1. Square wave guide Consider
a waveguide that is filled with a dielectric that undergoes
breakdown (sparking) at an electric field of 10 kV/m. Calculate the
maximum power that can be carried by the TE1,0 mode without
breakdown if the dimensions of the wave guide are 5 cm by 5 cm.
Assume that the frequency is twice the cutoff frequency. Your may
express your answer in terms of the index of refraction.
Homework Answers
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1. Square wave guide Consider
a waveguide that is filled with a dielectric that undergoes
breakdown...
4-9. The dominant mode TEio is propagated in a rectangular waveguide of dimensions a 2.25 cm and b-l cm. Assume an air dielectric with a breakdown gradient of 30 kV/cm and a frequency of 10 GHz. Ther...
4-9. The dominant mode TEio is propagated in a rectangular waveguide of dimensions a 2.25 cm and b-l cm. Assume an air dielectric with a breakdown gradient of 30 kV/cm and a frequency of 10 GHz. There are no standing waves in the guide. De- termine the maximum average power that can be carried by the guide
4-9. The dominant mode TEio is propagated in a rectangular waveguide of dimensions a 2.25 cm and b-l cm. Assume an air dielectric...
3. A TE wave propagating in a dielectric-filled waveguide of unknown permittivity has dimensions a =...
3. A TE wave propagating in a dielectric-filled waveguide of unknown permittivity has dimensions a = 10 cm and b = 6 cm. If the x-component of its electric field is given by Ex = -36 cos(40tex)sin(100ny) sin(2.41 x 1040t - 52.9nz) (V/m) determine: (a) mode numbers (m, n) (b) er of the material in the guide (©) cutoff frequency (d) expression for Hy
Power capacity of a rectangular waveguide. (a) Consider a WR-284 rectangular air waveguide with inner dimensions...
Power capacity of a rectangular waveguide. (a) Consider a WR-284 rectangular air waveguide with inner dimensions 7.214 cm x 3.404 cm to operate in the dominant mode at 2.45 GHz. Assuming the breakdown electric field of air to be 15 kV-(cm)-1 (with a safety factor of 2 at sea level), calculate the maximum time-average power that can be carried by this waveguide. (b) Another waveguide (WR-430 air-filled, with inner dimensions 10.922 cm x 5.461 cm) is proposed to increase the...
3) As in Figure 2, the rectangular waveguide with air filled (? = ?0, ? =...
3) As in Figure 2, the rectangular waveguide with air filled (?
= ?0, ? = ?0) and dimensions a = (2.75 + d) cm and b = (1.5 + h) cm
operates under the operating frequency of 7.580 GHz.
d = 8/10 h = 6/10
According to this,
a) Which wave mode is the dominant mode (dominant mode)? Why?
Figure 2- Rectangular Wave Guide
b) Calculate the Z, β, up and λg values for the dominant wave
mode.
b
4. Consider the cylindrical waveguide below, which has an electromagnetic wave propagating in the space between...
4. Consider the cylindrical waveguide below, which has an
electromagnetic wave propagating in the space between the inner and
outer conductors, which is a gap where air exists. The radius of
the inner conductor is a, while the inner radius of the outer
conductor is b (as shown). The fields in the air-gap have the form
E = E0r cos (kz z ωt) B = B0r cos (kz z ωt) where E0 and B0 are
constants, r is the radial...
What are the answers and how did you get to the answers? Consider the electromagnetic wave...
What are the answers and how did you get to the answers?
Consider the electromagnetic wave shown in the diagram. The wave is propagating through a vacuum along the z-axis. The electric field of the wave is parallel to the y-axis. It is a sine wave of amplitude 15 V/m. The accompanying magnetic field is parallel to the x-axis. See Figure (which is a snapshot at a particular instant) 23 cm 2 6) What is the frequency fof this electromagnetic...
1. The magnetic field of a wave propagating through a certain nonmagnetic material is given by...
1. The magnetic field of a wave propagating through a certain nonmagnetic material is given by H-x30cos(10%-0. Sy) (mA/m) Find the following: (a) The direction of wave propagation. (b) The phase velocity (c) The wavelength in the material. (d) The relative permittivity of the material (e) The electric field phasor 2. A 60-MHz plane wave traveling in the -x-direction in dry soil with relative permittivity &4 has an electric field polarized along the z-direction. Assuming dry soil to be approximately...
1.Vp and Vg are the phase velocity and group velocity, respectively, of the de Broglie wave...
1.Vp and Vg are the phase velocity and group velocity, respectively, of the de Broglie wave for an electron moving with the velocity V, and C is the velocity of light in free space. Which of the following is incorrect? (a) Vp> Vg (b) Vp>C (c) Vg<C (d) Vg=V (e) Vp=V 2.An atomic force microscope (AFM) probe is essentially a cantilever with a nanosized tip at the free end. One scan mode of AFM is to drive the probe as...
4-9. The dominant mode TEio is propagated in a rectangular waveguide of dimensions a 2.25 cm and b-l cm. Assume an air dielectric with a breakdown gradient of 30 kV/cm and a frequency of 10 GHz. There are no standing waves in the guide. De- termine the maximum average power that can be carried by the guide
4-9. The dominant mode TEio is propagated in a rectangular waveguide of dimensions a 2.25 cm and b-l cm. Assume an air dielectric...
3. A TE wave propagating in a dielectric-filled waveguide of unknown permittivity has dimensions a = 10 cm and b = 6 cm. If the x-component of its electric field is given by Ex = -36 cos(40tex)sin(100ny) sin(2.41 x 1040t - 52.9nz) (V/m) determine: (a) mode numbers (m, n) (b) er of the material in the guide (©) cutoff frequency (d) expression for Hy
3) As in Figure 2, the rectangular waveguide with air filled (?
= ?0, ? = ?0) and dimensions a = (2.75 + d) cm and b = (1.5 + h) cm
operates under the operating frequency of 7.580 GHz.
d = 8/10 h = 6/10
According to this,
a) Which wave mode is the dominant mode (dominant mode)? Why?
Figure 2- Rectangular Wave Guide
b) Calculate the Z, β, up and λg values for the dominant wave
mode.
b
4. Consider the cylindrical waveguide below, which has an
electromagnetic wave propagating in the space between the inner and
outer conductors, which is a gap where air exists. The radius of
the inner conductor is a, while the inner radius of the outer
conductor is b (as shown). The fields in the air-gap have the form
E = E0r cos (kz z ωt) B = B0r cos (kz z ωt) where E0 and B0 are
constants, r is the radial...
What are the answers and how did you get to the answers?
Consider the electromagnetic wave shown in the diagram. The wave is propagating through a vacuum along the z-axis. The electric field of the wave is parallel to the y-axis. It is a sine wave of amplitude 15 V/m. The accompanying magnetic field is parallel to the x-axis. See Figure (which is a snapshot at a particular instant) 23 cm 2 6) What is the frequency fof this electromagnetic...
1. The magnetic field of a wave propagating through a certain nonmagnetic material is given by H-x30cos(10%-0. Sy) (mA/m) Find the following: (a) The direction of wave propagation. (b) The phase velocity (c) The wavelength in the material. (d) The relative permittivity of the material (e) The electric field phasor 2. A 60-MHz plane wave traveling in the -x-direction in dry soil with relative permittivity &4 has an electric field polarized along the z-direction. Assuming dry soil to be approximately...
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