Sri Venkateswara College of Engineering s2

SRI VENKATESWARA COLLEGE OF ENGINEERING

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

UNIT-V-PART-B

1. A rectangular air filled copper waveguide with a a=2.28 cm and b=1.01 cm across section and l=30.48 cm is operated at 9.2 GHz with a dominant mode. Find the cut off frequency, guide wavelength, phase velocity and characteristics impedance. [Nov/Dec 2014]) 2. Explain the principles of the following. (i) Excitation of waveguides. (ii) Guide termination and resonant Cavities. [Nov/Dec 2014]

3. (i)Describe the propagation of TE waves in a rectangular waveguide with necessary expressions for the field components. [ May/June 2014] (ii)An air filled rectangular waveguide of dimensions a = 6cm and b=4cm operates in the TM 11 mode. Find the cut off frequency guide wavelength and phase velocity at a frequency of 3 GHz.

4. (i)Describe the principle and operation of rectangular cavity resonators with relevant expressions. (ii) Give a brief note on excitation of modes in rectangular waveguides. [May/June 2014]

5. Derive the field expressions for transmission of TE waves between Parallel Planes. [Nov/Dec 2014]

6. (i)Discuss the transmission of TM waves between parallel perfectly conducting planes with necessary expressions for the field components. (ii)Discuss the characteristics of TE and TM waves between the parallel planes. [May/June 2014]

7. Discuss the transmission of TM waves between parallel perfectly conducting planes with necessary expressions for the field components. Discuss briefly the manner how the wave travels and phase and group velocities between the two parallel planes. [May/June 2014] [Nov/Dec 2013] 8. (i)Describe the field components of TE waves in a rectangular waveguide with necessary ex-

pressions and also plot the field configurations for the TE10 mode. [Nov/Dec 2013] (NOV 2009)

(ii)A rectangular waveguide measuring a=4.5 cm and b=3 cm internally has a 9 GHz signal propagated in it. Calculate the cutoff wavelength, guide wavelength, phase and group velocities and characteristic wave impedance for TM11 mode. 9. Give brief note on the transmission of TEM waves between parallel planes.

[Nov/Dec 2013] 10. Derive the field expression for TE waves between a pair of parallel perfectly conducting planes of infinite extent in the Y and Z directions. The planes are separated in X direction by ‘a’ meter. [May/June 2013] 11. (i)Discuss the characteristics of TE and TM waves and also derive cutoff frequency and phase velocity from the propagation constant.[May/June 2013]

(ii) A parallel perfectly conducting plates are separated by 7 cm in air and carries a signal with frequency (f) of 6GHz inTE1 mode. i. The cut-off frequency (fc) ii. Phase constant iii. Attenuation constant and Phase constant for f=.8fc and iv. Cut off wavelength [May/June 2013](May 2007)

12. Explain briefly the propagation of TM waves in a circular waveguide with necessary expressions for the field components.

[May/June 2013] [Nov/Dec,2013] (NOV 2009)

13. (i) A rectangular cavity resonator excited by TE101 mode at 20G Hz has the dimension a = 2 cm, b = 1 cm. Calculate the length of the cavity.

(ii)With neat diagrams, explain the concept of excitation of modes. [May/June 2013] 14. (i)Derive the field expression for TM wave propagation in rectangular waveguide stating the necessary assumptions. (Nov/Dec 2012,R8) [Nov 2010,R8]

(ii) A rectangular waveguide measuring a = 4.5 cm and b = 3 cm internally has a 9 GHz signal propagated in it. Calculate the guide wavelength, phase and group velocities and characteristic impedance for the dominant mode. 15. (a)Explain the concept of excitation of waveguides. b) Discuss the structure, advantages and disadvantages of resonant cavities. (Nov/Dec 2012,R8)

16. (i)Discuss the characteristics of TM waves in circular waveguides.

(ii)A 10 G Hz signal is to be transmitted inside a hallow circular conducting pipe. Determine the inside diameter of the pipe such that its lowest cut off frequency is 20%below this signal frequency. [Apr/May 2012, R8] 17. (i)Discuss the principle of rectangular cavity resonator.

