This document describes an antipodal linearly tapered slot antenna (LTSA) fed by a substrate parallel plate waveguide. It analyzes the propagation characteristics of the parallel plate waveguide, showing it supports a TEM mode. An LTSA element is designed using this feeding structure, fabricated and tested. Both simulated and measured results show the LTSA has very wide bandwidth, from 12 GHz to over 50 GHz. Radiation patterns are also measured at two frequencies, showing narrow beamwidths and gains of 8-9.5 dBi. The substrate parallel plate waveguide is proposed as a good feeding structure for wideband LTSA designs.