Find the attenuation constant (write exact ansuwer upto 3 decimal places) for a lossy transmission line which has resistance per unit length = 0.05 Ohm/m. The line is distortionless and has a characteristic impedance of 50Ohm.
Question
Find the attenuation constant (write exact ansuwer upto 3 decimal places) for a lossy transmission line which has resistance per unit length = 0.05 Ohm/m. The line is distortionless and has a characteristic impedance of 50Ohm.
Solution
To find the attenuation constant for a lossy transmission line, we can use the formula:
Attenuation constant (α) = √(Resistance per unit length * Conductance per unit length)
Given that the resistance per unit length is 0.05 Ohm/m, we need to find the conductance per unit length.
The conductance per unit length (G) can be calculated using the formula:
G = 1 / Characteristic impedance
Given that the characteristic impedance is 50 Ohm, we can substitute this value into the formula to find the conductance per unit length:
G = 1 / 50 Ohm
G = 0.02 S/m
Now, we can substitute the values of resistance per unit length and conductance per unit length into the formula for the attenuation constant:
α = √(0.05 Ohm/m * 0.02 S/m)
α = √(0.001 Ohm-Siemens/m)
Calculating the square root, we find:
α ≈ 0.031
Therefore, the attenuation constant for the given lossy transmission line is approximately 0.031 (up to 3 decimal places).
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