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ABSTRACT
This article deals with the basis of the theory of linear electrical circuits with localized constants. The topology of circuits (notion of nodes, meshes and branches) and the nature of the signals leading to Kirchhoff's laws are presented. The behavioral characteristics of passive elements (resistor, capacitor, inductance coil, coupled coils, ideal transformer) and sources (of voltage or current, independent or linked) involved in the circuit. This article also presents, via mathematical tools, permanent causal linear systems (Laplace transform, complex rating) as well as various theorems specific to these systems and whose results facilitate the study of circuits. To conclude, the modeling of real elements (non-ideal) is dealt with.
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André PACAUD: SUPELEC engineer
INTRODUCTION
Permanent, causal, linear electrical circuits with localized constants assume that signal propagation does not occur in the circuit. This means that the wavelength of the signals in the circuit is large relative to its dimensions.
The study of these circuits usually involves calculating the response (voltage across a dipole, current flowing through an impedance, etc.) to one or more given actions. This study is based on the basic laws of electrical circuits (Kirchhoff's laws, behavioral definitions of elementary components and sources encountered in practice) and using the mathematical tools of permanent linear causal systems.
The specificity of electrical circuits in this field of linear systems has led to the establishment of special theorems to facilitate the study of these circuits (linearity, substitution, Thévenin / Norton, reciprocity, Kennelly, Tellegen).
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Linear electrical circuits
Kirchhoff circuits: definitions, constitution, general laws
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