# Fluctuation-Enhanced Sensing (FES): A Promising Sensing Technique
## 6 Reducing Errors and Enhancing the Sensory Information Channel Capacity
### Dedicated Instrumentation
A fully differential input low noise amplifier can be derived from the circuit in Figure 11 for noise measurement across a DUT with none of the two terminals grounded [105]. Voltage noise measurements are typically employed for low to moderate impedances for the DUTs (from a few \(\Omega\) up to a few tens of k\(\Omega\)), where all the conditions that allow to simplify the measurement set up discussed above can be met. For much higher impedances, current noise measurements are usually more easily implemented. In principle, one could assume that current noise measurements present issues that are dual with respect to the case of voltage noise measurements, but in the case of low frequency noise measurements this is seldom the case. As we have discussed above, in the case of voltage noise measurements, AC coupling down to the tens of mHz range for removing the DC component can be obtained with simple \(RC\) networks (\(R_{A}C_{A}\) in Figure 9) with reasonable values (M\(\Omega\) for the resistances and tens of \(\upmu\)F for the capacitances) with the capacitors only marginally deviating  
Figure 11: Complete schematic of the Low Noise Voltage Amplifier (LN-VA) proposed in [96]. from ideality. In the case of current noise measurement, we would require an input AC coupling network capable of separating the DC bias current from the current fluctuations down to the mHz range. This could be done, in principle, by employing the circuit configuration in Figure 12 in which the \(L_{A}R_{A}\) network would operate dually with respect to the \(R_{A}C_{A}\) network in Figure 11. However, even assuming a resistance \(R_{L}\) in the order of 1 k\(\Omega\) (in the case of current measurements \(R_{L}\) must be much lower with respect to the impedance of the DUT for its attenuation effect to be negligible) the value of \(L_{A}\) that would be required to obtain a low frequency corner below 100 mHz would be larger than 1 kH, that is, to say the least, completely outside the range of values that can be realized, at least with high quality and for signal applications. This means, as it is shown in Figure 9, that the first stage (the transimpedance amplifier) is always coupled in DC, and this translates in an important constraint in the performances that can be obtained by a low noise transimpedance amplifier as we shall presently discuss. To this purpose, rather than dealing with the general circuit configuration in Figure 9 it is convenient to refer to the actual circuit configurations employed for the realization of Low Noise Transimpedance Amplifier (LN-TIA). In almost any instance of low frequency noise measurements, the basic circuit configuration that is employed is shown in Figure 12.  
The operational amplifier in Figure 13 is a JFET or MOSFET input operational amplifier, so that the current noise sources that are present at its inputs can be typically neglected with respect to other sources of noise [106]. The operational amplifier equivalent input voltage noise source \(e_{Vn}\) is shown explicitly in the figure as its effect can be relevant especially at higher frequencies and in the case of DUTs with large capacitive components, as it will be presently discussed. With the equivalent circuit in Figure 10 in mind, in the assumption of virtual short circuit between the inverting and non-inverting inputs of the operational amplifier, the transresistance gain \(A_{R}\) can be calculated to be -\(R_{R}\) while for the equivalent input voltage and current noise sources \(e_{n}\) and \(i_{n}\) we have:  
\[ \begin{array}{c}i_{n}=-\frac{e_{Vn}}{R_{R}}-\frac{e_{Rn}}{R_{R}}\\ e_{n}=-e_{Vn}\end{array}  \tag{11}\]  
As it is apparent from Equation (11), the equivalent sources \(i_{n}\) and \(e_{n}\) are correlated since \(e_{Vn}\) contributes to both sources.