(a) A transmission line has a length, ℓ, of 0.4λ. Determine the phase change, βℓ, that occurs down the line.
(b) A 50Ω lossless transmission line of length 0.4λ is terminated in a load of (40 + j30) Ω. Determine, using the equation given below, the input impedance to the line.
[see attachment for equation]
The Attempt at a Solution
(a) β = ω / fλ
∴ βℓ = ω 0.4λ / fλ
= ω 0.4 / f
= 0.4x2π f / f
= 0.8π (=2.513 to 3d.p.)
(b) Zin = 50 x [ (40cos0.8π) / ( 50cos0.8π + 30sin0.8π) ]
= 70.91 ohms
Do these answers look correct? Seems worryingly straightforward.