Passive RLC Cascade Circuit Synthesis
The theory of synthesis of LC filters dates from the very beginning of filter circuit implementations. The theory of synthesis of LC filters dates from the very beginning of filter circuit implementations. Here, however, following the overall concept of the book, only cascade synthesis will be described. It creates a cascade of cells realizing one transmission zero each. To that end cells realizing zeros: in the origin, at infinity, at a frequency on the ω-axis, in the left half plane, and in the right-half plane are encompassed. Depending of the numerical values of the transmission zeros, alternative circuits realizing the same transmission zero will be necessary. That is most frequently related to the necessity to avoid implementation of transformers or coupled inductances. In order to simplify the synthesis use of circuit transformations in place of frequency transformations is exemplified for non-low-pass filters. The order of extraction of the transmission zeros is discussed and advice is given. Three examples are elaborated realizing a low-pass filter having transmission zeros at the ω-axis and a complex pair, a band-pass, and an all-pass filter. The synthesis needs solution of a polynomial of order twice the order of filter. In addition, polynomial subtraction and division are undertaken frequently. To cope with numerical problems of that kind use of extended precision arithmetic is advised.
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