# Research on Wide Input Voltage LLC Resonant Converter and Compound Control Strategy

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## Abstract

**:**

## 1. Introduction

## 2. LLC Resonant Converter Topology and Characteristics’ Analysis

_{1}–Q

_{4}. The resonant network consists of the resonant capacitor C

_{r}, resonant inductance L

_{r}, and excitation inductance L

_{m}, while the resonant capacitor C

_{r}also prevents the DC component of the square wave generator’s output voltage flowing to the transformer while balancing the magnetic flux to prevent magnetic circuit saturation. The rectifier filter network is a double half-wave rectifier with a center tap on the secondary side of the transformer.

_{m}< f

_{s}< f

_{r}; the operating waveform in this frequency range is shown in Figure 3. When the excitation current is equal to the resonant current, the voltage across L

_{m}is no longer clamped, and L

_{r}, C

_{r}, and L

_{m}resonate together. From Figure 3, it can be seen that the diode on the secondary side achieves zero-current shutdown.

_{in}, as shown in Figure 2. The bridge arm’s diagonal switch transistor is simultaneously adjusted on and off, and the two groups of transistors perform complementary conduction; then, the resonant network input voltage V

_{AB}has a duty cycle of 0.5. The amplitude of the periodic square wave is V

_{in}. Figure 4 shows the equivalent topology diagram of the conversion of the rectifier filter network to the primary side of the transformer.

_{AB1}is the input voltage of the resonant network after conversion; nV

_{sec}is the output voltage of the resonant network after conversion.

_{s}is the switching angular frequency.

_{N}is the normalized frequency, f

_{N}= f

_{s}/f

_{r}.

_{N}= 1, the converter can be divided into three operating zones:

_{N}= 1. At this time, the gain M is less than 1; in the inductive operating area, the buck mode is operational, and the LLC resonant converter is in the ZVS state.

_{N}= 1. At this time, the gain M is more than 1; in the inductive operating area, the boost mode is operational, and the LLC resonant converter is in the ZVS state.

_{N}= 1. At this time, the gain M is variable in the capacitance-operating area, and the LLC resonant converter is in the zero-current switching (ZCS) state.

## 3. Composite Control Strategy

#### 3.1. FM Control

#### 3.2. Phase Shift Control

_{1}–Q

_{4}is adjusted, which can be divided into two groups according to the phase angle difference between the leading bridge arm and the lagging bridge arm. Q

_{1}and Q

_{3}are leading bridge arms, while Q

_{2}and Q

_{4}are lagging bridge arms. The output characteristics are then changed by the phase angle difference between the leading and lagging bridge arm. The operating waveform in the phase shift mode is shown in Figure 8.

_{1}, θ

_{2}, and θ

_{3}are the angles at moments t

_{2}, t

_{4}, and t

_{5}, respectively; I*

_{m}is the current standard value when the excitation current and resonance current are equal; and V*

_{Cr}(0) is the resonant capacitor’s zero-moment voltage standard value.

_{1}, θ

_{3}, and I*

_{m}are expressed as:

_{y}is the duty cycle.

_{N}can be identified as known quantities. In addition, the load condition determines the quality factor Q. Figure 9 shows the variation curve of the duty cycle Dy versus the input–output voltage ratio M for different values of the quality factor Q. In the graph, the inductance factor is taken as 4, and the normalized frequency is f

_{N}= 1.

_{y}changes, the value of M is less than 1. Under the phase shift mode control, the LLC resonant converter operates in step-down mode. It can also be clearly seen from Figure 5 that the gain characteristics of the resonant converter are difficult to adjust in terms of frequency when operating in region 1. Based on the FM control strategy, the rectifier on the secondary side of the transformer cannot achieve ZCS. Therefore, there is a reverse recovery problem and the loss increases. Thus, the phase shift control strategy makes up for the shortcomings of the FM control strategy in the buck mode. The phase shift control strategy is shown in Figure 10.

#### 3.3. Composite Control

_{r}and C

_{r}co-resonance takes place. f

_{r}is taken as the highest switching frequency. This is the mode-switching point of the two control strategies. That is, when f

_{s}= f

_{r}, the phase shift angle is 0, the electrical energy is directly converted, and the converter efficiency is at its best.

