Question

A lossless transmission line of 2.5 m length is driven by a 100 V, 400 MHz sinusoidal with no phase offset; the line has L = 0.25 μH/m, C = 100pF/m. The line is connected to loads of 0, 25, 50, 100 and an open-circuit load.

For each of these determine:
the reflection coefficient at the load;

Answer 1

To determine the reflection coefficient at the load for a lossless transmission line driven by a sinusoidal source, use the formula \(\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}\), where \(Z_L\) is the load impedance and \(Z_0\) is the characteristic impedance. Substitute different load values to find the reflection coefficients.

Step-by-step explanation:

The reflection coefficient at the load can be determined using the formula:

\(\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}\)

Where:

\(\Gamma\) is the reflection coefficient,

\(Z_L\) is the load impedance, and

\(Z_0\) is the characteristic impedance of the transmission line.

To calculate the reflection coefficients for the different loads:

1. For the 0 Ω load, \(Z_L = 0\) Ω. Substitute the values in the formula to find \(\Gamma\).
2. For the 25 Ω load, \(Z_L = 25\) Ω. Substitute the values in the formula to find \(\Gamma\).
3. For the 50 Ω load, \(Z_L = 50\) Ω. Substitute the values in the formula to find \(\Gamma\).
4. For the 100 Ω load, \(Z_L = 100\) Ω. Substitute the values in the formula to find \(\Gamma\).
5. For the open-circuit load, \(Z_L = \infty\) Ω. Substitute the values in the formula to find \(\Gamma\).

By calculating the above expressions, we can find the reflection coefficients at the different loads. Note that \(\Gamma\) is a complex number representing the magnitude and phase of the reflection.