Circuits and Signals in Power Engineering

Subject description

Definition, characteristics and limitations of the built-linear circuits, the characteristics of ideal elements.

Basic electrical signals: the harmonic signal, unit step, unit impulse and operations on signals.

Topological circuit description, the incidence array, the array of graph windows, loop and nodal method of setting circuit equations.

Theory of the source transformation, and Tellegen theorem.

Classical Analysis: System differential equation and its solution, initial conditions and interpretation solutions.

Convolution.

AC analysis: indicators, system function, imitance and transfer function, complex power, Tellegen theorem and Bode plot

Single input circuits, Thevenin and Norton equivalent circuit, theorem of maximum power transmission, resonance.

Two port circuits: the reciprocity theorem, the parameters of port circuits, the equivalent circuit and integration. The input impedance, impedance mapping and impedance adaptation, conductivity and transfer function.

Spectral analysis: Signal spectrum, using Fourier trigonometric and exponential type and integral in the analysis of linear circuits.

Laplace transform: Laplace transform, circuit model in the complex frequency domain, the initial state of the circuit, system function, circuit analysis with Laplace transform. Calculating the inverse transformation.

Objectives and competences

The objective of the course is to familiarize students with basics of time continuous linear circuits and systems including the relationship of signal representation domain and type of system analysis.

Basic understanding of linear circuits and systems. Understanding of the relationship between continuous time signal representations and linear system analysis. Recognition of a system type according to types of their components. Recognition and understanding of selected phenomena in linear systems in terms of power systems and mechatronics.

Teaching and learning methods

Lectures provide theoretical backgrounds and basic reasoning supported by illustrative examples. Tutorials adds more examples and focus on improvement of analytical skills of students. Both methods are supported by a web based linear system simulator allowing hands-on learning and voluntary student’s work at home. It covers analyzable examples of linear systems in terms of system response. Signal representations on different domains are supported by web based Jupyter Python system.

Expected study results

After completing this course the student will be able to:

• Classify system according to linearity, time invariance and causality;
• Perfrom basic operations on signals;
• Analyse system response in terms of transients and stationary states, and in terms of zero-input response;
• Select the analysis method based on the input signal type;
• Perform complex signal analysis, including amplitude and phase spectrum calculation;
• Perform harmonic analysis of the system including one-port and two port circuits;
• Replace complex two-port circuits with simplified two-port circuits with correctly calculated parameters.

Basic sources and literature

1. B. P. Lahti: Linear Systems and Signals, Oxford university press, 2005
2. P. D. Cha, J. I. Molinder: Fundamentals of Signals and Systems, Cambridge university press, 2006
3. J. Mlakar: Linearna vezja in signali, Založba FE in FRI, 2002
4.  A. Košir: Linearna vezja in signali, zbirka rešenih vaj, Založba FE in FRI, 2005.

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University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana