# A VHF Circularly Polarized Turnstile Antenna with Balun for Meteor Radar
## 5 Results Comparison and Discussion  
### Experiment 2  
Figure 11 shows the measured phase difference and magnitude of ports in the improved feeding network. The measurements are taken with a vector network analyzer and only two-port scattering parameter measurements are taken with the other port terminated with a standard 50 \(\Omega\) load. Within the operation band from 38.5 MHz to 39.5 MHz, the phase difference between Port2 and Port3 of the feeding network ranges from 87.3\({}^{\circ}\) to 90\({}^{\circ}\). Achieving circular polarization or elliptical polarization is an essential prerequisite for successful feeding. The maximum phase unbalances from 180\({}^{\circ}\) between Port2 and Port3 are 1.3\({}^{\circ}\) and 1.05\({}^{\circ}\) at the operation band, respectively. The maximum amplitude unbalances of Port2 and Port3 are 0.215 dB and 0.24 dB. The new baluns are designed to be inserted at the two ports of the antenna. In addition, the improved antenna forms an array that can be applied in the meteor radar system. The new round of verification experiments is taken from 20 to 24 August 2022. As shown in Figure 12 and Table 4, the antenna equipped with the new feeding network can detect a greater number of meteors, and the azimuth distribution correlation can reach 0.8467, as compared to the data from the ATRAD radar. This indicates the good radiation performance and the application ability of the designed antenna. Figure 11: Measurement results of magnitude unbalance and phase unbalance of new feeding network. Figure 10: The prototype of the improved feeding network. (a) the circuit principal diagram of balun and (b) photo of feeding network. Figure 12: Comparison of count and azimuth distribution of meteors. Meteor radar with antennas of Chinese Meridian Project (**a**,**c**) and proposed and improved (**b**,**d**). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Time** & **Meteor Radar with ATRAD** & **Meteor Radar with Proposed** \\
**(UT Hour)** & **Antennas** & **Antennas** \\ \hline
0–24 & 13,874 & 13,866 \\
24–48 & 13,156 & 14,394 \\
48–72 & 12,359 & 15,435 \\
72–96 & 12,890 & 15,749 \\
96–120 & 14,871 & 15,569 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statics table of meteor quantity with improved antenna. Discussion  
The balun plays an important role in the designed antenna. The prototype of the balun (shown in Figure 10) is proposed in reference [23]. This type of balun is similar to a single bifilar winding transformer, except for an additional length of winding being added. Under the condition of low loss and phase shifting, the characteristics of the current distribution on the three wires are as follows [24,25]:  
1. Equal current always flows through two of the three wires;
2. The sum of the currents is equal to the current flowing through the other wire in the opposite direction;
3. The points at both ends of the three wires are distributed evenly. The equations are listed as:  
\[V_{1}-V_{2}=V_{2}\cos\beta l+jI_{2}Z_{oo}\sin\beta l \tag{3}\]  
\[I_{1}=I_{2}\cos\beta l+j\frac{V_{2}}{Z_{oo}}\sin\beta l \tag{4}\]  
\[V_{2}=V_{3}\cos\beta l+jI_{2}Z_{oo}\sin\beta l \tag{5}\]  
\[I_{1}=I_{2}\cos\beta l+j\frac{V_{3}}{Z_{oo}}\sin\beta l \tag{6}\]  
where, \(V_{1}\) and \(V_{2}\) are termination voltages, and \(I_{1}\) and \(I_{2}\) are termination currents. \(Z_{oo}\) is the odd mode impedance and \(\beta l\) is electrical length with a unit of rad of windings. \(R_{g}\) is the power impedance and \(R_{b}\) is the load input impedance. Then, when \(R_{g}=R_{b}\), the transmission coefficient (\(T\)) of the transformer can be described as:  
\[T=\cos^{2}\beta l+\frac{1}{4}\bigg{(}k+\frac{1}{k}\bigg{)}\sin^{2}\beta l \tag{7}\]  
\[k=\frac{2Z_{oo}}{\sqrt{R_{g}R_{b}}} \tag{8}\]  
Equations (7) and (8) indicate that the optimum transmission condition is \(R_{g}=R_{b}\). This just meets the demand of the designed antenna. During the experiment, it was also found that this kind of transformer can be used for broadband RF devices. This idea will also be included in the next research.