The article is dedicated to the development of the mathematical model of the resonant frequency converter with pulse-density control in the part of determining the functional of the carrier voltage pulses, which allows calculating the time sequence of the inverter’s control pulses. The authors have determined that the functional here is the dependence of the average value of the carrier voltage pulse of the resonant capacitor on its duration. Its duration, on its turn, depends on the instantaneous filter current value at the beginning of the control pulse for the half-bridge transistors. The analytic expressions for determining the exact and approximate average values of the quasi-sinusoidal voltage pulses at the resonant capacitor during the time interval between two serial control pulses are obtained. Due to the gotten expressions, the error in the application of the approximate model is estimated.Comparing the average value of the carrier resonant voltage pulse with the average value of the desired output voltage during the time interval between two serial control pulses, allowed to obtain the frequency converter pulse-density control law, which considered and compensated the inaccuracy of the approximate value of the chosen functional. To observe the functionality of the frequency converter, which operates according to the designed control law, its load characteristics were built and compared to the characteristics of the converter, which control law used the approximate model but did not consider its inaccuracy.In the case of the resonant current amplitude exceeding 1.2 times over the load current one, the maximum calculating error of the average value of the carrier voltage pulses is 0.01%. This makes possible to simplify the real time calculation of the control pulses sequence by using the approximate average value of the resonant voltage to ensure the hard pattern of the load characteristic in the case of load resistance varying within two orders. The comparison of the frequency converters load characteristics in the cases of various control laws shows the prolonged hard pattern of the load characteristic in the case of considering the inaccuracy of the chosen functional.The research results can be applied in the design of the highly efficient secondary power supplies with improved electromagnetic compatibility with the load and the network. Thus, the received functional of the carrier sinusoidal voltage pulses allows the real time calculation of the control pulses time sequence for the power transistors of the resonant inverter in accordance to the developed pulse-density control law.Ref. 10, fig. 5.
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