Optimal nonuniform distributed networks |
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| Authors: | TN Lee |
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| Institution: | Department of Electrical Engineering and Computer Science, The George Washington University, Washington, DC 20052, USA U.S.A. |
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| Abstract: | Techniques developed in the Sturm—Liouville problem and its Inverse problem are well known in solving the analysis and synthesis problems of non-uniform distributed networks (or NUDN) (1)-(6), (15). However, very few practical results have been obtained from the theory, especially as regards the synthesis part of the problem. In this paper, we show that the chain matrix of an inhomogeneous ladder network (or IHLN) of N sections has undergone exactly the limit process of first-order difference equation approximation of the corresponding differential equation converges to the chain matrix of the corresponding NUDN uniformly on every compact subset of p = z(s)y(s) plane. Therefore an optimal NUDN is proven to be either symmetrical or antimetrical (7). Specifically, a class of optimal NUDN which is optimal on every subinterval of O,L] has closed-form solutions, and is proven to be both symmetrical and antimetrical. |
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