(ii)Determine the dominant modes and their frequencies is an air filled rectangular cavity resonator for [Apr/May 2012, R8] 1) a > b > d

2) a > d > b

3) a = b = d where a, b and d are dimensions is the x, y and z directions, respectively.

18. Explain the concept of transmission of TM waves and TEM waves between parallel plates. (Nov/Dec 2012,R8)

19. Derive the relation among phase velocity, group velocity and free space velocity. . (Nov/Dec 2012,R8) [Nov/Dec2010]

20. (i)Discuss the transmission of TM waves between parallel planes.

(ii)Write the instantaneous field expressions for TM1 mode in a parallel plate waveguide. [Apr/May 2012,R8]

21. (i) Discuss the transmission of TE waves between parallel planes

(ii)Sketch the field lines of TE1 mode parallel plate waveguide. [Apr/May 2012,R8]

22. A rectangular air-filled copper waveguide with dimension 0.9 inch 0.4 inch cross section and 12 inch length is operated at 9.2 GHZ with a dominant mode. Find cut-off frequency, guide wave-length, phase velocity, characteristics impedance and the loss [Nov/Dec 2011,R8]

23. (i) Find the resonant frequencies of first five lowest modes of an air-filled rectangular cavity of dimensions 5 cm ×4 cm × 2.5 cm. List them in ascending order [Nov/Dec 2011,R8]

(ii) An air-filled circular waveguide having an inner radius of 1 cm is excited in dominant mode at 10 Ghz. Find cut-off frequency of dominant mode, guide wavelength, wave impedance and the bandwidth for operation in dominant mode only (Given [X11 ′ =1.84 ; X01 =2.40]

24. Explain in detail [Apr/May 2011,R8] (i)Excitation of wave guides (ii)Resonant cavities 25. A rectangular wave guide with dimensions a = 2.5 cm, b =1 cm is to operate below 15 GHz. How many TE and TM modes can the waveguide transmit if the guide is filled with a medi-

um characterized by σr= 0 , ε=4ε0 µr=1? Calculate the cutoff frequencies of the modes.

[Apr/May 2011,R8]

26. (i)Derive the equations that are the result of introduction of restrictions on time to Maxwell’s equations [Nov/Dec 2011,R8]

(ii)Derive the field equations for TE waves between parallel planes. A TEM wave at 1 MHz propagates in the region between conducting planes which is filled with dielectric material of r μ = 1 and r ε = 2. Find the phase constant and characteristic wave impedance. (Nov/Dec 2010, R8)

27. (i) Write a detailed note on impossibility of TEM waves in waveguides.

(ii)In an air filled rectangular waveguide the cut off frequency of a TE10 mode is 5 G Hz , Whereas that of TE10 mode is 12 G HZ. Calculate the dimensions of the guide and cut off frequencies of the next three higher TE modes such as TE01 , TE11 , TE20 . [Nov/Dec2010]

28. (i) Derive the expressions for the field components of TEM waves.

(ii) Discuss wave impedances in detail (April 2010) 29. (i) Derive the field expression for Transverse Magnetic waves between a pair of parallel perfectly conducting planes of infinite extent in the Y and Z directions. The planes are separated in X direction by ‘a’ meter. [Nov 2010]

(ii) A parallel perfectly conducting plates are separated by 10 cm and filled with paper whose dielectric constant is 7. This arrangement need to support TE1 mode. Find the cut off frequency. 30. (i) Discuss the characteristics of TE, TM, and TEM waves between parallel conducting planes and derive the cut off frequency and phase velocity.

31. (ii) Describe the velocity of propagation of wave between a pair of perfectly conducting plates. . [Nov 2010]

32. Explain the propagation of electromagnetic waves in a cylindrical waveguide with suitable expressions. (16) [Nov 2010,R8]

33. (i) Derive the TM wave components in circular wave guides using Bessel function.

(ii)Write a brief note on microwave cavities. [Nov/Dec 2010] 34. Derive the expression for the following parameters in rectangular cavity resonator support-

ing TE101 mode.

