Digital Circuit Boards: Mach 1 GHz

3.9 Magnetic Component of Cross Coupling

The magnetic flux generated by the culprit line current crosses the conducting path of the victim line. By Lenz's law, a changing current on the culprit line induces a negative current on the victim line. This current is associated with a negative voltage wave that travels to the right and a positive voltage wave that travels to the left. The associated fields have directions that satisfy the requirements of Poynting's vector.

In Figure 3.7, the culprit line is short and it couples to the middle of the victim line L2. Notice L1 is terminated in its characteristic impedance so the culprit wave is absorbed when the wave reaches the end of the line.

As the culprit wave progresses along L1 the only magnetic flux in transition is along the leading edge. In effect, the coupling is limited to the region where flux (current) is changing on L1. The coupling takes energy from L1 and adds it to L2 on a continuous basis. Each increment of transmission line couples an increment of current to a forward and reverse traveling wave. The coupled forward wave and the culprit wave move to the right at the same velocity, so there can be no coupled energy ahead of the leading edge. The induction process causes a negative pulse of voltage on L2 that increases in amplitude as the culprit wave moves to the right down the line. The pulse width is equal to the rise time of the culprit wave.

A reverse wave moves to the left on L2 as the culprit wave moves to the right. ...