Advanced Topics in Electric Circuits

This book offers effective tools to facilitate the study of all those circuits and systems that are increasingly penetrating our world, helping to discover their hidden beauty. This book is intended for researchers and practitioners in the theory and applications of electric circuits. It also serves as a textbook for Ph.D. students examining the applications of modern mathematics to important issues emerging nowadays more and more often in advanced electrical and electronic systems.

The material is presented in twelve chapters divided into sections. Usually, the first sections are of an introductory nature, explain studied phenomena, and announce numerical results. More advanced investigations are presented in the subsequent sections. The center of concern is set on existing modern methods as well as continuously emerging new methods of investigations useful for researchers, engineers, and practitioners active in many and often interdisciplinary fields, where physics, electrochemistry, and electric circuits play a key role.

Coverage includes:

- Principles of optimal operation of electrical circuits.

- The equilibrium state of the circuit as a stationary point of its power functional.

- The Gibbs effect and its consequences for circuit analysis.

- Accurate calculation of complex dynamic circuits operating in non-sinusoidal periodic states. -Energy hysteresis loops in a non-sinusoidal periodic state of the circuit.

- Optimal transformations of elements in three-phase circuits.

- Analog and digital filters.

- Fractals and their structures and measures.

- Fibonacci circuits.

- Sierpinski circuits.

- Cantor circuits.

-Chaotic states in electrical circuits.

-Electrochemical impedance spectroscopy.

-Circuits with special nanostructures and their properties.

-Circuits of fractional orders.

-AI in the study of electrical circuits.

This is the first extensive description of these topics and the interpretations of analytical results and those obtained from computer simulations with the MATLAB environments.

Special attention is paid to nonlinear electric circuits and finally the presentation is extended to effective applications of the achievements of modern AI.