Signal Integrity and Radiated Emission of High-Speed Digital Systems

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 L_e associated with one conductor is used here to compute the voltage drop V(t) = L_e 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 L_et = L_e1 + L_e2. For two conductors with currents flowing in the same direction (i.e. parallel connection) the overall inductance is L_et = L_e1L_e2/(L_e1 + L_e2).

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 L_p function of the length l and wire radius r_w [1]. The low-frequency expression includes the internal wire inductance L_int = 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 ...