Symbolic solution of the multiconductor transmission-line equations for lines containing shielded wires

The multiconductor transmission line equations that characterize crosstalk in a multiconductor transmission line containing a shielded wire are solved in symbolic form, that is, the resulting crosstalk voltages are determined in terms of symbols rather than numerical values. The resulting solutions show the frequency range for which the widely used, low-frequency, inductive-capacitive coupling model is a valid representation. The solution shows that the inductive-capacitive coupling model is an adequate characterization of crosstalk for lines that are electrically short and whose termination impedances do not differ substantially from the characteristic impedances of the lines that are involved. For lines whose termination impedances differ drastically from the line characteristic impedances, the inductive-capacitive coupling model is valid only for frequencies where the line is extremely short, electrically. For higher frequencies of excitation, the model may give predictions that are substantially below the true crosstalk even for frequencies where the line is electrically short