Waveguides
Practice QuestionsMarks 1
1
Consider an air filled rectangular waveguide with a cross-section of $$5\,\,cm\,\, \times \,\,3\,cm$$. For this waveguide, the cut-off frequency (in MHz) of $$T{E_{21}}\,$$ mode is __________________
GATE ECE 2014 Set 3
2
The modes in a rectangular waveguide are denoted by $$T{E_{mn}}\,$$/$$T{M_{mn}}\,$$ where m and n are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of the following satements is TRUE?
GATE ECE 2011
3
Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?
GATE ECE 2009
4
The phase velocity of an electromagnetic wave propagating in a hollow metallic rectangular waveguide in the $$T{E_{10}}$$ mode is
GATE ECE 2004
5
The phase velocity for the $$T{E_{10}}$$ mode in an air-filled rectangular waveguide is
GATE ECE 2002
6
The phase velocity of waves propagating in a hollow metal waveguide is
GATE ECE 2001
7
The dominant mode in a rectangular waveguide is $$T{E_{10}}$$, because this mode has
GATE ECE 2001
8
Indicate which one of the following modes do NOT exist in a rectangular resonant cavity.
GATE ECE 1999
9
A rectangular air-filled waveguide has a cross section of $$4\,cm\,\, \times \,\,10cm$$. The minimum frequency which can propagate in the waveguide is
GATE ECE 1997
10
The interior of a $${{20} \over 3}\,\,cm\,\, \times \,\,{{20} \over 4}\,\,cm$$ rectangular waveguide is completely filled with a dielectric of $${ \in _r} = 4$$. Waves of free space wave-lengths shorter than .........can be propagated in the $$T{E_{11}}$$ mode.
GATE ECE 1994
Marks 2
1
A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10$$-$$4 cm, with air as the dielectric. Assume the speed of light in air to be 3 $$\times$$ 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/are ___________.
GATE ECE 2022
2
Standard air filled rectangular waveguides of dimensions a = 2.29cm and b = 1.02cm are designed for radar applications. It is desired that these waveguides operate only in the dominant $$T{E_{10}}$$ mode with the operating frequency at least 25% above the cut-off frequency of the $$T{E_{10}}$$ mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency f is
GATE ECE 2017 Set 2
3
Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. The increasing order of the cut-off frequencies for different modes is
GATE ECE 2016 Set 3
4
Consider an air-filled rectangular waveguide with dimensions a = 2.286cm and b = 1.016cm. At 10GHz operating frequency, the value of the propagation constant (per meter) of the corresponding propagation mode is _____________________
GATE ECE 2016 Set 3
5
An air-filled rectangular waveguide of internal dimension $$a\,\,cm\,\, \times \,\,b\,\,cm$$ (a > b) has a cutoff frequency of 6 GHz for the dominant $$T{E_{10}}$$ mode. For the same waveguide, if the cutoff frequency of the $$T{E_{11}}$$ mode is 15 GHz, the cutoff frequency of the $$T{E_{01}}$$ mode in GHz is _____________
GATE ECE 2015 Set 2
6
The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression $${H_z}(x,\,y,\,z,\,t) = \,0.1\,\cos \,(25\,\,\pi \,x)\,\cos \,(30.3\,\pi y)$$
$$\cos \,(12\,\pi \, \times \,{10^9}\,t\, - \beta \,z)(A/m)$$
The cross-sectional dimemsions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is
GATE ECE 2015 Set 1
7
For a rectangular waveguide of internal dimensions $$a\,\, \times \,\,b$$ (a > b), the cut-off frequency for the $$T{E_{11}}$$ mode is the arithmetic mean of the cut-off frequencies for $$T{E_{10}}$$ mode and $$T{E_{20}}$$ mode. If a $$ = \sqrt 5 \,cm$$, the value of b (in cm) is
GATE ECE 2014 Set 2
8
The magnetic field along the propagation direction inside a rectangular waveguide with the cross section shown in the figure is $${H_Z} = 3\,\,\cos \,\,(2.094\,\, \times \,\,{10^2}x)\,\,\,\cos \,(2.618\,\, \times \,\,{10^2}y)$$
$$\cos \,\,(6.283\,\, \times \,\,{10^{10}}t\, - \beta \,z)$$
