Influence of the direct response on the heterodyne sensitivity of hot electron bolometer mixers

The data is taken at the optimally pumped $IV$ curve of the device discussed in Ref. 13.

Note that the current bias of the mixer in the presence of the direct detection effect is determined by the LO power and the load temperature. The usual approach that $G$ and $TN$ are a function of LO power alone is no longer valid. Hence in the presence of the direct detection effect$G=G(V,I)=G(V,[PLO,Tload])$ and $TN=TN(V,[PLO,Tload])$⁠. This also implies that the definition of the $Y$ factor is strictly speaking invalid in the presence of a direct detection effect since the $Y$ factor definition requires that $Ghot=Gcold$⁠. Hence only the small signal $Y$ factor is a correct parameter, and the normal, conventional $Y$ factor is not. This is due to the bias current change associated with the direct detection effect, which results in $Ghot≠Gcold$ because $Ihot≠Icold$ and $G$ depends on the bias current (which is a combination of LO power and load temperature). This is, however, a small effect that is ignored in the paper.

We use a low frequency mixer to be able to use a LO and a signal source, since $2THz$ sources were not available.

The relation $T=1−R$ relies on the assumption that the characteristic impedance of the directional coupler is identical to the impedance of the isolator in front of the amplifier. Hence the use of an isolator is crucial in this experiment, since the input match of a typical low noise amplifier can in general not be described by a $50Ω$ real impedance.

The bias current as shown in Figs. 3–6 is given by $Ihot$⁠, which is chosen arbitrarily. Note however that $IDD⪡Ihot$⁠, so using $Icold$ in stead of $Ihot$ would not change the graphs appreciably.