Abstract: In this paper we focus mainly on the investigation of the performance of a quasi-optical (planar log-spiral antenna) phonon-cooled NbN superconducting hot electron bolometer (HEB) mixer, which is cryogenically cooled by a close-cycled 4-K cryocooler, at 500 and 850 GHz frequency bands. The mixer's noise performance, stability of IF output power, and local oscillator (LO) power requirement are characterized for three NbN superconducting HEB devices of different sizes. The transmission characteristics of Mylar and Zitex films with incidence waves of an elliptical polarization are also examined by measuring the mixer's noise temperature. The lowest receiver noise temperatures (with no corrections) of 750 and 1100 K are measured at 500 and 850 GHz, respectively. Experimental results also demonstrate that the bigger the HEB device is, the higher the stability of IF output power becomes.