(i) Energy stored in electric field

(ii) Power loss in two side walls, bottom, top, front and back walls of the rectangular cavity. [Nov/Dec 2010]

35. (i) Distinguish between TE and TM modes of the rectangular guide

(ii) Derive the equations to give the relationships among the fields within the rectangular guide. (May 2010)

36. (i) A rectangular air-filled copper guide with 0.9 inch x 4 inch cross section and 12 inch length is operated at 9.2 GHz with a dominant mode. Find the cut-off frequency, the phase velocity and the characteristic impedance.

(ii) A standard air-filled rectangular guide with dimensions a=8.636cm. b=4.318 cm is fed by a 4 GHz carrier from a coaxial cable. Determine whether a TE10 mode is propagated. If so, calculate the phase velocity and the group velocity. (May 2010) 37. (i)Derive the solution of field equations using cylindrical coordinates (April 2010) (ii)Draw the field configuration of different TM and TE modes for a circular guide

38. Derive the expression for the field components existing in a rectangular cavity. (April 2010/Nov 2009)

39. Deduce the expressions for the field components of TM waves guided along a rectangular wave guide. (May 2009)

40. A pair of perfectly conducting planes are separated by 3.6cm in air .For TM10 mode determine the cut-off frequency and cut-off wavelength, if the operating frequency is 5GHz (May 2009)

41. For a frequency of 10 GHz and plane separation of 5 cm in air, find the cutoff ,find the cut- off wavelength ,phase velocity and group velocity of a wave (May 2009)

42. A parallel perfectly conducting planes are separated by 5cm in air and carries a signal with frequency of 10GHz in TM11 mode .Find the cut-off frequency and cut-off wavelength (Nov 2008) 43. Derive the expression of wave impedance for TE and TM waves guided along rectangular waveguide (April 2008/Nov 2007/May 2009) 44. A TE10 mode is propagated through a waveguide with α=10 cm at a frequency of 2.5 GHz. Find cut-off wavelength, phase velocity, group velocity and wave impedance (May 2009)

45. (i) Explain the methods of excitation of circular waveguides. (Nov 2008/April 2008)

(ii) Starting from Maxwell’s equation obtain the field components for the Transverse Electric waves of circular waveguides. (April 2008)

46. (i) What is an electromagnetic cavity resonator? Describe the excitation of TM waves in the class of cavity resonators produced by placing plane end faces on a length of cylindrical waveguide. (ii) Discuss the significance of Q-factor of a rectangular cavity resonator Excited in TE011 mode. Calculate the Q-factor of a cubic resonator supporting TE011 mode and resonant at 3 GHz. Resistivity of the resonator wall is 1.7*10 -8ohm meter. (April 2008)

47. (i) Using Bessel function derive the TE wave components in circular wave guides. (April 2008/May 2009)

(ii) Calculate the resonant frequency of an air filled rectangular resonator of dimensions a=2cm, b=4cm and d=6 cm operating in TE101 mode. (April 2008)

48. Derive the field configuration ,cut-off frequency and velocity of propagation for TE waves in rectangular waveguide (Nov 2008)

49. A TE10 wave at 10GHz propagates in a X band copper rectangular waveguide whose inner dimension are ‘a’=2.3cm and ‘b’=1cm,which is filled with Teflon ὲr=2.1cm and μr=1.Calculate the cut-off frequency ,velocity of propagation ,phase velocity , phase constant ,guide wavelength and wave impedance. (Nov 08)

50. Evaluate the ratio of the area of a circular waveguide to that of a rectangular one if both are to have the same cut off frequency for dominant mode. ( April 2008)

51. A rectangular guide has cross section dimensions a=7 cm, b=4cm. Determine all the modes which will propagate at a frequency of (1) 3000MHz (2) 5000MHz (April 2008)

52. Derive the field configuration, cut off frequency and velocity of propagation for TM waves in rectangular waveguide. (April 2008)

53. (i) TEM wave cannot exist in a single-conductor waveguide – Justify the statement using Maxwell’s equation. (i) A X-band air filled rectangular waveguide has inner dimensions of ‘a’=2.3cm and ‘b’=1cm. Calculate the cutoff frequencies in the following modes: TE10, TE20, TM11, TM12. Also check which of the modes will propagate along the waveguide when the signal frequency is 10GHz. (April 2008)

54. (i) Derive the expressions for the field components of TM waves between parallel plates, propagating in Z direction.

