# Low-Noise Programmable Voltage Source
## 3 Test of the Designed Voltage Source
### Test Results
In the case of Figure 4b, we can clearly distinguish the noise of the voltage source since it is well above the background noise of the measurement amplifier down to 0.001 Hz. It is important to observe that in the case of Figure 4b, we can conclude that the noise, in the low-frequency region, is mainly due to the JFET. In fact, if a significant contribution from \(e_{nDA}\) was present, it should also show in Figure 4a since the DA operates in almost the same condition for the same output voltage (small differences are only due to small differences in the \(V_{GS}\) required in the cases of \(R_{S}\) = 100 \(\Omega\) and \(R_{S}\) = 1 k\(\Omega\)). Since the noise introduced by the JFETs appears to be the most relevant source of noise, it is conceivable that by using JFETs characterized by better noise performances, we can obtain even lower levels of output noise. In order to test this hypothesis, we replaced the parallel combination of four 2 SK3557-6s with the parallel combination of two ultra-low-noise JFET IF9030s (InterFET). These transistors are characterized by a _VSD_ of about 1.5 nV/Hz, 0.6 nV/Hz and  
Figure 4: Voltage spectral density for two output voltages and four paralleled 2 SK3557-6s used as an output JFET (Junction Field-Effect Transistor) buffer (\(T_{1}\)). The spectra with \(R_{\text{s}}\) = 100 \(\Omega\) (**a**) and \(R_{\text{s}}\) = 1 k\(\Omega\) (**b**) at the input of the amplifiers and the background noise (BG, input of the amplifier shorted) are also shown. 0.5 nV/Hz for frequencies of 1 Hz, 10, and above 100 Hz, respectively [36]. In order to perform a meaningful comparison between two solutions in the case of \(R_{S}=100\)\(\Omega\) (that is, the case in which we obtain the lowest level of noise), it is mandatory to reduce the background noise of the voltage amplifier used for the measurement, otherwise, as can be seen in Figure 4a, we cannot obtain a correct estimation of the actual noise produced by the voltage source. In order to obtain a background noise below that introduced by the voltage preamplifier, we resorted to a cross-correlation approach. In this approach, two identical JFET input and low-noise voltage preamplifiers are employed. The voltage sources associated with each amplifier are uncorrelated to one another and their contribution to the final estimate of the noise to be measured can be reduced by proper averaging of the cross-spectrum between the two amplifying channels [37; 38; 39]. In our set-up, the gain of each channel was 80 dB and the equivalent input \(VSD\) of each amplifier was about 5 nV/\(\sqrt{\text{Hz}}\), 1 nV\(\sqrt{\text{Hz}}\) and 0.6 nV/\(\sqrt{\text{Hz}}\) at 1 Hz, 10 Hz and above 100 Hz, respectively. The results of noise measurements when using the cross-correlation approach in the same conditions as in Figure 4a (\(R_{S}=100\)\(\Omega\), \(V_{out}=50\) mV and 1 V) are reported in Figure 5a; the results obtained in the case in which the four 2 SK3557-6s are replaced by two IF9030s in parallel are reported in Figure 5b. For a better comparison among the performances in the two cases, the values of the voltage noise recorded at 1 Hz, 10 Hz and 100 Hz are reported in Table 2. To test measurement set-up, in the first step, the VSDs of known \"calibration resistors\" \(R_{CAL}\) were extracted. For measurements with Ultra-Low Noise Amplifier (ULNA) and cross-correlation, 1 k\(\Omega\) and 100 \(\Omega\) were used respectively as a \(R_{CAL}\). The obtained spectra correspond to thermal noise of the used resistors. In the case of cross-correlation, the shown spectra (Figure 5a,b) are characterized by lower resolution due to a shorter time of measurements (shorter data vector).