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In this paper, we discuss and analyze the design of a high-frequency, broadband distributed amplifier (DA) based on a 2-D array of field-emission nanotriodes (FENT) consisting of self-aligned gate around a nanomaterial field emitter. We propose here a physics-based device model to characterize dc properties of individual FENTs and a transmission-line circuit for evaluating and optimizing relevant ac properties, including power gain and impedance matching. Our discussion starts from the FENT array's dc characteristics and covers its radio frequency and microwave properties, considering effects of array density, geometry, FENT dimensions, and nanoemitter work function, in order to maximize power gain and bandwidth for high-frequency applications (30-100 GHz). Finally, we consider the practical design of a transmitter front end for wireless systems, combining the FENT-array DA with a tapered open-ended waveguide antenna, significantly improving matching and power radiation efficiency. Our results are of interest for imaging, sensing, satellite communications, defense, and security at 94 GHz.