= ;I

Lest the large L values (60 and 2 henries) and low-frequency ranges just quoted mislead the reader, we should indicate that many practical inductors of millihenry and microhenry value work in high kilohertz and megahertz frequency ranges. A 0.15-!lH inductor is about 0.1 inch in diameter and 0.4 inches long, with a DC resistance of 0.02 ohms and a Q of about 65 at 25 MHz, the frequency at which L was measured. If we take the simple definition of Q as wLj R in this example, we predict a Q of 1180, much higher than the value actually measured. One explanation of this discrepancy lies in the so-called skin effect, which makes the resistance at high frequency much higher than its DC value. At DC and low frequencies, the current is uniformly distributed over the cross section of a conductor, while at high frequency it is "crowded" toward the surface, making the effective cross section smaller and thus raising the resistance. This is caused by self-induced emfs set up by variations in the internal flux in the conductor. In our numerical example, it appears that at 25 MHz the effective resistance is about 1180/65 = 18 times the DC value. Part of this resistance could also be caused by the core losses mentioned earlier. The skin effect is not peculiar to inductors; it occurs in all conductors at high frequency and provides an explanation of several otherwise puzzling observed phenomena, so add it to your "catalog" of useful electrical effects.