How do you relay EM wave parameters to Transmission line parameters?

In summary: So the equation linking the L,C of unit length to \epsilon and \mu is just the physics expressions for the propagation constant?Yes, that is correct. Thanks, I think I got it. So the equation linking the L,C of unit length to \epsilon and \mu is just the physics expressions for the propagation constant?Yes, that is correct.
  • #1
yungman
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I am studying EM wave and transmission lines. I see both derive equations for propagation constant [tex]\gamma[/tex]:

Plane wave velocity is 1/[tex]\sqrt{\mu\epsilon}[/tex] and [tex]\eta[/tex] = [tex]\sqrt{\mu/\epsilon}[/tex]

Transmission line velocity is 1/[tex]\sqrt{LC}[/tex] and Z0=[tex]\sqrt{L/C}[/tex].

From that the book just to say the velocity of both are the same and [tex]\mu[/tex] [tex]\epsilon[/tex] = LC

I see they both are propagation constant, but I don't see they are the same! Can anyone explain to me how they relate together?

Thanks
 
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  • #2
The first pair of equations is the physics representation, using the permeability of the medium per unit length and the permitivity per unit length. The latter two equations are the engineering equivalents, for example in a coaxial transmission line, where L and C are the inductance per unit length and capacitance per unit length. As an exercise, calculate L and C for RG-8 cable, with the velocity of propagation equal to about 2/3 the velocity of light, and Z = 50 ohms (impedance of free space = 377 ohms).
 
  • #3
Bob S said:
The first pair of equations is the physics representation, using the permeability of the medium per unit length and the permitivity per unit length. The latter two equations are the engineering equivalents, for example in a coaxial transmission line, where L and C are the inductance per unit length and capacitance per unit length. As an exercise, calculate L and C for RG-8 cable, with the velocity of propagation equal to about 2/3 the velocity of light, and Z = 50 ohms (impedance of free space = 377 ohms).

Thanks for the reply.

I know the result is true, I am not question the validity of the equation, just I cannot find the physics to link the two. I can derive the formulas of the transmission line and plane wave and arrive the equations in the book. Just that the book simply claim the two propagation constants are the same...WHY? What is the equation linking L,C of unit length to [tex]\epsilon[/tex] and [tex]\mu[/tex]?

Can you point me to material that link the two? Not just the Helmholtz's equation or the general wave equations that give the propagation constant.
 
  • #4
yungman said:
I know the result is true, I am not question the validity of the equation, just I cannot find the physics to link the two. I can derive the formulas of the transmission line and plane wave and arrive the equations in the book. Just that the book simply claim the two propagation constants are the same...WHY? What is the equation linking L,C of unit length to [tex]\epsilon[/tex] and [tex]\mu[/tex]?

Take your derivations for L and C per unit length, form the ratios and products as per the expressions for the propagation velocity and impedance, and cancel out all the 2 pi's etc. You should get the physics expressions.
 
  • #5
Bob S said:
Take your derivations for L and C per unit length, form the ratios and products as per the expressions for the propagation velocity and impedance, and cancel out all the 2 pi's etc. You should get the physics expressions.

Thanks, I think I got it.
 

1. How are EM wave parameters related to transmission line parameters?

The relationship between EM wave parameters and transmission line parameters is established through Maxwell's equations. These equations describe the propagation of electromagnetic waves through a medium, and they can be used to derive the parameters of a transmission line, such as impedance, propagation constant, and characteristic impedance.

2. What are the key EM wave parameters that need to be considered when analyzing transmission lines?

The main EM wave parameters that are important for analyzing transmission lines are frequency, wavelength, and phase velocity. These parameters determine the behavior of the wave on the transmission line, such as how it travels and reflects along the line.

3. How do you convert EM wave frequency to transmission line frequency?

To convert EM wave frequency to transmission line frequency, the relationship between wavelength and frequency must be taken into account. The transmission line frequency is equal to the EM wave frequency divided by the velocity factor of the transmission line, which is determined by the type of material the line is made of.

4. What is the role of characteristic impedance in the transmission line parameters?

Characteristic impedance is a crucial parameter in transmission line analysis as it represents the ratio of voltage to current along the line. It determines the amount of power that can be transferred along the line and is also used in matching the impedance between different parts of a circuit to minimize signal reflection.

5. How do you calculate the propagation constant of a transmission line from EM wave parameters?

The propagation constant of a transmission line can be calculated by taking the square root of the product of the line's inductance and capacitance per unit length. These parameters can be derived from the EM wave parameters, such as the velocity of propagation and characteristic impedance, which can be calculated from frequency and wavelength.

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