# Transmission lines

Discussion in 'Homework Help' started by Biggsy100, Mar 16, 2015.

1. ### Biggsy100 Thread Starter Member

Apr 7, 2014
88
1

1. The characteristic impedance of a transmission line is given by the equation:

zo = R + jwL W G + jwC

A transmission line-under-test has the following primary constants:

L = 100 x 10-9 Henries per metre

R = 4 x 10-3 Ohms per metre

G = 1 x 10-7 Siemens per metre

C = 20 x 10^-2 Farads per metre

Calculate the magnitude of the characteristic impedance with an 8 kHz line
signal frequency. Comment on the result and mention any reasonable

1. Am I correct to square root this equation?
2. Now I have completed the equation, should I have broken it down into stages to reach a resolution?

2. ### MrChips Moderator

Oct 2, 2009
13,363
3,746
Why would you want to take the square root of the right hand part of the equation?
That would alter the dimensions and make the equation invalid.

$Z_0 = \sqrt{\frac{(j\omega L+ R)}{(j\omega C + G)}}$

http://www.amanogawa.com/archive/docs/C-tutorial.pdf

3. ### Biggsy100 Thread Starter Member

Apr 7, 2014
88
1
I am not sure why I would want to square root it at all, that is why I asked?

On your picture it shows the how equation square rooted? I assumed that's what I had to do here? Are you suggesting from your notes that you supplied (many thanks) that I follow the whole process?

4. ### MrChips Moderator

Oct 2, 2009
13,363
3,746
You cannot just take the square root of one side of an equation willy nilly.

Here is a simple example:

Distance travelled = velocity/time

If I were to square the right-hand side of the equation for whatever whim, that would result in (velocity/time) squared which would give area as the result. Obviously, distance cannot be equal to area.

The dimensions of $(j\omega L + R)$ are Ohms.
The dimensions of $\frac{1}{(j\omega C + G)$ are Ohms.

Hence when we take the product the result is in $Ohms^2$.

Taking the square root makes the equation dimensionally balanced.

5. ### Biggsy100 Thread Starter Member

Apr 7, 2014
88
1
So I square root the answer?

6. ### MrChips Moderator

Oct 2, 2009
13,363
3,746
If this is your equation, no, you cannot take the square root.

zo = R + jwL W G + jwC

If you examine this equation you will notice that this equation is dimensionally unbalanced and therefore incorrect.

The dimensions of jωC are not Ohms.

I suggest you review the notes in the link provided and find the proper equation.

The lesson here is: check the dimensions of both sides of the equation.