## 3 Communication System Design  
### Forward Communication Based on Full-Bridge Inverter  
On the primary side, a full-bridge inverter that works in phase-shifting mode is employed to regulate input power for resonant tank, as shown in Figure 5a. The output voltage and output current are defined as \(V_{\rm inv}\) and \(i_{\rm p}\), respectively. In terms of the modulator, as shown in Figure 5b, the main counter and the shift counter are used to generate digital count values, and they share a same clock source (CLK). Comparing the value of the two counters with the half count value will generate a square wave signal with 50% duty cycle. Unlike the main counter, the initial value of the shift counter is determined by the transmitted data shown in (15). Finally, the obtained four signals (\(\rm{PWM}_{1}\sim\rm{PWM}_{4}\)) are used to drive the four MOSFETs (\(Q_{1}\sim Q_{4}\)), respectively. The output voltage of full-bridge inverter with Fourier series form is expressed as  
\[V_{\rm inv}=V_{\rm dc}\frac{4}{\tau}\sum_{n=1,3,\ldots}^{\infty}\frac{1}{n} \cos\left(n\omega t+\frac{n\varphi_{\rm p}}{2}\right)\sin\left(\frac{n\varphi_ {\rm p}}{2}\right). \tag{13}\]  
where, \(n\) represents the number of harmonic components, and \(V_{\rm dc}\) is the voltage on the DC bus. \(\omega\) is the operation angular frequency of WPT system, and \(\varphi_{\rm p}\) is the phase-shifting angle of the full-bridge inverter. For the SS compensated WPT system, the resonant tank composed of compensation circuitsand coils is regarded as a band-pass filter, and only the fundamental component of \(V_{\rm inv}\) is considered in the power loop. As a result, Equation (13) can be simplified as Equation (14). \[V_{\rm inv,1}=V_{\rm dc}\frac{4}{\pi}\cos\left(\omega t+\frac{\varphi_{\rm p}}{2 }\right)\sin\left(\frac{\varphi_{\rm p}}{2}\right) \tag{14}\]  
From (14), the output voltage of inverter is regulated by \(V_{\rm dc}\) and \(\varphi_{\rm p}\). In practice, the value of \(V_{\rm dc}\) is constant, and \(\varphi_{\rm p}\) will vary with different power demand and coupling inductance. Here, a differential phase-shifting angle \(\Delta\varphi_{\rm p}\) is added into \(\varphi_{\rm p}\), so that the full-bridge inverter is capable of information transmission. Taking binary symbol communication as an example, the changes of phase-shifting angle during the modulation of bit \"1\" and bit \"0\" is given by (15). \[\left\{ \begin{array}{cc}\varphi_{\rm p}-\Delta\varphi_{\rm p}\to\varphi_{ \rm p}+\Delta\varphi_{\rm p}&\mbox{``1''}\\ \varphi_{\rm p}&\mbox{``0''}\end{array} \right. \tag{15}\]  
When bit \"0\" is sent, the phase-shifting angle maintains its initial value for two switching cycles. When bit \"1\" is sent, the phase-shifting angle is set to \(\varphi_{\rm p}-\Delta\varphi_{\rm p}\) in the first switching cycle, and then becomes \(\varphi_{\rm p}+\Delta\varphi_{\rm p}\) in the next switching cycle. Since the change of phase-shifting angle is differential and complementary, the modulation method is defined as differential phase shifting keying (DPSK). To ensure the stability of power transmission, the value of \(\Delta\varphi\) should be designed as small as possible. However, the detection of information transmission depends on the fluctuation of secondary current, which requires higher value of \(\Delta\varphi\). Therefore, the value of \(\Delta\varphi\) is determined by the reliability of communication as well as the performance of power transmission. To further illustrate the working principle of the modulator designed above, bit \"1\" and bit \"0\" are sent, and the corresponding waveforms of the full-bridge inverter and modulator are depicted in Figure 6.  
When considering the fundamental component of the power loop, the output voltage of the full-bridge inverter satisfies \(V_{\rm p}=V_{\rm inv}\).