## 2 System Description
### RF AC-DC Converter with Input Impedance Matching
* Step 4: Derivation of the frequency ratio \(\alpha_{f}\) The frequency ratio \(\alpha_{f}\) The frequency ratio \(\alpha_{f}\) is defined as Figure 8:6 (35) where \(f_{in}=\omega_{in}/2\pi\) is the frequency of the input voltage, and Figure 8:7 (36) is the resonant frequency of the rectifier. \(\alpha_{f}\) can be derived from numerical analysis based on circuit simulation as Figure 8:8 (37)
* Step 5: Derivation of a non-dimensional parameter \(\beta\) \(\beta\) is a non-dimensional parameter defined as Figure 8:9 (38)  
\(\beta\) needs also to be derived from numerical analysis based on circuit simulation. The approximation formula is expressed by  
Figure 7:0
* Step 6: Calculation of the resonant inductance \(L_{1}\) Once \(\beta\) is calculated, the resonant inductance \(L_{1}\) can be calculated from (38). * Step 7: Calculation of the resonant frequency \(f_{re}\) The resonant frequency \(f_{re}\) can be get by substituting the calculated \(\alpha_{f}\) into (35). * Step 8: Calculation of the resonant capacitance \(C\) The resonant capacitance \(C\) can be get by substituting the calculated \(L_{1}\) and \(f_{re}\) into (36). The resonant parameters of the AC-DC converter used in the system were determined according to the steps above. Table 2 lists all the parameters of the AC-DC converter. These parameters were confirmed by a PSpice (Cadence Design Systems Inc., San Jose, CA, USA) simulation. Figure 10 shows the simulation waveforms in one period of the input voltage. A commercial PKB4713 PINB 5-V output isolated step-down DC-DC module (Ericsson AB, Stockholm, Sweden) is used as the DC-DC converter in the system. The use of a commercial off-the-shelf module instead of a custom designed converter allows a fast and stable system implementation. The circuits and one of the transducers of the system are shown in Figure 7:1 The component values in Table 1, as well as those in Figure 3, were rounded to find appropriate \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Parameter**} & \multicolumn{1}{c}{**Symbol**} & **Value** & **Unit** \\ \hline \multirow{4}{*}{Design input parameters} & Input impedance & \(Z_{in,\ AC-DC}\) & \(50+j0\) & \(\Omega\) \\  & Input frequency & \(f_{in}\) & 944.6 & kHz \\  & Input power & \(P_{in}\) & 20.0 & W \\  & Rectifier output voltage & \(V_{con}\) & 50.0 & V \\ \hline \multirow{2}{*}{Design output parameters} & Resonance inductance & \(L_{1}\) & 8.3 & μH \\  & Resonance capacitance & C & 989 & pF \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the AC-DC converter used in the system. Figure 10: PSpice simulation waveforms of the AC-DC converter used in the system: (**a**) Waveforms of the input voltage and input current; (**b**) Waveforms of the voltages across \(C_{1}\) and \(C_{2}\); (**c**) Waveforms of the currents through \(C_{1}\) and \(C_{2}\); (**d**) Waveforms of the currents through \(D_{1}\) and \(D_{2}\). commercial off-the-shelf components. The inductors are from Coil-Craft Inc. (Cary, IL, USA) and Wirth Elektronik GmbH & Co. KG (Niedernhall, Germany). The capacitors are from Murata Manufacturing Co., Ltd (Nagaokokayo-shi, Kyoto, Japan). The diodes are silicon carbide (SiC) Schottky barrier diodes from Cree Inc. (Durham, NC, USA).