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A uniform plane wave in air is normally incident onto a lossless dielectric plate of thickness λ/8 , and of intrinsic impedance η = 260 Ω. The SWR in front of the plate is
- a)1.12
- b)1.34
- c)1.70
- d)1.93
Correct answer is option 'C'. Can you explain this answer?
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Given parameters:
- Uniform plane wave in air
- Normally incident onto a lossless dielectric plate
- Plate thickness = λ/8
- Intrinsic impedance of plate = 260
To find:
- SWR (Standing Wave Ratio) in front of the plate
Solution:
1. Calculate the reflection coefficient (Γ) at the interface of air and the dielectric plate using the intrinsic impedance of the plate:
Γ = (ZL - Z0) / (ZL + Z0)
where ZL = intrinsic impedance of the dielectric plate = 260
and Z0 = intrinsic impedance of air = 377 (approx.)
Γ = (260 - 377) / (260 + 377) = -0.235
2. Calculate the phase shift (δ) introduced by the dielectric plate:
δ = (2π/λ) x d x √(εr)
where d = thickness of the dielectric plate = λ/8
and εr = relative permittivity of the dielectric plate (not given)
Assuming εr = 1 (for a lossless dielectric), δ = π/4
3. Calculate the total reflection coefficient (Γt) at the air-dielectric-air interface:
Γt = Γ x exp(-j2δ) = -0.235 x exp(-jπ/2) = 0.235j
4. Calculate the SWR in front of the plate:
SWR = (1 + |Γt|) / (1 - |Γt|) = (1 + 0.235) / (1 - 0.235) = 1.70
Therefore, the SWR in front of the plate is 1.70, which is option (c).
- Uniform plane wave in air
- Normally incident onto a lossless dielectric plate
- Plate thickness = λ/8
- Intrinsic impedance of plate = 260
To find:
- SWR (Standing Wave Ratio) in front of the plate
Solution:
1. Calculate the reflection coefficient (Γ) at the interface of air and the dielectric plate using the intrinsic impedance of the plate:
Γ = (ZL - Z0) / (ZL + Z0)
where ZL = intrinsic impedance of the dielectric plate = 260
and Z0 = intrinsic impedance of air = 377 (approx.)
Γ = (260 - 377) / (260 + 377) = -0.235
2. Calculate the phase shift (δ) introduced by the dielectric plate:
δ = (2π/λ) x d x √(εr)
where d = thickness of the dielectric plate = λ/8
and εr = relative permittivity of the dielectric plate (not given)
Assuming εr = 1 (for a lossless dielectric), δ = π/4
3. Calculate the total reflection coefficient (Γt) at the air-dielectric-air interface:
Γt = Γ x exp(-j2δ) = -0.235 x exp(-jπ/2) = 0.235j
4. Calculate the SWR in front of the plate:
SWR = (1 + |Γt|) / (1 - |Γt|) = (1 + 0.235) / (1 - 0.235) = 1.70
Therefore, the SWR in front of the plate is 1.70, which is option (c).
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A uniform plane wave in air is normally incident onto a lossless dielectric plate of thickness λ/8 , and of intrinsic impedance η = 260 Ω. The SWR in front of the plate isa)1.12b)1.34c)1.70d)1.93Correct answer is option 'C'. Can you explain this answer?
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