# Specific Resonant Properties of Non-Symmetrical Microwave Antennas
## 3 Results and Discussion
### Resonance Properties of Measured Classical Cylindrical Antennas  
Our original research aimed to experimentally verify the above facts, i.e., how the dimensions, shape and material of their components affect the resonant frequencies of antennas. Results similar to the illustrated graphs in Figure 7 were expected, but with real measured values of resonant frequencies, as per Figure 8. In these graphs it is possible to quickly orientate for the purpose of the production of antenna models, operating in the required frequency band, to use them in measurements on aircraft models. Although the implemented and measured sets included antennas with six different diameters \(\phi=\) (6, 8, 10, 12, 15, 25) mm, only antennas with three diameters \(\phi=\) (6, 12, 25) mm are used for the graph plots below in this article. Based on the measured values of the resonant frequency of each antenna, the corresponding wavelength, \(\lambda_{res}=c/f_{res}\), was determined from a known relationship. By defining the wavelength of the resonant frequency \(\lambda_{res}\) for a particular antenna in terms of its length \(l\) and diameter \(\phi\), it was possible to determine its ratio \(l/\lambda_{res}\). Since this was the first resonant frequency (also called the serial or quarter-wave frequency), the value of this ratio is always less than 0.25. The calculated values of resonance points as values of the ratio \(l/\lambda_{res}\) of individual types of measured cylindrical antennas are shown in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline
**20** & **30** & **40** & **50** & **60** & **70** & \(I\) **[mm]** \\ \hline
0.196 & 0.200 & 0.209 & 0.225 & 0.237 & 0.245 & (\(\phi=6\) mm) \\
0.189 & 0.194 & 0.202 & 0.215 & 0.225 & 0.234 & (\(\phi=12\) mm) \\
0.181 & 0.187 & 0.193 & 0.205 & 0.213 & 0.223 & (\(\phi=25\) mm) \\ \hline \end{tabular}
\end{table} 
Table 1: Values of resonance points \(l/\lambda_{res}\) of cylindrical antennas. Figure 7: The graphical course of resonant frequencies depending on the slenderness of the dipole. Based on the explanation of the general impedance dependence of the antenna on the \(l/\lambda\) ratio, presented in Figures 5 and 6, only three calculated values of \(l/\lambda_{res}\) from the measured values in Figure 6 were selected from Table 1 and subsequently plotted in the graphs in Figure 7. To be able to align the measured values of the antennas with the respective values given in Table 1 with their graphical representation in Figures 8 and 9, the numerical values and their respective graphic waveforms are highlighted and aligned. Figure 9 shows the resonant points of cylindrical antennas on the axis of the \(l/\lambda_{res}\) ratio, when the respective antenna is in resonance and thus when the reactance value of the antenna is \(X=0\). The resonant points corresponding to a thin antenna with a conductor diameter \(\phi=6\) mm are presented in Figure 9a. The resonant points corresponding to an antenna conductor with a mean value of the diameter of \(\phi=12\) mm are shown in Figure 9b. The resonant points corresponding to a thick antenna with a conductor diameter \(\phi=25\) mm are in Figure 9c. Depending on the length of the antenna (shown only for 20, 50 and 70 mm), each trio of antennas of the respective diameter (6, 12, 25) mm forms a slightly slim, slim, and very slim cylindrical antenna:  
\[ \begin{array}{l}\text{Low-height antennas ($l=20$ mm) are slightly slim antennas }\Omega_{\phi 6}\;l_{20},\;\Omega_{\phi 12}\;l_{20},\;\Omega_{\phi 25}\;l_{20} \text{Medium height antennas ($l=50$ mm) are slim antennas }\Omega_{\phi 6}\;l_{50},\;\Omega_{\phi 12}\;l_{50},\;\Omega_{\phi 25}\;l_{50} \text{High-height antennas ($l=70$ mm) are very slim antennas }\Omega_{\phi 6}\;l_{70},\;\Omega_{\phi 12}\;l_{70},\;\Omega_{\phi 25}\;l_{70}.\end{array} \]  
Figure 8: Dependence of resonant frequencies of cylindrical antennas on their length.