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We report a noise bandwidth of 7 GHz in the new generation of NbN hot-electron bolometer (HEB) mixers that are being developed for the space observatory Millimetron. The HEB receiver driven by a 2.5-THz local oscillator offered a noise temperature of 600 K in a 50-MHz final detection bandwidth. As the filter center frequency was swept this value remained nearly constant up to the cutoff frequency of the cryogenic amplifier at 7 GHz. We believe that such a low value of the noise temperature is due to reduced radio frequency (RF) loss at the interface between the superconducting film and the gold contacts. We have also performed gain bandwidth measurements at the superconducting transition on HEB mixers with various lengths and found them to be in excellent agreement with the results of the analytical and numerical models developed for the HEB mixer with both diffusion and phonon cooling of hot electrons.