Digital Circuit Boards: Mach 1 GHz

3.10 Capacitive Component of Cross Coupling

Capacitive coupling contributes to waves traveling in both directions on the victim line. The coupled current that flows to the right is positive and the coupled current that goes to the left is negative. These polarities satisfy the requirements of Poynting's vector.

The capacitively coupled reverse voltage pulse is approximately given by

3.4

where V is the culprit voltage, C_M is the mutual capacitance per unit length, and C is the capacitance per unit length used to calculate the characteristic impedance of the victim line. The reverse wave lasts twice as long as the forward wave and half the current is supplied to the forward wave. This accounts for the factor of 4 in Equation 3.4.

The rise time of the reverse wave is double the rise time of the culprit wave.

The amplitude of the forward capacitively coupled current component is given by

3.5

where V is the culprit voltage, t is the time of transit of the culprit wave, and τ_r is the rise time. The factor 1/2 results because half the current goes into the reverse wave.

The capacitively coupled wave forms are shown in Figure 3.9.

Figure 3.9 Capacitive coupling between transmission lines.