A lossless transmission line is terminated in a load which reflects a part of the incident power. If VSWR is 2, the reflection coefficient will be : 

Explanation:

Lossless Transmission Line and VSWR:

Definition: A lossless transmission line is a theoretical transmission line in which there is no dissipation of electrical energy as heat. This means that the conductors and the dielectric material between them are perfect, resulting in no energy loss as the signal propagates along the line.

VSWR (Voltage Standing Wave Ratio) is a measure of how efficiently RF power is transmitted from the power source, through a transmission line, into the load. It is defined as the ratio of the maximum voltage to the minimum voltage in a standing wave pattern along the transmission line.

The VSWR is given by:

VSWR = (1 + |Γ|) / (1 - |Γ|)

Where |Γ| is the magnitude of the reflection coefficient.

The reflection coefficient (Γ) represents the fraction of the incident power that is reflected back from the load. It is a measure of the impedance mismatch between the transmission line and the load.

Calculation of Reflection Coefficient:

Given that the VSWR is 2, we can use the VSWR formula to find the reflection coefficient.

VSWR = (1 + |Γ|) / (1 - |Γ|)

Substitute VSWR = 2 into the formula:

2 = (1 + |Γ|) / (1 - |Γ|)

To find |Γ|, we solve the equation step-by-step:

Step 1: Cross-multiply to eliminate the fraction:

2 * (1 - |Γ|) = 1 + |Γ|

Step 2: Distribute the 2 on the left-hand side:

2 - 2|Γ| = 1 + |Γ|

Step 3: Combine like terms to isolate |Γ|:

2 - 1 = 2|Γ| + |Γ|

1 = 3|Γ|

Step 4: Solve for |Γ|:

|Γ| = 1 / 3

Therefore, the reflection coefficient (|Γ|) is 1/3.

Correct Option Analysis:

The correct option is:

Option 1: 1/3

This option correctly represents the calculated value of the reflection coefficient when the VSWR is 2.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: 3/4

This option is incorrect. If we use 3/4 in the VSWR formula, we would get:

VSWR = (1 + 3/4) / (1 - 3/4) = 7 / 1 = 7

This does not match the given VSWR of 2.

Option 3: Thu Jan 02 2025 00:00:00 GMT+0530 (India Standard Time)

This option is clearly irrelevant to the calculation of the reflection coefficient.

Option 4: Mon Feb 03 2025 00:00:00 GMT+0530 (India Standard Time)

Similar to option 3, this option is irrelevant to the calculation of the reflection coefficient.

Conclusion:

Understanding the relationship between VSWR and the reflection coefficient is crucial for analyzing transmission line performance. The reflection coefficient (|Γ|) provides valuable insight into the impedance matching of the transmission line and the load. In this case, with a VSWR of 2, the reflection coefficient is accurately calculated to be 1/3, confirming that option 1 is correct.