Signal Integrity Applications of Mathcad, Part 2

摘要

Mathcad offers efficiency and flexibility for solving mathematical equations. It can treat analytical expressions having scalar (a single number), vector (column of numbers) and matrix (a rectangular array of number). An array is a general term for vector or matrix. The Mathcad logarithmic features include ln(z) which returns the natural log of z (z ≠ 0) and log(z,b) which outputs the base b logarithm of z (z or b ≠# 0). If b is omitted, then log(z,b) equals the base 10 logarithm. Hence, log(z) returns the common logarithm of nonzero z. Let us analyze, applying Mathcad, the concept of coupling even and odd mode impedances. The electric and magnetic fields associated with coupled traces (i.e., traces located in close proximity) will interact in manners that depend on each line's signal patterns. The effective characteristic impedance and velocity of the transmission will be altered due to such interactions. FIGURE 5 displays the computed (using HyperLynx from Mentor Graphics) odd and even electric (in blue) and magnetic (in red) field distributions for a coupled microstrip.