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The performance of a NbN based phonon-cooled Hot Electron Bolometric (HEB) quasioptical mixer is investigated in the 0.65-3.12 THz frequency range. The device is made from a 3 nm thick NbN film on high resistivity Si and integrated with a planar spiral antenna on the same substrate. The in-plane dimensions of the bolometer strip are 0.2/spl times/2 /spl mu/m. The best results of the DSB noise temperature at 1.5 GHz IF frequency obtained with one device are: 1300 K at 650 GHz, 4700 K at 2.5 THz and 10000 K at 3.12 THz. The measurements were performed at 4.5 K ambient temperature. The amount of local oscillator (LO) power absorbed in the bolometer is about 100 nW. The mixer is linear to within 1 dB compression up to the signal level 10 dB below that of the LO. The intrinsic single sideband conversion gain measured at 650 GHz is -9 dB, the total conversion gain is -14 dB.