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A transmission line is lossless and is 25 m long. It is terminated with a load of zL =40+j30Ω at a frequency of 10 MHz. The inductance and capacitance of the line are L - 300nH/m, C = 40pF/m.
Q.
Find the input impedance at the mid-point of the line.
  • a)
    47.175 +jO.768 Ω   
  • b)
    47.175 - j0.768 Ω
  • c)
    0.768 + j 47.175Ω   
  • d)
    0.768 -j 47.175Ω
Correct answer is option 'B'. Can you explain this answer?
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A transmission line is lossless and is 25 m long. It is terminated wit...
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A transmission line is lossless and is 25 m long. It is terminated wit...
Given:
Length of the transmission line (l) = 25 m
Load impedance (ZL) = 40 j30 ohm
Frequency (f) = 10 MHz
Inductance (L) = 300 nH/m
Capacitance (C) = 40 pF/m

To find: Input impedance at the mid-point of the line

Solution:

Step 1: Calculation of wavelength (λ)
λ = c/f
where c is the speed of light = 3 x 10^8 m/s
λ = 30 m

Step 2: Calculation of electrical length (βl)
β = 2π/λ
β = 0.2094 rad/m
βl = β x l/2
βl = 2.61 rad

Step 3: Calculation of characteristic impedance (Z0)
Z0 = √(L/C)
Z0 = 300/40 = 7.5 ohm

Step 4: Calculation of reflection coefficient (Γ) at the load
Γ = (ZL - Z0)/(ZL + Z0)
Γ = (40 j30 - 7.5)/(40 j30 + 7.5)
Γ = 0.6677 - j0.4709

Step 5: Calculation of input impedance (Zin) at the mid-point of the line
Zin = Z0 [ZL + jZ0 tan(βl)]/[Z0 + jZL tan(βl)]
Zin = 7.5 [40 j30 + j7.5 tan(2.61)]/[7.5 + j40 j30 tan(2.61)]
Zin = 47.175 - j0.768 ohm

Therefore, the correct answer is option 'B' (47.175 - j0.768 ohm)
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A transmission line is lossless and is 25 m long. It is terminated with a load of zL =40+j30Ωat a frequency of 10 MHz. The inductance and capacitance of the line are L - 300nH/m, C = 40pF/m.Q.Find the input impedance at the mid-point of the line.a)47.175 +jO.768 Ω b)47.175 - j0.768 Ωc)0.768 + j 47.175Ω d)0.768 -j 47.175ΩCorrect answer is option 'B'. Can you explain this answer?
Question Description
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