3.3  Inductor

To limit the current at the input of the voltage multiplier an inductor is connected between the output of the IGBT - switch and the input of the voltage multiplier (Figure 3.26, L1). The simulation showed that a minimum of 0.5mH is needed to limit the current to a maximum of 30A and a maximum of 2kV can occur at the inductor. A toroidal shape minimises EMI, an air coil ensures minimal loss at high frequencies.

According to [Yung], the inductance of a toroid with rectangular cross section is:

            N         =          number of turns

            r_o         =          outer radius

            r_i          =          inner radius

            h          =          height

            μ          =          μ_r · 4 π 10^-7

The formula for the length of the winding cable is:

Solving (3-1) for N and combining it with (3-2) gives the cable length. This length is dependent on the dimensions and the inductance:

To minimise the length of the winding wire, a graph (Figure 3.8) was plotted with Gnuplot. It is a visualisation of (3-2. Following settings:

set cntrparam levels 20

set contour base

set xlabel "height"

set ylabel "Ro, outer radius / m"

set xlabel "h, height / m"

set zlabel "lc, length of cable"

splot [h=0.1:0.2] [p=0.2:0.25] (2 * h + 2 * (p - 0.11)) * (sqrt((0.0005) / (0.0000002 * log(p / 0.11)*h)))

Figure 3.8:Gnuplot - graph for optimisation of the inductor

Figure 3.8 shows, that a rectangular cross-section is the optimal (minimal cable length) shape for the toroidal inductor. The minimum length is given by the restriction, that (at a one - layer winding) the inner radius is limited by the diameter of the cable and the number of turns.

d_cable   =          cable - diameter

Figure 3.9: Inductor: Photo of the frame

Figure 3.9 shows the wooden frame that the winding cable was wound around. A slot was left in the frame to enable the winding process. The wound inductor is shown in Figure 3.10.

Figure 3.10: Inductor: Photo

Figure 3.11 is an engineering drawing of the inductor frame.

Figure 3.11: Engineering drawing: Inductor frame

This page is part of a Frameset: Electrodynamic Sculpture: A Thesis by Rafael Bräg.