Transmission Line (simple Prob)

[tim9000]

Homework Statement

Incase formatting of numerical answers below is weird, please see attached picture of question.

"Consider a distortionless transmission line with impedance 50 Ω, capacitance 0.1
nF/m and attenuation 0.01 dB/m. Find:
(a) the resistance, inductance and conductance of the line
(b) the wave propagation velocity in the line
(c) the relative amplitude of a voltage after it has traveled a distance of 2 km in
the line.
[Ans. (a) R = 0.057 Ω/m, L = 2.5 x 10
-7
H/m, G = 2.3 x 10
-5
S/m; (b) v = 2 x 10
8
m/s;
(c) 10%]."

Homework Equations

Zo = SQRT(L/C)

For distortionless line

R/L = G/C

The Attempt at a Solution

Part b) is easy (from u = 1/Sqrt(LC))

However, I assume Zo = 50 ohms, as it let's me find L = 50²*0.1n = 2.5E-7

But then what the devil do they mean in the numerical answer given for R = 0.057ohm/m?
and what is with the conductance G? that isn't 1/any R value. Is that conductance and R wrong?

More pressingly though, my log is really rusty! this is where I'm most confused, I've been messing around with e^-attenuationconstant*distance and a loss = 0.01dB = 20 log(V1/V0) formula but I'm not sure if that's the right approach as I'm not getting anywhere?

Could anyone offer an opinion and if possible show me how the loss is 10% over 2km?

Thanks heaps!

 

[rude man]

If you're given attenuation you can immediately get R since you know Z_zero.
Then, what relates R,L,C and G in a distortionless line?

Knowing just L and C enables you to find the phase (wave propagation) velocity.
Part (c) should be evident from the attenuation number. You know the attenuation constant and the line length ...

 

[tim9000]

So as I said, R = Zo right?
Well why is that R = 0.057 ohm/m and not 50ohm/m? In the numerical solution (in picture)
And G, what R is that the inverse of? Thanks

 

[rude man]

So as I said, R = Zo right?

Well why is that R = 0.057 ohm/m and not 50ohm/m? In the numerical solution (in picture)
And G, what R is that the inverse of?
Thanks

Because R = α Ro, not Ro, where Ro = Re{Zo}.

G is not the inverse of anything significant. G is the conductive leakage per unit length of one conductor to the other. Units are Siemens/m.

BTW what are the units of α in the above expression?

 

[tim9000]

Because R = α Ro, not Ro, where Ro = Re{Zo}.

BTW what are the units of α in the above expression?

Oh, R = α Ro; Alpha is Neper/m, which is 0.115129dB*0.01*50

that makes sense, I'm really confused as to why I'm only learning that is what R is now and why I've never seen that written anywhere before.

So conductance is RC/L.

Thanks, you really cleared that up!

 

[rude man]

Oh, R = α Ro; Alpha is Neper/m, which is 0.115129dB*0.01*50

that makes sense, I'm really confused as to why I'm only learning that is what R is now and why I've never seen that written anywhere before.

So conductance is RC/L.

Thanks, you really cleared that up!

You're on top of it now!