Fractal-pyramid fractance approximation circuit—scaling extension and optimization design principle

Abstract:

Analyze the characteristics of B-type fractal-pyramid fractance approximation circuit, which has only negative half-order operational performance. According to scalingextension theory, a fractance approximation circuit with arbitrary real-order calculus operator is obtained——a scaling fractal-pyramid fractance approximation circuit, which then can be described by anirregular double scaling equation. The operational performance and approximation performance of this fractance approximation circuit is analyzed. The typical numerical solution algorithmsare used to analyze the frequency-domain characteristics and operational characteristics, the effects of different initial impedance values on the pole-zero distributions and frequency-domain curves are compared. By combining the operational characteristic curves and thedifferent values of scalingfeature parameters, the optimization principle of the scaling fractalpyramid fractance approximation circuit is theoretically analyzed and a specific optimization method is given. The approximation performance before and after the optimization of the scaling fractal-pyramid fractance approximation circuit is comparatively analyzed, and the operational oscillation phenomenon isquantitatively analyze.The actual circuit design scheme of the scaling fractal-pyramid fractance approximation circuit is introduced and an example is given. Resistors,capacitors, and active devices are used to generalize the operational order of this fractance from-1<μ<0 to 0<|μ|<2. Scalingfractal-pyramid fractance approximation circuit and its optimized circuit provide new ideas for the construction and application of fractance.