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A popular time evolution algorithm for solving Maxwell's equations for electromagnetic problems is the Yee's finite difference time domain (FDTD) algorithm. This algorithm introduces a non physical algorithmic anisotropic dispersion error and limited stability range. A new improved algorithm with isotropic dispersion error, better stability and faster execution is introduced in this paper. In this study, we compared the results of our improved isotropic algorithm, for simple and well-known problems, to that of the exact solution and that of the Yee algorithm. These comparisons show more accurate results for our improved isotropic algorithm compared to that for the Yee Algorithm. For practical application problems where solutions are too complicated to be solved analytically, we compared our algorithm to that of Yee and found that our algorithm simulate such problems faster and with smaller error.

SUMMARYThe trend in high-speed digital circuits is to increase speed and density and to operate at lower voltage. This fast increase in the switching speed combined with the decrease of the operating voltage causes the allowable absolute voltage variations to decrease, which makes the PDS design a more challenging task than ever.Moreover, the complex 3D nature of the modern PDS causes it to be more sensitive to capacitors' placement as well as capacitance value.In this paper, we introduce an efficient complete solution for the design of high-speed digital PDS. This solution (a) takes the effects of the decoupling capacitor placement into consideration through a 3D electromagnetic simulation of the PDS, (b) defines a more-realistic PDS design target, and (c) presents a clear capacitor value selection methodology. Finally, we applied our methodology to an industrial test case, compared its results with that of industrial design, and showed its advantages.