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When the load impedance is equal to the characteristic impedance of the transmission lines, then the reflection coefficient and standing wave ratio are, respectively _________.
- a)1 and 1
- b)0 and 0
- c)1 and 0
- d)0 and 1
- e)All of these
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
When the load impedance is equal to the characteristic impedance of th...
Reflection Coefficient and Standing Wave Ratio (SWR) when the Load Impedance is Equal to the Characteristic Impedance of the Transmission Lines:
Reflection Coefficient:
The reflection coefficient measures the amount of power reflected back from the load compared to the power incident on the load. It is denoted by the symbol Γ (gamma) and is a complex quantity.
When the load impedance is equal to the characteristic impedance of the transmission line, the reflection coefficient is zero. This means that there is no reflection of power from the load, and all the power is absorbed by the load. Mathematically, the reflection coefficient can be expressed as:
Γ = (ZL - Z0) / (ZL + Z0)
Where ZL is the load impedance and Z0 is the characteristic impedance of the transmission line.
If ZL = Z0, then the numerator of the above equation becomes zero, resulting in a reflection coefficient of zero.
Standing Wave Ratio (SWR):
The Standing Wave Ratio (SWR) is a measure of how well a load is matched to the characteristic impedance of the transmission line. It is defined as the ratio of the maximum voltage to the minimum voltage on the transmission line.
When the load impedance is equal to the characteristic impedance of the transmission line, the SWR is 1. This indicates a perfect match between the load and the transmission line. There are no reflections, and the voltage remains constant along the line.
Mathematically, SWR can be calculated as:
SWR = (1 + |Γ|) / (1 - |Γ|)
Where |Γ| is the magnitude of the reflection coefficient.
If the reflection coefficient is zero, i.e., |Γ| = 0, then the SWR becomes:
SWR = (1 + 0) / (1 - 0) = 1
Therefore, the SWR is 1 when the load impedance is equal to the characteristic impedance of the transmission line.
Conclusion:
When the load impedance is equal to the characteristic impedance of the transmission line, the reflection coefficient is zero, indicating no power reflection from the load. Additionally, the SWR is 1, indicating a perfect match between the load and the transmission line.
Reflection Coefficient:
The reflection coefficient measures the amount of power reflected back from the load compared to the power incident on the load. It is denoted by the symbol Γ (gamma) and is a complex quantity.
When the load impedance is equal to the characteristic impedance of the transmission line, the reflection coefficient is zero. This means that there is no reflection of power from the load, and all the power is absorbed by the load. Mathematically, the reflection coefficient can be expressed as:
Γ = (ZL - Z0) / (ZL + Z0)
Where ZL is the load impedance and Z0 is the characteristic impedance of the transmission line.
If ZL = Z0, then the numerator of the above equation becomes zero, resulting in a reflection coefficient of zero.
Standing Wave Ratio (SWR):
The Standing Wave Ratio (SWR) is a measure of how well a load is matched to the characteristic impedance of the transmission line. It is defined as the ratio of the maximum voltage to the minimum voltage on the transmission line.
When the load impedance is equal to the characteristic impedance of the transmission line, the SWR is 1. This indicates a perfect match between the load and the transmission line. There are no reflections, and the voltage remains constant along the line.
Mathematically, SWR can be calculated as:
SWR = (1 + |Γ|) / (1 - |Γ|)
Where |Γ| is the magnitude of the reflection coefficient.
If the reflection coefficient is zero, i.e., |Γ| = 0, then the SWR becomes:
SWR = (1 + 0) / (1 - 0) = 1
Therefore, the SWR is 1 when the load impedance is equal to the characteristic impedance of the transmission line.
Conclusion:
When the load impedance is equal to the characteristic impedance of the transmission line, the reflection coefficient is zero, indicating no power reflection from the load. Additionally, the SWR is 1, indicating a perfect match between the load and the transmission line.
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Community Answer
When the load impedance is equal to the characteristic impedance of th...
The voltage standing wave ratio is defined as the ratio of the maximum voltage (or current) to the minimum voltage (or current).
VSWR is also given by:
Γ = Reflection coefficient, defined as:
ZL = Load impedance
Z0 = Characteristic Impedance
For ΓL varying from 0 to 1, VSWR varies from 1 to ∞.
Application:
Given ZL = Z0
The reflection coefficient is calculated to be:
VSWR for Γ = 0 equals 1, which is the minimum value (because it varies from 1 to ∞)
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When the load impedance is equal to the characteristic impedance of the transmission lines, then the reflection coefficient and standing wave ratio are, respectively _________.a)1 and 1b)0 and 0c)1 and 0d)0 and 1e)All of theseCorrect answer is option 'D'. Can you explain this answer?
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