# Source/Load-Pull Noise Measurements at K\({}_{\text{a}}\) [PERSON]
## 2 Materials and Methods
### Formalism of Forward and Reverse Noise Measurements
Since cold-source measurements [18] will be considered in this work, (5) is rewritten to make explicit the role of the directly measured quantities, i.e., \(T_{out}\) and \(G_{av}\):  
\[\frac{T_{eq,NT}}{T_{0}}\cdot G_{S}=\frac{T_{out}/G_{av}-T_{S}}{T_{0}}\cdot G_{ S}=\left|Y_{S}\right|^{2}\hat{c}_{11}+2G_{S}\text{Re}[\hat{c}_{12}]-2B_{S} \text{Im}[\hat{c}_{21}]+\hat{c}_{22}. \tag{10}\]  
As to the reverse case, the relevant configuration comprises the small-signal parameters of the reversed noiseless 2-port and the reversed noisy thru: see right side of Figure 1.  
Figure 1: Model of a generic linear noisy 2-port network. (**Left**): forward case. (**Right**): reverse case. The reverse case can be viewed as reversing the noisy thru and the noiseless 2-ports individually and then swapping them. It can be observed that: \(Y_{S,NT}=Y_{S}\), \(T_{eq,NT}=T_{eq}\); \(Y_{S,NT}^{\prime}=Y_{out}^{\prime}\), \(T_{eq,NT}^{\prime}=T_{out}^{\prime}-T_{S}G_{av}^{\prime}\). * **Small-signal:** the SPMT switch is set so as to connect the throw to the VNA's port 1; the DPDT switch is set to vertical connections. * **Pre-characterization:** the SPMT switch is set so as to connect the throw to one of the terminations; the DPDT switch is set to vertical connections. * **Noise calibration:** the DPDT switch is set to vertical connections. * **Noise measurement:** the SPMT switch is set so as to connect the throw to one of the terminations; the DPDT switch is set to horizontal connections. The first configuration is common to small-signal calibration and measurement. The only, obvious difference is that either calibration standards or the DUT are placed between sections _s-D1_ and _s-D2_. Whereas the calibration is performed once as the first step of the measurement campaign, the DUT will be repeatedly measured, i.e., in conjunction with the selection of each termination. In this work, a thru-reflect-line (TRL) calibration was performed, with custom on-wafer standards replicating exactly the access structures of the DUT. Thus, the DUT's reference planes were easily set in correspondence with the center section of the physical 'thru' standard. The second configuration is used to characterize the source loads seen by the DUT. To ensure consistency, the same calibration performed in configuration 1 is exploited. Since the reference planes are at the center of the physical 'thru' standard, the measured \(S_{22}\) coincides with the sought-for \(\Gamma_{S}\) associated with the selected termination. The third configuration allows to acquire two noise power readings from the receiver (from section _s-REC_ rightwards), relevant to the cold and hot states of the solid-state noise source. To that end, notice, the noise source's noise temperatures must be shifted to section _s-REC_[23]. In turn, this requires an accurate knowledge of the passive network (BLK0) interposed between section _s-NS_ and section _s-REC_. The fourth configuration allows the actual noise measurement. Specifically, a noise power reading is acquired, associated with the selected termination. Notice that the receivers noise factor and gain are nominally the same as in the third configuration, due to the presence of a common isolator just ahead of section _s-REC_. Similar to the calibration step, processing the reading will require knowledge of the passive network (BLK2) interposed between section _s-D2_ and _s-REC_. The small-signal parameters of the isolator alone and of the whole BLK0 are assumed to be known by way of a dedicated coaxial calibration. As to BLK2, it can be characterized as follows. First, apply the 'adapter removal' technique with a coaxial first tier at sections _s-P1_ and _s-ISO_ and an on-wafer second tier at sections _s-D1_ and _s-D2_. The result will be the scattering parameters of the passive network between sections _s-P1_ and _s-D1_ (BLK1) and of the passive network between sections _s-D2_ and _s-ISO_. Cascading the latter to the small-signal parameters of the isolator will yield the sought-for characterization of BLK2.