# Design and Experiment of Magnetic Antenna Vibration and Noise Reduction System
## 2 Demand Analysis of Vibration Reduction  
In essence, the induced noise of magnetic antenna motion is caused by the change of magnetic flux caused by the vibration of coil in the geomagnetic field, which mainly comes from fluid excitation and transmission vibration. Not long ago, [PERSON] et al. (2017) built a magnetic antenna test platform and simulated its working environment in underwater electromagnetic signal detection. By observing the measured spectrum of vibration acceleration signal, the signal spectrum at the concerned frequency \(f\) = 60 Hz in vibration state is about \(-\)65 dB, which translates to an acceleration of about 562 ug.  
The structure of the magnetic antenna is shown in Figure 1. It is a rod-shaped structure, which is internally wrapped with magnetic cores and coils, with total length \(l_{m}\) = 0.8 m and weight \(m\) = 6.5 kg. Due to the strength of geomagnetic field \(H_{earth}\)\(\approx\) 0.3 guass, according to the formula of electromagnetism \(B\) = \(\mu\)\(\times\)\(H_{earth}\), the magnetic induction intensity \(B\) is 30 T. As the sensitivity of the magnetic antenna receiving signal acquisition equipment is 0.8 V/nT, and the effective signal amplitude is 200 fT (2017), multiplication of the receiver sensitivity by the effective signal amplitude can obtain the corresponding induced voltage of 0.00016 V. In order to collect a valid signal, the induced electromotive force generated by the coil vibration must be less than 0.00016 V. The relevant parameters are listed in Table 1.  
Assume that the relative vibration acceleration and velocity of the two ends of the magnetic antenna with time are:  
\[a=A\cdot\sin(2\pi ft) \tag{1}\]  
\[v=-\frac{A}{2\pi f}\cdot\cos(2\pi ft) \tag{2}\]  
Therefore, the maximum angular velocity of antenna rotation is given as:  
\[\omega_{\max}=\frac{V_{\max}}{l}=\frac{A_{\max}}{2\pi fl} \tag{3}\]  
where \(l\) is the length of the antenna coil, Substitution into the induced electromotive force equation [18] yields the correlation formula of maximum induced electromotive force and maximum acceleration:  
\[\varepsilon_{\max}=nBS\omega_{\max}=nBS\cdot\frac{V_{\max}}{l}=nBS\cdot\frac{A _{\max}}{2\pi fl} \tag{4}\]  
Substitution of the parameters of antenna into Equation (4) can obtain the maximum vibration acceleration of magnetic antenna is \(A_{\max}\approx 5\times 10^{-5}\) m/s\({}^{2}\).  
Therefore, at a frequency of 60 Hz, the vibration reduction system of the magnetic antenna must reduce the vibration acceleration transmitted to the magnetic antenna by the environment where the antenna is located to below \(5\times 10^{-5}\) m/s\({}^{2}\), to 5 ug. According to the above, the vibration acceleration of the simulated magnetic antenna underwater  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Physical Quantity** & **Symbol** & **Unit** & **Value** \\ \hline Length of the antenna coil & \(l\) & m & 0.512 \\ \hline Magnetic core permeability & \(\mu\) & / & \(1\times 10\)\({}^{6}\) \\ \hline Number of turns & \(n\) & / & 32,000 \\ \hline Cross-sectional area & \(S\) & m\({}^{2}\) & \(2.52\times 10^{-3}\) \\ \hline Strength of geomagnetic field & \(H_{\textit{drift}}\) & guass & 0.3 \\ \hline Concerned frequency & \(f\) & Hz & 60 \\ \hline Magnetic field strength & \(B\) & T & 30 \\ \hline Maximum induced electromotive force & \(\varepsilon_{\max}\) & V & 0.00016 \\ \hline Maximum vibration acceleration & \(A_{\max}\) & g & to be determined \\ \hline \hline \end{tabular}
\end{table}
Table 1: The parameters of the antenna.  
Figure 1: Schematic diagram of magnetic antenna structure in the magnetic field.  
detection is about 562 ug, so the vibration transfer rate of the vibration reduction system should be less than 0.01 (\(-\)40 dB).