We measure the direct response of a Nb diffusion-cooled hot-electron bolometer mixer in a frequency range between 0.5 and 3.5 THz. The mixer consists essentially of a twin-slot antenna, a co-planar waveguide transmission line and a Nb superconducting bridge. It is designed for use in receivers with astronomical and atmospherical applications around 2.5 THz. We calculate the impedance of the antenna, the transmission line, and the bridge separately using models which are developed for frequencies below 1 THz and predict the direct response of the mixer. We demonstrate that these models can be applied to much higher frequencies. However, the measured central frequency is 10%-15% lower than predicted.
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