# Flicker-Free LED Driver Based on Cuk Converter with Integrated Magnetics

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Operating Principle

_{1}, inductors L

_{1}and L

_{2}, the coupling capacitors C

_{1}and C

_{2}with large voltage ripple, diode D

_{1}, transformer T

_{r}in which L

_{P}and L

_{S}are the primary and secondary inductance of the transformer, and LED load. The transformer T

_{r}is introduced to separate the input and output. The two inductors and the transformer are wound on an EI magnetic core to achieve magnetic integration. In the proposed circuit, the transformer wire is wound around the center leg3, and two conductors’ wire are wound around the two side leg—leg1 and leg2 with a very small air gap. Mutual inductance exists between the two inductors by this method and ensures decoupling integration between the two inductors and the transformer. Due to the mutual inductance, the voltage can be shared and the voltage on the inductors can be reduced [19,20]. Then the twice-line-frequency LED current ripple of the LED driver based on the Cuk converter with integrated magnetics can be greatly reduced.

- Both input and output are connected to inductors, making both input and output currents continuous and the pulsating currents of both are small, which is convenient for filtering at the input and output.
- The output voltage of Cuk converter can be larger or smaller than the input voltage, which increases the application range of the converter.
- The Cuk converter has better anti-interference performance because the switching tube short-circuits the interference at the input during the switching tube conduction and the diode short-circuits the interference at the input during the switching tube turn-off.
- If the input inductor and output inductor are integrated into one core, the output ripple can be reduced by half, and by choosing a suitable inductor value or increasing the operating frequency of the converter, the output current can theoretically achieve zero ripple.

_{1}switched on and D

_{1}switched off and (2) Q

_{1}turned off and D

_{1}turned on. Figure 2 shows the equivalent circuit of proposed LED driver in each mode of operation. Figure 3 shows the key voltage and current waveforms.

- All electronic devices are ideal, ignoring their parasitic parameters.
- The switching frequency f
_{S}is much larger than the grid frequency f_{L}, that is to say the input voltage is approximately constant over a switching period; - Capacitors C
_{1}, C_{2}, and C_{O}are large enough to keep the voltage constant approximately; - Since the decoupling integration mainly affects the volume and loss of the magnetic components, the influence on voltage and current is very small, the interaction between the inductors and the transformer can be neglected.

_{0}–t

_{1}]: At t

_{0}, the switch Q

_{1}is turned on and diode D

_{1}is turned off because of the reverse voltage. The equivalent circuit is shown in Figure 2a. The voltage on the inductor L

_{1}is input voltage v

_{in}and it is charging during this period. The voltage on the primary winding N

_{L}is equal to the voltage of the capacitor C

_{1}. At the same time, the voltage induced by the secondary winding N

_{S}and capacitor C

_{2}supplies to LED load together. The current flowing through L

_{2}increases and L

_{2}stores energy. According to Figure 2a, the equation can be expressed as

_{L}

_{1}and V

_{L}

_{2}are the voltages on the L

_{1}and L

_{2}respectively, V

_{C}

_{1}and V

_{C}

_{2}are the voltages on the C

_{1}and C

_{2}respectively, M is the mutual inductance between L

_{1}and L

_{2}, N = N

_{S}/N

_{P}is the transformer turns ratio.

_{1}–t

_{2}]: At t

_{1}, the switch Q

_{1}was turned off and diode D

_{1}was turned on to provide an afterflow for L

_{S}and L

_{2}. At this time, L

_{1}is discharging and provides energy to C

_{1}. Meanwhile, the voltage induced by the secondary winding is charging C

_{2}through D

_{1}. L

_{2}provides energy to LED load through D

_{1}as well. According to Figure 2b, the equation can be expressed as

_{1}, L

_{2}) over a switching period T

_{S}, we can get

_{1}.

_{L}

_{1}and Δi

_{L}

_{2}are the increment of i

_{L}

_{1}and i

_{L}

_{2}from t

_{0}to t

_{1}.

