Detailed derivation and minimization of the equivalent parasitic capacitance of a high voltage multiplier based on the complete model

This is a follow-up paper to the publication [1]. The previous paper presents the complete model of parasitic capacitances of a high voltage (HV) multiplier, which is employed as a capacitive rectifier in HV generator in 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 HV generator. Without detailed explanation about derivation of analytical expression of C_em, its dependence on the component parameters are directly shown, which leads to guidelines for minimization of C_em. However, the complete model shows a capacitance network with complicated structure and containing voltage-dependent capacitances and constant 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 can give readers a clear understanding of the voltage dependence of C_Dcht. Besides the derivation, a design procedure for minimization of C_em is created based on the proposed guidelines in [1], accompanied by a case study. It gives designers step-by-step rules to make an optimal HV multiplier with a minimum C_em.