This paper reports on the design of frequency-dependent feed networks for linear antenna arrays with minimum half-power beamwidth (HPBW) variation in more than one octave of the frequency spectrum. The proposed approach is based on: i) frequency-dependent power dividers that gradually shift the RF power from the outer elements of the array to the inner ones with the increase of frequency and ii) uniformly or non-uniformly-spaced directive antenna elements. The operating principles and design trade-offs of the concept are presented through ideal simulations of four- and six-element antenna arrays shaped by isotropic or directive radiators. It is shown that by employing directive antenna elements and non-uniform spacing, minimum HPBW variation can be obtained in a broad bandwidth (BW, e.g., 3:1). For physical verification purposes, two frequency-dependent feed networks and Vivaldi antenna elements were designed, manufactured, and measured. The first network feeds a uniformly-spaced four-element array of Vivaldi antennas and demonstrates a 58% HPBW variation in a 3:1 of BW. The second network feeds a non-uniformly-spaced six-element Vivaldi array and results in a 67% HPBW variation in a 2.5:1 of BW.