_{1}, the ripple current of the inductor L

_{2}reaches zero, and the input current i

_{L}

_{1}remains the same as the case of no coupling. Therefore, the output current ripple is only related to inductor L

_{1}, the mutual inductance M between two inductors, and the transformer turns ratio N. The mutual inductance M is an intrinsic parameter between the coils and related to the turns of the inductors, the dimension, the position, and the magnetic medium. Anyhow, the output current ripple can be much smaller than that of the discrete magnetics.

## 3. Critical Design Parameter

#### 3.1. Inductors L_{1} and L_{2}

_{1}and L

_{2}must ensure this operating condition so that all the relationships established in the theoretical analysis are valid. From (4), we have

_{1}is chosen as 20%. According to the increase of i

_{L}

_{1}from t

_{0}to t

_{1}, the expression is shown in (7)

_{O}is the power of LED, T

_{S}is the switching period of Q

_{1}and T

_{S}= 1/f

_{S}.

_{O}is zero in a grid period, so the current flowing through the LED load is equal to the current flowing through L

_{2}and the maximum ratio of the current ripple through L

_{2}is chosen as 5%. The expression is shown in Equation (9)

#### 3.2. Capacitors C_{1}, C_{2}, and C_{O}

_{O}equal to the current ripple of L

_{2}, which results in the voltage ripple on C

_{O}. The equation of output voltage ripple is shown as (11).

_{O}is 0.1 V

_{CO}

_{O}is obtained as

_{1}(is equal to C

_{2}) transfers energy from input to output and in order to balance the instantaneous input and output power, the maximum voltage ripple on C

_{1}(or C

_{2}) is 0.5 V

_{C}

_{1}(or 0.5 V

_{C}

_{2}). The computational procedure is same as C

_{O}.

_{1}, C

_{2}, and C

_{O}are CBB capacitor because of low loss, low absorption coefficient, good frequency characteristic, good self- healing effect, and high reliability [22].

#### 3.3. MOSFET Q_{1} and Diode D_{1}

_{1}and voltage applied on D

_{1}are similar to that of transistor Q. According to the above analysis, the circuit specifications and parameters designed in this paper are listed in Table 1.

## 4. Small-Signal Analysis and Controller Design

_{1}is around the upper side leg1 with N

_{1}turns of conductor, the magnetic flux is φ

_{1}, the reluctance is R

_{1}; the L

_{2}is wound on the lower side leg2 with N

_{2}turns of conductor, the magnetic flux is φ

_{2}, the reluctance is R

_{2}; the primary and secondary side of the transformer are wound in center leg3 with the magnetic flux φ

_{C}and the reluctance R

_{C}. Thus, according to Ohm’s law based on the magnetic circuit, we can get the following equation:

_{1}= φ

_{2}+ φ

_{C}, then (6) can be rewritten as

_{1}(t) ϕ

_{2}(t) v

_{O}(t) v

_{C1}(t) v

_{C2}(t)]

^{T}, the input variable u(t) is [v

_{in}(t)]

^{T}, the state-space equation in mode 1 can be expressed as

_{1}and B

_{1}can be expressed as follows ngs and their implications should be discussed in the broadest context possible. Future research directions may also be highlighted.

_{2}and B

_{2}are

_{vd}(s) can be expressed as

_{i}(I = 1, 2, 3, 4) and b

_{j}(j = 1, 2, 3, 4, 5, 6) are omitted for brevity.

_{1}is 9.5 × 10

^{9}A·t/Wb, reluctance R

_{2}is 1.27 × 10

^{10}A·t/Wb, reluctance R

_{C}is 1.14 × 10

^{10}A·t/Wb. Finally, we can calculate the G

_{vd}(s) based on MATLAB with the parameters in Table 1. The Bode diagram of G

_{vd}(s) is shown in Figure 5.

_{1}= 3.2 kHz and f

_{2}= 10.4 kHz and one zero resonance point f

_{3}= 10.6 kHz. The zero resonance point at f

_{3}balances the pole at f

_{2}, so there is no resonance peak in the Bode diagram, the circuit phase lags by 180 degree and its amplitude-frequency characteristic is declining by 40 dB/dec. Therefore, to make the circuit stable when wide range input voltage, phase compensation circuit should adopt the type II feedback network.

