## 3 Resonator Design  
### Data Coil Design  
Decoupling energy and data interface regardless of a close placement of the corresponding coils is the prerequisite to establish a stable and resilient data communication. The energy inductors used in  
Figure 2: System concept of this work: A separate inductive data communication interface is implemented by two additional coils, which can be subject to an individual optimization. The near-field communication interface is based on an active communication with digital modulators and demodulators, so that data are modulated on a rectangular wave, transmitted over an analog channel and converted back to a rectangular wave by a comparator stage in the receiver, where it gets demodulated by a fully digital circuit. this work are two capacitively segmented planar spiral coils with radii of 15 mm and 5 mm, respectively, which are designed by the authors of this paper in [28] for a high-efficiency wireless power transfer link operating at 40.68 MHz. Due to the capacitive elements included into the traces, the current distribution is uniform along the conductor and parasitic and lossy capacitive displacement currents are limited, so that high-frequency operation in biological tissue is possible without sacrificing efficiency: For coil separation distances of 20 mm, coil efficiency levels of up to 32% are achievable, while the maximum receivable power at the receiver is approximately 30 mW to fall below the regulatory limit of the specific absorption rate (SAR) of 1.6 W/kg. Creating a data coil on the same substrate now requires enclosing magnetic flux components of opposite sign, which basically leads to the winding designs shown in Figure 3: Here, the magnetic flux density \(B_{z}\) generated by a regular planar spiral energy coil normal to its surface is visualized for a uniform current distribution along its conductor trace and obtained from the numerical evaluation of the Biot-Savart law. The **C-shaped data coil** can now achieve zero mutual inductance to the energy coil by incorporating flux components of negative sign in the range of the outer winding part and flux components of positive sign along the inner winding part. As the inner winding part is the return line of the current and only the enclosed area contributes to the net flux such as given by (1), the center of the flux distribution does not affect the induced voltage. To include negative flux components, \(r_{\text{c1,i}}\) must be slightly larger than the radius of the energy coil, while \(r_{\text{c2,i}}\) is swept in a numerical simulation to yield a design with no coupling to the primary energy coil. The **butterfly-shaped data coil** follows the principles as elaborated in [17]: Every turn is split into two separate, but axis-symmetric parts with counter-rotating winding direction. If these are situated in a magnetic field of the same symmetry, both parts are subject to the same induced voltage, but, with the opposite sign, so that the overall output voltage and hence mutual inductance is zero. Due to the slightly asymmetric nature of the given energy coils (Archimedean spirals), a small spatial offset \(s_{\text{b,i}}\) is included to achieve zero coupling. The particular features of the butterfly-shaped coil is that the angular cutout, shown on the right side of Figure 3b, allows for implementing the feeding structure of the energy coil on a two-layer substrate, while the rounded outer contour line limits the size to that of the corresponding energy coil. It is now to be investigated how well these coil topologies perform in a data link and how they interfere with the second energy coil, which is not located on the same substrate. The notational convention used in the following is that the indices 1 and 2 denote primary and secondary energy coil,  
Figure 3: Data coil topologies to minimize mutual inductance to an energy coil on the same substrate and magnetic flux density distribution \(B_{z}\) of a planar spiral coil from [28].