I have an issue with my EM fields pre-lab that some night owl may be able to get to before my lab tomorrow. If not, I'll ask the T.A., though I'm still not getting what's going wrong here.

Problem:

A two-wire air line has the following line parameters:
R' = .404 mOhm/m
L' = 2.0 uH/m
C' = 5.56 pF/m
G' = 0
For operation at a frequency of 5kHz.

Find gamma, alpha, beta, Phase Velocity U[sub]p[/sub], Wavelength (lambda), and impedance (z[sub]0[/sub]).

Given the equation for gamma:

gamma = Sqrt[(R' + jwL')(G' + jwC')]
(w = omega = 2*pi*frequency
j = Sqrt(-1))

putting in for gamma:

gamma = Sqrt[(.404x10[sup]-3[/sup] + jw * 2x10[sup]-6[/sup])(0 + jw * 5.56x10[sup]-12[/sup])]

(R', L', and C' changed to be in units of Ohm/m, H/m, and F/m respectively)

which, multiplying out, gives us:

gamma = Sqrt[jw * 2.246x10[sup]-15[/sup] + (jw)[sup]2[/sup] * 1.112x10[sup]-17[/sup]]
= Sqrt[jw * 2.246x10[sup]-15[/sup]] + jw * 3.335x10[sup]-9[/sup]

given Sqrt[j] = e[sup]j*pi/4[/sup], we then get:

gamma = e[sup]j*pi/4[/sup]*Sqrt[w]*4.739x10[sup]-8[/sup] + jw * 3.335x10[sup]-9[/sup]

Expanding using Euler's:

gamma = Sqrt[w]*4.739x10[sup]-8[/sup]*(cos(pi/4) + j*sin(pi/4)) + jw * 3.335x10[sup]-9[/sup]

given that gamma = alpha + j*beta, for alpha we get:

alpha = 2.3696x10[sup]-6[/sup] Np/m

and for beta:

beta = 1.9045x10[sup]-5[/sup] rad/m

According to the answers given, I should have:

alpha = 3.37x10[sup]-7[/sup] Np/m
beta = 1.05x10[sup]-4[/sup] rad/m

Can anybody find where I'm doing my math incorrectly? Before 10am CST would be ideal, but if you get the right answer after that, I'd still like to know how you did it.

Expanding using Euler's:

gamma = Sqrt[w]*4.739x10-8*(cos(pi/4) + j*sin(pi/4)) + jw * 3.335x10-9

I was with you to there, but I've not done that in about 3 or 4 years so I can't help you any further than there. Everything up to there I agree with, that and beyond is stuff I can't remember how to do!

Euler's just says that e[sup]jw[/sup] = cos(w) + j*sin(w).

The Sqrt[w]*4.739x10[sup]-8[/sup] is the constant term that gets distributed.

Also, a little more clearly:

alpha = Re[gamma]
beta = Im[gamma]

Ah it all comes flooding back! I'll have a little look in half an hour when my lunch break starts proper.