Digital control of resonant converters: Resolution effects on limit cycles

The conditions for limit-cycle oscillations in digitally controlled resonant converters are explored theoretically and are tested by simulation and experiment. The analytical analysis reveals that in a manner similar to digital pulsewidth modulation (PWM) control, limit cycles occur in such systems when the LSB of the control changes the output by a value that is larger than the analog-to-digital converter (ADC) resolution. However, in resonant converters, unlike the case of PWM, limit-cycle oscillations depend on the steady-state control input, since both the power stage gain and the resolution of the digitally generated drive frequency are not constant over the operating frequency range. Consequently, at high gains (close to resonance), the required frequency resolution may not be supported by the digital core. A time-domain behavioral simulation model, developed, and experimentally verified, allows the steady-state behavior of digitally controlled resonant converters to be analyzed, including the phenomenon of limit cycles as well as the closed-loop response. A cycle-by-cycle Powersim (PSIM) simulation model of a digitally controlled resonant converter, developed in this study, includes a digital core realization using C code block. This simulation model enables the exploration of the system in fine details. The proposed method of static analysis and dynamic modeling is experimentally verified on a series-resonant parallel-loaded converter operated in closed-current loop. The digital control algorithm was implemented on a TMS320F2808 DSP core. Very good agreement is found between the analytical derivations, simulations, and experimental results.