Fundamentals of Electrical Circuits
Code  Completion  Credits  Range  Language 

AE2B31ZEO  Z,ZK  5  2+2s 
 Lecturer:
 Tutor:
 Supervisor:
 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, firstorder and secondorder 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. Basic quantities (electrical charge, voltage, current, power), special values. Sign conventions, fundamental topological terms (node, loop). 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 circuit analysis. Elementary analysis of linear resistive circuits. Circuits excited by one and several independent sources. Application of source equivalency method, load line.
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. General methods of resistive circuit analysis  nodal analysis.
5. General methods of resistive circuit analysis  circuit equations (circuit topology, loop analysis, nodal analysis). Comparison of distinct methods of analysis in DC, examples.
6. Sinusoidal steady state, representation of a sine wave as a phasor, circuit elements at sinusoidal excitation, impedance and admittance. Phasor diagrams. AC analysis.
7. Elementary and general methods of analysis of AC circuits. Power and power matching in AC circuits.
8. Frequency dependence of network functions (impedance, admittance, transfer function). Frequency response, its graphical representation, asymptotic approximation (Bode's plot).
9. Resonant circuits. Circuit equations in 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 analyses using Laplace transform.
13. Excitation by single pulses, unit impulse and unit step response. Relationship among description and behavior of circuits in time and frequency domain.
 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 twoport 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. Voltagecurrent 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 8001021270
[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 0131701797
[4] Alexander Ch. K., Sadiku M., N. O.: Fundamentals of Electric Circuits, 3rd ed., Mc Graw Hill, ISBN: 9780072977189
 Note:
 Further information:
 https://moodle.fel.cvut.cz/courses/AE2B31ZEO
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Cybernetics and Robotics  Robotics (elective course)
 Cybernetics and Robotics  Senzors and Instrumention (elective course)
 Cybernetics and Robotics  Systems and Control (elective course)
 Electrical Engineering, Power Engineering and Management  Applied Electrical Engineering (elective course)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (elective course)
 Communications, Multimedia and Electronics  Communication Technology (compulsory course in the program)
 Communications, Multimedia and Electronics  Multimedia Technology (compulsory course in the program)
 Communications, Multimedia and Electronics  Applied Electronics (compulsory course in the program)
 Communications, Multimedia and Electronics  Network and Information Technology (compulsory course in the program)
 Open Informatics  Computer Systems (elective course)
 Open Informatics  Computer and Information Science (elective course)
 Open Informatics  Software Systems (elective course)
 Electrical Engineering, Power Engineering and Management (elective course)
 Communications, Multimedia and Electronics (compulsory course in the program)
 Cybernetics and Robotics (elective course)
 Open Informatics (elective course)
 Communications, Multimedia and Electronics  Communications and Electronics (compulsory course in the program)