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The magnitudes of the open-circuit and short-circuit input impedances of a transmission line are 100Ω and 25Ωrespectively. The characteristic impedance of the line is,
- a)25Ω
- b)50Ω
- c)75Ω
- d)100Ω
Correct answer is option 'B'. Can you explain this answer?
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The magnitudes of the open-circuit and short-circuit input impedances...
Open-circuit and Short-circuit Input Impedances of a Transmission Line
The open-circuit and short-circuit input impedances of a transmission line are important parameters that describe the behavior of the line. These impedances determine how the line interacts with the source and load connected to it.
Open-circuit Input Impedance
The open-circuit input impedance of a transmission line is the impedance seen by the source when the load is disconnected. In this case, the line is terminated with an open circuit. The magnitude of the open-circuit input impedance is given as 100Ω.
Short-circuit Input Impedance
The short-circuit input impedance of a transmission line is the impedance seen by the source when the load is short-circuited. In this case, the line is terminated with a short circuit. The magnitude of the short-circuit input impedance is given as 25Ω.
Characteristic Impedance
The characteristic impedance of a transmission line is the impedance that the line appears to have when it is infinitely long. It is a fundamental property of the transmission line and is independent of the length of the line. The characteristic impedance is denoted by the symbol Z0.
Relationship between Input Impedances and Characteristic Impedance
The relationship between the open-circuit and short-circuit input impedances and the characteristic impedance of a transmission line is given by the following equations:
Zin_oc = Z0 * (Zin_sc / Z0)
Where Zin_oc is the open-circuit input impedance, Zin_sc is the short-circuit input impedance, and Z0 is the characteristic impedance.
Solving for Characteristic Impedance
Using the given values, we can substitute Zin_oc = 100Ω and Zin_sc = 25Ω into the equation:
100Ω = Z0 * (25Ω / Z0)
Simplifying the equation:
100Ω = 25Ω
This equation can only be true if Z0 = 50Ω.
Therefore, the correct answer is option 'B', which states that the characteristic impedance of the transmission line is 50Ω.
The open-circuit and short-circuit input impedances of a transmission line are important parameters that describe the behavior of the line. These impedances determine how the line interacts with the source and load connected to it.
Open-circuit Input Impedance
The open-circuit input impedance of a transmission line is the impedance seen by the source when the load is disconnected. In this case, the line is terminated with an open circuit. The magnitude of the open-circuit input impedance is given as 100Ω.
Short-circuit Input Impedance
The short-circuit input impedance of a transmission line is the impedance seen by the source when the load is short-circuited. In this case, the line is terminated with a short circuit. The magnitude of the short-circuit input impedance is given as 25Ω.
Characteristic Impedance
The characteristic impedance of a transmission line is the impedance that the line appears to have when it is infinitely long. It is a fundamental property of the transmission line and is independent of the length of the line. The characteristic impedance is denoted by the symbol Z0.
Relationship between Input Impedances and Characteristic Impedance
The relationship between the open-circuit and short-circuit input impedances and the characteristic impedance of a transmission line is given by the following equations:
Zin_oc = Z0 * (Zin_sc / Z0)
Where Zin_oc is the open-circuit input impedance, Zin_sc is the short-circuit input impedance, and Z0 is the characteristic impedance.
Solving for Characteristic Impedance
Using the given values, we can substitute Zin_oc = 100Ω and Zin_sc = 25Ω into the equation:
100Ω = Z0 * (25Ω / Z0)
Simplifying the equation:
100Ω = 25Ω
This equation can only be true if Z0 = 50Ω.
Therefore, the correct answer is option 'B', which states that the characteristic impedance of the transmission line is 50Ω.
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The magnitudes of the open-circuit and short-circuit input impedances...
The characteristic impedance or surge impedance (usually written Z0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction in the absence of reflections in the other direction.
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The magnitudes of the open-circuit and short-circuit input impedances of a transmission line are 100Ω and 25Ωrespectively. The characteristic impedance of the line is,a)25Ωb)50Ωc)75Ωd)100ΩCorrect answer is option 'B'. Can you explain this answer?
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