# A Magnetic-Balanced Inductive Link for the Simultaneous Uplink Data and Power Telemetry
## 7 Experimental Results
### Measurement Results  
Figure 11 shows the measured coupling coefficients (\(k_{13}\) and \(k_{23}\)) versus the distance (\(d_{13}\)). The coupling coefficients of the inductive link are measured by a network analyzer (E5071, Keysight, Santa Rosa, CA, USA) through using the method introduced in [15]. As seen, \(k_{13}\) could decrease to about zero when \(d_{13}=26\) mm, which agrees with the analysis in Section 4.1. The coupling coefficient (\(k_{23}\)) remains at a small, but adequate value. Therefore, the power carrier interference is substantially rejected while the intensity of the uplink signal remains adequate. Figure 11 also shows the simulated and calculated \(k_{13}\) and \(k_{23}\) versus the center distance (\(d_{13}\)). It can be seen that both the simulated and the calculated coupling coefficients almost agree with the measured results with some offsets, and the calculated coupling coefficients show better agreement. It can be proven that the calculation model is in good agreement with the real coils. Figure 12a,b shows the measured \(k_{12}\) and \(k_{23}\) over different coil separation (\(d\)), as \(k_{12}\) and \(k_{23}\) are the key parameters of the power link and the uplink, respectively. It can be seen that the coupling coefficient \(k_{12}\) is as low as 0.005, and \(k_{23}\) is as low as 0.001 when the coil separation is 60 mm. In addition, Figure 12b shows that \(k_{23}\) decreases when the coil separation is smaller than 15 mm, which agrees with the analysis in Section 4.2. Figure 13 shows the measured SIR and SNR of the uplink over different coil separations (\(d\)). The SIR and SNR are measured before the uplink receiving filter by using a spectrum analyzer (DSA815, RIGOL, Beijing, China). When measuring the SIR and SNR, the power delivered to the load (PDL) is kept as constant as 5 mW by adjusting the transmitting power of the class-E power amplifier (PA). When the coil separation (\(d\)) is 20 mm, the SIR before the uplink receiving filter is as large as \(-10.07\) dB. Compared with the two-coil inductive link in our previous work [11], the SIR of the magnetically-balanced inductive link has a significant improvement of 65.72 dB. When the coil separation (\(d\)) is as large as 60 mm (the maximum coil separation of our prototype to supply 5 mW of power to the load wirelessly), the SNR is about 14 dB, which is still adequate  
Figure 10: The prototype system is implemented to setup measurements of power and uplink data transmissions with beef tissue. to achieve BPSK demodulation, and the SIR is about \(-38\) dB, which can be improved by a fourth-order Butterworth low-pass filter. In addition, the SNR decreases when \(d=10\) mm, since \(k_{23}\) decreases. Thanks to the optimization of the skew distance \(d_{12}\), this decrease is avoided in our operating range (\(15\) mm \(\leq d\leq 40\) mm), so it does not affect the reliability of the uplink data transmission. Figure 11: Measured (Meas. ), simulated (Sim.) and calculated (Calc.) coupling coefficients (\(k_{13},k_{23}\)) versus the center distance (\(d_{13}\)), when the coil separation is \(d=20\) mm. Figure 12: (**a**) Measured and simulated coupling coefficient \(k_{12}\) versus the coil separation \(d\) in air and in tissue; (**b**) measured and simulated coupling coefficient \(k_{23}\) versus the coil separation \(d\) in air and in tissue. Figure 13: The measured signal-to-interference ratio (SIR) and the SNR of the uplink versus the coil separation \(d\). To measure the bit error rate (BER), a pseudo-random data sequence is transmitted continuously at a data rate of 50 kbps in half an hour for each measurement. When measuring the BER, the PDL is kept as constant as 5 mW by adjusting the transmitting power of the class-E PA. In the experiments, no bit error occurs in half an hour when the coil separation (\(d\)) is within the operating range (15-40 mm); thus, the BER is below \(1\times 10^{-8}\) in the operating range. When \(d\) is enlarged to 60 mm, the uplink is still reliable, and the measured BER is about \(1\times 10^{-7}\).