## 4 Simulation and Experiment
### Experimental Results  
Figure 16a shows the measured output voltage and current of the full-bridge inverter when the transmitted bits (Data in) are \"010\". The initial phase-shifting angle \(\varphi_{\mathrm{p}}\) and differential phase-shifting angle \(\Delta\varphi_{\mathrm{p}}\) are set to 90\({}^{\circ}\) and 30\({}^{\circ}\), respectively. The variations of \(\varphi_{\mathrm{p}}\) and \(\Delta\varphi_{\mathrm{p}}\) are consistent with the variations in Figure 6. In the forward modulation process, \(i_{\mathrm{p}}\) is almost in the phase of \(V_{\mathrm{inv}}\), and zero phase angle of inverter is achieved. Figure 16b shows the corresponding waveforms of \(i_{\mathrm{s}}\), \(V_{\mathrm{filter}}\) and received bits (Data out). The transmitted bits are successfully recovered from the demodulator on the secondary side. Figure 17a shows the measured input voltage and current of the S-BAR when the transmitted bits are \"010\". It can be seen that \(i_{\mathrm{s}}\) slightly leads \(V_{\mathrm{rec}}\) during the backward modulation but its peak value is almost stable. Similar to the forward communication, the transmitted bits are recovered from the demodulator on the primary side. Figure 15: Photograph of the experimental prototype. (**a**) Overall configuration of experimental prototype. (**b**) Demodulator circuit. (**c**) S-BAR circuit. To further verify the performance of the designed communication system, a bit frame \"10001000110\" produced by a random bit sequence generator is sent from primary side to the secondary side. After about 116 us, the transmitted bits are successfully recovered from secondary side, as shown in Figure 17(a). During the forward communication, the maximum fluctuation of \(V_{\text{out}}\) is about 300 mV at its rated output voltage 24 V, as shown in Figure 17(b), which is acceptable in practice. Thus, the information transmission has little impact on power transmission. Figure 18(a) compares the DC to DC efficiencies with and without communication under different coil distance. As the distance increases, \(\eta\) gradually decreases but the trends of three different conditions are similar. Because the modulation of backward communication changes the equivalent resistance of load, the system efficiency of backward communication is slightly lower than that of forward communication. Generally, the impact of the communication process on the system efficiency can be negligible. Figure 18(b) compares the measured bit error rate (BER) under different data rates (50 kbps, 25 kbps and 12.5 kbps) during the forward communication. As the distance increases, the BER under three rates rises significantly. Under the same distance, the BER at lower data rates is relatively small. Figure 16: Experimental results of forward communication. (**a**) Measured waveforms of \(V_{\text{inv}}\) and \(i_{\text{P}}\) when the transmitted bits are “010” (Data in) under \(\varphi_{\text{P}}=90^{\circ}\). (**b**) Measured waveforms of \(i_{\text{s}}\), \(V_{\text{filter}}\) and received data (Data out). Figure 17: Experimental results of backward communication. (**a**) Measured waveforms of \(V_{\text{rec}}\) and \(i_{\text{s}}\) when the transmitted bits are “010” (Data in) under \(\varphi_{\text{s}}=80^{\circ}\). (**b**) Measured waveforms of \(i_{\text{P}}\), \(V_{\text{filter}}\) and received data (Data out). When \(\varphi_{\text{p,s}}=90^{\circ}\), \(\Delta\varphi_{\text{p,s}}=30^{\circ}\), and \(R_{\text{L}}=20\)\(\Omega\), the fluctuation of secondary current \(\Delta i_{\text{s}}\) and primary current \(\Delta i_{\text{p}}\) are shown in Figure 20a,b, respectively. Due to the constant current characteristic, \(\Delta i_{\text{p}}\) in the backward communication is smaller than \(\Delta i_{\text{s}}\) in the forward communication. Because of the nonlinear characteristics of the rectifier and scattering resistance of the coils, there is a small difference between experiment and simulation results, especially when the coupling coefficient is lower than 0.2.