Fundamentals of electrical circuits

Esame Fundamentals of electrical systems

Facoltà Ingegneria dell'informazione iii

Appunti esame

Appunti dettagliati del corso presi a lezione, docente Fabio Freschi. Appunti in lingua inglese.

Part I: Preliminaries.
Basic definitions.
Models.
Electrical engineering and lumped circuit models: hypotheses.
Electrical components and terminals, two-terminal components.
Current e ammeter.
Voltage and voltmeter.
Passive and active sign convention.
electrical power (wattmeter) and energy, passivity.
Topology.
Operative definitions: node, branch, loop, mesh, graph.
Kirchhoffs current law (surface, node).
Kirchhoffs voltage law (closed path, mesh).
Two-terminal components and constitutive equations.
Constitutive equations.
Classifications: control type, linearity, time invariance.
Passive elements.
1. resistor (resistance, conductance), short circuit, open circuit, ideal switch.
2. electric energy and capacitor.
3. magnetic energy and inductor.
Active elements.
1. voltage generator.
2. current generator.
Solution of the fundamental problem of circuit theory
definition.
Linearly independent equations: KCL, KVL constitutive equations.
Method of sparse tableau.
Adynamic networks (algebraic equations), dynamic (differential equations), order of a network

Part II: Adynamic Circuits.
Special methods for the solution of electrical circuits.
Equivalence principle.
Series and parallel connection.
1. definitions.
2. series of resistors and voltage division.
3. parallel of resistors and current division.
4. examples.
5. series of generators.
6. parallel of generators.
Star and delta connection.
Superposition principle (proof).
Millmans theorem (proof).
Thevenins equivalent circuit (proof).
Nortons equivalent circuit (proof).
Tellegens theorem.
Maximum power transfer.
Circuits with controlled generators.

Parte III: Dynamic Circuits.
Transient analysis.
Constitutive equations of capacitor and inductor.
Series and parallel connection of capacitors and inductors.
Solutions of differential equations with constant coefficients: outline.
1. associated homogeneous equations.
2. particular solution.
3. initial conditions.
first order differential equations.
1. free and forced evolution.
2. transient and permanent evolution.
RC circuit.
RL circuit.
Solution of first order circuits with constant inputs (Thevenin, Norton).
Switches.
Sinusoidal steady state.
(summary of complex number algebra)
Sinusoidal waveforms.
Phasor of a sinusoidal waveform.
Properties of phasors.
Topological and constitutive equations in phasor domain.
Impedance, admittance and generalized Ohms law.
Generalization of principles and theorems in phasor domain.
Maximum power transfer in AC.
Phasor diagram.
Frequency response.
Power in sinusoidal steady state.
1. instantaneous power.
2. real and reactive power.
3. complex and apparent power.
Boucherots law.
Power factor correction of inductive single-phase loads.
Non sinusoidal periodic regime.

…continua

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