## 4 Power Flow Analysis
### Overall Efficiency  
The objective of this subsection is to calculate the efficiency of the proposed TIBuck DC/DC converter and to determine how that is affected by the different design parameters. With this efficiency being \(\eta_{\text{t}}\), the ratio between the output power, P\({}_{\text{out}}\), and the input power, P\({}_{\text{in}}\), by using Equations (29)-(31), \(\eta_{\text{t}}\) can be written as follows  
\[\eta_{t}=\frac{P_{out}}{P_{in}}=\frac{P_{out}}{\frac{P_{v2}}{\eta_{bu}}+\frac {P_{ti}}{\eta_{ii}}+P_{v1 fr}}. \tag{32}\]  
If Equations (17), (22), (27) and (28) are applied to Equation (32), it can be expressed in terms of the different design parameters:  
\[\eta_{t}=\frac{V_{o}\cdot I_{o}}{\frac{V_{2}\cdot(1-D_{li})\cdot I_{o}}{\eta_{ bu}}+\frac{(V_{o}-V_{2})\cdot I_{o}}{\eta_{ii}}+V_{2}\cdot D_{ti}\cdot I_{o}}. \tag{33}\]  
Equation (33) is the general approach of the efficiency, with no regard for the type of load or the type of application. Some of the values can be specified for a string of n HB-LEDs as a load in a VLC driver. The average output voltage value can be taken from Equation (2), giving  
\[V_{o}=nV_{th}(T)+n\frac{V_{\Omega}}{2}. \tag{34}\]  
As previously mentioned in Section 3 (Figure 9), the voltage feedback loop of the auxiliary Buck DC/DC converter changes the V\({}_{2}\) value to correct for the temperature changes of the HB-LED string. By using Equations (10) and (34) in (33), the following  
Figure 13: Power flow diagram of the proposed TIBuck DC/DC converter. expression for efficiency is obtained as a function of temperature with an HB-LED string as a load:  
\[\eta_{t}=\frac{V_{th}(T)+\frac{V_{\Omega}}{2}}{\frac{V_{th}(T)}{\eta_{hu}}(1-D_{ii} )+\frac{V_{\Omega}}{\eta_{ii}}+V_{th}(T)\cdot D_{ti}}. \tag{35}\]  
The output current, \(I_{o}\), and the number of HB-LEDs has been simplified. Therefore Equation (35) does not depend on them. The only parameter left is the duty cycle of the TIBuck DC/DC converter, \(D_{ti}\). Finally, adding Equations (10) and (34) into Equation (8) and solving for \(D_{ti}\) leads to  
\[D_{ti}=\frac{nV_{\Omega}}{2(V_{1}-nV_{th}(T))}. \tag{36}\]  
Temperature and Partial-Efficiency Dependencies of the Overall Efficiency of the Proposed TIBuck DC/DC Converter  
It can be seen from Equations (35) and (36) that \(\eta_{t}\) has a clear dependency on the efficiencies of the individual DC/DC converters (TIBuck and auxiliary Buck), as well as the HB-LED characteristics, some of which vary with temperature. To have a better idea about how the changes in these parameters affect the efficiency \(\eta_{t}\), a parametric analysis has been performed, sweeping through different values. In the first analysis, only one of the efficiencies of the individual converters has been swept. The HB-LED parameters were taken from standard parts, assuming no variation in temperature (i.e., \(V_{th}\) = 3 V and \(V_{\Omega}\) = 1 V). The value of \(V_{1}\) is obtained from Equation (9). Figure 14 shows how the overall efficiency of the proposed TIBuck DC/DC converter acting as a VLC driver, \(\eta_{t}\), varies with the variation in the efficiency of each individual DC/DC converter (i.e., with variations of \(\eta_{ti}\) and \(\eta_{bu}\)). In each sweep, the efficiency of one DC/DC converter varies from 0.8 to 1, while keeping the other efficiency at 1. It is clear that the efficiency of the proposed TIBuck DC/DC converter depends more strongly on the value of \(\eta_{bu}\). The auxiliary Buck DC/DC converter processes higher power, making its efficiency much more important. This becomes an important advantage, because the auxiliary buck converter operates at a lower switching frequency, and it is easier to achieve higher efficiency here than in the TIBuck DC/DC converter, which operates at a higher frequency. The same analysis of efficiencies of the individual DC/DC converters is shown in Figure 15, but at three different temperatures, with \(T_{1}\) > \(T_{2}\) > \(T_{3}\).