Lossless transmission line characteristic phase constant

In summary, a lossless transmission line has an inductance of 9.0 nH/m and a capacitance of 3.6 pF/m. The characteristic impedance of the line can be found using the formula Z0 = sqrt(R+j2piL/G+2jpiC), where R and G are both equal to 0 for a lossless transmission line. For part (b), the phase constant can be calculated using a simple formula relating the radian frequency, inductance per unit length, and capacitance per unit length.
  • #1
bergen89
12
0

Homework Statement



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.

Homework Equations



Equation of characteristic impedance of a transmission line:

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

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

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 don't 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?
 
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  • #2
bergen89 said:

Homework Statement



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.

Homework Equations



Equation of characteristic impedance of a transmission line:

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

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

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 don't 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?
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
rude man said:
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.
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 can't 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
bergen89 said:
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 can't find it. Also I have added what I done in the first task. Should I use the result from that? I got 50 ohm.
There are many places on the Internet where you can find that formula. No, that formula does not include the answer to part (a).
 

1. What is a lossless transmission line?

A lossless transmission line is a type of transmission line that has no resistance, capacitance, or inductance. This means that there is no loss of energy as the signal travels along the line.

2. What is the characteristic phase constant of a lossless transmission line?

The characteristic phase constant of a lossless transmission line is a measure of the rate at which the phase of the signal changes as it travels down the line. It is denoted by the symbol γ and is equal to the square root of the product of the line's inductance and capacitance per unit length (γ = √(L*C)).

3. How is the characteristic phase constant related to the propagation constant?

The propagation constant, denoted by the symbol α, is a measure of the rate at which the amplitude of the signal decays as it travels down the line. It is related to the characteristic phase constant by the equation α = γ * j, where j is the imaginary unit. This relationship holds true for lossless transmission lines.

4. What are the units of the characteristic phase constant?

The characteristic phase constant has units of radians per meter (rad/m) or neper per meter (Np/m). These units represent the change in phase per unit length along the transmission line.

5. How does the characteristic phase constant affect the behavior of a lossless transmission line?

The characteristic phase constant plays a significant role in determining the behavior of a lossless transmission line. It affects the phase and amplitude of the signal as it travels along the line, and also determines the input impedance of the line. Additionally, the characteristic phase constant is used in calculations for determining the reflection coefficient and standing wave ratio of the line.

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