## 8 Results
### Output Signals  
In the next step, the input voltage of the receiver's comparator \(u_{\text{c,in}}\), i.e., the output voltage of the complete wireless link including the analog interfaces, is analyzed for various levels of the mutual inductance \(M_{34}\), corresponding to variations in coil distance and alignment. The voltage is simulated with the harmonic balance algorithm implemented in _Keysight Advanced Design System 2016_. A SPICE model of the _BFR840_ transistor was used to simulate the receiving amplifier and the FPGA's output stage was modeled by an output resistance of \(R_{\text{TX,out}}=300\)\(\Omega\) and a voltage source alternating between 0 V and \(U_{\text{DD}}=1.8\) V; the measurement probe was modeled by a 8 pF capacitor to ground. Data were also acquired from on the prototype implementation presented above, using a _Tektronix MSO4104_ oscilloscope and a _PA6139A_ probe. As shown in Figure 19, the comparator input voltage can be reproduced by the numerical simulation and is highly sensitive to capacitive loading, so that a simulative de-embedding of the probe's capacitance is required (see blue curve). The output voltage is subject to compression for \(M_{34}>2\) nH due to the nonlinear behavior of the amplifier and drops below 60 mV (which will later to be determined as the sensitivity threshold) at \(M_{34}\approx 2\) nH, which corresponds to a distance of 15 mm.  
A snapshot of the link's most important intermediate and output signals is shown in Figure 20, which were simultaneously acquired by a _Salae Logic Pro 8_ multi-channel logic analyzer and a _Rigol MSO5074_ oscilloscope: The time sequence descriptively shows how the outgoing data stream is translated into a BPSK-modulated rectangular wave, which is then transmitted over the analog channel and recreated by the receiver's comparator. After RF detection and synchronization, the mixer's output signal \(s_{\text{m}}\) is low-pass filtered to obtain the received data sequence _data_rx_ and recovered clock _data_clk_, which corresponds to the incoming data sequence. Preamble and payload data are highlighted to show the identity of _data_tx_ and _data_rx_ and to prove the operability of the link.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Param.** & \(\mathbf{L_{3}}\) & \(\mathbf{L_{4}}\) & \multicolumn{4}{c}{\(\mathbf{M_{34}}\)} \\ \hline \(d_{34}\) & - & - & 5 mm & 10 mm & 15 mm & 20 mm \\ \hline sim. & 650 nH & 260 nH & 16.4 nH & 5.46 nH & 2.0 nH & 0.81 nH \\ \hline meas. & 680 nH & 270 nH & 15.8 nH & 5.50 nH & 2.02 nH & 0.85 nH \\ \hline dev. & 4.6 \% & 3.8 \% & 3.6 \% & 0.8 \% & 1.0 \% & 5.2 \% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Inductance values in simulation and measurement (in air).  
Figure 18: Frequency behavior of the effective coil resistances \(R_{i}\) and the mutual reactance \(X_{12}\) for the given data coil system at a coil separation distance of \(d_{34}=20\) mm in air and pork muscle tissue.  
Figure 19: Voltage at the comparator of the receiving stage \(u_{\text{c,in}}\) versus mutual inductance \(M_{34}\) of the data coils (in air). The simulated data was provided by a Harmonic Balance simulation using _Keysight Advanced Design System 2016_, the measurement was performed with the prototype circuits presented above.  
Figure 20: Transient behavior of important analog and digital signals within the near-field interface.