# How do I calculate the length of a transmission line?

A quick translation:

Generator has $Z_g = 50\Omega$ and 12 V. The line is loaded with an unknown RL. We observe we have a maximum of 8 V at 250 MHz and a minimum at 500 MHz.

1. Solution: Asks for the dielectrical permitivity and the $Z_o$ of the line

$$Z_o = \sqrt{L/C} = 50\Omega$$

and for the dielectrical permitivity of the dielectric it is

$$Z_o = \sqrt{\frac{\epsilon_o \epsilon_r}{\mu_o \mu_r}}$$

$$Z_o = 120\pi \cdot \sqrt{1/3}$$

from there we get the dielectrical permitivity.

2. This asks for the line length which is my initial question. Is wavelength same as the line length or am I wrong?

$$\lambda = \frac{v}{f} = 0.159 m$$

Thanks and sorry for my lack of English in Electrical Engineering subject.

• Perhaps you meant length? Jan 17, 2018 at 19:43
• yeah, i did mean that. Jan 17, 2018 at 19:52
• If 500MHz is 3/4λ and 250MHz is 1/2λ what is length? Jan 17, 2018 at 19:53
• My question: Calculating Lambda that way i did, the result is also the electrical length of the transmission line?. I mean, the line has a length of 0.159 meters? Jan 17, 2018 at 19:55

Signal Velocity = $v_s=\dfrac {c}{\sqrt{\epsilon _r}}$
$\lambda=\dfrac{v_s}{f}$