# A New Cuk-Based DC-DC Converter with Improved Efficiency and Lower Rated Voltage of Coupling Capacitor

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## Abstract

**:**

## 1. Introduction

_{2}) is transferred back to the supply, which can be undesirable and restrict the converter’s usability [16].

_{2}and the load simultaneously. Yet, unlike the Buck–Boost converter, when the switch is opened, the energy stored in L

_{2}is transferred to the load [16]. Despite these advantages, the Cuk converter does have some drawbacks; for example, the compensation circuit may be added to stabilize the converter, which reduces its response.

_{m}= ±100 V) compared to (V

_{m}= ±500 V) in the Cuck converter. A design example is presented to validate the functionality of the proposed converter, which is suitable for hybrid renewable energy systems and electric vehicle applications. Moreover, a low voltage–low power prototype of 12/−18 V, 3.24 W is established to verify the operation of the proposed converter, showing a close match between measurements and simulations.

## 2. Operating Modes, Duty Cycle, and Voltage Gain of the Proposed Converter

_{1}and L

_{2}, one coupling capacitance C

_{1}, one controlled switch M

_{1}, one diode D, and also a low pass filter includes C

_{o}in parallel with the load resistance.

#### 2.1. Operating Mode of the Proposed Converter

- When the switch M
_{1}is ON: the diode D is reversed biased. Figure 3a shows the equivalent circuit and current directions of this mode. The energy is transferred and stored in the coupling capacitor C_{1}. Meanwhile, both inductors L_{1}and L_{2}are energized. The current slope in the inductors is given according to the following equations:

_{1}is given by (4).

- When the switch M
_{1}is OFF: the diode is forward and conducts the current. Figure 3b shows this mode’s equivalent circuit and current directions. All the energy stored in C_{1}, L_{1}, and L_{2}is transferred to the load. The current slope in the inductors is given according to the following equations:

_{1}is given by (8).

_{1}is large enough, then, the average C

_{1}voltage has to be equal to the following equation:

_{1}depends on the voltage difference between the two inductors. In the proposed converter, the coupling capacitor’s average voltage is equal to zero. This means all the energy stored during the turn-on period is dissipated during the turn-off period. More details will be discussed in the Simulation Results Section.

#### 2.2. Duty Cycle and Voltage Gain of the Proposed Converter

_{s}) must equal zero. Then, once the switch M

_{1}is turned on, the inductor L

_{1}is energized from the input DC voltage V

_{in}. On the other hand, when the switch M

_{1}is turned off, the energy stored in L

_{1}is delivered to the load through the coupling capacitor C

_{1}and the diode D. Based on that, the inductor voltage function is given by:

_{1}and L

_{2}results in (12). By solving (12), the voltage gain can be produced as per (13).

_{G}is the voltage gain of the proposed converter.

## 3. Design Example and Parameters Selection

_{1}, L

_{2}currents are calculated as:

_{1}, the ripple in the output voltage should not exceed 20% of V

_{o}, thus it is found as per (19). Finally, the filter capacitor can be calculated by using (20). Thus, C

_{o}has a minimum value calculated as:

## 4. Simulation Results

_{L}

_{1}is given by (21). Based on the design example (21) gives 0.92 A. Otherwise, the ripple in I

_{L}

_{2}is calculated based on (22). It is also important to point out that the result of (21) is 1.3 A.

_{L}

_{1}is equal to 5 A, and the average inductor current I

_{L}

_{2}is equal to 3.3 A, with a ripple current percentage of less than 20% of both currents.

_{1}, the L

_{1}is clamped to V

_{in}. Meanwhile, the L

_{2}voltage to the difference between V

_{L}

_{1}and V

_{C}

_{1}. During the conduction period of the diode, the L

_{1}has a voltage of V

_{L}

_{2}+ V

_{C}

_{1}but in the reverse direction, and the L

_{2}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.

_{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 V

_{in}+ V

_{C}

_{1}+ V

_{o}. 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:

_{1}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.

_{critical}is equal to 0.16.

## 5. Experimental Results

#### 5.1. Experiment Setup

#### 5.2. Experimental Results and Discussion

_{1}voltage is plotted in Figure 17.

_{1}’s turn-on time. However, when the switch is turned off (with an off time of approximately 15 µs), the inductor voltage decreases to −6 V. Similarly, during the switch M

_{1}’s turn-on time, the inductor L

_{2}exhibits a voltage of a 3 V across its terminals. Conversely, when the switch M

_{1}is turned off, the inductor L

_{2}displays −10 V, see Figure 17 (Ch2). In addition, the coupling capacitor has 7 V across its terminal, which corresponds to the difference between the input and output voltage. Consequently, the rated voltage of the selected voltage of C

_{1}should be around 15 V. This confirms that the selected coupling capacitor has a lower rated voltage than the same one in the Cuk converter (in the Cuk converter case, the rating voltage of the coupling capacitor must be selected around 45 V. This reduces the selected rated voltage of C

_{1}in the proposed converter by 66.67% compared to the same capacitor of Cuk converter, as seen in Figure 18.

_{1}and the MOSFET’s parasitic capacitance during the energy transfer period. It is not possible to resonate L

_{2}and C

_{1}with L

_{1}, because the resonant frequency of this combination is about 28 kHz. Similarly, there is no possible resonant between L

_{2}and C

_{1}with L

_{1}, as their resonance frequency is about 40 kHz, significantly lower than the frequency depicted in Figure 19 and Figure 20.

