# Fluctuation-Enhanced Sensing (FES): A Promising Sensing Technique
## 6 Reducing Errors and Enhancing the Sensory Information Channel Capacity
### Dedicated Instrumentation
As far as \(S_{IBM}\) is concerned, a few designs for the realization of low noise current sources have been proposed [99; 100; 101; 102]. Depending on the current range to be sourced, the designs may vary considerably and, actually, there is no single approach than can be considered sufficiently general to be regarded as a reference design for the implementation of high sensitivity, low frequency voltage noise measurement systems. In most cases, if fine tuning of the current is not required, the current source in Figure 8 is obtained starting from a battery with a resistance in series that is much larger than the DUT impedance as in Figure 10.  
If the current supplied by the batteries (\(V_{BIAS}\)) is a small fraction of their maximum rated value, they behave as very low noise voltage sources, and if the resistance in series (\(R_{BIAS}\)) is a high quality metallic film resistance, its contribution can be reduced to its thermal noise. If, for the sake of simplicity, we assume the DUT to behave as a resistance with value \(R_{D}<<R_{BIAS}\), from Figure 10 we can calculate that the contribution to the voltage noise across the DUT as due to the bias network is:  
\[S_{IBM}\approx\frac{4 kT}{R_{BIAS}};\ S_{IBM}|Z_{DUT}|^{2}=4 KTR_{D}\frac{R_{D}} {R_{BIAS}}=S_{VTH}(R_{D})\ \frac{R_{D}}{R_{BIAS}} \tag{10}\]  
Figure 10: Block diagram for the calculation of the contribution to the voltage noise across the DUT as due to the bias network. Figure 9: Block diagram of basic set up for current noise measurements. where \(S_{VTH}(R_{D})\) is the thermal noise of the DUT. Equation (10) is particularly interesting when we observe that in order to detect low frequency noise generated by the DUT, its level must necessarily be above the thermal noise of the DUT. Therefore, since the noise contribution of the bias network is always below the thermal noise of the DUT (\(R_{D}<<R_{BIAS}\)), in the bias configuration in Figure 10 the noise introduced by the bias network is always negligible. Note that the condition \(R_{D}<<R_{BIAS}\) is also required since, in Figure 10, the contribution of the noise coming from the DUT is attenuated because of the presence of a finite \(R_{BIAS}\). However, as long as \(R_{BIAS}>>R_{D}\), the attenuation is small and can be usually neglected. As we have noted above, in order to obtain very low level of BN at very low frequencies (\(f<1\) Hz) we need to resort to discrete devices for the front end of the LN-VA. In order to understand the advantage that can be obtained in terms of BN when resorting to discrete JFETs, it is sufficient to observe that if we resorted to the conventional OA based voltage amplifier topology for the realization of the LN-VA, the equivalent input voltage noise source \(e_{n}\) in Figure 8 could be made to essentially coincide with the equivalent input voltage noise of the OA. The JFET input operational amplifiers with the lowest level of equivalent input voltage noise that we have been able to find are the ones belonging to the OPAx140 series by Texas Instruments [103]. Their equivalent input voltage noise is about 50 nV/VHz at 100 mHz, less than 16 nVHz at 1 Hz, and about 5 nVHz for \(f>1\) kHz. If, on the other hand, we design the LN-VA using the very large area IF3601 by InterFet [104], the equivalent input voltage noise can be as low as 5.6 nV/VHz at 100 mHz and 1.4 nV/VHz [95], with a gain, in terms of BN PSD reduction of 80 and 13 at 100 mHz and 1 Hz, respectively. While obtaining the ultimate noise performances in discrete JFET based amplifiers may require resorting to relatively complex circuitry [94; 95], optimized design aimed at simplifying implementation while maintaining excellent noise performances have been proposed. For instance, Figure 11 reports the complete schematic of the amplifier proposed in [96] that, with a very limited component count, allows to obtain an equivalent input noise of about 14, 1.4, and 0.8 nV/VHz at 100 mH, 1 Hz, and for \(f>1\) kHz, respectively.