# Design of Capacitive Paddy Moisture Sensor Based on Electrical Impedance Spectroscopy Analysis
## 3 Results and Discussion  
### Determination of Frequency  
Figure 2 shows the paddy capacitance in moisture ranged from 14% to 29% over the frequency ranged from 100 Hz to 1 MHz with the temperature ranged from 40 \({}^{\circ}\)C to 80 \({}^{\circ}\)C in a log-log plot. It can be seen clearly that the capacitance of the paddy had a negative relationship with frequency over 100 Hz to 1 MHz, and it decreased with increasing frequency. The variation of the paddy capacitance with frequency at different temperatures have the same trend. Except when the frequency was lower than 1 kHz, the capacitance fluctuated with increasing frequency in low paddy moisture content, especially in low temperature. The effect of frequency on the capacitance was more prominent at a higher paddy moisture. The dielectric constant is positively correlated with the paddy capacitance, as shown in the following equation:  
\[\epsilon=\frac{2\pi\epsilon_{0}L}{ln(R_{2}/R_{1})}*\epsilon \tag{1}\]  
where \(\epsilon_{0}\) is the vacuum dielectric constant, \(\epsilon\) is the relative dielectric constant of paddy samples, \(L\) is the high of coaxial cylindrical capacitor, \(R_{1}\) is the inner cylinder radius of coaxial cylindrical capacitor and \(R_{2}\) is the outer cylinder radius of coaxial cylindrical capacitor. It can be seen from Figure 2 that the paddy sample had a relatively stable relaxation process in the frequency range of 1 kHz to 1 MHz. The negative linear relationship between capacitance and frequency (1 kHz-1 MHz) could be because the relaxation polarization takes a certain time to complete under the action of an electric field. Therefore, when the frequency of an alternating electric field rises gradually from zero, the change of polarization direction cannot keep up with the change of electric field direction, so the relaxation polarization cannot be fully established [32; 33; 34]. Then the paddy capacitance decreases as the frequency increases and the energy is consumed because of the turning of the dipole moment and phase lag between the electrical fields. Figure 2: _Cont._Under the same temperature range of 40 \({}^{\circ}\)C to 80 \({}^{\circ}\)C and the same frequency range of 100 Hz to 1 MHz, define the difference between the maximum capacitance and the minimum capacitance divided by the moisture interval as the change rate of capacitance as follows:  
\[\textbf{{CTFC}^{t}}\textbf{{and}}\textbf{{f}}=\frac{\textbf{{C}^{t}}_{\textbf{ max}}^{\textbf{{and}}}\textbf{{-}}\textbf{{-}}\textbf{{C}^{t}}_{\textbf{min}}^{ \textbf{{and}}\textbf{{f}}}}{\textbf{{M}}\textbf{{t}}} \tag{2}\]  
where \(\textbf{{CTFC}^{t}}\textbf{{and}}\textbf{{f}}\) is the change rate of capacitance, \(\textbf{{C}^{t}}_{\textbf{max}}^{\textbf{{and}}\textbf{{f}}}\) is the capacitance of the experimental sample with maximum moisture content, and \(\textbf{{C}^{t}}_{\textbf{min}}^{\textbf{{and}}\textbf{{f}}}\) is the capacitance of the experimental sample with minimum moisture content in temperature **f** and frequency **f**. \(\textbf{{M}}\textbf{{t}}\) is the difference between the maximum moisture content and the minimum moisture content of experimental samples in temperature **t**. The greater the change rate of capacitance, the greater the change value of capacitance to the change of the paddy moisture content. Figure 3 shows the changing rate of capacitance over the frequency range from 100 Hz to 1 MHz with temperature range from 40 \({}^{\circ}\)C to 80 \({}^{\circ}\)C in a log-log plot. Figure 2: Frequency dependence of capacitance at temperature ranges of 40 to 80 \({}^{\circ}\)C.  
It can be clearly seen from the graph that, as the frequency increases, the change rate of capacitance gradually decreases. Paddy capacitance is more sensitive to a change of paddy moisture content at lower frequencies. It can be seen from the above analysis and Figure 3 that the lower the frequency, the higher the sensitivity of the capacitance to the change of the moisture.