Appendix A

Formulae for Partial Inductance Calculation

This appendix provides closed-form expressions for calculating partial inductances for round wires and busbars or strips useful for modeling connectors, vias, traces and planes in PCBs. The concept of effective inductance Le associated with one conductor is used here to compute the voltage drop V(t) = Le dI(t)/dt on the conductor that is caused by the current I(t). For two conductors with currents flowing in the opposite direction (i.e. series connection), the overall inductance is Let = Le1 + Le2. For two conductors with currents flowing in the same direction (i.e. parallel connection) the overall inductance is Let = Le1Le2/(Le1 + Le2).

A.1 Round Wires

A collection of formulae for round wire structures such as pin connectors or vias in PCBs, is shown in Table A.1. It is worth making the following observations:

  • Isolated wire. This is the situation that occurs when the current I on the conductor returns through another far away conductor and, therefore, the contribution of the mutual inductance can be neglected. The associated inductance is the self partial inductance Lp function of the length l and wire radius rw [1]. The low-frequency expression includes the internal wire inductance Lint = μ0/8π, and the resulting inductance is higher than the inductance at high frequency when the skin effect becomes dominant.
  • Two parallel wires. The mutual partial inductance is calculated as mutual inductance between two filaments and provides ...

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