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Inductance: Loop and Partial by CLAYTON R. PAUL

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6

PARTIAL INDUCTANCES OF CONDUCTORS OF RECTANGULAR CROSS SECTION

In this chapter we obtain the self and mutual partial inductances for conductors of rectangular cross section, referred to here as printed circuit board (PCB) lands. Figure 6.1 shows this type of conductor. The width is denoted as w, the length is denoted as l, and the thickness is denoted as t.

FIGURE 6.1. Printed circuit board land.

images/c06_image001.jpg

In previous chapters we have detailed the computation of inductances for conductors having circular, cylindrical cross sections (i.e., wires). The computation of the partial inductances of and between wires is fairly simple, for an important reason. We consistently made the assumption that the current carried by a wire is uniformly distributed over the cross section of the wire which is true for dc and widely spaced wires. In this case, for the purposes of computing the magnetic fields from that wire, we can replace the wire with a filament containing the total current l = JA, where J is the uniform current density distribution and A is the area of the wire cross section. This is an extraordinarily important simplifying assumption, for a number of reasons. First, we can equate the self partial inductance of a wire having a uniform current distribution over its cross section to the total magnetic flux threading the surface formed between the surface of the wire and infinity per unit ...

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