# Precision Calibration and Linearity Assessment of Thin Film Force-Sensing Resistors
## 3 Results and Discussion
### Equation of the Straight Line of the FSR Sensor Using Conductivity Data  
From the conductivity data, we derived equations of straight lines using the conductivity values at two specific loads (300 g and 500 g) within the applied load range for both sensors. Tables 3 and 4 show the equations for drawing a line based on conductivity data measured from the Flexiforce A201-1 and Interlink FSR-402 sensors, respectively. These equations allowed us to analyze the distribution of the measured values and assess the linearity of the sensors. Figure 8a shows the distribution of the conductivity values for the Flexiforce A201-1 sensor with a fixed resistance of 10 k\(\Omega\), which is the standard recommended by the manufacturer. The conductivity values at loads other than the two calibration points align closely with a straight line, indicating that the Flexiforce A201-1 sensor exhibits good linearity across the applied loads. Similar trends were observed when using other fixed resistances, with the exception of 100 k\(\Omega\) and 200 k\(\Omega\), where some deviation was noted. This suggests that the Flexiforce A201-1 sensor maintains consistent linearity regardless of the resistance value used in the measurement circuit (Figure 8b). Figure 7: Conductivity load comparison of Flexiforce A201\(-\)1 and Interlink FSR\(-\)402. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Fixed Resistance (f)**} & \multicolumn{2}{c}{**Conductivity**} & \multirow{2}{*}{**Equation of the Straight Line**} & \multirow{2}{*}{**Note**} \\ \cline{2-2} \cline{4-4}  & **300 g** & **500 g** & \\ \hline
1 k & \(3.750\times 10^{-4}\) & \(5.497\times 10^{-4}\) & \(y=8.735\times 10^{-7}x+1.1295\times 10^{-4}\) & \\ \hline
4.7 k & \(3.171\times 10^{-4}\) & \(5.121\times 10^{-4}\) & \(y=9.75\times 10^{-7}x+0.246\times 10^{-4}\) & \\ \hline
5.6 k & \(3.530\times 10^{-4}\) & \(5.214\times 10^{-4}\) & \(y=8.42\times 10^{-7}x+1.004\times 10^{-4}\) & \\ \hline
10 k & \(3.520\times 10^{-4}\) & \(5.070\times 10^{-4}\) & \(y=7.75\times 10^{-7}x+1.195\times 10^{-4}\) & Standard \\ \hline
47 k & \(3.620\times 10^{-4}\) & \(5.174\times 10^{-4}\) & \(y=7.77\times 10^{-7}x+1.289\times 10^{-4}\) & \\ \hline
100 k & \(3.357\times 10^{-4}\) & \(5.352\times 10^{-4}\) & \(y=9.95\times 10^{-7}x+0.372\times 10^{-4}\) & \\ \hline
200 k & \(2.756\times 10^{-4}\) & \(5.137\times 10^{-4}\) & \(y=11.91\times 10^{-7}x-0.816\times 10^{-4}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The equations of straight lines for Interlink FSR-402 with fixed resistance. Figure 8: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Fixed Resistance (f)**} & \multicolumn{2}{c}{**Conductivity**} & \multirow{2}{*}{**Equation of the Straight Line**} & \multirow{2}{*}{**Note**} \\ \cline{2-2} \cline{4-4}  & **300 g** & **500 g** & \\ \hline
1 k & \(3.912\times 10^{-5}\) & \(6.432\times 10^{-5}\) & \(y=1.26\times 10^{-7}x+1.32\times 10^{-6}\) & \\ \hline
4.7 k & \(3.749\times 10^{-5}\) & \(6.608\times 10^{-5}\) & \(y=1.4295\times 10^{-7}x+5.935\times 10^{-6}\) & \\ \hline
5.6 k & \(4.010\times 10^{-5}\) & \(6.163\times 10^{-5}\) & \(y=1.0765\times 10^{-7}x+7.805\times 10^{-6}\) & \\ \hline
10 k & \(3.815\times 10^{-5}\) & \(6.458\times 10^{-5}\) & \(y=1.3215\times 10^{-7}x-1.495\times 10^{-6}\) & Standard \\ \hline
47 k & \(3.339\times 10^{-5}\) & \(5.837\times 10^{-5}\) & \(y=1.249\times 10^{-7}x-4.08\times 10^{-6}\) & \\ \hline
100 k & \(3.017\times 10^{-5}\) & \(4.974\times 10^{-5}\) & \(y=0.9785\times 10^{-7}x-0.815\times 10^{-6}\) & \\ \hline
200 k & \(3.749\times 10^{-5}\) & \(5.154\times 10^{-5}\) & \(y=1.086\times 10^{-7}x+3.258\times 10^{-6}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The equations of straight lines for Flexiforce A201-1 with fixed resistance. Figure 8: _Cont_. In Figure 8c, the Interlink FSR-402 sensor shows a similar tendency, with conductivity values at various loads aligning well with the straight line derived from the 10 k\(\Omega\) resistance data.