# A Hybrid Constant On-Time Mode for Buck Circuits

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## Abstract

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## 1. Introduction

Algorithm 1 COT voltage mode. |

1: U_transistor = 0; 2: L_transistor = 1; 3: while 1 { 4: If V_FB < V_ref 5: { U_transistor = 1; 6: L_transistor = 0; 7: delay(t_on); 8: //Delay for a period of time// 9: //which lasts t_on. //10: U_transistor = 0;11: L_transistor = 1;12: delay(t_off);13: //Delay for a period of time//14: //which lasts t_off. //15: }16: } |

## 2. Modeling

## 3. Proposal of the Algorithm

Algorithm 2 Proposed PD-COT voltage mode. |

01: U_transistor = 0;02: L_transistor = 1;03: while 1 {04: If V_FB < V_ref05: { V_dy_ref = Delta(V_ref);}06: Else if V_FB > V_ref07: { V_dy_ref = - Delta(V_ref);}08: If P * (V_FB - V_ref) + D *09: Diff(V_FB) < V_dy_ref10: { U_transistor = 1;11: L_transistor = 0;12: delay(t_on);13: //Delay for a period of time //14: //which lasts t_on. //15: U_transistor = 0;16: L_transistor = 1;17: delay(t_off);18: //Delay for a period of time //19: // which lasts t_off. //20: }21: } |

## 4. Operating Frequency Analysis

## 5. Comparison and Application Analysis

## 6. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The schematic diagram of the Buck circuit. (

**a**) A typical Buck circuit; (

**b**) simplified form of (

**a**). ESR: equivalent serial resistance; COT: constant on-time.

**Figure 5.**The output voltages of the Buck circuit in the proposed PD-COT mode with different time delays.

Parameters | Definitions | Default Values | Parameters | Definitions | Default Values |
---|---|---|---|---|---|

${U}_{in,max}$ | Maximum input voltage | 90.0 V | ${U}_{in}$ | Input voltage | N/A |

${U}_{in,min}$ | Minimum input voltage | 70.0 V | ${R}_{DS\left(on\right)}$ | On-resistance of the transistor | N/A |

${f}_{in}$ | Variation frequency of input voltage | 100 Hz | ${U}_{out}$ | Output voltage | N/A |

${U}_{GND}$ | Ground voltage | 0 V | ${R}_{Load}$ | Load resistance | N/A |

${R}_{DS\left(on\right),upper}$ | On-resistance of the upper transistor | 10.0 m$\mathrm{\Omega}$ | ${V}_{FB}$ | Feedback voltage | N/A |

${R}_{DS\left(on\right),lower}$ | On-resistance of the lower transistor | 10.0 m$\mathrm{\Omega}$ | P | Proportional coefficient | N/A |

L | Inductor | 20.0 μH | D | Differential coefficient | N/A |

C | Capacitance | 5.00 × 10${}^{3}$ μF | $d{V}_{ref}$ | Adjustment value of dynamic reference voltage | N/A |

${r}_{ESR}$ | Equivalent series resistance of the Capacitance | 2.40 m$\mathrm{\Omega}$ | ${U}_{L}$ | Voltage of the inductor | N/A |

${U}_{out,set}$ | The set value of output voltage | 12 V | ${U}_{C}$ | Voltage of the capacitance | N/A |

${I}_{out,max}$ | Maximum value of ${I}_{out}$ | 60.0 A | ${U}_{R}$ | Voltage of the load resistance | N/A |

${I}_{out,min}$ | Minimum value of ${I}_{out}$ | 0.10 A | ${U}_{ESR}$ | Voltage of the ESR | N/A |

${f}_{out}$ | Variation frequency of load resistance | 100 Hz | ${I}_{L}$ | Current of the inductor | N/A |

${V}_{ref}$ | Reference voltage | 2.5 V | ${I}_{C}$ | Current of the capacitance | N/A |

${I}_{out}$ | Expected current output | ${U}_{out,set}/{R}_{Load}$ | ${I}_{R}$ | Current of the load resistance | N/A |

${t}_{ON}$ | Length of time to input ${U}_{in}$ | 2.0 μs | ${t}_{delay}$ | Total delay of the controller | N/A |

${t}_{OFF}$ | Length of time to input ${U}_{GND}$ | ≥0.50 μs |

[6] | [7] | This Work | |
---|---|---|---|

Input voltage | 5.0 V | 5.0 V | 5.0 V |

Output voltage | 1.15 V | 2.5 V | 1.15 V |

Maximum current | 1.0 A | 1.0 A | 1.0 A |

Minimum current | 0.1 A | 0.1 A | 0.1 A |

Off-chip capacitance | 47 μF | 47 μF | 47 μF |

Off-chip inductance | 0.47 μH | 0.47 μH | 0.47 μH |

Switching frequency | 3 MHz | 1.36 MHz | 2.3 MHz |

Recovery time | 12 μs | 12 μs | 4 μs |

Over/undershoot voltage | 35 mV | 5 mV | 25 mV/23 mV |

Ripple voltage | 30 mV | 6 mV | 14 mV |

[2] | This Work | |
---|---|---|

Input voltage | 5.0 V | 5.0 V |

Output voltage | 3.3 V | 3.3 V |

Maximum current | 0.5 A | 0.5 A |

Minimum current | 0.1 A | 0.1 A |

Off-chip capacitance | 8 μF | 8 μF |

Off-chip inductance | 4.7 μH | 4.7 μH |

Switching frequency | 1 Mhz | 1.225 Mhz (stable) |

Recovery time | 2 μs | 2 μs |

Overshoot voltage | 30 mV | 42 mV |

Ripple voltage | 20 mV | 4.5 mV |

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**MDPI and ACS Style**

Zhong, S.; Shen, Z.
A Hybrid Constant On-Time Mode for Buck Circuits. *Electronics* **2021**, *10*, 930.
https://doi.org/10.3390/electronics10080930

**AMA Style**

Zhong S, Shen Z.
A Hybrid Constant On-Time Mode for Buck Circuits. *Electronics*. 2021; 10(8):930.
https://doi.org/10.3390/electronics10080930

**Chicago/Turabian Style**

Zhong, Shun, and Ziqian Shen.
2021. "A Hybrid Constant On-Time Mode for Buck Circuits" *Electronics* 10, no. 8: 930.
https://doi.org/10.3390/electronics10080930