Question

[GATE E.C.E., 2011] 552. A \( 10 GHz \) plane wave travelling in free space has amplitude of \( 15 V / m \). The propagation coefficient \( \beta \) is (a) \( 209.4 rad / m \) (b) \( 173.6 rad / m \) (c) \( 543.5 rad / m \) (d) \( 3.97 \times 10^{-2} rad / m \)

Answer 1

A propagation constant is a measure of changes in a sinusoidal electromagnetic wave in terms of amplitude and phase while propagating through a medium. This can be a transmission line or free space.

Propagation constant (γ) = α + jβ

α = Attenuation constant. It causes the signal amplitude to decrease while propagating through a transmission line.

β = Phase constant. It is the imaginary component of the propagation constant. It gives us the phase of the signal along a transmission line, at a constant time.

Mathematically, β is defined as:

Calculation:

Frequency (f) = 10 GHz

Propagation coefficient (β) will be:

β = 209.4 rad/m