Graduate Thesis Or Dissertation
 

Synthesis of networks with complex terminations

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/5t34sn56f

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  • A method for the synthesis of networks with specified complex terminations is presented. The specification function is realized within a multiplicative constant. The technique presented differs somewhat from present methods employed in the synthesis of networks with resistive terminations. The technique is one of rearranging a transfer function and separating the specified load. The remaining portions are associated with realizable network functions which are synthesized by classical methods. The load is then added to the synthesized network. Through the analysis of a terminated network by the use of Thevenin's and Norton's theorems, the transfer function of the network can be generated in terms of the network characteristics and the termination. Having derived the general expression for the transfer function of a network, it is possible to separate a given transfer function with a specified termination in such a manner that it can be associated with the general expression. This separation process is the foundation of many of the operational steps of the procedure. In cases where the load is not already in the expression or not readily separable, it is inserted by multiplying and dividing or by adding and subtracting, whichever is appropriate. The separation, however, must yield network functions which are realizable. That is, driving point specifications must be positive real and transfer functions must satisfy similar requirements except that the degree of s in the numerator only has to be equal to or less than the degree of s in the denominator. The separation procedure consists of introducing a function, X (s), and then dividing the numerator and denominator of the transfer function by this function, X (s) is selected in such a manner that the restrictions placed on the expressions associated with the network specifications are maintained. A network can now be realized using a conventional method that is appropriate. The network is then connected to the termination and the overall transfer function is represented within a multiplicative constant.
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