The article presents the influence of the parameters of the high voltage direct current (HVDC) generator with a multiplier, such as: leakage inductance of the high voltage (HV) transformer, capacitance, and the number of multiplier stages on the value of the output voltage, voltage ripple, power and frequency of the supply voltage as a function of the output current. The presented characteristics were obtained under the synchronization conditions of the inverter output voltage and current that powers the multiplier. The presented results will be useful when designing HVDC generators with Cockcroft-Walton multipliers.