Generalized Fractional-Order Chebyshev Filters via Pole Placement in <i>F-</i> Plane

This paper presents a novel and efficient methodology for designing generalized fractional-order Chebyshev filters using pole placement in the F-plane. By directly placing poles within the stable region of the F-plane, the proposed approach ensures inherent stability and precise control over the filter frequency response, while avoiding the computational complexity and stability uncertainties associated with optimization-based methods. The method is particularly effective for realizing irrational-order filters, which cannot be reliably handled using conventional s-plane- or W-plane-based techniques.To demonstrate feasibility and practical relevance, a √2-order Chebyshev filter is implemented using a fractional-order Sallen–Key circuit. The proposed design achieves improved performance in terms of passband gain, roll-off rate, phase linearity, and group delay characteristics. Comprehensive validation through MATLAB and PSpice simulations, including Monte Carlo analysis, confirms strong robustness against component variations and practical non-idealities.The proposed F-plane pole-placement framework extends fractional-order Chebyshev filter design to both rational and irrational orders in a stable and deterministic manner. This work advances fractional-order filter synthesis and supports sustainable electronic design aligned with the United Nations Sustainable Development Goals (SDG 9: Industry, Innovation, and Infrastructure; SDG 12: Responsible Consumption and Production), with applications in signal processing, control systems, and communication technologies.