Abstract
In this chapter, we introduce a two-port component with memory, called coupled inductors. The dynamics of higher-order circuits are analyzed by resorting to the complementary component representation and to the state variables method, thus generalizing the concepts introduced for first-order circuits. Methods for the analysis of stability and for finding the circuit response to various inputs, including also discontinuous functions, are provided.
Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less.
Marie Skłodowska-Curie
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Notes
- 1.
For instance, real closely coupled inductors are devices largely used in electric grids to step up the voltage exiting a power plant (AC voltage with amplitude on the order of \(10^4\) V) to a high voltage (with amplitude on the order of \(10^5\) V) so that it can be transmitted with great efficiency, and to step it down at the distribution end to levels (on the order of \(10^2\) V) appropriate to homes and factories.
- 2.
In this circuit there is only one SSV and therefore one natural frequency, due to the inductor cut-set, which determines the algebraic constraint \(i_1 = i_2\).
- 3.
Fourier series are named after Jean-Baptiste Joseph Fourier (1768–1830), a French mathematician and physicist who made important contributions to the study of trigonometric series. He introduced these series for solving problems of heat transfer and vibrations.
- 4.
This name derives from the concept of overtones or harmonics in musical instruments: the wavelengths of the overtones of a vibrating string or a column of air are derived from the string’s (or air column’s) fundamental wavelength.
- 5.
The theorem is named after Marc-Antoine Parseval des Chênes (1755–1836), a French mathematician. His theorem presaged the unitarity of the Fourier transform.
References
Apostol T (1967) Calculus, vol 1. Wiley, New York
Budak BM, Fomin SV (1973) Multiple integrals, field theory and series. MIR Publishers, Moscow
Golub G, Van Loan CF (2013) Matrix computations. The Johns Hopkins University Press, Baltimore
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Parodi, M., Storace, M. (2020). Basic Concepts: Linear Two-Ports with Memory and Higher-Order Linear Circuits. In: Linear and Nonlinear Circuits: Basic and Advanced Concepts. Lecture Notes in Electrical Engineering, vol 620. Springer, Cham. https://doi.org/10.1007/978-3-030-35044-4_11
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DOI: https://doi.org/10.1007/978-3-030-35044-4_11
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