Question

During wave propagation in an air-filled rectangular waveguide:

1) Wave impedance is never less than the free-space impedance

2) Propagation constant is an imaginary number

3) TEM mode is possible if the dimensions of the waveguide are properly chosen

Which of the above are correct?

1. 1 and 2 only
2. 1 and 3 only
3. 2 and 3 only
4. 1, 2, and 3

Answer 1

Correct Answer - Option 1 : 1 and 2 only

In an air-filled Rectangular waveguide, during the wave propagation, the wave impedance for TE mode is given by:

\({\eta _{TE}} = \frac{{{\eta _0}}}{{\sqrt {1 - {{\left( {\frac{{{f_c}}}{f}} \right)}^2}} }}\)

And for TM mode, the wave impedance is given by:

\({\eta _{TE}} = {\eta _0}\sqrt {1 - \left( {{f_c}/f} \right)} \)

For wave propagation in a waveguide:

f > f­c­ so η_TE > η₀ and η_TM < η₀

So statement (1) will correct when we consider TE mode and statement (1) will incorrect when we consider TM mode.

Propagation Constant (γ):

γ = ∝ + jβ

α = attenuation constant

β = Phase constant

if α = 0: then γ = jβ i.e. purely imaginary quantity, and in this case, the wave will not attenuate during the propagation

If β = 0: then γ= α i.e. purely Real Quantity and in this case, the wave will be attenuate and not propagate inside the waveguide.

If ∝ ≠ 0 and β ≠ 0, then some part of the wave will attenuate during propagation.

So, statement (2) is correct.

TEM Mode: Transverse electric magnetic mode is not possible in the rectangular waveguide for any dimensions, because no component of the Electric field and magnetic field exists inside the waveguide. (i.e E_z = 0 and H_z = 0)

So Statement (3) is incorrect.

Hence, if we are considering the TE mode of propagation, then option (a) will be the correct answer.

And if we are considering TM mode Propagation, then no option will be correct for this question.