## 5 Results and Discussion
### Evaluation of the Output Power of the ALMA Band 3 Local Oscillator  
The performances of a receiver based on an SIS mixer depend on the pumping levels applied by the local oscillator [45]. Laboratory measurements were performed to study the optimum output power level of the ALMA Band 3 local oscillator to bias the SIS junction of the mixer. A signal generator (model SMF100A from Rohde & Schwarz [40]), a digital oscilloscope (model RTO 1044 from Rohde & Schwarz [40]), and a power meter (model PM5 from Erickson [46]) were used to perform these measurements. The Raspberry Pi 2 was programmed to enable the control of the laboratory instruments to run the tests. The frequency and amplitude sweep of the signal, synthesised by the signal generator and directly connected to the input of the ALMA Band 3 local oscillator, were varied in pre-established steps. The power meter, connected to the output of the local oscillator, measured the output power levels and saved the data simultaneously. These data were compared with the nominal power levels required for the SIS mixer biasing. The order of magnitude of the LO pumping power level required at the junction, named \(P_{LO}\), is given by the following formula (we assume to bias the mixer on the first photon step below the gap voltage of the superconductor) [45]:  
\[P_{LO}=\frac{\left(N\!\cdot\!h\!\cdot\!\
u_{LO}\right)^{2}}{2\!\cdot\!R_{N}\! \cdot\!e^{2}} \tag{1}\]  
where \(N\) represents the number of the SIS mixer junctions in series, \(h\) is the Planck's constant, \(\
u_{LO}\) is the LO frequency, \(R_{N}\) is the normal-state resistance of the current-voltage (I-V) SIS junction characteristic, and \(e\) the electron charge. The minimum required LO power level at the SIS junctions is of the order of 10 nW at 100 GHz for an SIS mixer with a single junction (\(N=1\)) and 40 nW for a two-junction series array (\(N=2\)), like the one used in the ex-PdBI 3 mm band SIS mixer. The attenuation of each component between the local oscillator injection coupler and the SIS mixer module is considered for the evaluation of the LO output power levels required for the local oscillator at the WR10 LO waveguide output flange of the cryostat. In detail, the LO coupler module (attached to the SIS mixer module is connected through a waveguide transition (with an insertion loss of approximately 6 dB) to the WR10 waveguide output of the ALMA Band 3 local oscillator (located outside the cryostat). The LO coupler (see Figure 1) has a coupling value of approximately \(-28\) dB. The coupling value is small so as to minimise the noise added to the signal path. The LO output power required at the WR10 output waveguide flange of the PA be more than three orders of magnitude greater than the nominal power level calculated using (1). The minimum value of the required LO power is taken to equal to 2 mW across the 92-108 GHz band. Figure 11 shows the plot of the output power of the local oscillator (channel 1). The drain and gate voltage values are set at 1.67 V and \(-\)0.1 V, respectively. The curve shows a peak power of approximately 7 mW at 98 GHz. The minimum value of 2 mW (highlighted in red) is exceeded in almost all local oscillator bandwidths from 85.75 to 114.25 GHz. These requirements can be easily achieved by optimising the drain and gate voltages. After the evaluation of the output power levels of the local oscillator, the I-V characteristic of the SIS junction of the two-junction array mixer is measured [47]. The measurement is carried out by connecting the digital oscilloscope to the SIS mixer junction bias module of the control system. In Figure 12, the measurement results are shown. In particular, the curve of Figure 12a shows the I-V characteristic of the mixer without the local oscillator power applied, where a spurious Josephson current is present (unsuppressed, as the mixer does not have a magnetic circuit), whereas the curve of Figure 12b represents the case with the local oscillator biasing at 87.5 GHz.