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The design of a combined mixer/antenna for submillimeter wavelengths has been given. The antenna consists of a substrateless cavity-backed planar log-periodic element with a single pair of radiating teeth. The pattern and impedance variation with frequency, as measured on microwave scale models of the antenna, were found to be small over a period and an antenna bandwidth of 20 % was easily obtained. The calculated illumination efficiency for a parabolic reflector is close to 75 %. The most serious limitation is the high level of cross polarization which may be due to a TEM type bow-tie mode on the antenna. The antenna input impedance is fairly constant although high (typically 200 Ohm real part) over moderate bandwidths. All of the antenna properties were found to be insensitive to dimensional tolerances. The mixer diode is mounted across the center of the antenna and extended bonding pads are used in a transmission line matching structure to reduce the antenna input impedance to a value which is more optimum for the diode (at the sacrifice of instantaneous bandwidth).