Final answer:
The input return loss of a transmission line with a complex load can be calculated using the reflection coefficient. The formula for calculating the reflection coefficient involves the normalized admittance of the transmission line and the complex admittance of the load.
Step-by-step explanation:
The input return loss of a transmission line with a complex load can be calculated using the formula:
RLᵢₙ = 20 log10(|Γᵢₙ|)
where Γᵢₙ is the reflection coefficient. The reflection coefficient is given by:
Γᵢₙ = (Y₁ - YL) / (Y₁ + YL)
where Y₁ is the normalized admittance of the transmission line and YL is the complex admittance of the load. In this case, Y₁ is 1 / Z₀, where Z₀ is the characteristic impedance of the transmission line.
Substituting the given values, we have:
Z₀ = 50Ω
YL = 0.01 + j0.01S
Y₁ = 1 / Z₀ = 1 / 50Ω
Γᵢₙ = (Y₁ - YL) / (Y₁ + YL) = (1/50Ω - (0.01 + j0.01S)) / (1/50Ω + (0.01 + j0.01S))
Using this value of Γᵢₙ, we can calculate the input return loss in dB using the formula mentioned earlier.