high voltage (HV) transformer newly dimensioned. This single phase system supplies a voltage doubler and current stabilizer circuit, which supplies a single magnetron. Then, by star connecting the three identical models of the single-phase power supply for one magnetron, we obtain a new character three-phase high voltage power supply for industrial microwave generators with one magnetron per phase. The simulation with EMTP (Electro Magnetic Transcients Program) in nominal operation has given the theoretical results close to the experimental measurements. Finally, the magnetrons' failure of the microwave generator was also treated and allowed to observe the interaction's influence between magnetrons; also the regulation of the anode current has been achieved successfully.
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