(ii) For a frequency of 6 GHz and plane separation = 7 cm. Find the following for the TE10 made: (1) Cutoff frequency (2) Phase and group velocity (Nov 2007)

55. (i) Explain wave impedance and obtain the expressions of wave impedance for TE and TM waves guided along parallel planes. Also sketch the variation of wave impedance with frequency.

(ii) For a frequency of 5 GHz and plane separation of 8 cm in air, find the following for TM10 mode (2) Cut-off wavelength (3) Characteristic impedance (4) Phase constant. (Nov 2007)

56. A rectangular waveguide measures 3X4.5cm internally and has a 10 GHz Signal propagated in it. Calculate the cut-off wavelength, the guide Wavelength and the characteristic wave impedance for the TE10 mode (Nov 2007) 57. (i) Discuss the attenuation of electromagnetic waves guided along rectangular waveguide. (ii)What are the dimensions of a waveguide with the following specifications? (iii)At a frequency of 9959.5 MHz, the guide wavelength for TE10 mode is 87.57% of the cut-off wavelength. (iv)TE30 and TE12 mode have the same cut-off frequency. (Nov 2007)

58. Derive the field configuration, cut off frequency and velocity of propagation for TM waves in rectangular waveguide. (May 2007)

59. (i) Obtain the expression for resonant frequency of circular cavity resonator. (May 2010/Nov 2007) (i) Calculate the resonant frequency of a rectangular resonator of dimensions a=3cm, b=2cm and d=4cm if the operating mode is TE101. Assume free space within the cavity. (Nov 2007)

60. (i) Derive the TM wave components in circular wave guides using Bessel function. (May 2007/Nov 2009) (ii)Calculate the resonant frequency of an air filled rectangular resonator of dimensions a=3 cm, b=2cm and d=4cm operating in TE101 mode. (May 2007)

61. Derive the Q-factor of a rectangular cavity resonator for TE101. (May 2007) 8 62. A TE10 wave at frequency 10GHz propagates with the velocity 2X10 m/sec in a brass 7 σc=1.57X10 s/m rectangular waveguide with inner dimensions a=1.5cm and b=0.6cm, which is filled with polyethylene εr =2.25, µr =1. Calculate the phase constant, Guide wavelength, phase velocity, wave impedance. Which signal among the two separate signals with frequency 5GHz and 15GHz will be supported by the rectangular waveguide for propagation through it? (May 2007)

63. (i) Determine the solution of electric and magnetic fields of TE waves guided along rectangular waveguide. (ii) An air filled rectangular waveguide with dimensions of a=8.5cm and b=4.3 cm is fed by a 4 GHz carrier from co-axial cable. Determine the cut-off frequency, phase velocity and group velocity for TE11 mode. (Nov 2006)

64. (i) Explain wave impedance of a rectangular waveguide and derive the expression for the wave impedance of TE, TM and TEM waves (ii) The cut-off wavelength of a rectangular waveguide are measured to be 8 cm and 4.8 cm for TE10 and TE11 mode respectively. Determine waveguide dimensions. (Nov 2006)

65. An air-filled rectangular waveguide has dimensions of copper a=1cm and b=0.6cm and is excited at 18GHz. Find a. modes of propagation b. guide wavelength c. wave impedances of the modes d. Attenuation constant for the excited modes. ( Nov 2006)

66. A rectangular waveguide (aXb) is excited in dominant TE10 mode field Hz=cos(πx/a) for propagation +z direction a. Find expressions for broad wall and narrow wall currents b. Expressions for the rate of energy flow along the guide. (Nov 2006)

67. Show that for TMmn mode of a rectangular waveguide the cut off wavelength λc is (λc)mn = 2/√(m/a)2+(n/b)2 meters. (Nov 2006) Where a and b are the width and height of the cross section of the waveguide.

68. (i)Derive the expressions for cut-off frequency, phase shift constant and velocity of propagation of waves in a circular waveguide. (ii) Sketch the electric and magnetic field configurations for TE01 mode in a circular waveguide. (iii) Given a circular waveguide of internal diameter 12 cm operating with a 8 GHz. Signal propagating TM22 mode. Calculate λ1, λc, λg an