## 3 The Use of the TIBuck DC/DC Converter as a VLC Driver  
### The Proposed TIBuck DC/DC Converter with Only One Input Voltage Source  
The proposed version of the TIBuck DC/DC converter with only one input voltage source is shown in Figure 8. For the analysis, two individual converters can be considered: the TIBuck DC/DC converter and the auxiliary Buck DC/DC converter. The V\({}_{2}\) for the TIBuck DC/DC converter can be obtained from V\({}_{1}\) with the simple addition of an auxiliary Buck DC/DC converter. This auxiliary buck converter does not need either high switching frequency or fast output voltage response, achieving high efficiency.  
With d\({}_{\text{bu}}\) the duty cycle of the auxiliary Buck DC/DC converter, voltage V\({}_{2}\) can be written as  
\[V_{2}=d_{bu}\cdot V_{1}. \tag{11}\]  
Substituting Equation (11) into Equation (8), the output voltage, v\({}_{\text{o}}\)(t), can be written in terms of the duty cycle of both DC/DC converters (TIBuck and auxiliary Buck) as  
\[v_{o}(t)=(V_{1}-V_{2})\cdot d_{ti}(t)+d_{bu}\cdot V_{1}. \tag{12}\]  
As mentioned previously, the duty cycle of the TIBuck DC/DC converter d\({}_{\text{ti}}\)(t) comes from modulating a communication signal with the DPWM. The communication signal has  
Figure 8: The proposed TIBuck DC/DC converter with only one input voltage source, V\({}_{1}\), provided by the auxiliary Buck DC/DC converter.  
Figure 7: Representation of the output voltage range of the Buck and TIBuck DC/DC converters versus the useful voltage range of the HB-LED load and their impact on resolution to track the output voltage.  
an average value and a time variant value, so \(\rm d_{ii}(t)\) also has them. Therefore, \(\rm d_{ti}(t)\) can then be written in terms of its average value \(\rm D_{ti}\) and the variations \(\rm\Delta d_{ti}(t)\)  
\[d_{ti}(t)=D_{ti}+\Delta d_{ti}(t). \tag{13}\]  
As highlighted previously in Figure 7, to maximize both the amplitude of the communication signal and the resolution for tracking the output voltage, using the whole \(\rm d_{ti}(t)\) range, \(\rm D_{ti}\) must be equal to 0.5, meaning that \(\rm\Delta d_{ti}(t)\) can vary from \(-0.5\) to 0.5.  
If the switching frequency of the auxiliary Buck DC/DC converter is at least one order of magnitude lower than that used in the TIBuck DC/DC converter, during a whole switching period of the auxiliary Buck DC/DC converter, the effective value of \(\rm d_{ti}(t)\) can be replaced by its average value \(\rm D_{ti}\). This quasistatic condition simplifies the calculation of the average output voltage \(\rm V_{o}\), which can be deduced from Equation (12) as  
\[V_{o}=avg(v_{o}(t))=0.5\cdot(1+d_{bu})\cdot V_{1}. \tag{14}\]  
According to Equation (14), the control of the average output voltage, Vo, can be implemented throughout \(\rm d_{bu}\). This means that the average current driven by the HB-LEDs, \(\rm I_{bias}\), and the average emitted light, \(\rm\Phi_{avg}\), (depicted in Figure 1) only depends on the auxiliary Buck DC/DC converter control. Therefore, to achieve good performance over temperature changes, the auxiliary Buck converter DC/DC converter would work in a closed loop. On the other hand, the TIBuck DC/DC converter could work in an open loop, simplifying the control design and maximizing bandwidth. Finally, it is important to note that during the switching period of the TIBuck DC/DC converter, the voltage \(\rm V_{2}\) can be considered constant. This means that the instantaneous value of the output voltage \(\rm v_{o}(t)\) is controlled throughout \(\rm d_{ti}(t)\), according to Equation (12).