Detailed Derivation and Minimization of the Equivalent Parasitic Capacitances of a High-Voltage Multiplier Based on the Complete Model

The authors´ previous paper presents the complete model of parasitic capacitances in a high-voltage (HV) multiplier in the HV generator in a medical X-ray machine. The equivalent parasitic capacitance of the multiplier C_em based on the model is exhibited to interpret the role of the parasitic capacitances in circuit operation of the generator. Without derivation of the analytical expression of C_em, its dependence on the component parameters is directly shown, which leads to guidelines for minimization of C_em. However, the complete capacitance model has a complicated structure and contains voltage-dependent capacitances and voltage sources, which gives complexity to derivation of C_em as well as difficulties to clear understanding of the voltage dependence of C_em. Thus, this paper presents the detailed derivation and analytical expression of C_em. Exactly speaking, the key part of C_em, namely, the total chain capacitance C_Dcht that determines the voltage dependence of C_em, is conducted. A simple way is presented for the derivation of C_Dcht. The derivation enables a clear understanding of the voltage dependence of C_Dcht. Moreover, a design procedure for minimization of C_em is created, accompanied by a case study. It gives designers step-by-step rules to make an optimal HV multiplier with a minimum C_em.