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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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The propagation constant of a transmission line is 0.15×10–³ + j1.5×10–³. The wavelength of the traveling wave is
2π15×10−3
1.5×10−32π
π15×10−3
15×10−3π
1.5×10−32π
The propagation constant γ of a transmission line is given by γ=α+jβ, where α is the attenuation constant and β is the phase constant. The wavelength λ is related to the phase constant β by the formula λ=β2π.
The propagation constant γ of a transmission line is given by γ=α+jβ, where α is the attenuation constant and β is the phase constant. The wavelength λ is related to the phase constant β by the formula λ=β2π.
γ=α+jβ — Propagation constant
λ=β2π — Wavelength definition
In a transmission line, the wave travels with a phase shift defined by β (radians per unit length). Since a full cycle corresponds to 2π radians of phase change, the distance traversed in one cycle is the wavelength λ=β2π. Here, the imaginary part of the propagation constant is β=1.5×10−3.
The propagation constant is complex: γ=α+jβ.
Real part α represents attenuation in Np/m.
Imaginary part β represents phase shift in rad/m.
Wavelength is the distance over which the phase shifts by 2π radians.
Allows calculation of physical distance between voltage maxima.
Essential for impedance matching and stub design.
Assumes a linear, time-invariant transmission line model.
Applicable only for sinusoidal steady-state analysis.
RF transmission line design.
Power system traveling wave fault location.
Given γ=0.15×10−3+j1.5×10−3.
Therefore, β=1.5×10−3 rad/m.
Calculating: λ=1.5×10−32π.
B is correct — The wavelength is calculated as β2π, where β is the imaginary part of the propagation constant, resulting in 1.5×10−32π.
Always ensure you distinguish between α (real part) and β (imaginary part) of the propagation constant to avoid errors in wavelength or velocity calculations.