# Isotropic IoT-Based Magnetic Flux Density Meter Implementation for ELF Field Measurements +
## 4 The Proposed ELF Isotropic Sensor Implementation  
Winding a coil with a certain number of turns and specific dimensions may constitute the magnetic field probe of the ELF meter. Suppose that the \(V_{\rm rms}\) voltage needs to be 1.2 V when the coil is placed inside a 2.3 \(\mu\)T (RMS) magnetic field. According to (25), the following equation should be satisfied:  
\[A\ N=0.05166\ m^{2} \tag{27}\]  
In our initial prototype implementation [30], by choosing a coil with 100 turns, each turn should include an area of 516.6 \(\times\) 10\({}^{-6}\) m\({}^{2}\). The desired area for a rectangular  
Figure 5: The output voltage of the proposed RMS detector is a function of the magnetic flux density.  
cross-section coil can be achieved if each turn is 43.05 mm \(\times\) 12 mm. Thus, the meter coil in the initial design consisted of 100 turns of 43.05 mm \(\times\) 12 mm rectangular cross-sections.  
In this study, the sensor of the proposed meter consists of three identical square probes in vertical alignment, providing isotropic \(H\)-field measurements from the X, Y, and Z planes, respectively, as shown in Figure 6. Each probe should also satisfy Equations (25) and (27) considering that the initial dimensions should be appropriately changed to achieve the cubic structure of the proposed isotropic sensor. The coil of each axis probe consists of 28 turns of 43.05 mm \(\times\) 43.05 mm square cross-sections to feed the identical electronic circuits of the meter (Figure 6b), to enhance the work in [30].  
The measured incident magnetic field of the proposed sensor with three identical square coils is given by the following equation [14]:  
\[\left|\,H_{inc}\right|\,=\sqrt{k_{x}V_{x}^{2}+k_{y}V_{y}^{2}+k_{z}V_{z}^{2}} \tag{28}\]  
where \(V_{x}\), \(V_{y}\), and \(V_{z}\) are the voltages at the outputs of the probe coils of the meter, and \(k_{x}\), \(k_{y}\), and \(k_{z}\) are the respective coefficients that are derived from calibrating the device against other available laboratory-calibrated equipment, as the Narda PMM EHP-50C.  
For the system's frequency response validation, a TTi TG230 function generator was used to feed a pair of Helmholtz coils to provide a homogeneous magnetic field at the laboratory. Keeping constant the generator's signal amplitude (and at the same time the intensity of the emitted magnetic field at about 2 uT), the operating frequency of the generator was changing in the ELF band (1 Hz-100 kHz) to achieve the frequency response curve of the proposed meter, as shown in Figure 7a. Experimental measurements show an almost flat response over the frequency range from 40 Hz to 10 kHz, as shown in Figure 7b, respectively. Table 2 shows the comparison of the proposed meter with similar high-precision and ultra-high-cost ELF measurement equipment solutions.  
Figure 6: (**a**) The sensor implementation of the proposed ELF meter consists of three identical square probes in vertical alignment, providing isotropic \(H\)-field measurements from the X, Y, and Z planes. (**b**) The main parts of the proposed magnetic field meter are the isotropic probes, the Arduino board, and the identical electronic circuits.