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# 1.9 E Fields Inside Conductors

If there is current flow in a conductor, a small E field must exist inside that conductor. At dc, this field will be the same at any depth. In most of our applications the ratio of external to internal field strength is about 20,000:1. A changing magnetic field associated with current flow forces the current to stay near the surface of the conductors. This applies to logic operations, where currents flow very near to the surface of the conductors. This is known as skin effect. For a sine wave current at 1 MHz, the skin depth for copper is only 0.066 mm. This means that the current at this depth is the surface current reduced by 8.68 dB. At 100 MHz, the skin depth is 0.0066 mm. Most of the current flows in the first three skin depths.2

N.B.
Very small E fields are required to cause typical current flow in conductors.

When a step voltage is first applied to a trace over a ground plane, the charges that move are on the surface of that trace and on the surface of the ground plane under the trace. Consider a fixed point on a long transmission line. As time progresses, the current that flows begins to penetrate into both conductors. After a few milliseconds, there will be very little skin effect present.

N.B.
Current patterns in traces and ground planes are very complex. Fortunately, in digital circuits, these patterns do not require extensive analysis. Current only flows in a conductor where there are fields present.

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