Resistance and Inductance of Copper Foil

The graphic on the right is a schematic diagram of the cross-section of a PCB. These are the basic construction and characteristics of a board, and so they should be remembered. The main points are listed below.

• Often the copper foil layers on the top and bottom surfaces are different in thickness from those on the inner layers.
• Often the copper foil layers on the core material are thicker, to increase heat dissipation.
• Core materials have general-use thicknesses, with the thickness adjusted using pre-preg.
• There are materials in which migration may occur, depending on the core material and the pre-preg type, and in some cases such materials cannot withstand high-humidity testing.

Of course, copper foil (wiring) has electrical resistance. Under conditions in which a large current flows, conduction losses, that is, a voltage drop and heat generation, occur. Hence where large-current lines are concerned, it is important to review the resistance values of copper foil layers.

The resistance of copper foil is described as a value per unit area. Figure 10 indicates the resistance values per unit area of copper foil. The resistance values are for the generally application conditions of a copper foil thickness of 35 μm, width 1 mm, and length 1 mm.

The following equation is used for general calculations of resistance.

Figure 11 shows calculated values for copper foil inductance. As is clear from the graph, there is surprisingly little decrease in the inductance even when the line width is doubled.

In order to suppress the effects of parasitic inductance, the best approach is to shorten wiring lengths.

If the current propagating in printed wiring with inductance L (H) changes by i (A) in time t (s), then the following voltage appears across the ends of the printed wiring.

For example, if a 2 A current flows for 10 ns in printed wiring with a parasitic inductance of 6 nH, then the following voltage occurs.