General Mathematics

   

On the Affine Nonlinearity in Circuit Theory

Authors: Emanuel Gluskin

According to the definition of the linear operator, as accepted in system theory, an affine dependence is a nonlinear one. This implies the nonlinearity of Thevenin's 1-port, while the battery itself is a strongly nonlinear element that in the 1-port's "passive mode" (when the 1-port is fed by a "stronger" circuit) can be replaced by a hardlimiter. For the theory, not the actual creation of the equivalent 1-port, but the selection of one of the ports of a (linear) many-port for interpreting the circuit as a 1-port, is important. A practical example of the affine nonlinearity is given also in terms of waveforms of time functions. Emphasizing the importance of the affine nonlinearity, it is argued that even when straightening the curved characteristic of the solar cell, we retain the main part of the nonlinearity. Finally, the "fractal-potential" and "f-connection-analysis" of 1- ports, which are missed in classical theory, are mentioned.

Comments: 34 Pages. This is the set of the slides for my first NDES 2012 lecture, which significantly extends the content of the associated proceedings article.

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[v1] 2012-08-06 05:59:47

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