Fundamentals of Electrical Circuits

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Code Completion Credits Range Language
BE5B31ZEO Z,ZK 5 2P+2S English
Garant předmětu:
Jiří Hospodka
Pavel Máša
Pavel Máša
Department of Circuit Theory

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.


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.Basic quantities (electrical charge, voltage, current, power), special values. Sign conventions, fundamental topological terms (node, loop). Kirchhoff's circuit laws.

2.Basic ideal passive circuit elements. Electrical devices and its models, practical circuit element.

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

4.Elementary analysis of linear resistive circuits ? step by step simplification, superposition, load line. Maximum power transfer.

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

6.General methods of resistive circuit analysis - circuit equations - mesh analysis. Circuits containing controlled sources.

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

8.Power and power matching in AC circuits. Frequency dependence of network functions (impedance, admittance, transfer function).

9.Frequency response, its graphical representation, asymptotic approximation (Bode?s plot). Resonant circuits.

10.Circuit equations in time domain and frequency p domain, transients in electrical circuits. Transients in the 1st order circuit excited by DC source ? introduction.

11.Transients in the 1st order circuit excited by DC and AC source.

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

13. Excitation by single pulses, unit impulse and unit step response.

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.

3. Ideal passive and active circuit elements, Ohm's law, electrical circuit. 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 voltage 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 mesh analysis of resistive circuits. Input and output resistance of two-port circuit, including circuits with controlled sources.

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. Resonant circuits. Voltage-current relationship of 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 analyses using Laplace transform, excitation by single pulses, unit impulse response, and unit step response. 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:

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

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

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

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

Further information:
Time-table for winter semester 2024/2025:
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The course is a part of the following study plans:
Data valid to 2024-04-17
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