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# First-Term Examination

Sixth Semester [B.Tech] - February 2006

 Paper Code : ETEC – 304 Subject : Microwave Engineering
 Time : 11/2 Hours Maximum Marks : 30
 Note : Attempt any 3 questions in all. Q1 is compulsory. Each question carries 10 marks.

 Q1 ( a ) Draw the field patterns fro the following modes: i) TE10   ii) TE11 2 ( b ) Derive the expression for the resonant frequency of the rectangular and circular waveguides. 2 ( c ) Why at low frequency, a wave cannot propagate in a waveguide. 2 ( d ) What is the dominant mode in a rectangular waveguide and why? 2 ( e ) Why TE00, TE01 and TE10 modes can't exist in a circular waveguide? 2

 Q2 ( a ) Derive the field expression for the TMmnp modes in a rectangular cavity resonator. 5 ( b ) For TE101 mode in a rectangular cavity resonator of width 'a', height 'b' and length 'd', show that the frequency of resonance is given by: 3 ( c ) For a=2cm, b=1cm, find d so that the cavity will resonate at 20GHz.

 Q3 ( a ) Why is a hybrid E-H plane teeis known as magic tee. Derive the scattering matrix for it. 5 ( b ) The scattering matrix of a two port is given by Find the distance that the position of port 1 should be adjusted to the left so that S12 and S21 will be real. Given that the phase constant beta=12.5rad/m. 5

 Q4 ( a ) An air filled rectangular waveguide has 2.254*1.5cm sides operating in dominant mode, transports energy at the rate of 1HP. If the frequency is 30GHz, what is the peak value of the electric field occurring in the waveguide? 4 ( b ) Determine the cutoff wavelength for the dominant mode in a rectangular waveguide of breadth 10cm. For a 2.5GHz signal propagated in this waveguide in the dominant mode. Calculate the guide wavelength, group velocity and phase velocity. 4 ( c ) Starting from Maxwell's equations, prove that Electromagnetic Waves propagate with a velocity of light. 2