Synthesis of circuit element with fractal dynamics

Abstract

The first aim of this diploma thesis is to clarify problems with circuit elements described by the fractional-order dynamics, show their basic properties and possible applications in circuits with lumped parameters. The second topic is covering the synthesis of two-terminal devices which have different fractional-orders for requested phase shifts. For this kind of devices, the thesis also describes their optimization and approximation in the frequency domain and subsequent implementation in the form of passive ladder structures. The final part of diploma work will be focused on practical realization of universal fractional PID controller and the verification of proper function of this multi-port in various configurations to prove its correct function via real measurement of frequency and time responses