# Low-Voltage Plasma Generator Based on Standing Wave Voltage Magnification

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- N—number of maximum points due to standing wave;
- L—secondary winding wire length;
- v
_{p}—propagation velocity, usually considered as the speed of light; - f
_{sw}—transmission line switching frequency; - λ —wavelength of propagated signal.

- 6.
- C
_{parasitic}—parasitic capacitance; - 7.
- D—winding diameter;
- 8.
- p—winding pitch;
- 9.
- d—wire diameter.

- 10.
- L—secondary side inductance;
- 11.
- μ
_{0}—vacuum magnetic permittivity; - 12.
- N—number of windings on the secondary side;
- 13.
- A—cross-sectional area of winding;
- 14.
- τ —winding pitch (distance between two distinct windings).

- 15.
- f
_{resonance}—natural frequency; - 16.
- L—secondary side inductance;
- 17.
- C—distributed parasitic capacitance.

_{0}), can be tuned using either the number of spires (N) or length (l) with a fixed cross-section area (A).

## 3. Results

#### 3.1. Circuit Components

#### 3.1.1. Secondary Side

_{0}the natural frequency.

#### 3.1.2. Primary Side

#### 3.2. Simulation Model

#### 3.3. Physical Prototype

- Top load torus. This part represents the top load capacitance
- Helical resonator secondary winding. The primary winding is overlaid at the bottom of secondary onto this part and insulated. An air-core transformer is implemented here, corresponding to the coupled inductors from Figure 5;
- Spark gap (gasoline engine spark plug). As represented in Figure 5. Distancing is 2.5 mm;
- High-voltage capacitors. The bank from the left has a total capacitance of 0.6 nF, while the one from the right has 1 nF. These components are connected in parallel;
- Flyback transformer. This component is used to supply power to the high voltage circuit, namely components connected to the primary side of the air-core transformer;
- MOSFET control circuit. This part uses the IRS2153DPBF integrated circuit, keeping an oscillating magnetic flux through the primary side of the high voltage transformer;
- MOSFET mounted on heatsink and overvoltage protection circuit;
- Optional modulation circuit. An “AND” logic operation is performed on the MOSFET gate, allowing this resonator to control the output power (number of spark gap breaks per second) in an open loop. The control signal is a PWM (pulse width modulation) signal;
- DC power supply. Its output voltage is close to 12 volts. This supply is used to emulate a solar panel or geothermal-probe-regulated output voltage. The average supplied current is around 4 amperes for this setup.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Helical resonator air-core transformer, Reprinted from Janis Voitkans and Arnis Voitkans (2015) [12]. Possibility for primary side natural frequency adjustment: (

**a**) L1 has a low inductance value due to winding pitch and area; (

**b**) L1 has a higher inductance value compared to the previous case.

**Figure 2.**Illustration of secondary wire length versus the propagated wave for one-quarter and three-quarters wavelength resonators.

**Figure 3.**Field distribution in quarter-wave and three-quarter wave topologies (ideal transmission line).

**Figure 5.**SPICE simulation model, used as a reference in finding the natural frequency of the experimental design.

**Figure 6.**Comparison between natural frequency determined by model (red characteristic) and the mathematically and experimentally confirmed natural frequency (blue dashed line).

**Figure 7.**Helical resonator propagation modes at one-quarter of wavelength. An air-core transformer is formed between the primary side winding (red line) and secondary side wire (black line). In all cases, the current must propagate through the secondary side as sinking and/or sourcing the helical resonator top load capacitors, depending on circuit design. (

**A**) The primary side current direction is arbitrary; the standing wave has one maximum point. (

**B**) The secondary side current direction is found using Lenz’s Law and Fleming’s Right-Hand Rule, assuming the illustrated primary side current; similarly, the propagation leads to one single maximum point. (

**C**) The primary side current direction is arbitrary; wave propagation through the secondary side leads to two maximum points.

