1.8 Mutual and Self-Capacitance

In a typical capacitor, the electric field lines start on one conductor and terminate on the second conductor. The conductor at zero volts is often called the reference conductor. The ratio of charge on the first conductor to the charge on that of the second conductor is called self-capacitance. The capacitors used in a circuit all have self-capacitances.

When there is a group of conductors as in a circuit, the concept of capacitance must be extended to allow for cross coupling. As an example, consider traces over a ground plane as in Figure 1.2. The ground plane can be considered the reference conductor at zero volts.

Figure 1.2 Mutual capacitance between traces on a circuit board.

Assume that one of the traces is at a voltage V₁ and all the other conductors are at zero volts. By definition the self-capacitance C₁₁ of trace 1 is the ratio of charge on trace 1 to the voltage on trace 1 or Q₁/V₁. When trace 1 is at potential V₁, some of the electric field lines terminate on trace 2. This represents an induced charge Q₂ on this conductor. The ratio of Q₂/V₁ = C₂₁ is called a mutual capacitance. Since the field lines always terminate on charges of opposite polarity this ratio is always negative.

Mutual capacitance can allow an induced current to flow in nearby circuits. The coupled current flow depends on the rate of change of voltage and the resulting voltage depends on the victim circuit impedance. This coupling can be a problem when traces on a circuit board run in parallel for a long distance. Mutual capacitance can be measured by placing a sinusoidal voltage on one conductor and observing the current flow on a second conductor. A small series resistor can be used to sense the current in the second conductor.

Later, we will show that in cross coupling, coupling current can be introduced only when a logic signal is in transition.