## 1 Introduction  
Honey has been around since 7000 BC in the Stone Age [1]. It contains components such as organic acid, minerals and protein [2]. Honey products are usually directly consumed, and some of its products are used in the food industry for such things as infant food and ice cream. They also play a role in pharmaceuticals such as in the flavor of medicines [3]. The International Food Regulations have specified that pure honey must not contain any additives. However, additive sweeteners and water are widely used in honey. This adulteration is intended to increase volume and reduce cost, which is a major issue, since the contamination affects the nutritional value of honey. The color, concentration and viscosity of adulterated honey are quite similar to pure honey, making the adulterated honey even harder to detect by consumers. Consumers typically detect adulteration by sensory observations of the honey's physical characteristics, which include color, viscosity and crystallization. The contamination can be detected by chemical analysis in the laboratory using methods such as chromatography, optical transmission analysis [3] and mass spectrometry [4]. These methods are complex processes. As such, the development of a fast, simple and low-cost method for honey adulteration detection is absolutely necessary. Based on previous studies, many researchers have measured the complex relative permittivity and physical properties of materials associated with medical, constructional, industrial, or agricultural applications [5, 6, 7]. In [8], an open-ended coaxial probe is used to measure the complex relative permittivity of apples in a frequency range of 10-1800 MHz. The obtained relative permittivity can be used to determine properties such as moisture content and pH value of apples. A waveguide and coaxial transmission line technique are applied to measure the complex relative permittivity of eggs to predict the quality index of eggs [9]. In addition, the dielectric properties of honeybee melons are measured in order to compare it to the quality of honeybee melons [10]. There are also many other researchers interested in measuring the physical properties of food and agricultural materials [11, 12, 13, 14, 15]. Water, a main component in agricultural products i.e., honey, is sensitive to applied microwave frequencies and therefore the complex relative permittivity is dominantly influenced by the water content. The complex relative permittivity of a substance in an aqueous solution depends on water content. A water molecule is dipolar, which can be polarized in the range of microwave frequencies, and produce a tetrahedral molecular structure [4]. However, when other substances dissolve in water, the molecular structure of water changes, affecting polarization properties in the microwave frequency range, leading to a change in complex relative permittivity [4]. Measurement of the complex relative permittivity of honey sample can be applied to determine water content in honey sample, which is an indicator of honey quality in food industries. Understanding of the complex relative permittivity of honey is necessary to develop a model and thus assess the quality of honey. Although the dielectric properties of some agricultural materials have been studied, not many studies of the agricultural materials investigate the electrical conductivity and the phase constant with different microwave frequencies in the agricultural materials. There is little knowledge of how water content affects the complex relative permittivity, the electrical conductivity, and the phase constant of honey at microwave frequencies. The complex relative permittivity (\(\varepsilon_{r}\)) of materials can be written as shown in Equation (1) [5]:  
\[\varepsilon_{r}=\varepsilon_{r}^{\prime}-j\varepsilon_{r}^{\prime\prime}, \tag{1}\]  
where \(\varepsilon_{r}^{\prime}\) is the real part of complex relative permittivity, and \(\varepsilon_{r}^{\prime\prime}\) is the imaginary part of complex relative permittivity.