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A uniform plane EM wave incident normally on a plane surface of a dielectric material is reflected with a VSWR of 3. What percentage of incident power that is reflected?
- a)10%
- b)25%
- c)50%
- d)75%
Correct answer is option 'B'. Can you explain this answer?
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Reflection Coefficient and VSWR
When an electromagnetic (EM) wave is incident normally on a dielectric material, a portion of the wave is reflected back. The reflection coefficient (Γ) represents the ratio of the amplitude of the reflected wave to the amplitude of the incident wave.
The Voltage Standing Wave Ratio (VSWR) is a measure of the amount of reflected power on a transmission line. It is given by the equation:
VSWR = (1 + |Γ|) / (1 - |Γ|)
where |Γ| is the magnitude of the reflection coefficient.
Given Information
In this case, the VSWR is given as 3. We need to find the percentage of the incident power that is reflected.
Calculating the Reflection Coefficient
We can rearrange the VSWR equation to solve for |Γ|:
|Γ| = (VSWR - 1) / (VSWR + 1)
Substituting the given VSWR value of 3 into the equation, we get:
|Γ| = (3 - 1) / (3 + 1)
|Γ| = 2 / 4
|Γ| = 0.5
Calculating the Percentage of Reflected Power
The percentage of reflected power can be calculated using the reflection coefficient. The power reflection coefficient (Γ^2) represents the ratio of the reflected power to the incident power.
Γ^2 = |Γ|^2 = 0.5^2 = 0.25
To find the percentage, we multiply the power reflection coefficient by 100:
Percentage of Reflected Power = 0.25 * 100 = 25%
Therefore, 25% of the incident power is reflected.
Conclusion
When a uniform plane EM wave is incident normally on a plane surface of a dielectric material and is reflected with a VSWR of 3, 25% of the incident power is reflected.
When an electromagnetic (EM) wave is incident normally on a dielectric material, a portion of the wave is reflected back. The reflection coefficient (Γ) represents the ratio of the amplitude of the reflected wave to the amplitude of the incident wave.
The Voltage Standing Wave Ratio (VSWR) is a measure of the amount of reflected power on a transmission line. It is given by the equation:
VSWR = (1 + |Γ|) / (1 - |Γ|)
where |Γ| is the magnitude of the reflection coefficient.
Given Information
In this case, the VSWR is given as 3. We need to find the percentage of the incident power that is reflected.
Calculating the Reflection Coefficient
We can rearrange the VSWR equation to solve for |Γ|:
|Γ| = (VSWR - 1) / (VSWR + 1)
Substituting the given VSWR value of 3 into the equation, we get:
|Γ| = (3 - 1) / (3 + 1)
|Γ| = 2 / 4
|Γ| = 0.5
Calculating the Percentage of Reflected Power
The percentage of reflected power can be calculated using the reflection coefficient. The power reflection coefficient (Γ^2) represents the ratio of the reflected power to the incident power.
Γ^2 = |Γ|^2 = 0.5^2 = 0.25
To find the percentage, we multiply the power reflection coefficient by 100:
Percentage of Reflected Power = 0.25 * 100 = 25%
Therefore, 25% of the incident power is reflected.
Conclusion
When a uniform plane EM wave is incident normally on a plane surface of a dielectric material and is reflected with a VSWR of 3, 25% of the incident power is reflected.
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A uniform plane EM wave incident normally on a plane surface of a dielectric material is reflected with a VSWR of 3. What percentage of incident power that is reflected?a)10%b)25%c)50%d)75%Correct answer is option 'B'. Can you explain this answer?
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