ANALYSIS OF MATERIAL POSITION AND SIZE IN A WAVEGUIDE FED RESONATOR

The main factors that affect electric field distribution, and therefore heat distribution, are the dimensions of the resonator, heating frequency, shape and dielectric properties of the material to be heated, position of the material to be heated within the resonator and the position of the feed guide on the resonator. From among these factors that directly affect heating, this work examined the material thickness. The purpose of this study was to determine the material thickness that will minimise the reflection coefficient. The accuracy of the results obtained by means of the mode matching method was demonstrated by comparing those results with the results obtained through Ansoft’s High Frequency Structure Simulator.


INTRODUCTION
Today, there are many papers being published on microwave heating, the use of which is very common (Jia, 1993, Liu et. al., 1994, Iskander et. al., 1994, Zhao and Turner, 1996, Dibben and Metaxas, 1996, Sunberg et. al., 1996, Liu et. al., 1996, Reader and Chan, 1998, Hallac and Metaxas, 2003).frequency (Requena-Perez et. al., 2004, Monzo´-Cabrera et. al., 2004, Plaza-González et. al., 2005, Pedreno-Molina et. al., 2006, Süle and Kent, 2010).In the present study, however, the effect of material thickness, a component that has not been thoroughly examined, on the variation of the reflection coefficient was examined.In the analysis, the position in which the reflection coefficient is minimised and the thickness of the material were determined by holding the resonator dimensions, feed position, and operating frequency fixed and varying the material thickness.
There are two primary innovations that are introduced with the conducted analysis.While the first of these is the obtainment of the reflection coefficient on the basis of material thickness, the second is the fact that results were obtained in a short period of time.As it is necessary with the use of Ansoft HFSS, which works on the basis of Finite Element Method (FEM) and was used in this study, or Finite Difference Time Domain (FDTD) method to make a new model for each position and thickness value of the material, obtaining the reflection coefficient takes a very long time.Yet, by means of the position and thickness information that can be defined as variables in the algorithm through the mode matching method in this study, the variation of the reflection coefficient according to the position and thickness of the material can be obtained in a very short period of time and with a high level of accuracy.

FORMULATION
We can divide the resonator into four basic parts as shown in Figure 1.The variable c 1 is the starting point of the feeding guide's x coordinate, and c 2 is the last point of the feeding guide's x coordinate.In the same way, v 1 is the starting point of the feeding guide's y coordinate, and v 2 is the last point of the feeding guide's y coordinate.The variable t is the slab thickness and, d and l are the empty spaces of the resonator.The variables a and b are, respectively, the resonator's x and y dimensions.
where k is the mode propagation constant, e h is the normal TE mode vector, h h is the normal TM mode vector, m and, n are mode indices, E t is the tangential electric field, H t is the tangential magnetic field.
For z=0 By finding the reflection coefficient in the second part, which is indicated with a minus sign, the equation below, which consists of the effects of the third and fourth parts, can be used as follows : We can write the approximate magnetic current as follows: The magnetic current is approximated with a truncated set of independent basis functions: By solving the above matrix equation, it is possible to determine the a mnx and a mny coefficients.The B coefficients can be obtained by means of (26).On the condition that the waveguide is between c 1 and c 2 in the x direction and between v 1 and v 2 in the y direction the base and weighting functions can be presented as follows (Terril, 1998):

NUMERICAL RESULTS
In this study, the amplitude of the reflection coefficient according to the change in material thickness was found in relation to the different positions of the material within the resonator.The results obtained with the mode matching method were compared with the results obtained through Ansoft HFSS.The variations in the reflection coefficient were determined by changing the material thickness within the range of 10 mm and 85 mm for different material positions.While the dielectric constant of the material was taken as 4.17-1.55i,the dimensions of the resonator were taken as 378 mm along the x axis, 258 mm along the y axis and 325 mm along the z axis.
Examining Figure 2 reveals that, for a height of d=60 mm, the minimum reflection coefficient value is obtained when the material thickness is t=80 mm.Material thicknesses of t=20 mm and t=40 mm are the other thickness values that result in low reflection coefficients.

