1.6 Current
The charges that create a static electric field are located on the surface of conductors. In every circuit with operating voltages, there are surface charges. These surface charges must move if the voltages change value. The pattern of charge motion can best be appreciated by noting the pattern of electric field lines that terminate on a conductor. Charges tend to concentrate where there are sharp bends or transitions. This means that if the field pattern changes, current flow must occur when the pattern changes. If there are no field lines terminating on a part of a conductor then there will be no current flow on that part of the conductor. This means that parts of a ground plane are often not used for current flow. Figure 1.1 shows the E field pattern around a typical trace over a ground plane.
Figure 1.1 The electric field pattern around a typical circuit trace.
The field pattern shows that the charges concentrate on one side of the trace and on that portion of the ground plane under the trace. No current flows on the other side of the ground plane. This charge pattern is essentially independent of frequency. Every E field line terminates on a unit of charge. The unit of charge is selected to best show the shape of the field. Note that the electric field lines terminate perpendicular to conducting surfaces. The lines that are shown parallel to the ground plane represent equipotential surfaces. The trace (conductor) itself is an equipotential surface at voltage V. The ground plane is an equipotential surface at zero volts. The dielectric normally present under a trace is not shown. A dielectric would not significantly change the field pattern, but it would increase the amount of stored charge.
The field pattern is shown for a voltage V. As V is increased, the number of lines also increases. If the voltage is a sine wave the field intensity pattern is also sinusoidal.
If there is sinusoidal current flow below a few kilohertz, a very small horizontal component of the E field penetrates into the conductors to move the charges. As the frequency increases, the penetration depth decreases and current flow concentrates closer to the surface. Above a megahertz, the current flow in conductors is basically at the surface. This surface flow phenomena is called skin effect (Section 1.8).
The velocity of electrons in a typical circuit is extremely low. In a typical geometry, it is not too difficult to show that the average velocity is less than 1 cm/s. This occurs because the electron density in a conductor is extremely large. What is important is the nature of the electric and magnetic fields. Fields carry signals and energy at the speed of light. For this reason, we must concentrate on the movement of fields and not on the flow of electrons. We need to know the value of current flow to calculate voltage drop, power losses, and magnetic field strength. This is a good example of where circuit theory can be put to good use.