# A New SEPIC-Based DC-DC Converter with Coupled Inductors Suitable for High Step-Up Applications
## 4 Design Example for the Proposed Converter  
In the design example, the converter is used in a PV system and, therefore, the requirements for the proposed SEPIC-based converter depend on the PV panel characteristics. Two PV modules MWG-20 will be used for the experiments. The PV modules will be connected in series, in order to increase the input voltage. In standard test conditions (STC) for a solar irradiance \(G=1000\) W/m\({}^{2}\) and temperature \(T=25\)\({}^{\circ}\)C, one PV module has the following parameters: \begin{tabular}{l} Peak power: \(P_{max}=20\) W \\ Maximum power point current: \(I_{mp}=1.14\) A \\ Maximum power point voltage: \(V_{mp}=17.49\) V \\ Short circuit current: \(I_{sc}=1.22\) A \\ Open circuit voltage: \(V_{oc}=21.67\) V \\ The converter was designed according to the following parameters: \\ Input voltage range was between: \(V_{g}=30\div 35\) V \(-\) correlated to \(V_{mp}\) \\ Maximum output power: \(P_{o}=40\) W \\ Switching frequency: \(f_{s}=100\) kHz \\ Output voltage: \(V_{o}=120\) V \\ Output voltage peak-to-peak ripple: \(\Delta V_{C2}=300\) mV \\ Transformer ratio: \(n=0.5\) \\ \end{tabular}   
The minimum and maximum static conversion ratios are obtained from Equation (8):  
\[M_{min}=\frac{V_{o}}{V_{gmax}}=3.42 \tag{30}\]  
\[M_{max}=\frac{V_{o}}{V_{gmin}}=4 \tag{31}\]  
The necessary duty cycle range can be calculated using (29) and will result in \(D\in[0.6070,\,0.6375]\). The value for the load resistor is given by:  
\[R=\frac{V_{o}^{2}}{P_{o}}=360\;\Omega \tag{32}\]  
Imposing the peak-to-peak magnetizing inductor current ripple given by (21) not to exceed 25% of the dc magnetizing inductor current value (11), the magnetizing inductor can be calculated. The condition will be:  
\[\Delta I_{LM}\leq\;\frac{1}{4}\times I_{LM} \tag{33}\]  
From Equations (33), (21) and (11) the minimum magnetizing inductor formula can be found:  
\[L_{M}\geq\frac{4\times(1-D)^{2}\times R}{D\times(n+D)\times(1+n)\times f_{s}} \tag{34}\]  
In a similar way, the condition for \(L_{3}\) inductor current will look like:  
\[\Delta I_{L3}\leq\;\frac{1}{4}\times I_{L3} \tag{35}\]and from (35), (22), and (12) the minimum inductor \(L_{3}\) value can be found as follows:  
\[L_{3}\geq\frac{4\times(1-D)\times R}{f_{s}} \tag{36}\]  
The equations for the inner and output capacitors are designed imposing that the voltage ripple across the inner capacitor be less than ten percent of its dc value and for the output capacitor to ensure an output voltage ripple less than the value imposed by the specifications. Using (6) and (23) the minimum required value for the internal capacitor, and from (7) and (24) the minimum required value for the output capacitor can be calculated:  
\[C_{1}\geq\frac{10\times D^{2}}{(1-D)\times R\times f_{s}} \tag{37}\]  
\[C_{2}\geq\frac{D^{2}\times(n+D)\times V_{g}}{n\times(1-D)\times R\cdot f_{s} \times\Delta V_{\text{C2}}} \tag{38}\]  
The minimum value of the magnetizing inductor \(L_{M}\) calculated with Equation (35) will be equal to the value of inductor \(L_{1}\), \(L_{M}=L_{1}=1.7\) mH. The value for \(L_{2}\) is determined using \(L_{2}=n^{2}\cdot L_{M}\), so \(L_{2}=425\) uH. The minimum inductor value \(L_{3}\), calculated from (36) is \(L_{3 min}=5200\) uH. The minimum value of the inner capacitor was obtained from (37) and that for the output capacitor from (38), and they are \(C_{1 min}=0.26\) uF and \(C_{2 min}=6.72\) uF. The inductors were manufactured in the laboratory with the following values: \(L_{1}=2\) mH, \(L_{2}=503\) uH and \(L_{3}=5900\) uH. Taking into account the practical values obtained in the laboratory for \(L_{1}\) and \(L_{2}\), the transformer ratio \(n\) resulted as \(n=0.5014\). For the capacitors, the following standard values were chosen: \(C_{1}=0.33\) uF and \(C_{2}=10\) uF. The transistor voltage stress can be calculated from (13), and it is \(V_{S}=197\) V. According to (14), its average current will be \(I_{S}=1.33\) A.