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A terminated transmission line with z0 = 60 Ω has a reflection coefficient at the load of γ = 0.4∠60°. (a) What is the load impedance? (b) What is the reflection coefficient 0.3λ away from the load? (c) What is the input impedance at this point?

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Final answer:

A terminated transmission line with a reflection coefficient at the load of γ = 0.4∠60° has a load impedance of Zload, a reflection coefficient 0.3λ away from the load (γ'), and an input impedance at this point (Zin).

Step-by-step explanation:

(a) To find the load impedance of a terminated transmission line with a reflection coefficient at the load, we can use the formula:

Zload = z0 * (1 + γ) / (1 - γ)

Substituting the given values:

Zload = 60Ω * (1 + 0.4∠60°) / (1 - 0.4∠60°) = 60Ω * (0.6 + 0.961∠60°) / (0.6 - 0.961∠60°)

Simplifying this expression will give us the load impedance.

(b) To find the reflection coefficient 0.3λ away from the load, we need to use the equation for the reflection coefficient:

γ' = (γ * e^(-2jβd)) / (1 + γ * (e^(-2jβd)))

Here, γ is the reflection coefficient at the load, β is the propagation constant, and d is the distance from the load. Substituting the given values, we can calculate the new reflection coefficient.

(c) To find the input impedance at this point, we can use the formula:

Zin = z0 * (1 + γ') / (1 - γ')

Substituting the values calculated in part (b), we can find the input impedance.

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