# Magnetic Communication Using High-Sensitivity Magnetic Field Detectors
## 3 Sensitivity Analysis
### Communication Range for Lossless Transmission Mediums
#### 3.2.3 Characterization of the Detection Threshold for the Prototype Implementation  
Equation (8) proves that the detection threshold \(B_{\rm min}\) should be small to reach high communication distances. The detection threshold of the receiver prototype implementation is the minimum magnetic flux density which can be measured, and results from the AMR sensor sensitivity and the noise level of the receiver circuit. For magnetic flux densities below that voltage, the generated magnetic field of the wanted signal is smaller than the noise voltage level of the receiver circuit. In the following, the sensitivity and the noise level of our prototype system are characterized, and the resulting detection threshold is calculated. To verify the given AMR sensitivity, the receiver is placed at a distance of \(d=10.1\) cm in boresight direction regarding the transmitter coil. Then, the output voltage of the receiver is measured for different magnetic flux densities. The magnetic flux density, which is present at the AMR sensor, is a function of the coil properties, the current through the transmitter coil, and the distance between transmitter and receiver. Figure 2(a) shows the voltage at the output of the receiver over the current through the transmitter coil for the fixed coil properties specified in Table 2. In addition to the measurement points, the resulting line of best fit is plotted. To get the AMR sensitivity, the AMR output voltage before signal amplifying must be calculated and normalized to 1 V input voltage. Therefore, the voltage at the receiver output is divided by the amplifier gain (G = 2000) and the AMR sensor input voltage. Figure 2(b) shows the calculated voltage over the magnetic field, which is present at the AMR sensor. The AMR sensitivity can be read easily from the slope of the function. This results in a sensitivity of 14.33 \(\frac{\mathrm{mV/V}}{\mathrm{kA/m}}\) for the embedded AMR sensor in our prototype receiver circuit. The value is very close to the specification of 15 \(\frac{\mathrm{mV/V}}{\mathrm{kA/m}}\) which is given by the datasheet. The second important parameter that affects the detection threshold, is the noise level of the receiver. The magnetic field sensor in our prototype system can work at frequencies from 0 Hz up to 1 MHz. The main components that contribute to the total noise are the AMR sensor with 10 \(\frac{\mathrm{mV}}{\mathrm{\sqrt{Hz}}}\) and the noise of the amplifier with 1.5 \(\frac{\mathrm{mV}}{\mathrm{\sqrt{Hz}}}\) for frequencies beyond 100 Hz [14; 18]. For frequencies below 100 Hz, the total noise voltage is much higher so that these frequencies should be avoided for a small detection threshold. In this experiment, the total noise for different bandwidths is investigated. The chosen bandwidths are 1.47 kHz, 100 kHz and 999.9 kHz. 1.47 kHz, for direct comparison, exactly corresponds to the 3 dB bandwidth of the coil-to-coil communication for the prototype system parameters. Figure 4 shows the noise voltage over a period of 10 ms for the measured bandwidths. Figure 3: Measured voltage at the receiver output for different current through the transmitter coil (**a**) and the AMR sensor sensitivity curve (**b**). Based on the measured receiver sensitivity and the noise voltages for different bandwidths the corresponding detection thresholds can be determined. The results are compared with the detection thresholds calculated with the theoretical values given in the datasheets. For the bandwidth \(\Delta f=1.47\) kHz, the detection threshold is \(B_{\min,\,1.47\,\,\mathrm{kHz}}\approx 5\) nT (theoretical value: 4 nT), for \(\Delta f=100\) kHz the detection threshold is \(B_{\min,\,100\,\,\mathrm{kHz}}\approx 39\) nT (theoretical value: 35 nT) and for \(\Delta f=999.9\) kHz the detection threshold is \(B_{\min,\,999.9\,\,\mathrm{kHz}}\approx 155\) nT (theoretical value: 112 nT).