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- 2001 [2]
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Boolean or switching equations are powerful mathematical tools for digital logic. Several problems in digital circuit design, such as automatic test pattern generation, could be efficiently solved if fast procedures for solving Boolean equations were available. Several methods for solving this class of equations have been developed, but their efficiency is a problem. A new formulation for the computation of Boolean operations based on cubic representation of Boolean functions, termed the cube set method, is presented. The solutions provided by this approach are given as a set of cubes satisfying the disjoint property. Some definitions and theorems are given to describe the method and experimental results are presented.
Obtaining the steady-state operation of a power electronic device by means of brute force computer simulation is not feasible in many practical cases. Fast steady-state algorithms that formulate the steady-state problem as a boundary problem and solve it using Newton's method have been proposed to overcome this difficulty. These algorithms are known as shooting algorithms. An extension of the shooting algorithm for piecewise linear circuits is provided. The complete Jacobian matrix that takes into account the switching instants variation is analytically derived for a state variable formulation of the steady-state problem of a piecewise linear circuit. A computer program PWiseSS based on this algorithm is used to solve a previously proposed test circuit of difficult convergence as well as to solve a realistic six-pulse converter of interest to the power electronics engineer.
