Imbalance in Phased Arrays of Dipoles Induced by Scanning

Dipoles driven by baluns can become unbalanced by external influences. Such dipole elements in a phased array can become unbalanced due to the phase shift factor u
₀
used to scan the array. This scanning-induced imbalance is distinct from imbalance at the edge of the array induced by truncation. In a large array the scanning-induced imbalance is the only significant imbalance in the interior. For progressive phasing, like the active element reflection coefficients, the scanning-induced imbalances of the interior elements of a large array are all approximately identical. When the baluns are 180° hybrids, a measure for the scanning-induced imbalance of an element is the outgoing voltage at the sum port of the element's respective hybrid. An analytical expression for this quantity is derived using a two-port model for the balun-driven dipoles. In the interior of the array this expression is simplified and it is shown that it is zero with no scanning, maximum with u
₀
= 90°, and zero again for u
₀
= 180°. Additionally, an expression for the active reflection coefficient is given. The scanning-induced imbalance in the interior is an odd function of u
₀
while the active reflection coefficient is an even function of u
₀
.