_{s}= f

_{r}is retained. As the regulation duty cycle decreases, the resonant network gain decreases, which is suitable for the case of a higher input voltage.

_{0}, and the resonant frequency is set as the switching frequency by comparing it with the given reference voltage V

_{0_ref}. When the operating frequency of the resonant converter is less than the set value, the phase shift angle is equal to 1, and the FM mode is used to change the frequency f

_{s}of the switching transistor to adjust the output voltage V

_{0}. However, increasing the resonant converter’s operating frequency to the set value still cannot regulate the voltage. The operating frequency is maintained as the resonant frequency is unchanged, and the phase shift angle d

_{s}is changed to adjust the output voltage V

_{0}. Depending on the input voltage, the control strategy switches the mode to change only one of the variables, the frequency or phase angle, ensuring independence between the two.

_{s}≤ f

_{r}is selected. Since the efficiency is highest and the loss is lowest when f

_{s}= f

_{r}and the frequency remains the same in the case of phase-shifting control, the resonant frequency is chosen as the operating frequency in this case. Based on the above analysis, the mode-switching point selects the point where the operating frequency is the resonant frequency when the resonant network gain is 1, and the switching transistor duty cycle is 1.

_{in_min}, is set to one-half the maximum value of the input voltage, V

_{in_max}:

_{N})

_{_max}. Correspondingly, when the input voltage is the highest value, the phase shift control mode holds, and the resonant network gain is the minimum value, M(D

_{y})

_{_min}. Since the output voltage is kept constant, then:

_{max}. In addition, it can be seen in the frequency gain curve that the gain M decreases with the increase in Q. To ensure that the voltage increase in the rated operating condition is large enough, this paper considers that the gain of the lower limit of the input voltage V

_{in_min}is M(f

_{N})

_{_max}in the rated operating condition. At this time, the quality factor Q takes the maximum value Q

_{max}, and Q

_{max}= 0.5 is considered. Figure 12 shows that in the leaving margin, M(f

_{N})

_{_max}and f

_{N_min}are 1.33 and 0.75, respectively. It can be deduced from Equation (14) that the control mode’s switching point voltage is:

_{y})

_{min}can then be derived:

_{y_min}= 0.42.

_{s_min}for different input voltages and loads, while the high-voltage, full-load duty cycle approximately reflects the minimum duty cycle, which is considered as the minimum duty cycle D

_{y_min}.

## 4. System Parameter Design

_{F}is the diode’s on-state voltage drop, taking the value of 0.966 V.

_{r}= 100 kHz, and the resonant capacitance is given by:

## 5. Simulation Analysis

#### 5.1. Output Voltage Waveform at Different Input Voltages

#### 5.2. Other Major Waveform

_{r}and i

_{m}, are shown in Figure 17. The phase shift mode waveform is shown in Figure 18, and the overall waveform is shown in Figure 19.

_{s1}and i

_{s2}waveforms are shown in Figure 20 and Figure 21, respectively. It can be seen the LLC resonant converter can achieve the ZCS of the secondary side rectifier in both the FM and phase shift modes.

_{Cr}, waveform at both ends of the resonant capacitor is shown in Figure 22 and Figure 23. After regulating the control strategy, the resonant capacitor voltage is an AC waveform with an amplitude of 400 V.

_{AB}) waveform of the resonant network is shown in Figure 24 and Figure 25. The input voltage waveform of the resonant network for different DC voltage inputs is consistent with the principle analysis of the different control strategies that were presented in the previous section.

_{1}and Q

_{3}drive waveforms are complementary, and the Q

_{2}and Q

_{4}are synchronized with the Q

_{3}and Q

_{1}drive waveforms, respectively. In the phase shift mode, the Q

_{1}and Q

_{3}drive waveforms are ahead, while the Q

_{2}and Q

_{4}drive waveforms are lagging.

## 6. Experimental Verification

_{1}in FM mode and Phase shift mode. It can be seen that the voltages at the two ends of the switch transistor and the drive signal exhibit slight interleaving. That is, the voltage at the end of the switch transistor has dropped to 0 before the drive signal drives on it, and, thus, the ZVS is achieved. Due to the stray capacitance, the voltage hysteresis across the switching transistor increases and the deactivation loss is reduced. The rest of the switching transistors are similar to Q

_{1}.

