# Simple Lossless Inductive Snubbers-Assisted Series Load Resonant Inverter Operating under ZCS-PDM Scheme for High-Frequency Induction Heating Fixed Roller

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## Abstract

**:**

## 1. Introduction

## 2. Schematic of Induction Heating Fixed Roller and Its Equivalent Circuit

#### 2.1. Schematic Structure of Induction Heating Fixed Roller

#### 2.2. Transformer Circuit Model for IH Load

_{1}and L

_{2}, the winding resistance R

_{1}and the effective resistance R

_{2}, considering the skin effect of the heating object. The equivalent circuit parameters of Figure 2a are assumed to be constant as the quasi-steady state. Resistance R

_{1}is small enough and uses the litz wire, which reduces the skin effect, and therefore, it is ignored. Resistance R

_{2}is based on the current penetration depth, and the skin effect is related to the high-frequency inverter switching frequency.

_{1}and φ

_{2}are expressed as follows:

_{1}and φ

_{2}from Equation (2) into Equation (1), the following equation can be obtained:

_{2}and L

_{2}if these values’ ratio is constant for a certain value of k. The electromagnetic coupling degree with the heating coil and the heating body is represented by the parameter k. The IH load time constant is represented by parameter τ. The L

_{1}value is the heating coil self-inductance as measured on the transformer model primary side, with the secondary side open-circuited. Further, this L

_{1}value equals the heating coil self-inductance with a heating object with zero conductivity and a nonmagnetic heating body under the no-load condition using materials such as stainless steel or aluminium.

#### 2.3. Theoretical Analysis of IH Load Parameters

_{1}, the equivalent inductance L

_{a}and the equivalent resistance R

_{a}, as shown in Figure 2c.

_{AB}= R

_{a}+ jωL

_{a}

_{a}and inductance L

_{a}can be expressed as follows:

_{1}−L

_{a}can be calculated as follows:

_{1}, L

_{a}and R

_{a}as follows:

_{1}, τ and k.

## 3. ZCS Series Load Resonant High-Frequency Inverter Employing PDM Control

#### 3.1. Circuit Description

_{1}and S

_{2}active power switches; C

_{r}, a resonant capacitor in series with IH load; and L

_{S2}and L

_{S1}, two ZCS-assisted snubber inductors, which are in series with S

_{1}and S

_{2}, respectively.

#### 3.2. Principle of Operation

_{PDM}, the PDM duty ratio, is described as follows:

_{S1}and L

_{S2}allow soft-switching ZCS commutation for the active power switches S

_{1}and S

_{2}, which provide the overlapping current mode in S

_{1}/D

_{S}

_{2}and S

_{2}/D

_{S}

_{1}when they are in the continuous load current mode. The range of ZCS of the proposed inverter covers all ranges of inverter power regulation. Additionally, the commutation of the ZCS theoretically causes the IGBTs to have zero tail current. Thus, S

_{1}and S

_{2}in the proposed inverter have extremely low switching power losses. Furthermore, power losses are non-existent in this PDM scheme during the non-injected power period compared with the series load resonant inverters employing control methods such as PFM and PWM in light load conditions.

