The superconducting HEB device is so far the most promising low noise mixer in the THz frequency range. It out-performs other existing receiver systems because it has low noise temperature and sufficient bandwidth for applications in the FIR range such as astronomy, remote sensing and plasma diagnostics. This work investigates the linear and nonlinear characteristics of NbN Hot Electron Bolometer (HEB) devices. First of all, a thorough expression of the Johnson noise and the thermal fluctuation noise has been re-derived. Our circuit model is more preferable for the HEB devices than the traditional one being used for the semiconductor bolometer. Secondly, the equivalent noise temperature of our receiver system has been significantly improved: the noise temperature went from the original 5800K to a record of 500K for silicon substrate devices. We are also getting improved noise performance for the new MgO substrate devices. The simulation results agree with the measured data very well around the optimum operating point. Finally, the device in the unstable region can be stabilized by connecting a series resistor with higher resistance than the negative resistance of the device. Two frequencies are related to the oscillation waveforms of the voltage and the current of the device. The first one is the repetition frequency that is actually related to the external circuit. The second one is the relaxation frequency that is related to the intrinsic phenomena of the device itself. The domain wall velocity and the relaxation oscillation frequency have been calculated both theoretically and experimentally. The calculated results are within a satisfactory range compared with the measured data. Also, a thorough explanation of the device oscillation process has been presented.