Optimization of Fractional-Order RLC Filters

This paper introduces some generalized fundamentals for fractional-order RLβCα circuits as well as a gradient-based optimization technique in the frequency domain. One of the main advantages of the fractional-order design is that it increases the flexibility and degrees of freedom by means of the fractional parameters, which provide new fundamentals and can be used for better interpretation or best fit matching with experimental results. An analysis of the real and imaginary components, the magnitude and phase responses, and the sensitivity must be performed to obtain an optimal design. Also new fundamentals, which do not exist in conventional RLC circuits, are introduced. Using the gradient-based optimization technique with the extra degrees of freedom, several inverse problems in filter design are introduced. The concepts introduced in this paper have been verified by analytical, numerical, and PSpice simulations with different examples, showing a perfect matching.