# Influence of MOSFET Parasitic Capacitance on the Operation of Interleaved ZVS Boost Converters
## 7 Possible Output Voltage Regulation Method  
Applying the analyzed converter in any real energy generation system, for example as a boost stage in a photovoltaic inverter, requires a control method that allows to regulate the output voltage to be developed. The voltage ratio plot, presented in Figure 4, can be used to propose such a controller. Voltage ratio \(G\) and normalized load resistance \(\overline{R}\) are variables that change in a renewable energy  
Figure 10: Plot of the voltage ratio \(G\) as a function of normalized switching frequency with parasitic capacitance considered for \(V_{\rm in}=50\) V, \(N=2\), \(R=50\)\(\Omega\). generation system, as the input voltage and the load vary. Thus maintaining constant output voltage \(V_{\mathrm{o}}\) requires switching frequency \(f_{\mathrm{s}}\) to change as the input voltage \(V_{\mathrm{in}}\) and load resistance \(R\) fluctuate. Equation (13) allows for plotting normalized switching frequency \(f_{\mathrm{s}}\)/\(f_{0}\) as a function of normalized load resistance \(\overline{R}\) by assuming that supply voltage \(V_{\mathrm{in}}\) = const. and voltage ratio \(G\) = const. Such a plot, for several given values of voltage ratio \(G\) is presented in Figure 11. The plot reveals the main limitation of the converter, namely that it is not possible to keep the voltage ratio low at low load condition (when the load resistance is high). For example keeping the voltage ratio at \(G\) = 2.5 at normalized load resistance \(\overline{R}\) greater than 7 would require normalized switching frequency \(f_{\mathrm{s}}\)/\(f_{0}\) to be above 1. However, Figures 4 and 11 combined, show that it is indeed possible to control the output voltage by changing the switching frequency. A simplified schematic of the proposed controller is presented in Figure 12. This method requires the output voltage and drain-source voltages of the transistors to be measured. A PI controller is used to change the switching frequency in order to change the output voltage. A zero-crossing detection block is needed to ensure that the switches are turned on in zero-voltage conditions. Figure 11: Plot of the normalized switching frequency \(f_{\mathrm{s}}\)/\(f_{0}\) as a function of normalized load resistance \(\overline{R}\) for given values of voltage ratio \(G\). In order to confirm feasibility of the proposed control method a simulation model was built in GeckoCircuits software. An overview of the model is presented in Figure 13. All circuit parameters are the same as in the experimental converter. The model allows for simulation of certain dynamic states--step of desired output voltage and sudden load resistance variation. Both the PI controller and ZVS synchronization block were programmed in Java programming language. The resonant frequency is around 813 kHz, thus the switching frequency was limited to the range of 50-800 kHz. The PI controller was tuned by trial and error method while analyzing the step response. The output value of the PI controller is the switching frequency which is then the input of the ZVS synchronization block, which has additional inputs--drain-source voltages of the MOSFETs. The MOSFETs are turned on when their drain-source voltage reaches zero, while turn-offs result from the switching period. The same block is also responsible for phase shifting both control signals. However, when the output voltage is too low, i.e., when the voltage ratio \(G\) is below 2, for example during the converter start-up, zero-voltage switching is not achievable as was shown before. Therefore control signals would not be turned high at any point. Thus another condition was implemented--when the output voltage \(V_{\mathrm{o}}\) is lower than 210% of the input voltage \(V_{\mathrm{in}}\) the MOSFETs are switched with a constant duty cycle \(D\) = 0.5 and switching frequency\(f_{\mathrm{s}}\) = 50 kHz. After \(V_{\mathrm{o}}\) reaches 2.1\(V_{\mathrm{in}}\) control signals are synchronized to ZVS conditions.