# Using Modeling to Select the Type of Microwave Field Emitter for Dense-Layer Grain Dryers
## 2 Materials and Methods
### Features of Electromagnetic Field Transmission by Horn Waveguides  
According to the classification, horn antennas belong to the aperture class antennas. They have emitting elements in the form of planar aperture in which angular distribution of the microwave field is achieved. Among advantages of these antennas are a relatively simple and reliable design, convenience of connecting to waveguide transmission lines, rather low energy loss and wide bandwidth [29; 30]. Horn antennas are applied in a broad frequency interval ranging from decimeter to millimeter waves. Typical horn antenna design structure is a smooth transition interface between the waveguide's open end and the radiating surface (aperture). The latter is of large size in order to enhance its radiation directionality and, therefore, to attain better matching between the radiator and the feeder transmission line. The authors used a combination of \(H\)-sectorial and pyramidal horns (see Figure 6a,b). The upper plane of the horn has \(H\)-sectorial form while the lower one is made in the form of a pyramidal horn (Figure 6c). This design is adopted to have the ability to control the direction of the electromagnetic field as it propagates through the grain layer. Since the microwave convective processing system is assembled from modules, one of which is depicted in Figure 1, this waveguide construction allows for directional changes based on the module's position. For instance, when grain enters the upper microwave convective module from the receiving hopper, a downward-directed horn is used. This is done to prevent the microwave field from exiting the system when the grain level in the receiving hopper decreases. In the lower modules of the system, near the discharge hopper, a downward-directed horn is also utilized. This enables the propagation of the electromagnetic field in the lower part of the system. The opposite direction of the field of the horns in two consecutive zones is used in the lower half of the processing plant, where the moisture content in the processed grain  
Figure 6: Horn antennas and the antenna used in the processing plant under studies [13]: (**a**) \(H\)-sectorial horn; (**b**) pyramidal horn; and (**c**) combined-type horn. becomes lower and, consequently, the intensity of the microwave field acting on the grain layer can be increased. The directional gain (DG) of an aperture-type antenna is defined from the following formula [31]:  
\[D=\frac{4\pi S}{\lambda^{2}}\gamma, \tag{5}\]  
where \(S\) is the aperture area surface (m\({}^{2}\)), \(\lambda\) is the radiation wavelength (m), and \(\gamma\) is the aperture efficiency (AE) depending on the field amplitude and phase distribution in the radiator aperture (a.u.). The maximum value of AE (\(\gamma\) = 1) is attained in conditions of uniform and coherent excitation of the aperture. In a first approximation, the field amplitude distribution in the horn aperture has a sinusoidal form, in the plane of vector \(H\)[32]:  
\[\frac{E(y)}{E_{max}}\approx\sin\left(\frac{\pi y}{B}\right), \tag{6}\]  
where \(B\) is aperture area dimension along axis \(y\) (m),  
\(E(y)\) is electromagnetic field intensity along axis \(y\), (V/m), and  
\(E_{max}\) is the maximum value of electromagnetic field, in the aperture (V/m). The phase of the field in the aperture changes in accordance with nearly a square law because of the curvilinear form of the wave edge surface. The change in the direction of the electromagnetic field (and its power) at the output of the horn radiator can be described by a second-order equation. The phase displacement has its maximum \(\Phi max\) on the borders of the aperture area and is equal to:  
\[\Phi_{max}\approx\frac{\pi A^{2}}{4\lambda R}. \tag{7}\]  
For a constant length \(R\) of the horn, the aperture area \(S\) grows with the aperture size \(A\) (Figure 7), resulting in decreasing AE due to the increasing phase nonuniformity. The gain of a horn antenna reaches its maximum at specific values of the aperture size (phase error at the edge of the aperture).