A Lossy Transmission Line Model for the Scan Impedance of the Infinite Dipole Array

In this paper, an analytical formulation of the infinite dipole array scan impedance is presented. The primary contribution of this work is the introduction of a lossy transmission line analogue which simultaneously models the Floquet modal impedances as well as the reactive properties of the dipole's physical geometry. A scan dependent line inductance is implemented, resulting in accurate impedance predictions at extreme scan angles. The model accurately predicts the input scan impedance of tightly-coupled arrays and connected arrays for a variety of element geometries. Ground planes, substrates, superstrates, and feed structures are also incorporated in the model. Calculated impedances are compared to full-wave electromagnetic models, demonstrating high accuracy predictions from broadside to near 90° in each scan plane. Finally, an array which scans to 60° in each scan plane is rapidly optimized using only the transmission line model and compared to full-wave simulations, achieving a 3:1 VSWR over a 6.1:1 bandwidth, demonstrating the value of the model as a starting point for array design.