**2. High Output Gain Modified Cuk Converter ´**

The developed Cuk converter is depicted in Figure ´ 1. A classical Cuk converter was modified ´ with an additional inductor (L3) and capacitor (C2). Figure 2a and b provides the equivalent circuit representation of the modified Cuk converter with the semiconductor switch S turned ON and ´ OFF, respectively.

**Figure 1.** Topology of proposed novel Cuk converter. ´

**Figure 2.** Circuit configuration (**a**) ON state; (**b**) OFF state.

When the switch S is turned ON and OFF, the following inductance voltage equations can be written to the circuit over one period for steady-state conditions. When the S is ON:

$$V\_{L1} = V\_{1\prime} \, V\_{L2} = V\_o - V\_{C2} - V\_{C1\prime} \, V\_{L3} = -\, V\_{C2} \tag{1}$$

When the S is OFF:

$$V\_{L1} = V\_1 - V\_{C1}, \; V\_{L2} = -\; V\_o + V\_{C2}, \; V\_{L3} = V\_{C1} + V\_{C2} \tag{2}$$

According to Faraday's Law, the average voltage across an inductor is zero at steady-state. Hence, the voltage gain ratio of the converter can be obtained by starting the commonly used equation given below.

$$
\delta\,V\_{L(ON)} = (1 - \delta)V\_{L(OFF)}\tag{3}
$$

The term *δ* means the duty ratio of the switch S. Equation (3) will be written for *L*1, *L*2, and *L*3, and required voltage gain ratio equation will be obtained.

First, (3) is written for *L*1, and the equation given below is obtained;

$$
\delta\,V\_1 = (1 - \delta)(V\_1 - V\_\mathbb{C})\tag{4}
$$

The above Equation (4) can be simplified as:

$$(2\ \delta - 1)V\_1 = (\delta - 1)\ V\_{\mathbb{C}1} \tag{5}$$

Second, (3) can be written for *L*<sup>2</sup> as given below:

$$
\delta \left( V\_o - V\_{\subset 2} - V\_{\subset 1} \right) = (1 - \delta)(V\_o + V\_{\subset 2}) \tag{6}
$$

Equation (6) can be arranged as given below:

$$V\_{\mathcal{O}} \text{ (2 }\delta - 1) = V\_{\mathcal{C}2} + \delta \text{ }V\_{\mathcal{C}1} \tag{7}$$

Finally, (3) can be written for *L*3:

$$
\delta V\_{C2} = (1 - \delta)(V\_{C1} + V\_{C2}) \tag{8}
$$

This simplifies to:

$$V\_{C2} = (1 - \delta)V\_{C1} \tag{9}$$

If (5), (7), and (9) are combined, the duty ratio of the converter can be obtained. If (9) is inserted into (7),

$$V\_o \text{ (2 }\delta - 1) = V\_{C1} \tag{10}$$

If (10) is inserted into (5), the duty ratio of the system can be finalized.

$$\frac{V\_o}{V\_i} = -\frac{1}{1-\delta} \tag{11}$$

A sample design circuit can be conducted by using the circuit parameters given in Table 1 in MATLAB/Simulink. Different *δ* values are applied in the simulation, as shown in Figure 3c. Output voltage (*Vo*) and input current (*ii*) curves change accordingly, as shown in Figure 3a,b, respectively. Output voltage and input currents are zoomed; it is observed in simulations that the frequency of the ripples is equal to the SF (150 kHz).

**Table 1.** Design parameters of Modified Cuk Converter. ´


The performance of the modified Cuk converter was compared to classical ´ Cuk and buck/boost ´ converter circuits. Figure 4a shows *δ* comparison of converters. A simulation platform is constructed in MATLAB/Simulink with the same parameters given in Table 1. Theoretical and simulation values of the modified Cuk converter validate the results. Efficiency comparison of simulated buck/boost, ´ Cuk, and ´ modified Cuk converter is depicted in Figure ´ 4b. Modified Cuk converter efficiency is higher than classical ´ Cuk and buck/boost converter. It can be stated that the proposed modified ´ Cuk converter produces ´ higher efficiency due to the inclusion of additional passive elements. This reduces several parasitic effects and switching/conduction losses and increases voltage gain ratio, as emphasized in [37].

**Figure 3.** Simulation of modified Cuk converter. ( ´ **a**) Output Voltage (V); (**b**) Input Current (A); (**c**) *δ*.

**Figure 4.** Comparison of buck/boost, Cuk, and modified ´ Cuk converter. ( ´ **a**) Duty Ratio; (**b**) Efficiency.
