19
Use a 2-D field solver, such as the code provided in [5].
Sometimes odd and even mode impedances are provided rather than the inductance and capacitance
matrices. The even and odd mode characteristic impedances are related to L, C, LM and
CM in the following way:
Zoe = SQRT((L + e*LM)/(C - e*CM))
Zoo = SQRT((L + o*LM)/(C - o*CM))
Tde = SQRT((L + e*LM)(C - e*CM))
Tdo = SQRT((L + o*LM)(C - o*CM))
Zoe and Zoo are the even and odd mode impedances, respectively, and Tde and
Tdo are the corresponding delays. The coefficients e and o are the even and
odd mode eigenvalues of the matrix [L][C], and come out to e=SQRT(2)/2 and
o=-SQRT(2)/2 for two symmetric lines.
L, C, Lm and Cm are found by solving the 4 equations above in terms of Zoe, Zoo,
Tde, and Tdo.
Modeling R and G at high frequencies
Twinax attenuation curves have an a + b*sqrt(f) frequency dependence, similar to coax. The same
method as suggested for coax may be used to model R and G for twinax.
Unshielded Twisted Pair (UTP) Modeling
Unshielded twisted pair (UTP) can not be used at higher frequencies, as can STP.
Modeling L and C
A simple for formula for the characteristic impedance of two parallel wires is
Where d is the diameter of the conductor, and s is the separation between wire centers. The propagation
delay is
For UTP, the inductance in the region below ~500KHz can vary slightly with frequency. The distributed
lossy transmission line model allows R and G to depend on frequency, but not L. The best solution is to
pick the value of L for the frequencies of interest.
)
2
ln(
120
0
d
s
Z
r
) / ( 85 in ps t r d
