# Isotropic IoT-Based Magnetic Flux Density Meter Implementation for ELF Field Measurements +
## 3 The Electronic Circuit of the Proposed EMF Magnetic Flux Density Meter (Analog Section)  
Figure 4 presents the proposed magnetic field meter's basic electronic circuit (analog section). The Op-Amp A is used as a typical non-inverting amplifier with \(G_{a}\) gain:  
\[G_{\alpha}=1+\frac{R_{2}}{R_{1}} \tag{16}\]  
The gain \(G_{a}\) is defined by \(R_{1}\) and \(R_{2}\) as described in Equation (16); it is equal to 101 and does not depend on frequency. Practically, the gain of the amplifier would be less than 101 for frequencies lower than 40 Hz. The design characteristics of the Op-Amp A  
Figure 4: The basic electronic circuit of the proposed magnetic flux density meter. For the implementation of an isotropic meter, 3 identical circuits are also needed for ELF measurements in the X, Y, and Z planes. limit the amplifier's responsiveness at higher frequencies (the gain-bandwidth product). Nevertheless, from 40 Hz to 10 kHz, the amplifier response is almost flat, and the gain is approximately equal to the theoretical value with a potential error of less than 1 dB if 1% accuracy resistors are used for \(R_{1}\) and \(R_{2}\). The integrator follows the amplifier, implemented from Op-Amp B, \(R_{4}\), \(R_{3}\), and \(C_{2}\). The response of the integrator is inversely proportional to the frequency due to \(C_{2}\). If the integrator is analyzed as a typical inverse amplifier, it is observed that its gain \(G_{b}\) is equal to  
\[G_{b}=-\frac{R_{F}}{R_{3}} \tag{17}\]  
The \(R_{F}\) value is the impedance resulting from the parallel combination of resistor \(R_{4}\) and the \(X_{c}\) impedance (reactance) of \(C_{2}\). That is,  
\[R_{F}=X_{c}/\,/\,R_{4}=R_{4}X_{c}/\,(R_{4}+X_{c}) \tag{18}\]  
Knowing that \(X_{c}\) reactance is equal to:  
\[X_{c}=\frac{1}{2\pi f\cdot C_{2}} \tag{19}\]  
The rectifier circuit is subsequent to the integrator, implemented from the Op-Amp C. Since there is no diode anywhere, the rectification circuit is uncommon. The rectification is carried out because the negative half-period of the signal is simply cut off. The Op-Amp C along with the resistors \(R_{5}\), \(R_{6}\), \(R_{7}\), and \(R_{8}\) is a typical differential amplifier circuit (subtraction). The voltage applied to the left end of \(R_{5}\) is subtracted from the voltage applied to the left end of \(R_{6}\). The output of the subtractor will always have a voltage equal to zero since the left edges of \(R_{5}\) and \(R_{6}\) are short-circuited, only in the case of DC. Contrariwise, for the \(AC\) signal, the capacitor \(C_{3}\) acts as a short circuit and grounds the non-inverting input of Op-Amp C. This method converts the subtractor into an inverting \(AC\) amplifier with an amplification of \(R_{7}/R_{5}\) = 2.2. The previous analysis demonstrates that Op-Amp C eliminates the DC component of the signal and amplifies the remaining AC signal by a factor of 2.2. Furthermore, Op-Amp C performs a half-rectification of the signal at 0 V reference level without negative supply voltage. Consequently, it can only amplify the positive half-period of the signal, and during the negative half-period, its output is zero (i.e., half-phase rectification occurs). Op-Amp C output produces a semi-rectified signal containing a DC component and some harmonics (according to the Fourier series analysis mentioned above). The harmonics are filtered out from a simple low pass filter formed by \(R_{9}\) and \(C_{4}\). The cut-off frequency of this specific filter is equal to \(1/2\pi R_{9}C_{4}\) = 4.5 Hz, which is a very low one and the filter passes only the DC component. Normally, the \(DC\) component of a half-rectified signal is equal to \(\sqrt{2}/\pi\) of the RMS value of the input signal of the rectifier. The term \(\sqrt{2}/\pi\) is equal to about 1/2.2. However, since we use amplification equal to 2.2 in the rectifier, we make the half-rectified signal have a DC component equal to the exact \(RMS\) value of the input signal (by cancelling out the 1/2.2 factor).