#### 3.3. Operation of the Circuit

- Mode 1
- With switch S
_{1}in the conduction mode, the power is delivered to the resonant capacitor C_{r}, snubber inductor L_{S1}and the IH load. The attenuated sinusoidal resonance starts through the IH load. - Mode 2
- When load current i
_{L}decreases through S_{1}to zero at t = t_{1}, anti-parallel diode D_{S}_{1}is naturally turned on. At turn-off transition, this results in S_{1}achieving complete ZCS-and-ZVS hybrid soft commutation. - Mode 3
- While diode D
_{S}_{1}is in conducting mode, the S_{2}switch turns on at t = t_{2}. Consequently, the D_{S}_{1}current commutates to S_{2}. Eventually, the D_{S}_{1}current is completely transferred to switch S_{2}by snubber inductor L_{S2}. Therefore, switch S_{2}achieves ZCS turn-on. - Mode 4
- While switch S
_{2}is still in conduction mode, the diode D_{S}_{1}current becomes zero at t = t_{3}. Then, C_{r}delivers the output power to the IH load. This results in the attenuated sinusoidal resonance starting through the IH load. - Mode 5
- As the load current i
_{L}increases, the S_{2}current decreases to zero at t = t_{4}. As a result, anti-parallel diode D_{S}_{2}is naturally turned on and S_{2}turns off by complete ZVS and ZCS throughout this operating mode. - Mode 6
- While diode D
_{S}_{2}is still in conduction mode, switch S_{1}turns on at t = t_{5}. The D_{S}_{2}current begins to commutate to switch S_{1}. Eventually, the D_{S}_{2}current is completely transferred to switch S_{1}due to snubber inductor L_{S1}. As the result, switch S_{1}is turned on with the ZCS condition, and the circuit operation Modes 1–6 repeat.

## 4. Experimental Results and Performance Evaluations

#### 4.1. Voltage and Current Waveforms

_{S1}and L

_{S2}are set to 12 µH, as determined by the IGBT’s peak voltage of 350 V. For this circuit, the di/dt

_{max}stress is 12.5 A/µs dynamic switch current and 3.8 µs current overlapping time. Figure 6 shows the IH fixed roller and installed heating coil self-inductance L

_{1}. The heating coil, shown in Figure 6b, has a diameter of 50 mm and a width of 350 mm.

_{L}and load current i

_{L}for PDM duty ratios D

_{PDM}= 0.8 and 0.2 are given in Figure 7. They show that the proposed high-frequency inverter can operate with PDM control.

_{1}and S

_{2}. These figures show that ZCS soft-switching commutation is achieved in the transitions from turn-on and turn-off. The waveforms of the current and voltage of switches S

_{1}and S

_{2}are shown in Figure 8c,d for the beginning interval of the injection of power. Observing waveforms in Figure 8c,d, the switches S

_{1}and S

_{2}also operate for PDM control implementation using complete ZCS soft-switching commutation.

#### 4.2. Power Conversion Efficiencies

_{PDM}causes linear regulation of the output. The PDM operates at D

_{PDM}= 1.0 in the printing mode and at D

_{PDM}= 0.05 in the stand-by mode. More than 94% power conversion efficiency η can be achieved with a D

_{PDM}= 0.05 to 1.0. Thus, the proposed IH fixed roller application in printing and copy machines can achieve high efficiency using the proposed high-frequency inverter system.

#### 4.3. Analysis of Power Loss

_{1}and snubber inductors L

_{S1}and L

_{S2}conduction losses are negligible due to litz wire usage. The IGBT conduction losses of the proposed high-frequency inverter are the main power losses. The IGBT voltage and current characteristics curves are used for conduction power losses calculations. Figure 10 shows the current and voltage characteristics of the IGBT and that its antiparallel diode has constant temperature conditions. Experimental results yielded the switching characteristics curves. Equations (13) and (14) represent the characteristic curves, which approximate quadratic polynomials in the low forward current area and linear functions in the high forward current area.

_{PDM}ratio of this PDM control scheme increases proportionately with the power losses increase. When the printing mode D

_{PDM}ratio reaches 1.0 (heaviest load), only 20% of the total power losses are stray power losses and 80% are conduction power losses. This results from the ZCS soft commutation display low power losses, as seen in Figure 11.

