Analytical broadband impedance matching using modified approximating functions with embedded transmission zeros

Abstract

This paper proposes a modified approximating function (MAF)-based analytical method for broadband impedance matching in radio-electronic systems. Unlike traditional Chebyshev and Butterworth approaches, which rely on fixed pole distributions and predefined amplitude responses, the proposed method analytically embeds load-specific transmission zeros directly into the approximation function. This modification enables more accurate reconstruction of frequency-dependent impedance behavior without increasing the network order or circuit complexity. The method establishes a unified analytical synthesis framework linking impedance modeling, ladder-network realization, and constrained optimization. Validation was performed over the 1–10 GHz band using numerical simulations, Monte Carlo tolerance analysis, and prototype measurements. Compared with classical Chebyshev and Butterworth designs, the MAF-based approach achieves a 15–25% reduction in maximum reflection coefficient, a 30–40% decrease in optimization iterations, and improved robustness, with reflection variations remaining within 2% under ±10% parameter deviations. The results confirm that the proposed method provides superior analytical flexibility, improved matching accuracy, and reduced computational effort, making it suitable for automated broadband radio frequency (RF) design applications.