# Specific Resonant Properties of Non-Symmetrical Microwave Antennas
## 3 Results and Discussion
### Resonance Properties of Measured Flat Microwave Antennas  
In our general determination of the resonant properties of antennas, measurements were performed on various types of antennas, like cylindrical, square, and rectangular. Measurements made on flat metal material of various thicknesses were also performed. These antennas are classified as flat microwave antennas. After manufacturing complete sets of these antennas with the appropriate dimensions, their resonant properties were measured and recorded. During the measurements (made by observing discrete values of resonant frequencies), it became apparent that the way frequency values change based on length in flat microwave antennas is different than antennas with cylindrical cross-sections. This can be demonstrated on a graph (Figure 11). Some types of flat microwave antennas, whose cross-sectional dimensions in both planes are not the same, show similar resonance dependences but are still different from cylindrical antennas. When enlarging only one of the transverse dimensions of the flat microwave antenna (like width), the course of the change of the frequency dependence on the length of the antenna does not have the same parallel curvature as for cylindrical antennas (Figure 8). In the case of the flat microwave antennas and other flat antennas, each set of antennas has a different curvature, a different steepness and, consequently, they intersect at one point. For the purposes of this article, we call this crossover value a \"significant\" point and it is marked with the letter \(S\). Based on the measured values of the resonant frequency of each antenna, the corresponding wavelength was determined similarly to cylindrical antennas. By knowing the wavelength of the resonant frequency and knowing the specific length of the antennas, it was possible to determine the \(l/\lambda_{res}\) ratio, which determines its resonant point. The values of resonance points calculated in this way of individual types of measured flat microwave antennas are shown in Table 3.  
Figure 10: Concentrated distribution of the position of the resonant points of a set of cylindrical antennas. Figure 12 shows the resonance points of flat microwave antennas when the reactance value of the antenna is zero. In Figure 12a are points corresponding to a thin antenna with a strip width w = 5 mm. The points corresponding to a medium-thick antenna with a bandwidth \(w\) = 10 mm are in Figure 12b. The points corresponding to a thick antenna with a bandwidth \(w\) = 30 mm are shown in Figure 12c. Depending on the length of the antenna, \(l\) = (20, 55, 70) mm, each triple of antennas of corresponding strip width \(w\) = (5, 10, 30) mm forms a low-slim, slim, and very slim flat microwave antenna. Even in this case, antennas with a small height (20 mm) are low-slim antennas with slimness coefficients \(\Omega_{w5}\) \(l_{20}\), \(\Omega_{w10}\) \(l_{20}\), \(\Omega_{w30}\) \(l_{20}\). Medium height antennas (55 mm) are medium slim antennas with slimness coefficients \(\Omega_{w5}\) \(l_{55}\), \(\Omega_{w10}\) \(l_{55}\), \(\Omega_{w30}\) \(l_{55}\). High height antennas (70 mm) are very slim antennas with slimness coefficients \(\Omega_{w5}\) \(l_{70}\), \(\Omega_{w10}\) \(l_{70}\), \(\Omega_{w30}\) \(l_{70}\). In the case of the whole measured set of 18 flat microwave antennas, the value of the resonance point changes from a maximum of 0.247 to a minimum of 0.139, which represents the total range of 0.108. This fact is known in antenna theory and used in antenna technology for the realization of small broadband antennas. The influence of the slimness coefficient change \(\Omega\) of the flat antenna on the change of the ratio \(l/\lambda_{res}\) due to changing its width \(w\) at the same height \(l\), or due to changing its height \(l\) at the same width \(w\) can be seen in Figure 12. Also, it can be quantified from Table 4.  
Figure 11: Dependence of resonant frequencies of flat microwave antennas on their length showing the significant crossover point \(S\).