# Isotropic IoT-Based Magnetic Flux Density Meter Implementation for ELF Field Measurements +
## 1 Introduction
The complex waveforms are weighted using a filter function that takes into account the waveforms' phase, as described by the following equation [7]:  
\[\left|\sum_{i}\frac{A_{i}}{E_{Li}}\cos(2\pi\;f_{i}t+\theta_{i}+\varphi_{i})\right|\leq 1 \tag{2}\]  
where \(t\) is the exposure time and \(A_{i}\) and \(E_{Li}\) are the harmonic component amplitude and the exposure limit at \(i\)th harmonic frequency \(f_{i}\), respectively. The phase and filter angles of the field at the harmonic frequencies are also described by \(\theta_{i}\), \(\varphi_{i}\). In addition, knowing that isotropic measurements should be along the \(X\), \(Y\), and \(Z\) axes, the total measured magnetic field \(H_{i}\) is described by Equation (3):  
\[H_{i}=\sqrt{H_{x,i}{}^{2}+H_{y,i}{}^{2}+H_{z,i}{}^{2}} \tag{3}\]  
The continuing interest in making reliable measurements concerning public exposure to extremely low frequency (ELF) magnetic fields has led researchers to implement measurement devices for several years. Strong magnetic field sources can be detected using an ELF magnetic field meter by taking the necessary precautions [3,8]. The authors in [9] introduced a broadband magnetic field meter at the National Bureau of Standards (NBS), in 1985. The proposed meter has an isotropic probe unit consisting of three mutually orthogonal loops, each 10 cm in diameter, for magnetic field measurements up to 30 A/m. The novelty of this implementation was based on several improvements over available instruments for that time, such as the dynamic range of 44 dB, the flat frequency response (about \(\pm\)1.0 dB), the isotropic response (about \(\pm\)0.3 dB), and the overload capability, using only one probe head. The work in [10] introduced a sensor for isotropic magnetic and electric field measurements at frequencies less than 100 kHz, determining the electromagnetic interferences specialized in the audio frequency band. Three orthogonally oriented coils are used as an EMF sensor by the authors in [11], introducing a measurement method that enables a precise analysis of the field distribution. The study suggests a research technique that involves evaluating the strength of the electromagnetic field produced by the emitting coil in a Wireless Power Transfer (WPT) system in terms of both magnitude and direction. Nowadays, the technology of Electric and Magnetic Fields (EMF) meters has advanced considerably, offering engineers measurements with less uncertainty and the feature of remote equipment real-time monitoring. A professional solution for continuous monitoring of the electric and magnetic fields is provided by the Narda PMM EHP-50C probe analyzer [12,13] which can begin its acquisition by storing the data over 24 h in the operating frequency range of 5 Hz to 100 kHz. The analyzer features a variety of operating modes, including stand-alone mode without an external apparatus connection and cooperation with a Pocket-PC or Narda PMM 8053A portable display unit via fiber optic communication. In [14], another analyzer for measuring magnetic and electric fields in the workplace \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Freq. Band**} & **Electric Field Strength** & **Magnetic Field Strength** & **Magnetic Field** \\  & **(V/m)** & **(A/m)** & **Induction (\(\mu\)T)** \\ \hline
0–1 Hz & - & 3.2 \(\times\) 10\({}^{4}\) & 4 \(\times\) 10\({}^{4}\) \\
1–8 Hz & 10,000 & 3.2 \(\times\) 10\({}^{4}\)/\(\hat{r}^{2}\) & 4 \(\times\) 10\({}^{4}\)/\(\hat{r}^{2}\) \\
8–25 Hz & 10,000 & 4000/f & 5000/f \\
0.025–0.8 kHz & 250/f & 4/f & 5/f \\
0.8–3 kHz & 250/f & 5 & 6.25 \\
3–150 kHz & 87 & 5 & 6.25 \\ \hline \hline \end{tabular} Where \(f\), is the frequency in Hz or kHz, depending on how it is defined in the table cell that is in the same row and column of the frequency band. No \(E\)-field value is defined for frequencies less than 1 Hz, which are essentially static electric fields.  
\end{table}