## 3 Materials and Methods
### Methodology to Conduct the Measures  
Firstly, we performed a fast sweep between the 10 kHz and 300 kHz in each prototype for all the configurations, to find the region in which the Vout was highest. Based on the results of previous experiments, the WF was found in the region with the maximum Vout. To find the WF, we used six samples for the calibration. We calibrated the prototypes using six samples, see Table 3. The measures of Vout were replicated three times for each prototype and configuration in order to discard any interferences. In addition, during each measurement, three values of Vout were gathered. The data used for the calibration represented the average value of Vout and the concentration of OF in g/L of each sample. The process to have the calibration was performed as follows. Initially, we essayed with the four prototypes, testing each one in a specific spectrum of frequency, from 10 to 300 kHz, to find the WF. It was done considering the four configurations of each prototype, as indicated in Figure 6. After analysing the range of frequency, where the P1, P2, and P3 were more affected by the concentration changes, we chose the WF for each prototype in the four studied configurations. Furthermore, we used the Vout values in the WF to obtain a mathematical model for the tested prototypes to verify which equation adjusted better to obtain data. To get this, we used specific software, Statgraphics [39], which is very useful for analysing the values. Figure 5: Tight model for OF concentration (g/L) vs. conductivity (mS/cm). \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Sample** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline OF (g/L) & 0 & 2.5 & 5 & 7.5 & 10 & 12.5 & 15 & 17.5 & 20 \\ Used for: & CalPr & VerPr & CalPr & VerPr & CalPr & VerPr & CalPr \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The concentration of OF in the experiment. Calibration process (CalPr) and Verification process (VerPr). Once the calibration test finished and calibration models were obtained, we used the other three samples (5 g/L, 12.5 g/L, and 17.5 g/L) to verify the calibrations and their mathematical models. With the data of verification, we calculated the Absolute Error (AE) and Relative Error (RE) between the real concentration of OF and predicted OF concentration based on measured Vout and the calibration models for the tested samples. Finally, we applied the ANOVA [40,41] procedure to verify if the obtained data were relevant. Likewise, we used the multiple range procedure to determine if the different concentrations of OF explained the variance of the variable Vout. We use the Least Significant Difference Turkey (LSD Tukey) method for significant differences between pairs of means for the comparisons among the concentrations of fertilizer. In this case, we obtained two indicators, Reason-F and Value-P. The former is used to determine whether, from among a group of independent variables, at least one has the ability to explain a significant part of the variation of the dependent variable. Moreover, Value-P is useful to know if the obtained results are the consequence of random sampling, or if they are statistically significant. This procedure is used to choose which prototype is the best one, in terms of its capability to differentiate the samples, to be selected as a sensor for measuring OF. Subsequently, we analyse the data for all cases in the three prototypes, using a single ANOVA operation to obtain the relevance of the measured values, and we evaluated the standard deviations of the prototypes for each configuration. Finally, we selected the best prototypes based on previous results. Since, in past experiences, we detected different behaviours of inductive coils, we set a series of requirements that prototypes must accomplish in order to be selected as a capable sensor. Those requirements are described below:  
1.