# A Magnetic-Balanced Inductive Link for the Simultaneous Uplink Data and Power Telemetry
## 5 Optimization of the Isolation Resistance \(R_{\text{isolate}}\)  
The resistance of \(R_{\text{isolate}}\) is a key circuit parameter, which needs to be optimized in this magnetically-balanced inductive link circuit. The uplink transmitter drives the implant coil though \(R_{\text{isolate}}\). \(R_{\text{isolate}}\) determines the transmitted power of the uplink transmitter. Furthermore, \(R_{\text{isolate}}\) could affect the loaded quality factor of the implant coil \(L_{2}\) as \(R_{\text{isolate}}\) is directly connected to the implant coil \(L_{2}\) in parallel. The loaded quality factor is a key factor to the PTE, and a higher loaded quality factor benefits higher power transfer efficiency [22]. The loaded quality factor \(Q_{\text{L\_Conventional}}\) of the conventional inductive link can be found from [23], as Equation (10) shows. Similarly, the loaded quality factor \(Q_{\text{L\_Proposed}}\) of our proposed inductive is shown in Equation (11). In order to reduce the impact of the uplink data transmission on the WPT while keeping the uplink signal intensity satisfied, the selection of \(R_{\text{isolate}}\) is a trade-off between the loaded quality factor and the received uplink signal power. \[Q_{\text{L\_Conventional}}=\frac{1}{\frac{R_{2}}{\omega_{\text{p}}L_{2}}+ \frac{\omega_{\text{p}}L_{2}}{R_{\text{L}}}}=\frac{1}{R_{2}\sqrt{\frac{C_{2} }{L_{2}}}+\frac{1}{R_{\text{L}}}\sqrt{\frac{L_{2}}{C_{2}}}} \tag{10}\]  
\[Q_{\text{L\_Proposed}}=\frac{1}{\frac{R_{2}}{\omega_{\text{p}}L_{2}}+\frac{ \omega_{\text{p}}L_{2}}{R_{\text{L}}}+\frac{\omega_{\text{p}}L_{2}}{R_{\text{ isolate}}}}=\frac{1}{R_{2}\sqrt{\frac{C_{2}}{L_{2}}}+\left(\frac{1}{R_{ \text{L}}}+\frac{1}{R_{\text{isolate}}}\right)\sqrt{\frac{L_{2}}{C_{2}}}} \tag{11}\]  
Figure 8 shows the calculated loaded quality factor \(Q_{\text{L\_Proposed}}\) and the Pspice simulated received uplink signal power versus \(R_{\text{isolate}}\) at the maximum coil separation (\(d=40\) mm) in our operating range. It shows that higher resistance of \(R_{\text{isolate}}\) leads to a higher loaded quality factor, but lower received uplink signal power. Figure 8 also shows the uplink receiver sensitivity, which is the minimal required signal power to ensure reliable receiving. The sensitivity is defined in Equation (12), where noise is the thermal noise floor (\(-174\) dBm/Hz); BW is the bandwidth (50 kHz); SNR is the required signal-to-noise ratio (11.5 dB for \(1\times 10^{-7}\) error probability of BPSK demodulation); NF is the noise figure (about 11 dB in our prototype); Loss is the implementation loss (about 12 dB in our prototype). Thus, the sensitivity of our uplink receiver is \(-174+47+11.5+11+12=-92.5\) dBm. The minimum uplink received power required is set to be \(-82.5\) dBm, including a 10-dB reliable margin. When the coil separation is maximal (40 mm), the received uplink signal power is minimal. If the minimal power of received uplink signal in the operating range is higher than the receiver sensitivity, it can be ensured that the uplink is reliable in the entire operating range. As Figure 8 shows, when \(R_{\text{isolate}}\) is larger than 50 k\(\Omega\), the minimal received uplink signal power will be lower than the sensitivity plus the reliable margin. Therefore, \(R_{\text{isolate}}\) is selected to be 50 k\(\Omega\) to achieve a higher loaded quality factor while at the same time fulfilling the constraint of the receiver sensitivity. \[\text{Sensitivity}=\text{Noise}+10\log\left(\text{BW}\right)+\text{SNR}+ \text{NF}+\text{Loss}. \tag{12}\]  
Through calculating and comparing \(Q_{\text{L\_Proposed}}=1.98\) and \(Q_{\text{L\_Conventional}}=2.06\), the decrease of the loaded quality factor caused by the isolation resistors is only 3.9% when \(R_{\text{isolate}}=50\) k\(\Omega\). In addition, \(R_{\text{isolate}}\) dominates the load impedance of the implant transmitter.