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A numerical direct solution approach for characteristic function in filter design
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DOI：10.1016/j.asej.2026.104314.png)
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Abstract
En 中文
This paper proposes a numerical direct solution approach (NDSA) for the characteristic function in filter design from a theoretical perspective. The method starts from the frequency domain of the filter and establishes a relationship between the magnitude of the filter network characteristic function |h(s)| , the target |S11|opt , and the selected transfer function f(s) . Furthermore, the phase of the characteristic function h(s) at each target frequency point is flexibly chosen, and a matrix equation for the characteristic function coefficients is constructed. The coefficients of the characteristic function are quickly obtained using a matrix solution approach. Subsequently, an optimization algorithm is employed to determine the phase θ and calculate the filter response that satisfies the performance requirements. All the filter parameters are extracted through network synthesis. Additionally, S11 and S21 under different θ values are analyzed to illustrate how phase θ affects S11 . As design examples, three types of filters—dual-band, harmonic control, and broadband filters—are designed, fabricated, and measured. The experimental results match well with the simulation results. The results demonstrate that the proposed method simplifies the design process, enabling the rapid and flexible synthesis of diverse filter responses. It complements existing design methodologies and provides a new perspective for the design of multiband/complex-response filters.
Keywords:
Filter
Numerical direct solution approach
Real frequency technique
Multiband/complex-response
Characteristic function
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