Frequency-Domain Method of Transient Simulations

There exist powerful simulation tools such as the EMTP and SPICE. Those tools, however, involve a number of assumpfions and the limit of the applications, which are not easy for a user to understand. Thus, it happens quite often that a simulation result is not correct due to the user s misunderstanding of fhe applicafion limifs related to the assumptions of the tools. To avoid this kind of an incorrecf simulation, the best way is to develop a user s own simulation tool. For this purpose, an FD method of transient simulations is the easiest one, because the method is entirely based on the theory explained in Chapter 1 and Section 1.5, and requires only numerical transformation of a frequency response into a time response by adopting Fourier/Laplace inverse transform. The theory of a distributed-parameter circuit, a transient analysis in a lumped-parameter circuit, and the Fourier/Laplace transform is given as an undergraduate course in electrical engineering department in most universities all over the world. This section explains how to develop a computer code of the FD transient simulations. 

A numerical calculation code of Fourier/Laplace transform is prepared in commercial softwares MATLAB , MAPLE, etc., even in Excel. Therefore, it is easy to carry out an inverse transform provided that all the frequency responses are given by a user. Similarly, if a user can prepare a time response of a transient voltage, for example, as digital data of a measured result, then the user can easily obtain its frequency response by the software. However, it is better to understand the basic theory of the Fourier/Laplace transform. 

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