A load of 3 + j4Ω is connected to a 1Ω lossless line. The magnitude of reflection coefficient at the load will be :

Explanation:

To find the magnitude of the reflection coefficient (Γ) at the load, we need to use the formula:

|Γ| = |(Z_L - Z₀) / (Z_L + Z₀)|

Where Z_L is the load impedance and Z₀ is the characteristic impedance of the lossless transmission line. Given:

• Z_L = 3 + j4Ω
• Z₀ = 1Ω

Step-by-Step Solution:

1. Calculate the numerator (Z_L - Z₀):

Z_L - Z₀ = (3 + j4) - 1 = 2 + j4

2. Calculate the denominator (Z_L + Z₀):

Z_L + Z₀ = (3 + j4) + 1 = 4 + j4

3. Find the magnitude of the numerator and the denominator:

|Z_L - Z₀| = |2 + j4| = √(2² + 4²) = √(4 + 16) = √20 = 2√5

|Z_L + Z₀| = |4 + j4| = √(4² + 4²) = √(16 + 16) = √32 = 4√2

4. Calculate the magnitude of the reflection coefficient:

|Γ| = |(Z_L - Z₀) / (Z_L + Z₀)| = |(2 + j4) / (4 + j4)| = (2√5) / (4√2) = (2√5) / (2√2 * 2) = √5 / (2√2) = (√5 / √2) / 2 = √(5/2) / 2

By simplifying √(5/2):

√(5/2) ≈ 1.58

Therefore:

|Γ| ≈ 1.58 / 2 ≈ 0.79

Hence, the magnitude of the reflection coefficient at the load is approximately 0.79. Therefore, the correct answer is Option 2.