The phase velocity $${V_p}$$ of the wave inside the waveguide satisfies
$$\cos \,\,(6.283\,\, \times \,\,{10^{10}}t\, - \beta \,z)$$
The phase velocity $${V_p}$$ of the wave inside the waveguide satisfies
GATE ECE 2012
9
A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm ) is to be operated in $$T{E_{11}}$$ mode. The minimum operating frequency is
GATE ECE 2008
10
The $$\mathop E\limits^ \to $$ field in a rectangular waveguide of inner dimensions $$a\,\, \times \,\,b$$ is given by
$$\mathop E\limits^ \to = {{\omega \,\mu } \over {{h^2}}}\,\left( {{\pi \over a}} \right)\,{H_0}\,\sin \,\left( {{{2\,\pi \,x} \over a}} \right)\,\,\sin \,(\omega \,t - \,\beta \,z)\hat y$$,
where $${H_0}$$ is a constant, a and b are the dimensions along the x-axis and the y-axis respectively. The mode of propagation in the waveguide is
GATE ECE 2007
11
An air-filled rectangular waveguide has inner dimensions of $$3\,cm\,\, \times \,\,2\,\,cm\,$$. The wave impedance of the $$T{E_{20}}$$ mode of propagation in the waveguide at a frequency of 30 GHz is (free space impedance $$\,{\eta _0} = \,377\,\,\Omega $$)
GATE ECE 2007
12
A rectangular waveguide having $$T{E_{10}}$$ mode as dominant mode is having a cutoff frequency of 18 GHz for the $$T{E_{30}}$$ mode. The inner broad-wall dimension of the rectangular waveguide is
GATE ECE 2006
13
Which one of the following does represent the electric field lines for the $$T{E_{02}}$$ mode in the cross-section of a hollow rectangular metallic waveguide?
GATE ECE 2005
14
A rectangular metal wave guide filled with a dielectric material of relative permittivity $${\varepsilon _r} = \,4$$ has the inside dimensions $$3.0\,cm\,\, \times \,\,1.2\,cm$$. The cut-off frequency for the dominant mode is
GATE ECE 2003
15
A rectangular waveguide has dimensions $$1\,\,cm\,\, \times \,\,0.5\,\,cm$$. Its cut-off frequency is
GATE ECE 2000
16
An optical fiber consists of a cylindrical dielectric rod of refractive index $$n_1$$, surrounded by another dielectric of refractive index $$n_2$$ where $$n_2$$ < $$n_1$$ as shown in the following Fig. If a ray is incident from air at angle i to the axis, then it undergoes total internal reflection at the interface AB if
GATE ECE 1993
17
Choose the correct statements.
For a wave propagating in an air filled rectangular wave guide
For a wave propagating in an air filled rectangular wave guide
GATE ECE 1990
18
For a normal mode EM wave propagating in a hollow rectangular wave guide
GATE ECE 1988
19
The cut-off frequency of a waveguide depends upon
GATE ECE 1987
Marks 5
1
Consider a parallel plate waveguide with plate separation d as shown in Fig. The electric and magnetic fields for the TEM mode are given by
$${E_x} = \,{E_0}\,\,{e^{ - j\,k\,z + j\,\omega \,t}},\,{H_y} = {{{E_0}} \over \eta }\,{e^{ - j\,k\,z + j\,\omega \,t}}$$
Where $$k = \,\,\eta \,\omega \,\, \in $$
(a) Determine the surface charge densities $${\rho _s}$$ on the plates at x = 0 and x = d
(b) Determine the surface current densities $$\mathop {{J_s}}\limits^ \to $$ on the same plates.
(c) Prove that $${\rho _s}$$ and $$\mathop {{J_s}}\limits^ \to $$ satisfy the current continuity condition.
GATE ECE 2002
2
Consider a parallel plate waveguide with plate separation d as shown in Fig. The electric and magnetic fields for the TEM mode are given by
$${E_x} = \,{E_0}\,\,{e^{ - j\,k\,z + j\,\omega \,t}},\,{H_y} = {{{E_0}} \over \eta }\,{e^{ - j\,k\,z + j\,\omega \,t}}$$
Where $$k = \,\,\eta \,\omega \,\, \in $$
(a) Determine the surface charge densities $${\rho _s}$$ on the plates at x = 0 and x = d
(b) Determine the surface current densities $$\mathop {{J_s}}\limits^ \to $$ on the same plates.
(c) Prove that $${\rho _s}$$ and $$\mathop {{J_s}}\limits^ \to $$ satisfy the current continuity condition.
