Rectangular Waveguide Questions and Answers

Answer.3. Non-existent mode

Explanation:

TM₀₁ mode in the rectangular perfect metallic waveguide is a Non-existent mode. The condition where m = 0 or n = 0 is excluded as the field intensities all vanish and hence no TM₀₁, or TM₁₀ mode exists in a rectangular waveguide.

Answer.3. TEmn and TMmn (both m ≠ 0, n ≠ 0)

Explanation:

Degenerate Mode: Two or more modes having the same cut-off frequency are said to be degenerate modes, e.g. the corresponding TE_mn and TM_mn modes in the rectangular waveguide are always degenerate.

In a rectangular waveguide, TEmn and TMmn modes are always degenerate.

The above cutoff frequency is the same for both TE and TM waves.

For TE waves, E_z = 0 and TM waves have H_z = 0.

Answer.3. Low-loss dielectric substrate

Explanation:

A microstrip line consists of a single ground plane and a thin strip conductor on a low-loss dielectric substrate above the ground plate. Since the size of the microwave solid-state devices is very small (of the order 0.008 — 0.08 mm³), the technique of signal input to these devices and extracting output power from them uses microstrip lines on the surface on which they can be easily mounted.

Answer.1. Is greater than in free space

Explanation:

In the regime of loss-free wave propagation in the waveguide, the wavelength is always larger than the wavelength in free space. This means that the phase velocity of the wave within the waveguide is greater than the speed of light.

The wavelength in a waveguide is considered as a wavelength in the direction of wave propagation and its dependence on wave frequency is defined as follows:

${\lambda _x} = \frac{{{\lambda _0}}}{{\sqrt {1 – {{\left( {\frac{{{\lambda _0}}}{{{\lambda _c}}}} \right)}^2}} }}$

Where λ₀ is a wavelength in free space at a given frequency and λ_c stands for the cutoff wavelength for given waveguide dimensions and waveguide mode.

The wavelength of a wave in a waveguide is greater than in free space. The phase velocity is greater than the speed of light.

Answer.1. The TM10 mode of the waveguide does not exist

Explanation:

For a TE_mn mode to exist, We need to have m,n = 0,1,2,……

but does not exist for m = n = 0. For all other combinations, TE_mn exists.

For a TM_mn mode to exist, We need to have m,n = 1,2,3, ……. i.e m & n both must be non-zero

⇒ TM₀₁, TM₁₀ modes do not exist. The condition where m = 0 or n = 0 is excluded as the field intensities all vanish and hence no TM01 , or TM10 mode exists in a rectangular waveguide.

Answer.3. The group velocity

Explanation:

Group Velocity: The group velocity of a wave is the velocity with which the overall envelope shape of the wave’s amplitudes propagates through space.

Answer.4. 2 cm

Explanation:

The cutoff frequency of TE₁₁ mode in the rectangular waveguide is given as:

$\begin{array}{l} {f_{c\left( {11} \right)}} = \frac{c}{{2\pi }}\sqrt {{{\left( {\frac{\pi }{a}} \right)}^2} + {{\left( {\frac{\pi }{n}} \right)}^2}} \\ \\ = \frac{c}{2}\sqrt {{{\left( {\frac{1}{a}} \right)}^2} + {{\left( {\frac{1}{b}} \right)}^2}} \: \end{array}$

Given:

${f_c}\left( {T{E_{11}}} \right) = \frac{{{f_c}\left( {T{E_{10}}} \right) + {f_c}\left( {T{E_{20}}} \right)}}{2}$

$\begin{array}{l} \frac{c}{2}\sqrt {{{\left( {\frac{1}{a}} \right)}^2} + {{\left( {\frac{1}{b}} \right)}^2}} = \frac{{\frac{c}{{2a}} + \frac{c}{a}}}{2}\\ \\ \sqrt {{{\left( {\frac{1}{a}} \right)}^2} + {{\left( {\frac{1}{b}} \right)}^2}} = \frac{1}{{2a}} + \frac{1}{a} = \frac{3}{{2a}}\\ \\ {\left( {\frac{1}{a}} \right)^2} + {\left( {\frac{1}{b}} \right)^2} = \frac{9}{{4{a^2}}} \end{array}$

a = √5

$\begin{array}{l} {\left( {\frac{1}{b}} \right)^2} = \frac{5}{{4{a^2}}}\\ \\ b = \frac{{2a}}{{\sqrt 5 }} \end{array}$

b = 2 cm

Answer.1. Zero

Explanation:

• The cutoff frequency of TEM wave is zero.
• All electromagnetic waves consist of electric and magnetic fields propagating in the same direction of travel, but perpendicular to each other.
• Along the length of a normal transmission line, both electric and magnetic fields are perpendicular (transverse) to the direction of wave travel. This is known as the principal mode, or TEM (Transverse Electric and Magnetic) mode.
• This mode of wave propagation can exist only where there are two conductors, and it is the dominant mode of wave propagation where the cross-sectional dimensions of the transmission line are small compared to the wavelength of the signal.