Sectional view of the electric field distribution on the material when the material is 80 mm thick for d=60 mm
Examining the electric field distributions in Figures 3 and 4 shows that because the thickness of the material is large, the power had only a slight effect on the material.

Figure 5:
Reflection coefficient variation according to the material thickness for d=120 mm Figure 5 shows that at a height value of d=120 mm, the lowest reflection coefficient is obtained when the material thickness is t=55 mm; t=60 mm and t=65 mm are the other two material thickness values that resulted in low reflection coefficients.

Figure 6:
Top view of the electric field distribution on the material when the material is 55 mm thick for d=120 mm

Figure 7: Sectional view of the electric field distribution on the material when the material is 55 mm thick for d=120 mm
Examining Figures 6 and 7 show that the electric field distribution is not homogenous and local.

Figure 8: Reflection coefficient variation according to material the thickness for d=180 mm
From Figure 8, it can be observed that, at a height of d=180 mm, the reflection coefficient exhibits the lowest value when the material thickness is t=30 mm; t=60 mm and t=85 mm are the other two material thickness values that resulted in low reflection coefficients.Giving the reflection coefficient changes according to material thickness, figure 2, figure 5, figure 8 and figure 11 to obtain the sixty-eight different modeling was made by Ansoft HFSS.The method presented in this article, the reflection coefficient changes according to material thickness, with a single modeling, in a much shorter time and with high accuracy was obtained.

CONCLUSIONS
The objective in microwave heating is to uniformly distribute the field change on the material to be heated over as wide of an area as possible.In this way, homogenous heating can be achieved.A low reflection coefficient means that the power reflecting to the feed will be low.However, a low reflection coefficient does not necessarily mean that all the power will interact with the material to be heated.For instance, at a value that gives a low reflection coefficient, the power may be stored within the resonator.Nevertheless, to increase power efficiency within the oven, the material has to be placed at the position where the reflection coefficient is low.Doing so increases the possibility of the power interacting with the material.
The conclusions presented below are reached by examining the figures showing the electric field variation: When the material is positioned at a height of d=120 mm from the base of the resonator, the reflection coefficient is s 11 =0.0046 when the material thickness is t=55 mm.This indicates a power efficiency of 99.997 %.However, when the field changes on the material are examined, it is observed that the electric field affected the surface of the material as a hot point, and there was no significant effect within the material itself.This means that the electric field is mainly stored within the resonator.
When the material is positioned at a height of d=240 mm from the base of the resonator, the reflection coefficient is s 11 =0.1004 when the material thickness is t=25 mm.According to the formula p=1-(s 11 ) 2 , there is 98.991 % power efficiency.Examining the area changes on the material revealed that the electric field uniformly affected a wide area at the top of the material.The power was also effectively distributed within the material.Considering all of these data, it is possible to assert that the reflection coefficient variations obtained by alternating the position and the thickness of the material by means of a mode matching system is the first and the most important design phase for microwave ovens.By examining the field changes at the values for which the reflection coefficient is low, the position where the material will be placed within the resonator and the thickness of the material can be determined with a few electric field analyses.

Figure 1 :
Figure 1:Three dimensional rectangular cavity loaded with lossy slab When the basic equalities are taken into account and the equality of the tangential electric field compounds on the point of the first and the second area intersection on the aperture and mode matching equalities in the related boundaries are used, the equation for the electric field can be formed as follows:

Figure 2 :
Figure 2: Reflection coefficient variation according to the material thickness for d=60 mm

Figure 3 :
Figure 3: Top view of the electric field distribution on the material when the material is 80 mm thick for d=60 mm

Figure 9 :Figure 10 :
Figure 9: Top view of the electric field distribution on the material when the material is 30 mm thick for d=180 mm

Figure 11 :
Figure 11: Reflection coefficient variation according to the material thickness for d=240 mm

Figure 12 :Figure 13 :
Figure 12: Top view of the electric field distribution on the material when the material is 25 mm thick for d=240 mm )