GATE ECE 2002
3
Consider a parallel plate waveguide with plate separation d as shown in Fig. The electric and magnetic fields for the TEM mode are given by
$${E_x} = \,{E_0}\,\,{e^{ - j\,k\,z + j\,\omega \,t}},\,{H_y} = {{{E_0}} \over \eta }\,{e^{ - j\,k\,z + j\,\omega \,t}}$$
Where $$k = \,\,\eta \,\omega \,\, \in $$
(a) Determine the surface charge densities $${\rho _s}$$ on the plates at x = 0 and x = d
(b) Determine the surface current densities $$\mathop {{J_s}}\limits^ \to $$ on the same plates.
(c) Prove that $${\rho _s}$$ and $$\mathop {{J_s}}\limits^ \to $$ satisfy the current continuity condition.
GATE ECE 2002
4
A rectangular hollow metal waveguide has dimensions a = 2.29 cm and b = 1.02 cm. Microwave power at 10 GHz is transmitted through the waveguide in the $$T{E_{10}}$$ mode.
(a) Calculate the cut-off wavelength and the guide wavelength for this mode.
(b) What are the other (TE or TM) modes that can propagate through the waveguide?
(c) If a = b = 2.29 cm, what are the modes which can propagate through the waveguide?
(a) Calculate the cut-off wavelength and the guide wavelength for this mode.
(b) What are the other (TE or TM) modes that can propagate through the waveguide?
(c) If a = b = 2.29 cm, what are the modes which can propagate through the waveguide?
GATE ECE 2001
5
A 100 m section of an air-filled rectangular wave-guide operating in the $$T{E_{10}}$$ mode has a cross-sectional dimension of 1.071 cm $$ \times $$ 0.5 cm. Two pulses carriers of 21 GHz and 28 GHz are simultaneously launched at one end of the wave-guide section. What is the time delay difference between the two pulses at the other end of the waveguide?
GATE ECE 1999
6
The region between a pair of parallel perfectly conducting planes of infinite extent in the y and z directions is partially filled with a dielectric as shown in Figure. A 30 GHz $$T{E_{10}}$$ wave is incident on the air dielectric interface as shown. Find the
VSWR at the interface.
GATE ECE 1998
7
A rectangular waveguide with inner dimensions 6 cm $$ \times $$ 3 cm has been designed for a single mode operation. Find the possible frequency range of operation such that the lowest frequency is 5% above the cut off and the highest frequency is 5% below the cut off of the next higher mode.
GATE ECE 1998
8
In an air-filled rectangular waveguide, the vector electric field is given by
$$\mathop E\limits^ \to = \cos \,(20\,\pi \,y)\,\exp \,\,\left[ { - j\left( {{{40\,\,\pi } \over 3}} \right)\,z\, + j\,\omega \,t} \right]\,\hat i\,\,\,V/m$$
Find the vector magnetic field and the phase velocity of the wave inside the waveguide.
GATE ECE 1996
9
A rectangular hollow metal waveguide is required to be so designed to propagate a 9375 MHz signal in its $$T{E_{10}}$$-mode that the guide-wavelength equals the cut-off wavelength. Calculate the value of 'a' (breadth or the wider dimension of the waveguide). Take b = a/2. Also, calculate the cut-off frequency of the next higher order mode.
GATE ECE 1995
10
A rectangular hollow metal waveguide of internal cross-section of $$7.366\,\,cm\,\, \times \,\,3.556\,cm$$ carries a 3 GHz signal in the $$T{E_{10}}$$-mode. Calculate the maximum power handling capability of the waveguide assuming the maximum permissible electric field inside the waveguide to be 30 kV/cm
GATE ECE 1994
Marks 8
1
A rectangular waveguide with cross-section dimensions 5 cm by 3 cm is filled with a dielectric of relative permittivity 3.
(i) Determine the cutoff frequency of the$$T{E_{11}}$$ mode.
(ii) Determine the frequency at which this / mode has an attenuation of $$3\,\pi $$ nepers/m.
(i) Determine the cutoff frequency of the$$T{E_{11}}$$ mode.
(ii) Determine the frequency at which this / mode has an attenuation of $$3\,\pi $$ nepers/m.
GATE ECE 1988
2
A rectangular waveguide with cross-section dimensions 5 cm by 3 cm is filled with a dielectric of relative permittivity 3.
(i) Determine the cutoff frequency of the$$T{E_{11}}$$ mode.
(ii) Determine the frequency at which this / mode has an attenuation of $$3\,\pi $$ nepers/m.
(i) Determine the cutoff frequency of the$$T{E_{11}}$$ mode.
(ii) Determine the frequency at which this / mode has an attenuation of $$3\,\pi $$ nepers/m.
GATE ECE 1988