 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Fundamentals of Electrical Circuits

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Department of Circuit Theory
Synopsis:

The subject describes fundamental methods of electrical circuit analysis. After a brief introductory part where the difference between an electrical device and its models is introduced, the basic ideal passive and active circuit elements are then defined. Next, basic circuit quantities are defined; lectures are then focused on important laws and methods of analysis of electrical circuits. Circuit theorems, an analysis of DC circuits, AC circuits, first-order and second-order circuits are described. Finally, a brief description of more sophisticated methods of analysis (Laplace transform, pulse excitation) is done. The seminars are focused on getting a theoretical experience in analysis of electrical circuits, supplemented with simulations and simple measurement.

Requirements:

Assume from math student will know complex numbers, elementary integrals and derivatives, and Laplace transform fundamentals. He / she should know solving procedure of differential equation of the 1st and 2nd order. Student should be able solve system of equations. Basic knowledge of mathematical and simulation programs (Matlab, Maple) is welcomed.

Syllabus of lectures:

1.Electrical devices and its models. Circuit variables (voltage, current, power) and its basic quantities. Basic ideal passive and active circuit elements, Ohms'law.

2.Basic laws and theorems (Kirchhoff's circuit laws, Thévenin's and Norton's theorem, superposition theorem), examples of application (equivalence of circuit elements, voltage divider, current divider, actual sources).

3.Procedures and methods of electrical circuits analysis. Elementary analysis of linear resistive circuits. Circuits excited by one and several independent sources.

4.Power and power matching in resistive circuits. Working states of electrical circuits (transients, steady state). DC steady state, circuit model in DC steady state.

5.General methods of resistive circuits analysis - circuit equations (circuit topology, loop analysis, nodal analysis).

6.Sinusoidal steady state, representation of a sine wave as a phasor, circuit elements at sinusoidal excitation, impedance and admittance. Phasor diagrams.

7.Elementary and general methods of electrical circuits analysis in sinusoidal steady state. Power, power matching.

8.Frequency dependence of network functions (impedance, admittance, transfer function). Frequency response, its graphical representation, asymptotic approximation.

9.Resonance, resonant circuits and its frequency response. Linear circuit containing energy storage elements, circuit equations in the time domain.

10.Transients in electrical circuits. Transients in the 1st order circuit excited by DC source.

11.Transients in the 2nd order circuit excited by DC source - aperiodic and quasiperiodic case, oscillating RLC circuits.

12.Transients with sinusoidal excitation. Transient analysis using Laplace transform.

13.Excitation by single pulses. Relationship among description and behavior of circuits in time and frequency domain. Steady state in linear circuit excited by periodical non-sinusoidal source.

14.Recapitulation, comparison of methods of electrical circuits analysis. Some other problems of the circuit analysis.

Syllabus of tutorials:

1.Introduction. Electrical voltage and current, sources of electrical energy, loads, electrical circuit and its physical analogies.

2.Circuit variables and its basic quantities. Ideal passive and active circuit elements, Ohm's law, electrical circuit.

3.Kirchhoff's laws. Series and parallel connection of resistors (common voltage or common current), voltage divider and current divider. Connection of ideal independent sources.

4.Thévenin's and Norton's theorems, substitution of sources, loaded dividers. Superposition theorem. Elementary analysis of linear resistive circuits.

5.Series and parallel connection of actual electrical sources. Power supplied by the source, power absorbed by the resistor, power matching.

6.Nodal analysis and loop analysis of resistive circuits. Input and output resistance of two-port circuit.

7.Representation of a sine wave by a phasor, circuit elements at sinusoidal excitation, impedance and admittance. Simple circuits in the sinusoidal steady state, integrating and differentiating circuits.

8.Phasor diagrams. Power and power matching in the sinusoidal steady state. Nodal and loop analysis using phasors.

9.Frequency responses of integrating and differentiating circuit, frequency range of valid operation, PWM. Frequency response of more complex circuits.

10.Resonance, resonant circuits. Voltage-current relationship of an energy storage elements. Capacitor supplied by constant current, inductor supplied by constant voltage.

11.Transients in the 1st order circuits excited by DC (constant) source and/or by AC (sinusoidal) source.

12.Transients in the 2st order RLC circuits excited by DC (constant) source, aperiodic and quasiperiodic (damped oscillations) case.

13.Transient analysis using Laplace transform, excitation by single pulses.

14.Reserve, recapitulation, assessment.

Study Objective:

The aim is to unify different level of knowledge of students coming from schools of different categories and form the basis of knowledge necessary for next subjects. After finishing this subject each student should understand to fundamental principles of electric circuits, their behavior and fundamental methods of analysis.

Study materials:

 Mikulec M., Havlíček V.: Basic Circuit Theory, Vydavatelství ČVUT, Praha, 2008, ISBN 80-01-02127-0

 Irwin, J. D., Nelms R. M.: Basic engineering circuit analysis: / 9th ed., Wiley, 2008, ISBN 0470128690

 Floyd T. L.: Principles of Electric Circuits, Conventional Current Version, 8th ed., Pearsen Prentice Hall, ISBN 0-13-170179-7

 Alexander Ch. K., Sadiku M., N. O.: Fundamentals of Electric Circuits, 3rd ed., Mc Graw Hill, ISBN: 978-0-07-297718-9

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