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(3) For modes propagating in a waveguide, compute phase velocity and group velocity (10 pts)
Q3. (25 pts) A rectangular waveguide with sizes a = 10cm and b = 6cm is...
Q3. (25 pts) A rectangular waveguide with sizes a = 10cm and b = 6cm is filled with a dielectric material characterized by o = 0.2 = 1.5&g and p = Mo. The x-component of the TE wave propagating inside the waveguide is given by Ex = -24 cos(40mx) sin(100ry) sin(2.41 x 100+ - Bz) (V/m) Determine, (a) The mode of operation and the mode number (If there are more than one possible answer, proceed to remaining parts of the...
3.7. A certain type of electromagnetic wave propagating inside an empty waveguide with perfectly conducting walls...
3.7. A certain type of electromagnetic wave propagating inside an empty waveguide with perfectly conducting walls obeys the dispersion relationship 2 e) where m and n are integers and m and n a and b are the height and width of the waveguide; and c is the speed of light in free space. Find the phase and group velocity of these waves in terms of m, n, a, b, c, and ω only (your answer should not contain k). Discuss...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a f...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a function of frequency given by: I. Eo where co is radian frequency and o the "plasma frequency", which is assumed to be a constant related to the properties of the ionized gas. (a) 6 pts. Given the relation above, write an expression for the phase velocity in a plasma. (Assume μ-,-1). (b) 2 pts. Write an expression for the magnitude of...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a function of frequency given by: I. Eo where co is radian frequency and o the "plasma frequency", which is assumed to be a constant related to the properties of the ionized gas. (a) 6 pts. Given the relation above, write an expression for the phase velocity in a plasma. (Assume μ-,-1). (b) 2 pts. Write an expression for the magnitude of...
help me this exercise pls. Thank you Question 5 (3.5 pts) A parallel-plate waveguide has plate...
help me this exercise pls. Thank you
Question 5 (3.5 pts) A parallel-plate waveguide has plate separation d -1.2cm and is filled with a dielectric having dielectric constant ?:-2.8 a. Determine the maximum operating frequency such that only the TEM mode will propagate The operating wavelength is 2.5 mm b. How many waveguide modes will propagate? c. Find the group velocity of the TE and TM mode with m=2 and the mode w maximum m.
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
2. (10 pts). CH3F belongs to C3e group. Determine the symmetry of all the normal modes...
2. (10 pts). CH3F belongs to C3e group. Determine the symmetry of all the normal modes using group theory. Find out the modes that are IR active. Find out the modes that are Raman active.
A 10 cm long rectangular waveguide is designed with side lengths of 3 mm and 4mm....
A 10 cm long rectangular waveguide is designed with side lengths of 3 mm and 4mm. The waveguide is filled with a dielectric that has a refractive index n=1.3. a) Over what frequency range is this waveguide single mode? A 50 GHz signal is modulated into one short pulse, then sent into the waveguide. b) How many modes are supported by the waveguide? Also identify them by their name (for example TE32). c) Resulting from one pulse sent at the...
Deel 3 A waveguide Ral a square cross section one side 2a. For the TM modes...
Deel 3 A waveguide Ral a square cross section one side 2a. For the TM modes of wave vector K, the transverse em modes are obtained in terms of a function 4(x,y) which obeys the equation: le et saya + Cho key] 406,4)=0 with the boundary condition (ta,y)=40%, ta) so The frequency w of the lowest mode is : as we calka + 4/67) by welcoh (K 4x2/9) es und = ( 2 ( Kit tal Lane do we =...
Problem 2-For a rectangular metallic waveguide of width b-2 cm and height a-3 cm, calculate the...
Problem 2-For a rectangular metallic waveguide of width b-2 cm and height a-3 cm, calculate the following. (a) What are the supported mode(s) at 6 GHz? Calculate phase velocity and (b) What are the supported mode(s) at 8 GHz? Calculate phase velocity and (c) Plot the group velocity dispersion parameter β2 (-d+p) for the lowest order (d) Consider the lowest order mode supported in the rectangular waveguid<e group velocity of those mode(s) at 6GHz. group velocity of those mode(s) at...
Q3. (25 pts) A rectangular waveguide with sizes a = 10cm and b = 6cm is filled with a dielectric material characterized by o = 0.2 = 1.5&g and p = Mo. The x-component of the TE wave propagating inside the waveguide is given by Ex = -24 cos(40mx) sin(100ry) sin(2.41 x 100+ - Bz) (V/m) Determine, (a) The mode of operation and the mode number (If there are more than one possible answer, proceed to remaining parts of the...
3.7. A certain type of electromagnetic wave propagating inside an empty waveguide with perfectly conducting walls obeys the dispersion relationship 2 e) where m and n are integers and m and n a and b are the height and width of the waveguide; and c is the speed of light in free space. Find the phase and group velocity of these waves in terms of m, n, a, b, c, and ω only (your answer should not contain k). Discuss...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a function of frequency given by: I. Eo where co is radian frequency and o the "plasma frequency", which is assumed to be a constant related to the properties of the ionized gas. (a) 6 pts. Given the relation above, write an expression for the phase velocity in a plasma. (Assume μ-,-1). (b) 2 pts. Write an expression for the magnitude of...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a function of frequency given by: I. Eo where co is radian frequency and o the "plasma frequency", which is assumed to be a constant related to the properties of the ionized gas. (a) 6 pts. Given the relation above, write an expression for the phase velocity in a plasma. (Assume μ-,-1). (b) 2 pts. Write an expression for the magnitude of...
help me this exercise pls. Thank you
Question 5 (3.5 pts) A parallel-plate waveguide has plate separation d -1.2cm and is filled with a dielectric having dielectric constant ?:-2.8 a. Determine the maximum operating frequency such that only the TEM mode will propagate The operating wavelength is 2.5 mm b. How many waveguide modes will propagate? c. Find the group velocity of the TE and TM mode with m=2 and the mode w maximum m.
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
2. (10 pts). CH3F belongs to C3e group. Determine the symmetry of all the normal modes using group theory. Find out the modes that are IR active. Find out the modes that are Raman active.
Deel 3 A waveguide Ral a square cross section one side 2a. For the TM modes of wave vector K, the transverse em modes are obtained in terms of a function 4(x,y) which obeys the equation: le et saya + Cho key] 406,4)=0 with the boundary condition (ta,y)=40%, ta) so The frequency w of the lowest mode is : as we calka + 4/67) by welcoh (K 4x2/9) es und = ( 2 ( Kit tal Lane do we =...
Problem 2-For a rectangular metallic waveguide of width b-2 cm and height a-3 cm, calculate the following. (a) What are the supported mode(s) at 6 GHz? Calculate phase velocity and (b) What are the supported mode(s) at 8 GHz? Calculate phase velocity and (c) Plot the group velocity dispersion parameter β2 (-d+p) for the lowest order (d) Consider the lowest order mode supported in the rectangular waveguid<e group velocity of those mode(s) at 6GHz. group velocity of those mode(s) at...
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