- #1

David J

Gold Member

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- 15

## Homework Statement

A transmission line has the primary coefficients as given below.

##R=2\Omega/m##

##L=8 nH/m##

##G=0.5 mS/m##

##C=0.23 pF/m##

Determine the lines secondary coefficients ##Z0##. ##\alpha## and ##\beta## at a frequency of ##1 GHz##

## Homework Equations

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In my notes I am given

##\alpha=\frac{R}{2}\sqrt\frac{C}{L} +\frac{G}{2}\sqrt\frac{L}{C}## and ##\beta=\omega\sqrt{LC}##

## The Attempt at a Solution

[/B]

##\alpha=\frac{2}{2}\sqrt\frac{0.23 X 10^-12}{8 X 10^-9} +\frac{0.5 X 10^-3}{2}\sqrt\frac{8 X 10^-9}{0.23 X10^-12}##

##\alpha=1 X \sqrt{2.875 X 10^-5} + (2.4 X 10^-4)\sqrt{34,782.6}##

##\alpha=\sqrt{2.875 X 10^-5} + (2.4 X 10^-4)\sqrt{34,782.6}##

##\alpha=(5.362 X 10^-3) +0.044760 = 0.050121902## nepers per meter

I think this is correct. I am unsure how to input the single multiplication sign `X` in LaTeX form. I think my " to the power of`s" are correct for ##R, L, G## and ##C## but I am unsure about the final result in nepers per meter

For the second part I got the following:-

##\beta=\omega\sqrt{LC}##

##(2\pi)(1 X 10^9) \sqrt{(8 X 10^-9)(0.23 X 10^-21)}##

So I have ##6,283,185,307\sqrt{1.84 X 10^-21}##

So ##6,283,185,307(4.289522 X 10^-11)=0.269518623## radians

So ##\beta= 0.269518623## radians

This second answer I am not so sure as I have some very large numbers but I have followed the examples in my notes.

Any comments on the two attempts above would be appreciated.

Thanks