  We have developed, built, and tested a new feed design for interferometric
radio telescopes with "large-$N$, small-$D$" designs. Those arrays require
low-cost and low-complexity feeds for mass production on reasonable timescales
and budgets, and also require those feeds to be compact to minimize obstruction
of the dishes, along with having ultra wide bands of operation for most current
and future science goals. The feed presented in this paper modifies the
exponentially tapered slot antenna (Vivaldi) and quad-ridged flared horn
antenna designs by having an oversized backshort, a novel method of maintaining
a small size that is well-suited for deeper dishes ($f/D\leq 0.25$). It is made
of laser cut aluminum and printed circuit boards, such that it is inexpensive
($\lesssim$ 75 USD per feed in large-scale production) and quick to build; it
has a 5:1 frequency ratio, and its size is approximately a third of its longest
operating wavelength. We present the science and engineering constraints that
went into design decisions, the development and optimization process, and the
simulated performance. A version of this feed design was optimized and built
for the Canadian Hydrogen Observatory and Radio-transient Detector (CHORD)
prototypes. When simulated on CHORD's very deep dishes ($f/D=0.21$) and with
CHORD's custom first stage amplifiers, the on-sky system temperature
$T_\mathrm{sys}$ of the complete receiving system from dish to digitizer
remains below 30 K over most of the 0.3-1.5 GHz band, and maintains an aperture
efficiency $\eta_\mathrm{A}$ between 0.4 and 0.6. The entire receiving chain
operates at ambient temperature. The feed is designed to slightly
under-illuminate the CHORD dishes, in order to minimize coupling between array
elements and spillover.
