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

Abstract

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> , its dependence on the component parameters is directly shown, which leads to guidelines for minimization of C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> . However, the complete capacitance model has a complicated structure and contains voltage-dependent capacitances and voltage sources, which gives complexity to derivation of C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> as well as difficulties to clear understanding of the voltage dependence of C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> . Thus, this paper presents the detailed derivation and analytical expression of C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> . Exactly speaking, the key part of C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> , namely, the total chain capacitance C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dcht</sub> that determines the voltage dependence of C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> , is conducted. A simple way is presented for the derivation of C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dcht</sub> . The derivation enables a clear understanding of the voltage dependence of C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dcht</sub> . Moreover, a design procedure for minimization of C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> is created, accompanied by a case study. It gives designers step-by-step rules to make an optimal HV multiplier with a minimum C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">em</sub> .