_{AB}, V

_{Cr}, and i

_{r}in the resonant network are shown. Figure 34a shows the waveform of V

_{AB}, V

_{Cr}, and i

_{r}in the resonant network when the input voltage is 300 V at full load. At this time, the switching frequency is 75 kHz. Figure 34b shows the waveform of V

_{AB}, V

_{Cr}, and i

_{r}in the resonant network when the input voltage is 500 V at full load. At this time, the switching frequency is 100 kHz. In the FM control mode, V

_{AB}is approximated as a square wave with an amplitude of 300 V, and V

_{Cr}is approximated as an AC waveform of 300 V. In the phase shift control mode, V

_{AB}shows a stepped waveform and V

_{Cr}is an AC waveform of approximately 500 V. The voltage and current waveforms of the resonant network for different DC voltage inputs are consistent with the previous analysis. Figure 35 shows the waveform at no load and with full load switching applied. The output voltage exhibits a small fluctuation when the load is switched, and finally the output voltage is stabilized at 48 V. The experimental results and theoretical analysis show that in the full voltage and full load range, the converter can operate well in FM mode and phase shift mode.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 30.**Switching transistor Q

_{1}drive signal. (

**a**) FM mode switching transistor drive signal; (

**b**) Phase shift mode switching transistor drive signal.

**Figure 31.**Voltage surge experimental waveform. (

**a**) 300 V increased to 600 V; (

**b**) 600 V reduced to 300 V.

**Figure 32.**Light load (10% full load) experimental waveform. (

**a**) 300 V input (FM mode); (

**b**) 500 V input (Phase shift mode).

**Figure 33.**Half load experimental waveform. (

**a**) 300 V input (FM mode); (

**b**) 500 V input (Phase shift mode).

**Figure 34.**Full load experimental waveform. (

**a**) 300 V input (FM mode); (

**b**) 500 V input (Phase shift mode).

Symbol | Description | Value |
---|---|---|

V_{in_min} | Minimum input voltage | 300 V |

V_{in_max} | Maximum input voltage | 600 V |

V_{o} | Rated output voltage | 48 V |

f_{r} | Resonant frequency | 100 kHz |

f_{s_max} | Maximum switching frequency | 100 kHz |

f_{s_min} | Minimum switching frequency | 75 kHz |

Symbol | Description | Value |
---|---|---|

L_{r} | Resonant inductance | 49.97 μH |

C_{r} | Resonant capacitor | 50.7 nF |

L_{m} | Excitation inductance | 149.91 μH |

N | Transformer ratio | 8.2 |

C_{o} | Filter Capacitor | 2000 μF |

V_{in} | DC input voltage | 300–600 V |

V_{o} | DC output voltage | 48 V |

Symbol | Description | Value |
---|---|---|

L_{r} | Resonant inductance | 50 μH |

C_{r} | Resonant capacitor | 51 nF |

L_{m} | Excitation inductance | 150 μH |

N | Transformer ratio | 8.2 |

C_{o} | Filter Capacitor | 2000 μF |

V_{in} | DC input voltage | 300–600 V |

V_{o} | DC output voltage | 48 V |

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**MDPI and ACS Style**

Zhou, K.; Liu, Y.; Wu, X.
Research on Wide Input Voltage LLC Resonant Converter and Compound Control Strategy. *Electronics* **2022**, *11*, 3379.
https://doi.org/10.3390/electronics11203379

**AMA Style**

Zhou K, Liu Y, Wu X.
Research on Wide Input Voltage LLC Resonant Converter and Compound Control Strategy. *Electronics*. 2022; 11(20):3379.
https://doi.org/10.3390/electronics11203379

**Chicago/Turabian Style**

Zhou, Kai, Yang Liu, and Xiaogang Wu.
2022. "Research on Wide Input Voltage LLC Resonant Converter and Compound Control Strategy" *Electronics* 11, no. 20: 3379.
https://doi.org/10.3390/electronics11203379