**4. Simulation Results**

MATLAB 2020a is used to simulate the proposed converter, which can provide very close results to the real prototype. The simulation parameters are discussed in the previous section, whereas the simulation time is set to 1 s, and the solver is selected to be an ordinary differential equation ode23tb with a maximum step size is 250 μs and continuous simulation type. Moreover, the proposed converter is operating under the CCM mode with a hard-switching technique and constant duty cycle equal to 0.6.

The output voltage is plotted in Figure 5. It is seen that the average output is 297 V DC voltage with a ripple percentage in the voltage of around 6.7%, which is an acceptable value. Moreover, as the load is a pure resistance, the load current has the same voltage pattern but is scaled by (1/90), which gives the average load current 3.3 A. Thus, the current ripple in *IL*<sup>1</sup> is given by (21). Based on the design example (21) gives 0.92 A. Otherwise, the ripple

in *IL*<sup>2</sup> is calculated based on (22). It is also important to point out that the result of (21) is 1.3 A.

$$
\Delta I\_{L1} = \frac{V\_{\text{in}} D T\_{\text{s}}}{L\_1} \tag{21}
$$

$$
\Delta I\_{L2} = \frac{V\_o D T\_s}{L\_2} \tag{22}
$$

**Figure 5.** The output voltage of the proposed Mahafzah converter.

The continuous current operation in the proposed converter is clearly seen in Figure 6. As the inductance values of both inductors are the same, the difference in the slopes and their averages are related to the difference in the applied voltage across inductor terminals during the on/off periods. The average inductor current *IL*<sup>1</sup> is equal to 5 A, and the average inductor current *IL*<sup>2</sup> is equal to 3.3 A, with a ripple current percentage of less than 20% of both currents.

**Figure 6.** Inductor currents in CCM.

On the other hand, the inductors' voltages are illustrated in Figure 7. During the conduction of switch *M*1, the *L*<sup>1</sup> is clamped to *Vin*. Meanwhile, the *L*<sup>2</sup> voltage to the difference between *VL*<sup>1</sup> and *VC*1. During the conduction period of the diode, the *L*<sup>1</sup> has a voltage of *VL*<sup>2</sup> + *VC*<sup>1</sup> but in the reverse direction, and the *L*<sup>2</sup> voltage is clamped to the load voltage. In steady-state operation, the average inductor voltages are equal to zero. Figure 8 presents the coupling capacitor voltage and its current. Over one switching cycle, it is noticeable that the capacitor bypasses the energy from the input side to the output side without any remaining voltage across its terminals. This means the average capacitor voltage is zero based on Figure 8a. Additionally, the balance in the capacitor charge is illustrated in Figure 8b. Whereas, the average capacitor current over one switching cycle is zero in steady-state conditions.

**Figure 7.** The inductors voltages in CCM.

**Figure 8.** (**a**) The voltage of coupling capacitor *C*<sup>1</sup> (**b**). The current of coupling capacitor *C*1.

The merit of the proposed converter is the existence of an LCL tank connected with the switch *M*1, this connection offers a soft switching turn on and turn off. The voltage stress across the switch is illustrated in Figure 9a. The voltage reaches the sum of *Vin* + *VC*<sup>1</sup> + *Vo*. The same issue with the output diode. Figure 9b shows the switch and diode currents. The average switch and diode voltages are calculated, respectively, using the following equations:

$$I\_{M1} = \frac{V\_{in}D^2}{R\_o(1-D)^2} \tag{23}$$

$$I\_D = \frac{V\_{\text{in}}D}{R\_o(1 - D)}\tag{24}$$

The proposed converter is compared with the Cuk converter. The Cuk converter is simulated using the same design example discussed above to compare the results. Both converters' output voltages are shown in Figure 10a. It shows that the output voltage in both cases decreased to −300 V, but the proposed converter has more ripple in its voltage than the Cuk converter. Moreover, the proposed converter has an unrecognizable overshoot higher than the Cuk converter, but the proposed converter is faster than the Cuk converter in achieving the steady state period, see Figure 10b.

The coupling capacitor *C*<sup>1</sup> plays an important role in energy transfer in Cuk, SEPIC, Buck–Boost, and Luo converters, as well as it has a role in the proposed Mahafzah converter. The selected capacitor must be sized so that it has a rated voltage value that is higher than twice the voltage across its terminal. The higher rated voltage results in a higher size capacitor. Furthermore, the large size of this capacitor holds a rather large place on the PCB, thus reducing the cost of circuit manufacturing.

**Figure 9.** (**a**) The switch *M*<sup>1</sup> voltage (blue), and the diode *D* (red) voltage (**b**). The switch *M*<sup>1</sup> current (blue), and the diode *D* (red) current.

**Figure 10.** (**a**) The output voltage of both converters, (**b**) the zoomed in.

Figure 11a compares the two capacitor voltages in the proposed and Cuk converter. As noticed from Figure 11b, the coupling capacitor Cuk converter has a much higher applied voltage than its counterpart in the proposed converter. Similar to the Cuk converter, the proposed converter has the boundary characteristics shown in Figure 12. The coupling capacitor is selected to endure the applied voltage across its terminal in the Cuk converter. The critical value that separates the two modes is plotted in the cyan curve. The voltage gain as a function of the duty cycle and *K* value is given by (25). Then, according to (25), the critical value between CCM and DCM is given as described in (26). Accordingly, *Kcritical* is equal to 0.16.

$$V\_G(D\_\prime K) = \begin{cases} \begin{array}{c} \frac{-D}{(1-D)} & K > K\_{critical} \\ \frac{-D}{\sqrt{K}} & K > K\_{critical} \end{array} \end{cases} \tag{25}$$

$$K\_{critical} = \left(1 - D\right)^2\tag{26}$$

**Figure 11.** (**a**) The coupling capacitor voltage of both converters, (**b**) zoomed in during steady state.

**Figure 12.** Characteristics of the proposed converter.

As illustrated in Figure 11 and in Equation (19), the coupling capacitor value of the proposed converter is noticeably reduced by five times compared to the coupling capacitor value for the cuck converter under the same operating conditions. The loss components of the proposed converter can be divided into conduction losses, switching losses, and control losses [23,34]. It should be noted that these losses are associated with semiconductor devices. Table 3 illustrates all loss components and provides the related equation.


**Table 3.** Loss calculation of the proposed Mahafzah converter.

Using the presented equations in Table 2, the efficiency of the proposed converter is calculated when changing the load simultaneously. The efficiency of the proposed converter is compared with the Cuk converter, as illustrated in Figure 13. The efficiency of both converters is calculated based on the equations presented in [22–24,34]. The efficiency calculation considers all the loss components, including the conduction, switching, and control losses. The efficiency is also calculated when the load current is changed from 10% up to 100% of the rated current. As seen in Figure 13, the proposed converter has better efficiency than the Cuk converter when the load is increased. The efficiency of the proposed converter reaches around 88% at full load conditions, while the Cuk converter efficiency reaches 87% at the same rated conditions.

**Figure 13.** The efficiency of both converters.
