The Invariant Properties of Two-Port Circuits

Authors: Alexandr A. Penin

Abstract:

Application of projective geometry to the theory of two-ports and cascade circuits with a load change is considered. The equations linking the input and output of a two-port are interpreted as projective transformations which have the invariant as a cross-ratio of four points. This invariant has place for all regime parameters in all parts of a cascade circuit. This approach allows justifying the definition of a regime and its change, to calculate a circuit without explicitly finding the aparameters, to transmit accurately an analogue signal through the unstable two-port.

Keywords: Circuit regime, geometric circuit theory, projective geometry, two-port.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1061194

References:

[1] A. A. Penin,"Linear- fractional relation in the problems of analysis of resistive circuits with variable parameters", Electrichestvo, 11, 1999, pp.32-44, (Russian).
[2] A. A. Penin,"Determination of Regimes of the Equivalent Generator Based on Projective Geometry.The Generalized Equivalent Generator", International Journal of Electrical Systems Science and Engineering, vol.1, n.3, 2008, pp.169-177.
[3] C. A. Desoer and E. S. Kuh, Basic Circuit Theory, McGraw - Hill, New York, 1969.
[4] O. Veblen and J. W. A. Young, Projective Geometry, vol.1, Blaisdell, New York, 1938- 1946.
[5] C. K. Kittel, W. D. Knight and M. A. Ruderman,Mechanics: Berkely Physics Course, vol.1, McGraw - Hill, New York, 1973.
[6] A. I. Gerasimov and V. D. Masin, "Aplication of the properties of linear- fractional transformatoins in the measuring converters", Pribory, sistemy upravlenia, n. 9, 1983, pp. 22- 23, (Russian).
[7] A. A. Penin , "Projective- affine properties of the resistive twoport with the changeable load", Electrodinamika, n. 2, 1991, pp.38- 42, (Russian).