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

M. Deng, J. Wu

TL;DR

The paper addresses the challenge of characterizing the active impedance $z_a(\\theta,\\phi)$ in large uniform phased arrays, which depends on scan angle due to mutual coupling and is hard to relate to element behavior via traditional $Z$ or $S$ matrices. It introduces a beam-based derivation yielding the closed-form relation $z_a(\\theta,\\phi) = \\frac{E^I_0(\\pi-\\theta,\\phi-\\pi)}{E^V_0(\\pi-\\theta,\\phi-\\pi)}$, using two beam datasets from open-load and short-load configurations. The approach is validated with full-wave simulations of a 15-element array in HFSS, showing agreement in magnitude and phase between the conventional and beam-derived active impedance across scan angles. This beam-centric framework provides intuitive physical insight and can simplify measurement and optimization pipelines for next-generation large-scale phased arrays.

Abstract

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.

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

TL;DR

The paper addresses the challenge of characterizing the active impedance in large uniform phased arrays, which depends on scan angle due to mutual coupling and is hard to relate to element behavior via traditional or matrices. It introduces a beam-based derivation yielding the closed-form relation , using two beam datasets from open-load and short-load configurations. The approach is validated with full-wave simulations of a 15-element array in HFSS, showing agreement in magnitude and phase between the conventional and beam-derived active impedance across scan angles. This beam-centric framework provides intuitive physical insight and can simplify measurement and optimization pipelines for next-generation large-scale phased arrays.

Abstract

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.
Paper Structure (4 sections, 11 equations, 2 figures, 1 table)

This paper contains 4 sections, 11 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical Derivation
  3. Simulation Data
  4. Conclusion

Figures (2)

  • Figure 1: the Thevevin-equivalent circuit of a phased array and its feeding network system. The array consists of N elements. At each port, the feeding network is equalized as a voltage source in series with a source input impedance $z_S$.
  • Figure 2: The active impedance $z_a$ derived from conventional S-parameters and that from the beam with short/open load are compared along the $\phi=30$ slice at various $\theta$ scanning angle. The top left panel shows the beam data itself that is used for the derivation of the active impedance. The top right panel shows the magnitude comparison between the the active impedance $z_a$ from conventional S-parameters and $z_a$ from beam data directly. Bottom left panel shows the phase comparison between these two derivations of active impedance. Bottom right panel is the angle difference of the two traces in the bottom left panel.