## 3 Instrument Characteristics and Tests
### Characteristics of Radiometer Sub-Systems
#### 3.1.4 Characteristics of the Active Cold Source
This time period is selected in order to avoid disturbances caused by the galaxy passing through the field of view and to ensure the atmospheric conditions are comparable every day. The measurements are performed for \(T_{0}\) in the rangeof 21 \({}^{\circ}\)C-39 \({}^{\circ}\)C in steps of 3 \({}^{\circ}\)C. To give the temperature feedback loop sufficient time to settle before the next measurements, \(T_{0}\) is switched to the next higher value several hours before measuring. The voltages are recorded with the ADC sampling rate of \(f_{\mathrm{ADC}}\) = 800 Hz, which is twice the nominal -3 dB cut-off frequency of the low-pass filters LPA/b in front of the ADC. This implies that almost the maximum time resolution of nominally 2.5 ms of the radiometer output voltage is recorded. For the duration of data recording set to 10 seconds, this corresponds to the nominal total integration time of 10 seconds per voltage data record. As will be discussed in Section 3.2 (Table 2b), these settings yield data records with mean values \(\langle U_{\mathrm{sky,\;in}}\rangle\), \(\langle U_{\mathrm{RS}}\rangle\), \(\langle U_{\mathrm{ACS}}\rangle\) and very small standard deviations \(\sigma U_{\mathrm{sky,\;in}}\), \(\sigma U_{\mathrm{RS}}\), \(\sigma U_{\mathrm{ACS}}\). The crosses in the top panel of Figure 7 are the mean \(T_{\mathrm{ACS}}\) derived for a specific \(T_{0}\). The error bars indicate the associated standard deviations \(\sigma T_{\mathrm{ACS}}\leq\) 0.23 K and \(\sigma T_{0}\leq\) 0.1 K. This shows that the temperature feedback loop is able to keep \(T_{0}\) very stable for the ranges of ambient temperatures \(T_{\mathrm{amb}}\) indicated in the bottom panel of Figure 7. The variation \(\sigma T_{\mathrm{ACS}}\) is less than 1% of the measured mean \(T_{\mathrm{ACS}}\). It is assumed that most of these variations are due to errors introduced by the model (6), which uses \(T_{\mathrm{amb}}\) to correct for the noise contribution \(\Delta T_{\mathrm{B,\;FC}}\) of the FC to \(T_{\mathrm{sky}}\). The solid line in Figure 7 is the linear interpolation to the mean \(T_{\mathrm{ACS}}\):  
\[T_{ACS}[K]=T_{ACS,^{\prime}\mathrm{C}}+\frac{dT_{ACS}}{dt_{0}}\cdot T_{0}=31.56353K+0.23579\cdot T_{0}[^{\circ}\mathrm{C}] \tag{9}\]  
The positive temperature response \(dT_{\mathrm{ACS}}/dT_{0}\approx\) 0.24 K\({}^{\circ}\)C\({}^{-1}\) is mostly associated with the noise caused by the loss of the isolator (ISO2), which increases with \(T_{0}\) (Figure 2). Figure 7: Mean noise temperatures \(T_{\mathrm{ACS}}\) of the ACS measured for instrument set-point temperatures \(T_{0}\) = 21 \({}^{\circ}\)C, 24 \({}^{\circ}\)C, 27 \({}^{\circ}\)C, 30 \({}^{\circ}\)C, 33 \({}^{\circ}\)C, 36 \({}^{\circ}\)C, 39 \({}^{\circ}\)C (top panel), and ambient temperatures \(T_{\mathrm{amb}}\) measured during the calibration measurements (bottom panel). The calibration procedure based on sky and RS measurements is also applied to the HS. The measured noise temperatures of the HS for 21 \({}^{\circ}\)C \(\leq T_{0}\leq\) 39 \({}^{\circ}\)C are in the range of 630 K \(<T_{\rm HS}<\) 660 K, which is in good agreement with the estimated value given in Table 1. The temperature response \(dT_{\rm HS}/dT_{0}\approx\) 1.60 K \({}^{\circ}\)C-1 measured is highly linear for the temperature range considered and mostly due to the increasing noise of the 6 dB attenuator attached to the output of the ND (Figure 2).