A lossless transmission line with characteristic impedance of 600ohms is terminated in a purely resistive load of 900ohms. The reflection coefficient is?

Question

Answer

Calculation of Reflection Coefficient

Step 1: Calculate the mismatch loss

The mismatch loss (Lm) is given by Lm = (VSWR^2 - 1)/(VSWR^2 +1), where VSWR is the voltage standing wave ratio. Here, the load impedance (ZL) is greater than the characteristic impedance (Z0) of the transmission line, so the VSWR is given by VSWR = (ZL/Z0) = 1.5. Therefore, Lm = 0.111 or 11.1%.

Step 2: Calculate the reflection coefficient

The reflection coefficient (Γ) is given by Γ = (1 - e^-2Lm)/(1 + e^-2Lm) = 0.364 or 0.36 (rounded to two decimal places).

Explanation

When a transmission line is terminated in a load impedance that is different from its characteristic impedance, some of the incident power is reflected back towards the source. The amount of reflection depends on the magnitude and phase of the reflection coefficient. A reflection coefficient of 0 indicates that there is no reflection, while a reflection coefficient of 1 indicates that all of the incident power is reflected back towards the source. On the other hand, a reflection coefficient of -1 indicates that the reflected wave has the same magnitude as the incident wave but is 180 degrees out of phase, resulting in complete cancellation of the incident wave.

In this case, the load impedance is greater than the characteristic impedance of the transmission line, which results in a VSWR of 1.5 and a mismatch loss of 11.1%. The reflection coefficient is calculated to be 0.364 or 0.36, which indicates that some of the incident power is reflected back towards the source, but not all of it. The magnitude and phase of the reflection coefficient can be used to calculate the voltage and current standing waves on the transmission line, which can be used to determine the power loss and efficiency of the system.

Answer

1.5

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