# Fluctuation-Enhanced Sensing (FES): A Promising Sensing Technique
## 6 Reducing Errors and Enhancing the Sensory Information Channel Capacity
### Dedicated Instrumentation  
To overcome the problems evidenced in Section 5.4, dedicated instrumentation may be the optimal choice. To discuss the options that are available for the design of dedicate instrumentation, it can be useful to divide the possible measurement set-ups into two main categories, as quite different issues must be addressed in the two cases: Voltage Noise Measurements (VNM) and Current Noise Measurements (CNM). A block diagram of basic set ups for VNM and CNM in the case of a two terminals device (DUT) are shown in Figures 8 and 9, respectively. In the case of VNMs, the DUT is supplied with a constant current. If the input impedance of the Low Noise Voltage Amplifier (LN-VA) is sufficiently large and its Equivalent Input Current Noise (EICN) is sufficiently low, the DC component due to the bias can be removed before the input of the LN-VA that can be therefore DC coupled and, at the same time, characterized by high gain [94; 95; 96]. Typical gains for the LNVA stage are in the order of 40 dB. A second AC filter can be used to remove the offset at the output of the LNVA prior to the input to a second stage that acts as a gain stage to ensure a good coverage of the dynamic range of the signal sampler used to record and analyze the output signal. Due to the large gain of the first stage, the gain stage can often be realized employing low noise Operational Amplifier (OA) based amplifiers. On the other hand, the Equivalent Input Voltage Noise (EIVN) at the input of the LN-VA amplifier sets the ultimate level to the Background Noise (BN) that can be reached and, therefore, it is often obtained by resorting to discrete large area Junction Field Effect Transistors (JFETs) as the first amplifying device. Regardless of the particular architecture chosen for the realization of the LN-VA, the fact that it is based on discrete devices means that the output offset can be quite large, hence the need for a second AC coupling stage between LN-VA and the second stage [94; 95; 96]. When dimensioning the first AC coupling stage, attention must be paid to the fact that the resistance \(R_{A}\) introduces noise that may increase the BN of the system. Assuming that \(R_{A}\) can be made much larger than the DUT impedance, the thermal noise generated by \(R_{A}\) is filtered by the coupling capacitance C\({}_{A}\). In order to take full advantage of the low noise of the first stage the noise contribution coming from \(R_{A}\) must become negligible at the minimum frequency of interest\(f_{min}\), and this means, as it is discussed in [97; 98], that the frequency corner of the AC filter must be much smaller than \(f_{min}\). The resulting long time constant may cause transients that are very long (in the order of minutes) if \(f_{min}\) is in the hundred mHz range. Assuming the EICN of the LN-VA to be negligible and its input impedance to be extremely large, at frequencies at which the presence of the AC coupling filter can be neglected (both in terms of frequency response and noise contribution from \(R_{A}\)), we have that the voltage at the input of the LN-VA can be written as:  
\[V_{in}=i_{Bn}Z_{DUT}+e_{Dn}+e_{n} \tag{8}\]  
Figure 8: Block diagram of basic set up for voltage noise measurements. Assuming now, as it is often the case, that the noise introduced by the second stage is negligible, because of the large gain of the first stage, we can interpret the power spectral density (PSD) of the noise at the output of the amplifier as due to an equivalent input voltage PSD \(S_{Vin}\) given by:  
\[S_{Vin}=S_{IBM}|Z_{DUT}|^{2}+S_{VDN}+S_{VN} \tag{9}\]  
where \(S_{IBM}\) is the PSD of the noise source \(i_{Bn}\), \(S_{VDN}\) is the PSD of the noise source \(e_{Dn}\) (i.e., the noise source generated by the DUT), and \(S_{VN}\) is the PSD of the equivalent input noise source of the LN-VA.  
Clearly, \(S_{Vin}\) can be assumed to represent \(S_{VDN}\) only if \(S_{VN}\) and the effect of \(S_{IBM}\) are negligible.