A Novel, Beam-based Formalism for Active Impedance of Phased Arrays

The active impedance is a fundamental parameter for characterizing the behavior of large, uniform phased array antennas. However, its conventional calculation via the mutual impedance matrix (or the scattering matrix) offers limited physical intuition and can be computationally intensive. This paper presents a novel derivation of the active impedance directly from the radiated beam pattern of such arrays. This approach maps the scan-angle variation of the active impedance directly to the intrinsic angular variation of the beam, providing a more intuitive physical interpretation. The theoretical derivation is straightforward and rigorous. The validity of the proposed equation is conclusively confirmed through full-wave simulations of a prototype array. This work establishes a new and more intuitive framework for understanding, analyzing and accurately measuring the scan-dependent variations in phased arrays, which is one of the main challenges in modern phased array designs. Consequently, this novel formalism is expected to expedite and simplify the overall design and optimization process for next-generation, large-scale uniform phased arrays.