_{1}and the capacitance of parasitic capacitance of the used passive prob. The third possible reason may be related to the poor copper board used which causes some EMI issues. However, these reasons can be easily overcome with very good PCB design and using advanced measuring devices. In sum, Table 5 provides a comprehensive comparison between the Cuk converter and the Mahafzah converter, considering their main features under the same operating conditions.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**(

**a**) The switch M

_{1}voltage (blue), and the diode D (red) voltage (

**b**). The switch M

_{1}current (blue), and the diode D (red) current.

**Figure 11.**(

**a**) The coupling capacitor voltage of both converters, (

**b**) zoomed in during steady state.

Ref. | Year of Publication | Objective | Limitations |
---|---|---|---|

[12] | 2011 | A buck converter with coupled inductor for ZVS is proposed | Critical design of the coupled inductor |

[13] | 2020 | A different DC-DC converters with average model is presented | It is used for multi-phase applications with coupled inductor |

[15] | 2018 | Design quasi-SEPIC converter with high voltage gain capability | It uses a coupled inductor and the way to improve the magnetic core characteristics |

[16] | 2019 | Proposes a new Cuk converter fed switched reluctance motor | The circuit has additional semiconductor devices and many inductors |

[17] | 2021 | Proposed an interleaved Luo converter | The critical design of the magnetic circuit |

[18] | 2022 | Design a flyback with a ripple free in inductor current | Adding many passive components to the conventional flyback |

These Parameters Are Taken from the Application Proposed in [33] | The Calculated Parameters Based on Presented Equations | ||
---|---|---|---|

Parameter | Value | Parameter | Value |

P_{in}/P_{o} | 1 kW | I_{o} | 3.3 A |

V_{in} | 200 V | I_{L1} | 5 A |

V_{o} | −300 V | I_{L}_{2} | 3.3 A |

ΔI_{L}_{1} | 0.92 A | R_{o} | 90 Ω |

ΔI_{L}_{2} | 1.3 A | L_{1} | 6.5 mH |

ΔV_{C}_{1} | <0.1 | L_{2} | 6.5 mH |

K_{p} | 0.2 | C_{1} | 0.5 µF |

K_{i} | 0.001 | C_{o} | 5 µF |

Duty Cycle (D) | 60% | ||

f_{s} | 20 kHz |

Loss Component | Equation | Note |
---|---|---|

Conduction Loss | ${P}_{M1}={i}_{d}^{2}{R}_{ds-on}D$ | R_{on}: MOSFET on-state resistance |

${P}_{D}=({V}_{f}{i}_{d}+{i}_{d}^{2}{R}_{f})(1-D)$ | ||

Switching Loss | ${P}_{M1}=05{f}_{s}{C}_{oss}{(0.5{V}_{in}+{V}_{o})}^{2}$ | ${C}_{oss}$ is M_{1} output capacitance |

${P}_{D}=05{f}_{s}{C}_{d}{(0.5{V}_{in}+{V}_{o})}^{2}$ | ||

Control Loss | ${P}_{gates}={Q}_{g}{V}_{gs}{f}_{s}$ | ${Q}_{g}$ is the gate charge of M_{1} |

${R}_{L1}={R}_{1dc}{\left(\frac{D{T}_{s}{V}_{in}}{{L}_{1}}\right)}^{2}$ | ||

Passive Devices | ${R}_{L2}={R}_{2dc}{\left(\frac{D{T}_{s}{V}_{o}}{{L}_{2}}\right)}^{2}$ | Losses in each L_{1} and L_{2} based on using their DC resistance. The losses in the coupling capacitor are ignored due to its small ERS |

The Selected Parameters for Testing and Validation | |
---|---|

Parameter | Value |

P_{in}/P_{o} | 3.24 W |

V_{in} | 12 V |

V_{o} | −18 V |

MOSFET | IRF540N |

Driving Transistor | 2N3904 |

Diode | 1N4007 |

L_{1} = L_{2} | 1.2 mH |

C_{1} | 1 µF |

Duty Cycle | 70% |

f_{s} | 20 kHz |

Parameters | Converter Topology | |
---|---|---|

Cuk Converter | Mahafzah Converter | |

Component Count | Same | Same |

Coupling Capacitor Voltage | High | Reduced (√) |

Efficiency | Low | Improved (√) |

Ripple in Vo | Low (√) | High |

Transient Period | Long | Short (√) |

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## Share and Cite

**MDPI and ACS Style**

Mahafzah, K.A.; Al-Shetwi, A.Q.; Hannan, M.A.; Babu, T.S.; Nwulu, N.
A New Cuk-Based DC-DC Converter with Improved Efficiency and Lower Rated Voltage of Coupling Capacitor. *Sustainability* **2023**, *15*, 8515.
https://doi.org/10.3390/su15118515

**AMA Style**

Mahafzah KA, Al-Shetwi AQ, Hannan MA, Babu TS, Nwulu N.
A New Cuk-Based DC-DC Converter with Improved Efficiency and Lower Rated Voltage of Coupling Capacitor. *Sustainability*. 2023; 15(11):8515.
https://doi.org/10.3390/su15118515

**Chicago/Turabian Style**

Mahafzah, Khaled A., Ali Q. Al-Shetwi, M. A. Hannan, Thanikanti Sudhakar Babu, and Nnamdi Nwulu.
2023. "A New Cuk-Based DC-DC Converter with Improved Efficiency and Lower Rated Voltage of Coupling Capacitor" *Sustainability* 15, no. 11: 8515.
https://doi.org/10.3390/su15118515