# Source/Load-Pull Noise Measurements at K\({}_{\text{a}}\) [PERSON]
## 1 Introduction  
The noise behavior of a linear noisy 2-port network can be fully characterized in terms of four noise parameters, as known from well established theory [1, 2]. If the 2-port network is an active device and its small-signal equivalent circuit model is available, those parameters can be determined indirectly: namely, the noise temperatures of the equivalent circuit element are actually extracted [3, 4], then the noise parameters are computed [5]. In the absence of a suitable model, on the other hand, a black-box characterization becomes necessary, which has long been performed by means of source-pull noise measurements [6, 7] and, more recently, has been also carried out by source/load pull [8, 9, 10].  
It is worth noting that the noise temperature-based methods can benefit from source- or source/load-pull noise measurements, but they strictly require one physical termination only, although used across a broad frequency range. Black-box methods, on the other hand, require a set of different terminations at each frequency, which are usually obtained by means of electro-mechanical RF tuners [11, 12]. Tuners allow to synthesize virtually arbitrary terminations, which can be exploited to optimize the pattern of terminations at each extraction frequency [13, 14, 15]. Nevertheless, electro-mechanical tuners are rather costly and may present repeatability issues, so that alternatives have also been proposed, such as custom tuners [6], long lines [16, 17] and switching over a set of different physical terminations [18, 19]. When switching is adopted, the number of terminations is of course limited by the complexity of the available switching matrix and by the associated loss.  
In this paper, several of the previous ideas are reappraised and combined. First of all, a black-box approach is considered, with a small number (only four) of different terminations realized through electro-mechanical switching. To relieve this minimal condition, both forward and reverse noise measurements are taken, thus realizing a source/load pull. Finally, the idea of exploiting measurements at multiple frequencies to produce an extraction at asingle nominal frequency is adopted to further increase the number of _effective_ (as opposed to _physical_) terminations. This is justified if the noise correlation matrix can be linearized within some frequency interval. Notice, however, that no assumption is made about the behavior of the source terminations, as opposed to [16; 17].  
The proposed approach is applied to the black-box on-wafer characterization of a field-effect transistor realized in OMMIC's 60 nm gate length GaN-on-Si HEMT technology (D006 GH) [20]. The preliminary assessment of that process is one of the objectives of the MiGaNSOS project [21], funded by the European Commission. Other goals are the space-qualification of the analogous 100 nm process and demonstrating that both can be simultaneously used on the same chip [22; 23].  
The projects also aims at demonstrating future applications of the developed technologies in advanced space equipment. Due to the growing interest in the \(\mathrm{K_{a}}\) band for space applications, such as telecommunications and Earth observation [24; 25], a \(\mathrm{K_{a}}\)-band synthetic aperture radar (SAR) antenna has been taken as a reference in MiGaNSOS for the design of the test vehicles. More specifically, the project aims at the full integration of a single-chip front-end (SCFE) monolithic microwave integrated chip (MMIC) demonstrator replicating the basic building block of an active antenna operating in the 35-36.5 GHz frequency range [22; 26; 27].