The N Extra Element Theorem

Abstract

The N Extra Element Theorem (NEET) is an alternative means of analysis for any transfer function of any linear system model, not restricted to electrical systems. Its principal distinction from conventional loop or node analysis is that a simpler reference system model in the absence of N designated "extra" elements is solved first, and the N extra elements are then restored via a correction factor. Parameters in the correction factor are various single injection and null double injection driving point immittances seen by the extra elements, and are all calculated upon the reference model. Thus, no calculation is performed upon a model containing any of the designated extra elements, and the final result is obtained by assembly of sequentially obtained results in a "divide and conquer" approach that is potentially easier, shorter, and which produces lower entropy forms than does the conventional approach. The NEET correction factor is a simultaneous bilinear representation of the extra elements, which can be immittances or dependent generators in any combination, and thus exposes explicitly the contribution of each extra element. An especially useful implementation of the NEET is to designate all the reactances as extra elements. The frequency response of the transfer function is then contained entirely in the NEET correction factor, which emerges directly as a ratio of polynomials in complex frequency s. The zeros as well as the poles can thus be obtained directly from the driving point resistances seen by the reactances, and it can also be determined whether any of the zeros or poles are exactly factorable. The approach throughout is to show how the NEET theorem can be useful in practical Design-Oriented Analysis, and emphasis is on the criteria by which the designer-analyst can take maximum advantage of the numerous choices of which elements to designate as "extra," and which of the many versions of the theorem to adopt.

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