# Analysis and Design of a Transient-State Resonant Converter Used as a Frequency Multiplier
The transient design methodology presented in this work allows a resonant converter to act as a frequency multiplier, where the operating power is not limited only to low levels and brings advantages in the operation of the converter as well as in the reduction of losses in the switching stage. This design methodology is different from the harmonic selection technique for frequency multiplication, which has already been studied and applied to wireless power transmission [17; 18; 19]. It is important to clarify that this methodology is not aimed at communication applications, where frequencies in the GHz range are common. Excessively multiplying frequency would require extremely large inductors and very high-quality factors, impacting efficiency. This proposal mainly targets practical applications requiring relatively high frequencies (MHz) while using lower frequenciesat the switching stage, ideal for wireless power transfer, induction heating, and wireless charging of electric vehicles. The theoretical analysis of the multiplier circuit designed in transient and with underdamped response was presented in [20], where the operation of a series RLC circuit acting as a frequency multiplier was verified by simulation in SPICE, which reached the established operating parameters. This prior work provided the fundamental understanding of how the transient response of an underdamped RLC circuit could be leveraged to achieve frequency multiplication, without requiring harmonic filtering or direct high-frequency switching. The insights gained from this analysis were instrumental in developing the transient design methodology for the resonant converter presented in this work, extending the theoretical findings into a practical implementation. In this work, the analysis presented was used for the development of the transient design methodology of the resonant converter acting as a multiplier, since, as shown in Figure 1, it is only necessary to replace the bipolar DC voltage source by a full-bridge inverter in order to apply the transient analysis in a resonant inverter and then in a resonant converter. A detailed literature review revealed that no previous studies have reported resonant converters explicitly designed to operate in transient conditions. Existing works primarily focus on steady-state analysis using methods such as the First Harmonic Approximation (FHA) or other conventional modeling techniques. Therefore, this work represents the first experimental validation of a resonant converter designed specifically for transient operation, marking a novel contribution in the field of high-frequency power electronics. The resonant converter designed to operate in the transient state presented in this work was used in a wireless power transmission application, which is a currently relevant application and where the performance of the converter could be verified, since usually in this type of applications very high operating frequencies are required, with low levels of losses mainly in the switching stage. The converter complied with the established operating parameters, which were verified first by simulation in SPICE, and then during the experimental tests. The transient operation allowed to greatly reduce the losses in the switching stage, because it was possible to operate with a frequency much lower than the one present in the resonant tank. Regarding the losses in the inductive coupling between the transmitter-receiver inductor pair, these are not affected to a great extent by the transient operation, as well as the losses in the rectification stage, which was the one with the highest losses due to the high operating frequencies at which the rectifier was exposed. The transient operation to operate the resonant converter as a frequency multiplier only brought benefits to the inverter stage, which is in charge of providing the base switching frequency \(f_{sw}\). The analysis and design methodology used in this work, as well as the results obtained after the experimental tests, are presented below.