_{1}= 51 kΩ, R

_{f}= 270 kΩ, C

_{3}= 680 pF, C

_{f}= 470 nF.

- The low frequency band decreases at a slope of −20 dB/dec and has a certain height to ensure that the requirements of steady-state accuracy are met, followed by a slope of −40 dB/dec to increase the rapidity of the system.
- The middle frequency band should ensure that the cut-off frequency is large enough to meet the requirements of dynamic rapidity, and the amplitude-frequency characteristic curve at the 0 dB line should cross at −20 dB/dec and maintain a certain width to meet the requirements of the relative stability of the system.
- The amplitude-frequency characteristic curve of the high-frequency band should have a large negative slope, generally less than or equal to −40 dB/dec to improve the system’s ability to resist high-frequency interference.

## 5. Simulation and Results Analysis of Proposed LED Driver

_{in}and input current i

_{in}. It can be seen that the input voltage and current are nearly in the same phase, so the driver achieves unity power factor. Figure 8b shows the waveforms of the inductor current i

_{L}

_{1}, i

_{L}

_{2}and diode current i

_{D}

_{1}. It can be seen that the circuit works in CCM mode. Figure 8c gives the flux curves of the three legs. Obviously, φ

_{1}+ φ

_{2}+ φ

_{C}= 0, which is exactly the same as the theory.

_{1}:SPW20N60C3; free-wheeling diode D

_{1}: HFA25TB60S; control IC: UCC3844.

_{in}and current i

_{in}. The input current follows the voltage change and achieves high power factor. The measured PF value is 0.982. Figure 10 shows the waveforms of switching signal VGS and the freewheeling diode current iD1. The switching frequency is presented as 100 kHz and the duty ratio D is 31%. The freewheel diode operates in CCM mode, which is exactly the same as the theoretical analysis. Figure 11 shows the waveforms of filter capacitor voltage V

_{O}and LED current I

_{O}. The filter capacitor voltage contains AC component with twice the line frequency, but the LED current is a pure DC current, thus it basically eliminates the LED flicker. Figure 12 shows a comparison of the system output current before and after the adoption of the magnetic integration technique. It can be seen that the system output current ripple is significantly reduced after adopting the integrated magnetic technology.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Simulation results of Cuk circuit with integrated magnetics. (

**a**) Waveforms of v

_{in}and i

_{in}

_{.}(

**b**) Waveforms of i

_{L}

_{1}, i

_{L}

_{2}and current i

_{D}

_{1.}(

**c**) Waveforms of φ

_{1}, φ

_{2}and φ

_{3}.

Parameter | Value |
---|---|

Input voltage v_{in_RMS}/V | 220 |

Switching frequency f_{S}/Hz | 100 k |

Inductor L_{1}/mH | 1.6 (30 Ts) |

Inductor L_{2}/mH | 2.4 (42 Ts) |

Transformer turn ratio N_{P}:N_{S} | 60:12 |

Capacitor C_{1}, C_{2}/μF | 2.2 (650 V/CBB) |

Filter capacitor C_{O}/μF | 10 × 2 (160 V/CBB) |

Output voltage V_{O}/V | 33 |

Output current I_{O}/mA | 900 |

Duty cycle D | 0.31 |

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## Share and Cite

**MDPI and ACS Style**

Shen, Y.; Xia, J.; Cai, C.
Flicker-Free LED Driver Based on Cuk Converter with Integrated Magnetics. *World Electr. Veh. J.* **2023**, *14*, 75.
https://doi.org/10.3390/wevj14030075

**AMA Style**

Shen Y, Xia J, Cai C.
Flicker-Free LED Driver Based on Cuk Converter with Integrated Magnetics. *World Electric Vehicle Journal*. 2023; 14(3):75.
https://doi.org/10.3390/wevj14030075

**Chicago/Turabian Style**

Shen, Yanxia, Jintao Xia, and Chengchao Cai.
2023. "Flicker-Free LED Driver Based on Cuk Converter with Integrated Magnetics" *World Electric Vehicle Journal* 14, no. 3: 75.
https://doi.org/10.3390/wevj14030075