# Design of Typhoon Detection Downcast Device Based on Four-Arm Helical Antenna Structure
## 2 Theoretical Studies
### Radiation Principle of Four-Arm Helical Antenna  
When introducing the radiation principle of the four-armed helical antenna, the antenna can be equated to two orthogonal two-armed helical antennas with a 90-degree phase difference [16], as shown in Figure 4.  
Figure 3: Schematic diagram of a four-armed helical antenna.  
One of the parts was selected for analysis after the structural decomposition. When the antenna works, the current density on the double-armed helix varies, as the cosine current at the middle position of the helical arm is zero, and the current at the feed point and the open and short-circuit points is maximum. Therefore, a single part can be equated with a vertically placed magnetic oscillator and a horizontally placed electric oscillator structure, as shown in Figure 5. \(I_{L}\) is the current loop current, and \(I_{D}\) is the electric vibrator current.  
Similarly, another equivalent model can be obtained, and if the 0\({}^{\circ}\) and 90\({}^{\circ}\) equivalent models are combined, the complete four-arm helical antenna equivalent model can be achieved, as shown in Figure 6.  
After simplifying the equivalent model of the four-armed helical antenna, the magnitude of the superimposed electric field at a certain position in the far-field region can be calculated using a combination of individual electromagnetic oscillators according to the following equation:  
\[E_{\theta}=\frac{60\pi I_{D}\sin\theta}{r}\frac{L}{\lambda}e^{-jkr} \tag{2}\]  
\[E_{\varphi}=\frac{120\pi^{2}I_{L}\sin\theta}{r}\frac{A}{\lambda^{2}}e^{-jkr} \tag{3}\]  
Figure 4: Decomposition schematic of the structure of the four-armed helical antenna.  
Figure 5: Decomposition schematic of the structure of the four-armed helical antenna.  
Figure 6: Equivalent model of four-armed helical antenna.  
Simplification leads to the following:  
\[E_{\theta}=j\frac{K_{1}}{r}\sin\theta e^{-jkr} \tag{4}\]  
\[E_{\varphi}=j\frac{K_{2}}{r}\sin\theta e^{-jkr} \tag{5}\]  
In the above equation, \(L\) is the length of the electric oscillator; \(A\) is the area of the magnetic oscillator; \(\lambda\) is the working wavelength; \(r\) is the distance from any point (\(P\)) to the origin in free space; and \(k=2\pi/\lambda\), and \(K_{1}\) and \(K_{2}\) are different constants. Then, the electric fields in the far-field region of the two equivalent models of the decomposition are expressed as follows:  
\[\left\{\begin{array}{l}E_{\theta 1}=K_{1}e^{-j\left(kr-\frac{\pi}{2}\right)} \left(\sin\varphi+j\cos\varphi\sin\theta\right)\\ E_{\varphi 1}=K_{2}e^{-j\left(kr-\frac{\pi}{2}\right)}\left(\cos\varphi\cos \varphi-j\sin\theta\right)\end{array}\right. \tag{6}\]  
\[\left\{\begin{array}{l}E_{\theta 2}=K_{1}e^{-jkr}(-\cos\varphi+j\cos\theta \sin\varphi)\\ E_{\varphi 2}=K_{2}e^{-jkr}(\cos\theta\sin\varphi+j\cos\varphi)\end{array}\right. \tag{7}\]  
In the above equation, the addition of the \(e^{-j\frac{\pi}{2}}\) term indicates a 90\({}^{\circ}\) phase shift, which is superimposed to obtain the total far-field region electric field as follows:  
\[\left\{\begin{array}{l}E_{\theta}=E_{\theta 1}+E_{\theta 2}=(\cos\theta+1)e^{-j \varphi}\\ E_{\varphi}=E_{\varphi 1}+E_{\varphi 2}=(\cos\theta+1)e^{-\left(j\varphi- \frac{\pi}{2}\right)}\end{array}\right. \tag{8}\]  
In the above equation, it is easy to see that the direction diagram is presented as a cardioid line, indicating that the far-field region radiation characteristics of the equivalent model of the four-armed helical antenna are equivalent to two pairs of mutually orthogonal electromagnetic oscillator antennas.