## 3 Results and Discussions
A figure of merit (FOM1) for measuring the performance of this technique using the real part of complex relative permittivity is calculated in Equation (10). \[FOM1=\frac{\Delta\varepsilon_{r}^{\prime}}{\Delta(\%w/w)} \tag{10}\]  
The FOM1 can help to judge how well the performance of this technique using the real part of permittivity is. From Figure 8a, the measured results show that the difference of the real part of complex relative permittivity (\(\Delta\varepsilon_{r}^{\prime}\)) of pure honey and the honey sample (water adulteration for 30%\(w\)/\(w\)) is 33.24 at the frequency of 0.6 GHz and the temperature of 25 \({}^{\circ}\)C while the difference of water content of both samples is 30%\(w\)/\(w\). Therefore, the FOM1 is equal to 1.108 (\(\%w\)/\(w\))\({}^{-1}\) at the frequency of 0.6 GHz. Figure 11 shows the FOM1. The FOM1 is performed at the frequency of 4.0 GHz as well. Its FOM1 is equal to 0.715 (\(\%w\)/\(w\))\({}^{-1}\). From the results, it shows that the real part of the complex relative permittivity is the most appropriate indicator in water adulteration detection in honey at 0.6 GHz, and the FOM1 is equal to 1.108 (\(\%w\)/\(w\))\({}^{-1}\). Figure 9 shows the electrical conductivity of the adulterated honey samples with water in the range of 0-30%\(w\)/\(w\). The electrical conductivity increases when compared to pure honey. The electrical conductivity is slightly changed in the frequency range of 0.5-1.5 GHz while the significant increase occurs in the higher frequency range of 1.5-4.0 GHz. A figure of merit (FOM2) for measuring the performance of this technique using the electrical conductivity is described in Equation (11). \[FOM2=\frac{\Delta\sigma}{\Delta(\%w/w)} \tag{11}\]Figure 7: (**a**) Complex relative permittivity (**b**) electrical conductivity (**c**) phase constant of pure honey in the frequency range of 0.5–4.0 GHz at the temperature of 25 \({}^{\circ}\)C.  
Figure 8: (**a**) Real part (**b**) imaginary part of the complex relative permittivity of honey samples which are adulterated by water with different concentrations over the frequency range of 0.5–4.0 GHz at the temperature of 25 \({}^{\circ}\)C.  
Figure 12 demonstrates the FOM2 in the frequency range of 0.5-4.0 GHz. The maximum FOM2 is equal to 0.069 S/m * (%\(\omega\)/\(w\))\({}^{-1}\) at the frequency of 3.74 GHz. Therefore, the frequency of 3.74 GHz is the most appropriate frequency when the electrical conductivity is considered the indicator. Figure 10 shows the phase constant of the adulterated honey samples with water in the range of 0-30%\(\omega\)/\(w\). The phase constant increases when compared to pure honey. The significant change occurs in the frequency range of 1.5-4.0 GHz. A figure of merit (FOM3) for measuring the performance of this technique using the phase constant is given by Equation (12). \[FOM3=\frac{\Delta\beta}{\Delta(\%w/w)} \tag{12}\]  
Figure 13 depicts the FOM3 in the frequency range of 0.5-4.0 GHz. The maximum FOM3 is equal to 0.007 rad/mm * (%\(w\)/\(w\))\({}^{-1}\) at the frequency of 4.0 GHz. The frequency of 4.0 GHz is the most suitable frequency when the phase constant is considered the indicator. Figure 10: Phase constant of honey which is adulterated by water with different concentrations over the frequency range of 0.5–4.0 GHz at the temperature of 25 \({}^{\circ}\)C.  
Figure 7.0 Electrical conductivity of honey, which is adulterated by water with different concentrations over the frequency range of 0.5–4.0 GHz at the temperature of 25 \({}^{\circ}\)C.  
From the FOMs, it can be concluded in Table 2 according to the indicators for measurements. In regression analysis (R\({}^{2}\)) for the real part of complex relative permittivity, the electrical conductivity, and the phase constant, curve fitting is the process of determining which model best fits specific curves in the data set. It is found that the real part of complex