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A control scheme is presented for a high voltage output power supply based on an LCC resonant converter which exploits the flexibility of digital methods to attain high performance with simple algorithms. The control scheme uses voltage and current control operating modes; the interaction of these modes is analytically investigated. Optimally fast capacitor charging is attained by charging up using current control mode and switching to voltage control mode for approach of the reference voltage. An adaptive low-pass filter of the reference voltage is presented which guarantees zero reference overshoot for a wide range of resistive-capacitive loads. The devised scheme is simple, effective, and not specific to the system under study. Details of FPGA implementation and experimental results verifying the adaptive reference filter are presented.