# Lossless transmission line characteristic phase constant

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1. Sep 11, 2016

### bergen89

1. The problem statement, all variables and given/known data

A lossless transmission line has an inductance of 9.0 nH / m and a capacitance of 3.6 pF / m.
a) What is the line's characteristic impedance?
b) Calculate the phase constant of a frequency of 1 GHz.

2. Relevant equations

Equation of characteristic impedance of a transmission line:

Z0 = sqrt( R+j2piL / G+2jpiC )

Where R and G = 0, because lossless transmission line.

3. The attempt at a solution

For a I just used the equation above, but for task 2 I'm not sure what to do. I dont now how to get Sin/Cos to the equation so I can fint the phase constant. Do I need to do something to the equation above?

2. Sep 13, 2016

### rude man

For a lossless or for that matter distortionless line there is a very simple formula relating the phase constant to the radian frequency, inductance per unit length and capacitance per unit length, all of which you have. SI units are rad/m.

3. Sep 13, 2016

### bergen89

Thanks a lot for you respons. I really appreciate it. Do you know what the formula is, or where I could find it? I have seen in the book, but cant find it. Also I have added what I done in the first task. Should I use the result from that? I got 50 ohm.

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4. Sep 13, 2016

### rude man

There are many places on the Internet where you can find that formula. No, that formula does not include the answer to part (a).