# Analysis and Design of a Transient-State Resonant Converter Used as a Frequency Multiplier
## 4 Conclusions  
This paper presented the analysis and design of a class D resonant converter operating in the transient state and with underdamped response acting as a frequency multiplier for a wireless power transmission application (TPI), where the frequency multiplication occurs in the resonant tank which is equal to \"\(n\)\" times the switching frequency \(f_{o}=nf_{sw}\). The converter operated optimally, managing to meet the proposed operating specifications, operating in the transient state and with underdamped response. The experimental tests were able to verify the performance of the converter acting as a frequency multiplier, with multiplier values of \(n=3\), \(5\), \(7\) in the resonant tank. The experimental tests proved that using decay factors lower than \(d_{f}>0.90\) (waveform with amplitude decay) does not affect the circuit performance, and reduces the losses in the converter tank. In this TPI application, the losses in the inverter stage depend largely on the \(\rm V_{DC}\) supply voltage of the circuit, since as shown in (16) and (17), the higher the \(\rm V_{DC}\) voltage, the higher the energy stored by the output capacitance \(\rm C_{oss}\) and the higher the losses in the inverter. The transient operation of the converter acting as a frequency multiplier allowed reducing the losses in the switching of the inverter stage, due to the possibility of operating with a lower switching frequency than the operating frequency in the resonant tank, so that the losses are proportional to the low frequency in the inverter. Figure 19: Efficiency in the resonant tank by increasing the decay factor \(d_{f}\). Figure 18: Measurements on the input and output power in the tank of the resonant converter. A major contribution of this work is demonstrating that frequency multiplication can be achieved naturally through the underdamped transient response of the resonant tank, without requiring harmonic filtering. Unlike conventional approaches where the switching stage operates directly at high frequencies, this methodology allows obtaining high-frequency oscillations in the resonant tank while maintaining a lower switching frequency. This results in significantly reduced losses in the inverter stage, particularly in the charging and discharging cycles of the output capacitance \(\mathrm{C_{oss}}\), which would otherwise occur at a much higher rate in a conventional high-frequency resonant converter. The experimental results confirm that this approach enables efficient power conversion while simplifying the design and minimizing switching losses. In general, the transient design methodology of the converter to achieve frequency multiplication showed good results, where for its implementation, it is necessary to consider the use of magnetic cores and Litz wire suitable for the operating frequency at which you want to operate, as well as choosing the correct decay factor to reduce losses in the resonant tank. Conceptualization, M.P.-S., L.H.-G., S.E.D.-A. and R.E.L.-P.; methodology, J.L.R., M.P.-S., J.R.-H. and S.E.D.-A. ; software J.L.R., C.C.-G., J.R.-H. and R.E.L.-P.; validation, J.L.R., M.P.-S., L.H.-G., J.R.-H. and R.E.L.-P.; formal analysis, J.L.R., M.P.-S., C.C.-G. and S.E.D.-A. ; investigation, J.L.R., M.P.-S., C.C.-G., S.E.D.-A. and R.E.L.-P. resources, J.L.R., M.P.-S., L.H.-G. and O.U.J.-S.; data curation, C.C.-G., J.R.-H., O.U.J.-S. and R.E.L.-P.; writing--original draft preparation, J.L.R., M.P.-S. and S.E.D.-A. ; writing--review and editing, M.P.-S., L.H.-G. and C.C.-G.; visualization, C.C.-G., J.R.-H. and O.U.J.-S.; supervision, M.P.-S., S.E.D.-A. and R.E.L.-P.; project administration, M.P.-S., L.H.-G., O.U.J.-S. and R.E.L.-P.; funding acquisition, M.P.-S., L.H.-G. and O.U.J.-S. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors. The authors declare no conflicts of interest.