# Analysis and Design of a Transient-State Resonant Converter Used as a Frequency Multiplier  
[PERSON]  
1 Tecnologico Nacional de Mexico-CESNIDET, Av. Palmira s/n, Col. Palmira, Cuernavaca 62490, Mexico; d138 [EMAIL_ADDRESS] (J.L.R. ); [EMAIL_ADDRESS] (C.C.-C.); [EMAIL_ADDRESS] (S.D.-A.) [PERSON]  
1 Tecnologico Nacional de Mexico-CESNIDET, Av. Palmira s/n, Col. Palmira, Cuernavaca 62490, Mexico; d138 [EMAIL_ADDRESS] (J.L.R. ); [EMAIL_ADDRESS] (C.C.-C.); [EMAIL_ADDRESS] (S.D.-A.) [PERSON]  
2 Escuela Superior de Ingenieria Mecanica y Electrica, Unidad Culhuacan, Instituto Politecnico Nacional, Av. Santa Ana No. 1000, Col.  
and enhances the power density. Resonant converters are commonly employed in these applications because they allow for high frequency operation and soft switching, which significantly reduces switching losses [4]. The issue with these types of converters is that operating at frequencies above 1 MHz typically necessitates the use of expensive electronic cards in the control stage, special semiconductors, and control methods applied to the inverter/rectifier stage, increasing the circuit's total cost and complexity [5]. Typically, resonant converters are designed in a steady state and analyzed using the first harmonic approximation method, which is a modeling methodology that assumes only the first harmonic signal contributes to power transfer [6; 7]. The performance of resonant circuits operating in the transient state has not received much attention, and it is quite interesting to see what applications the analysis of resonant circuits operating in the transient state can be utilized for [8]. This paper presents the analysis and design in the transient state of a resonant converter acting as a frequency multiplier, where the oscillation frequency of the current in the resonant tank is equal to \"\(n\)\" times the switching frequency at the inverter stage (\(f_{o}=\eta f_{sw}\)), allowing it to operate at high resonant frequencies in the resonant network without needing a high switching frequency in the inverter. The concept of frequency multipliers is not new; numerous publications have already been published. A frequency multiplier is a DC circuit in which the frequency of the output signal is a harmonic component of the frequency of the supply signal. If the frequency of the input signal is \"\(f_{sw}\)\", a resonant tank can be used to filter out the unwanted frequency components and leave only the signal component whose frequency is \"\(nf_{sw}\)\" at the output [9; 10; 11; 12]. These circuits are commonly utilized in high-frequency RF applications where parasitic semiconductor components limit the maximum working switching frequency, such as switched mode inverters and power amplifiers. Unlike conventional frequency multipliers, which require decomposing a signal with harmonic content and then filtering out unwanted harmonics using bandpass circuits, the methodology presented in this work achieves frequency multiplication naturally through the underdamped transient response of a series RLC circuit. This approach eliminates the need for additional filtering and simplifies circuit design, allowing for higher power levels and reducing losses compared to conventional harmonic filtering-based frequency multipliers. These frequency multiplication approaches have been presented in the design of DC-DC converters, but they are not widely used since the output power of a frequency multiplying inverter is intrinsically low when compared to the ratings of the needed devices. The low power levels at which frequency multipliers usually work limit the applications in which they can be used, being used only in radio frequency applications, which is where power levels in the order of milliwatts are usually handled [13; 14; 15; 16].