#### 4.4. Halogen Lamp Heater Comparative Characteristics

## 5. Conclusions

_{PDM}is at a very small value, which is 0.05 in this experiment. This small output power requires only two or three cycles of injected current from the voltage power source. Therefore, the asymmetrical pattern of PDM pulses is employed so that the injected current becomes easily observable and the control circuit has enough time to get the heat response from the IH system. Then, the ZCS operations are verified at very light load conditions. The power conversion efficiency for power output ranges from 50 to 1200 W is achieved at η > 94%. Power loss calculations are verified through experimental i–v characteristics of the diode and IGBT. At heavy load conditions, the stray load power losses amount to be only 20% of the total power losses. This is due to the soft commutation of the ZCS, which yields very low switching power losses. At light load conditions, although the power conversion becomes less effective, the ZCS operations are still achieved. Additionally, the power losses saved by the operations are significant due to the fact that most of the printer operation time is in the stand-by mode. Importantly, the experimental results demonstrate good performance of the proposed high-frequency resonant inverter by replacing the conventional halogen lamp heater with the IH fixed roller. Therefore, the PDM-controlled series load resonant soft-switching high-frequency inverter is proved to be effective for IH applications. Future evaluations of this proposed high-frequency inverter are planned using new wide-bandgap semiconductors, such as GaN FET.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Induction heating fixed roller for copy and printing machines. (

**a**) Sectional view. (

**b**) Internal configuration. (

**c**) Toner fixing process.

**Figure 2.**Transformer circuit model for IH fixed roller. (

**a**) Transformer model. (

**b**) Transformer equivalent circuit model. (

**c**) L-R series equivalent circuit model.

**Figure 5.**Operating conditions. (

**a**) Circuit mode transitions. (

**b**) Operating waveforms by simulations.

**Figure 7.**Load current i

_{L}and voltage v

_{L}waveforms under PDM. (

**a**) Duty ratio D

_{PDM}= 0.2. (

**b**) Duty ratio D

_{PDM}= 0.8.

**Figure 8.**Current and voltage waveforms for switches S

_{1}and S

_{2}. (

**a**) Steady-state condition for switch S

_{1}. (

**b**) Steady-state condition for switch S

_{2}. (

**c**) Beginning of power injection for switch S

_{1}. (

**d**) Beginning of power injection for switch S

_{2}.

**Figure 10.**Current and voltage characteristics of IGBT and diode. (

**a**) IGBT for S

_{1}and S

_{2}. (

**b**) Diode for D

_{S}

_{1}and D

_{S}

_{2}.

Item | Symbol | Value |
---|---|---|

DC input voltage | V_{in} | 280 V |

Resonant capacitor | C_{r} | 0.49 µF |

Frequency of switching | f | 20 kHz |

Frequency of PDM | f _{PDM} | 400 Hz |

Snubber inductor | L_{S1}, L_{S2} | 12 μH |

Heating coil self-inductance | L_{1} | 90 μH |

IH load time constant | τ | 9.23 μs |

Electromagnetic coefficient of coupling | k | 0.48 |

IGBT (Mitsubishi: CT75AM-12) | I_{C} | 75 A |

V_{CE} | 600 V |

Item | IH Fixed Roller | Halogen Lamp Heater |
---|---|---|

Rise time to 185 °C | 27.9 s | 36.1 s |

Idling mode power consumption | 52 Wh | 57 Wh |

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## Share and Cite

**MDPI and ACS Style**

Ogura, K.; Chandhaket, S.; Kolhe, M.L.; Sakphrom, S.; Mekhilef, S.
Simple Lossless Inductive Snubbers-Assisted Series Load Resonant Inverter Operating under ZCS-PDM Scheme for High-Frequency Induction Heating Fixed Roller. *Appl. Sci.* **2022**, *12*, 1122.
https://doi.org/10.3390/app12031122

**AMA Style**

Ogura K, Chandhaket S, Kolhe ML, Sakphrom S, Mekhilef S.
Simple Lossless Inductive Snubbers-Assisted Series Load Resonant Inverter Operating under ZCS-PDM Scheme for High-Frequency Induction Heating Fixed Roller. *Applied Sciences*. 2022; 12(3):1122.
https://doi.org/10.3390/app12031122

**Chicago/Turabian Style**

Ogura, Koki, Srawouth Chandhaket, Mohan Lal Kolhe, Siraporn Sakphrom, and Saad Mekhilef.
2022. "Simple Lossless Inductive Snubbers-Assisted Series Load Resonant Inverter Operating under ZCS-PDM Scheme for High-Frequency Induction Heating Fixed Roller" *Applied Sciences* 12, no. 3: 1122.
https://doi.org/10.3390/app12031122