**Figure 9.**Electric field presence at the top of helical resonator: (

**a**) Discharge without backlight; (

**b**) Discharge shown using green backlight.

Secondary Side Variable | Meaning | Calculated Value |
---|---|---|

N | Winding number | 500 ^{1} |

μ_{0} | Vacuum magnetic permittivity | 4π × 10^{−7} Hm^{−1 1} |

r | Sectional area radius | 10.5 mm ^{1} |

τ | Winding distancing | 0.45 mm ^{1,2} |

A | Sectional area | 3.4 cm^{2} |

L | Secondary winding wire length | 35.3 m ^{3} |

f_{0} | Natural frequency | 2.1 MHz ^{4} |

L | Secondary side inductance | 0.6 mH ^{5} |

C | Distributed parasitic capacitance | 9.4 pF ^{6} |

^{ 1 }Designing started with these variables.

^{2}This value corresponds to the AWG25 wire size.

^{3}From Equation (9).

^{4}From Equation (2), replacing the transmission line length and propagation velocity.

^{5}From Equation (5).

^{6}From Equation (10), resulting in a capacitance specific to the propagation mode and not specific to the solenoid.

Primary Side Variable | Meaning | Calculated Value |
---|---|---|

N | Winding number of the primary side | 13 |

μ_{0} | Vacuum magnetic permittivity | 4π × 10^{−7} Hm^{−1} |

r | Sectional area radius | 11 mm |

τ | Winding distancing | 1 mm |

A | Sectional area | 3.8 cm^{2} |

f_{0} | Natural frequency | 1.99 MHz ^{1} |

L | Primary side inductance | 4.02 µH ^{1} |

C | Resulting high-voltage capacitance | 1.6 nF ^{1} |

D_{1} | Air spark gap length | 2.5 mm ^{2} |

^{ 1 }A greater capacitor value was used to compensate for a small difference in primary side inductance between the calculated and implemented values, resulting in a natural frequency closer to 2.1 MHz.

^{2}This value must be less than the length of an air gap having its breakdown voltage corresponding to the peak voltage of the high-voltage transformer.

**Table 3.**Data used in building the experimental prototype: mathematical approach based on the previous equations (Method 1, manual calculation), cascade LC resonance model (Method 2, mathematics by model), or experimental (Method 3, trial and error).

Experimental Prototype Part | Method Used |
---|---|

Step-up voltage circuit | Method 3 |

Primary side parameters frequency matching to the secondary side | Method 2 |

Secondary side natural frequency | Method 1 ^{1} |

Secondary side top-load capacitance | Method 3 ^{1,2} |

^{ 1 }Influenced by secondary side top-load capacitance.

^{2}Experimentally, it has been found that the top-load capacitance influences the secondary side natural frequency. Three different top loads were tested.

Top Load | Outcome |
---|---|

No top load | Standing wave not forming, no electric field present at top load |

Top load from Figure 8 (approximately 0.5 to 1.5 pF) | The electric field is present at the top load ^{1} |

Approximately 2 to 3 pF top load | Standing wave not forming, no electric field present at top load |

^{ 1 }This parameter corresponds to component C6 from Figure 5.

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**MDPI and ACS Style**

Covaci, M.A.; Szolga, L.A.
Low-Voltage Plasma Generator Based on Standing Wave Voltage Magnification. *Sustainability* **2022**, *14*, 2890.
https://doi.org/10.3390/su14052890

**AMA Style**

Covaci MA, Szolga LA.
Low-Voltage Plasma Generator Based on Standing Wave Voltage Magnification. *Sustainability*. 2022; 14(5):2890.
https://doi.org/10.3390/su14052890

**Chicago/Turabian Style**

Covaci, Mihnea Antoniu, and Lorant Andras Szolga.
2022. "Low-Voltage Plasma Generator Based on Standing Wave Voltage Magnification" *Sustainability* 14, no. 5: 2890.
https://doi.org/10.3390/su14052890