A simplified cross coupling model for multiple balanced transmission lines

Modeling of the coupling between transmission lines in the practical sense has been an elusive quarry. Since the favorite tool of signal integrity designers is SPICE, the ultimate goal should be translation of the mathematics of coupled mode analysis into a simple SPICE formulation. This investigation presents a method to simulate the parasitic coupling between transmission lines in structures where complete isolation is impractical. The conventional mathematical analysis of such coupling does not suggest a simple SPICE solution, so a farther analysis of cause-effect and elimination of unimportant terms resulted in a set of models which uses the transmission line capacitance matrix to create a direct input of parameters to a SPICE subcircuit. This SPICE subcircuit is utilized as an attachment to a previously designed lossy transmission line circuit. The resultant circuit models cross coupling originating from any number of culprits affecting one victim. The circuit requires one victim line and one culprit line, where the assumption is made that all culprit lines carry the same signal. The technique is applicable to single ended and differential pair transmission lines. An HSPICE subcircuit was included to illustrate the ultimate form of the model.