# Low-Voltage Plasma Generator Based on Standing Wave Voltage Magnification
## 5 Conclusions  
First and foremost, as shown by equations, standing wave constructive interference occurs inside any conductor when given an ideal power supply. In addition, the secondary-side frequency of a helical resonator was found based on the effect of the same phenomenon, representing a constraint in PCB design, namely transmission line reflections. Moreover, using conventional SPICE simulation software, a model was built to predict the natural frequency of such resonators using a different approach, the LC series resonance, considering the insulated wire capacitance and inductance. This method used by the model was initially thought to be the reason for voltage magnification, having the model using the parasitic capacitance as resulting from Equation (10) for one maximum point. Other scenarios for implementing such models would further investigate the differences that appear for more than one maximum point.  
The study shows that standing wave does occur only due to transmission line reflections, meaning that a further improvement to this design would be an even smaller size and higher operating frequency. Furthermore, given an ideal power supply capability, an X-ray generator would be indefinitely small due to a very short transmission line in which repeated wave reflections and summations occur, forming stationary waveforms. Moreover, the study shows that such helical oscillators could also be used as X-ray generators.  
Within this application, we also aimed to implement a low-power helical resonator that uses the stationary wave summation to concentrate the pulsating electric field in a single point as resulting from mathematics, thus achieving a high voltage gain. An innovative feature of this design is that it fully uses a flyback-derived step-up transformer starting at low voltage to achieve voltage magnification, possibly further improving this design for renewable energy. Thus, in the case of improving this design or using another topology (greater \"N\" values) for X-ray or ozone generation, better results can be obtained in certain conditions. However, due to several approximations when using a model, the actual natural frequency will differ from the calculated resonant frequency, as resulted from the model.  
While implementing the helical resonator, we aimed to use low-tolerance components and a high quality-to-price ratio. The study of this topic involved several stages. First, for a given number of windings, the coil's natural frequency was calculated as a function of inductance and self-capacitance in inductors, followed by a comparison to mathematical and experimental results. The high-voltage circuit was designed to match the two oscillating frequencies.  
In conclusion, following the specialized studies for each block component presented in this work and the simulations of electrical circuits, respectively building the prototype for obtaining the plasma ionization, the practical and functional implementation of the system was successful.  
Conceptualization, methodology, validation, supervision, project administration, funding acquisition, review and editing was done by L.A.S.; Conceptualization, methodology, validation, software, investigation, data curation, writing--original draft preparation, visualization was done by M.A.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the Romanian Ministry of Education and Research, grant number PN-III-P2-2-1-PED-2019-2601, \"REGRENIPOS\". The authors declare no conflict of interest.