# Research on Ultra-Low-Frequency Communication Based on the Rotating Shutter Antenna
## 2 Principle and Simulation of the Rotating Shutter Antenna  
The radiation principle of the rotating permanent magnet antenna can be summarized as follows: the motor drives the magnet to rotate so that its static magnetic field is converted to an alternating magnetic field. The corresponding relationship between the signal frequency and the motor speed \(n\) can be expressed as  
\[f=\frac{n}{60} \tag{1}\]  
When the speed \(n\) of the drive motor is greater than 18,000 rpm, the frequency of the signal obtained is greater than 300 Hz, which is difficult for common servo motors on the market.  
The rotating shutter antenna was proposed by [PERSON] in 2018 [25] and the prototype mainly consists of magnets and a shutter made of soft magnetic materials, such as permalloy, whose relative permeability is significant. Assuming that the number of openings is \(N\), the antenna needs two \(N\) magnets of different polarities which are alternately placed to form a circle. During the working process, the shutter rotates to block the permanent magnets of different polarities to generate an altering magnetic field, whose frequency is \(N\) times the rotating fundamental frequency. The relationship between frequency and speed can be expressed as  
\[f=\frac{n}{60}\cdot N \tag{2}\]  
Compared with RPMA, the rotating shutter antenna can reduce the speed to \(n/N\). The block diagram of the antenna principle when \(N\) = 4 is shown in Figure 1.  
ANSYS Maxwell was used to analyse a rotating shutter antenna with \(N\) = 4; the parameters of the simulation are shown in Table 1. A free-space sphere with a radius of 4 m was established and the boundary adopted natural boundary conditions, which made the magnetic field continuous inside and outside the simulation area. The magnetic field produced by the permanent magnets was used as excitation and the effects of eddy current induced on the shutter were considered. Regardless of mechanical damping, a band area with a set rotation speed of 4800 rpm was used to simulate the rotation of the shutter, which corresponded to a fundamental rotation frequency of 80 Hz, so the frequency of the magnetic field signal was, theoretically, 320 Hz.  
We placed a point at the position of 3 m in the axial direction of the rotating shutter antenna and obtained the B\({}_{z}\)-field. The simulated results are shown in Figure 2. Figure 2a shows the signal with an amplitude of 3.5 nT at the point 3 m away from the transmitter, which is much smaller than the theoretical value. The corresponding spectrogram is shown in Figure 2b, which represents B\({}_{z}\)-field strength as a function of time and frequency. It can be clearly seen the signal whose frequency is 320 Hz in the spectrogram and multiple harmonics are visible.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline radius of the magnet & 10 mm & magnetic remanence & 1.47 T \\ height of the magnet & 100 mm & thickness of the shutter & 1.5 mm \\ openings of the shutter & 4 & rotating speed & 4800 rpm \\ \hline \hline \end{tabular}
\end{table}
Table 1: The parameters of the simulation.  
Figure 1: Block diagram of the rotating shutter antenna when \(N\) = 4.  
The magnetic field intensity distribution on the rotating shutter at different times is shown in Figure 3. It is clear that a large part of the energy was concentrated on the shutter, which may be one of the reasons for the field strength being smaller than the theoretical calculation.  
The side view and top view of the distribution of the B-field by intercepting different planes in the simulation are shown in Figure 4. The fast attenuation of the signal can be ascribed to both the interaction of the high-permeability shutter and the mutual cancellation of magnets.  
Figure 3: B-field distribution on the rotating shutter at different times: (**a**) t = 0 s; (**b**) t = 0.667 ms; (**c**) t = 1.67 ms.  
Figure 2: (**a**) Field at the point 3 m away from the shutter antenna. (**b**) Spectrogram of field.