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The input impedance of lossless λ/8 transmission line with other end short circuited is given by ______. (Assume characteristic impedance Zo = 50Ω)
- a)50∠90ºΩ
- b)50∠180ºΩ
- c)50∠180ºΩ
- d)Zero
Correct answer is option 'A'. Can you explain this answer?
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Calculation of Input Impedance of λ/8 Transmission Line with Short Circuit
To calculate the input impedance of a lossless λ/8 transmission line with one end short-circuited, we can use the following formula:
Zin = jZo * tan(βl)
Given parameters:
- Characteristic impedance Zo = 50Ω
- Length of transmission line l = λ/8 = π/4
Calculation:
- β = 2π/λ = 2π/(4λ) = π/2
- Zin = j*50 * tan(π/2)
- tan(π/2) is undefined, so Zin approaches infinity
Therefore, the input impedance of a lossless λ/8 transmission line with one end short-circuited is an open circuit, which can be represented as 50∠90ºΩ.
To calculate the input impedance of a lossless λ/8 transmission line with one end short-circuited, we can use the following formula:
Zin = jZo * tan(βl)
Given parameters:
- Characteristic impedance Zo = 50Ω
- Length of transmission line l = λ/8 = π/4
Calculation:
- β = 2π/λ = 2π/(4λ) = π/2
- Zin = j*50 * tan(π/2)
- tan(π/2) is undefined, so Zin approaches infinity
Therefore, the input impedance of a lossless λ/8 transmission line with one end short-circuited is an open circuit, which can be represented as 50∠90ºΩ.
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