## 3 Instrument Control
### Back-End Configuration
#### 3.2.1 Power Measurements  
The power mode allows to get directly the power spectral density of the system noise measured by the SA. When several noise spectra are retrieved consecutively, their orderly aggregation conforms a spectrogram. The spectrogram allows to detect temporal changes in the spectrum, however, it requires larger communication bandwidth and acquisition time. Each point of the spectrum represents the radiometric noise power spectral density corresponding to a specific frequency in the span bandwidth, with a noise bandwidth equal to the resolution bandwidth of the SA. In order to understand clearly this last statement, the configurable SA parameters and their relationship with the radiometric performance are described subsequently. The _center frequency_\(f_{\mathrm{c}}\) determines the central point of the frequency band under analysis. According to the front-end design, there are eight usual values for this parameter, which are the center frequency of each band. The _span_\(B_{r}\) is the overall receiving bandwidth to be analyzed centered at \(f_{\mathrm{c}}\). As the previous parameter, it is usually defined as the bandwidth of the eight frequency bands supported by the front-end. The _resolution bandwidth_ RBW is the bandwidth of the last and narrower bandpass filter in the IF chain (see Figure 5). This value determines the noise power and resolution of each point of the spectrum. The possible values for RBW are increasing from 10 Hz to 10 MHz in 1, 3, 10 steps [26]. The _video bandwidth_ VBW is the bandwidth of the lowpass filter set after the detector. For radiometric purposes, this value is automatically set to ten times the resolution bandwidth, \(\mathrm{VBW}=10\times\mathrm{RBW}\), in order to ensure that the peak values of the voltage after the detector are not cut off by the video filter [26]. The _sweep time_ SWT is the time that the local oscillator takes to sweep the whole \(B_{r}\). This parameter is automatically set to its minimum value [26]  
\[\mathrm{SWT}=\mathrm{k}\frac{B_{r}}{\mathrm{RBW}^{2}}, \tag{1}\]  
where k is a is a constant internal parameter of the R&S(r)FSP40. The _number of sweep points_\(N_{\mathrm{SWP}}\) is the number of points obtained for each spectrum measurement. Given the SA structure, samples are statistically independent if the time difference between consecutive acquisitions is at least \(1/\mathrm{RBW}\). This means that the maximum number of statistically independent samples \(N_{\mathrm{IND}}\) taken for each \(B_{r}\) is equal to  
\[N_{\mathrm{IND}}=\frac{B_{r}}{\mathrm{RBW}}. \tag{2}\]  
However, \(N_{\mathrm{SWP}}\) can only be configured as one of the values of the set 8001, 4001, 2001, 1001, 501, 251, and 125. Therefore, this parameter is set automatically by the SA to the minimum value of the previous set that satisfies the inequality  
\[N_{\mathrm{SWP}}>\frac{B_{r}}{\mathrm{RBW}}. \tag{3}\]  
The _trace detector_ determines the algorithm used in the detection process. There are three types of detectors: _sample_ which uses a midpoint value for each sweep point, _peak_ which uses the maximum or minimum detected value for each point, and _average_ which uses all of the detected values within a point to calculate the final value. The default algorithm used in MERITXELL is the average of power using the Root Mean Square (RMS) of the input samples. The power spectrum retrieved with the RMS detector contains \(N_{\mathrm{SWP}}\) measurements of the radiometric noise in the whole bandwidth under analysis \(B_{r}\).