We present a detailed experimental and theoretical study of terahertz (THz) generation and beam propagation in an optoelectronic THz system consisting of a large-area (ZnTe) electro-optic emitter and a standard electro-optic detector, and provide a comparison to typical biased GaAs emitters. As predicted by theory, in the absence of saturation the generated THz pulse energy is inversely proportional to the area of the optical pump beam incident on the emitter, although the detected on-axis electric field amplitude of the subsequently focused THz beam is practically independent of this area. This latter result promotes the use of larger emitter crystals in amplifier-laser-based THz systems in order to minimize saturation effects. Moreover, the generation of an initially larger THz beam also provides improved spatial resolution at intermediate foci between emitter and detector.