# Low-Voltage Plasma Generator Based on Standing Wave Voltage Magnification
## 3 Results
### Simulation Model  
The main experimental circuit consists of an integrated MOSFET (Metal Oxide Semiconductor Field Effect Transistor) driver that switches the transistor on and off. The integrated circuit used in this study for driving the MOSFET transistor is IRS2153 DPBF, configured at 75 kHz. A flyback transformer generated high voltage, which charges the LC circuit up to the spark gap-breaking voltage. Due to leakage inductances, the Schottky diode prevents high-voltage spikes at the MOSFET drain.  
The schematic based on which the experimental prototype was built is presented below in Figure 5, and this circuit is also considered a simulation model. The actual value for a high-voltage capacitor is 1.6 nF, having used 2 nF as the initial value followed by impedance tuning.  
The oscillating circuits will be separated as the spark gap triggers due to a short circuit occurring at the high-voltage transformer secondary winding. Both LC circuits will enter a state of damped oscillations. For the circuit presented in Figure 4, the time for which the two circuits are separated depends on the gas used for ionization at the spark gap.  
By correlating Equation (1) with Figure 5, the resulting phase shift between the incident and top load wave corresponds to the phase shift obtained at resonance for an LC series circuit, which is used as a prototype to describe the natural frequency of the helical resonator.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Primary Side Variable** & **Meaning** & **Calculated Value** \\ \hline \(N\) & Winding number of the primary side & 13 \\ \(\mu_{0}\) & Vacuum magnetic permittivity & \(4\pi\times 10^{-7}\)\(\mathrm{H}\mathrm{m}^{-1}\) \\ \(r\) & Sectional area radius & 11 mm \\ \(\tau\) & 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 uH 1 \\ \(C\) & Resulting high-voltage capacitance & 1.6 nF 1 \\ \(D_{1}\) & Air spark gap length & 2.5 mm 2 \\ \hline \hline \end{tabular}  
* 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.  
\end{table}
Table 2: Primary side parameters.  
Figure 5: SPICE simulation model, used as a reference in finding the natural frequency of the experimental design.  
Its frequency response is shown below in Figure 6, compared to the experimentally and mathematically confirmed natural frequency.  
The predicted helical resonator natural frequency is 2.4 MHz using the SPICE simulation mathematics, close to the previously obtained result of 2.1 MHz using mathematics and manual calculation described using the previous equations. The difference occurs due to modeling the distributed parasitic capacitance as a series capacitor. The actual natural frequency is determined by transmission line length, having the physical prototype built using 2.1 MHz as natural frequency. The model predicts the natural frequency with a relative error close to 15% for this design.  
The secondary behaves as a transmission line similarly to the previously presented frequency response because the excitation occurs between the secondary top load and its ground terminal, as shown in Figure 7A,B. In this case, the standing wave constructive interference represents an approximate Bode chart gain characteristic.  
The previous figure shows that multiple topologies can achieve the standing wave voltage magnification. The reflection coefficient would have a higher value for Figure 7C than Figure 7A or 7B because the air ionizes at both top loads' ends.