Influence of the electrical parameters on the input impedance of a fractal structure realised on silicon

Abstract

We study here samples having “fractal tree” patterns. The frequency response analysis of their input impedance “ Z in ” has revealed the existence of a frequency band in which the input impedance Z in ≈( iω ) η , η being a fraction. The argument of Z in is constant, situated between 0 and −π/2 and called constant phase angle. This zone depends on the number of iterations for the patterns concerned and on the magnitude of parameters R s , C p and R p of the electrical model. We demonstrate here another approach in the utilisation of deterministic fractal, from an electronic component angle. Obtained by microelectronical process, this component can be used in stabilizer circuit such as phase correctors. The manufacturing process employed has aided in mastering the technological aspects (conducting trace length, oxide thickness, plate surface) of parameters of the electrical model which play a very important role in the choice of the frequency range in which the fractal zone must intervene. The objective was attained in two phases. At first, in simulation where the technological parameters were adjusted to obtain the appropriate electrical magnitudes was followed by the component manufacture based on simulation results. After, electrical measurements were undertaken on those components.