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Sixth Semester [B.Tech]  February 2006
Paper Code : ETEC – 304 Subject : Microwave Engineering 
Time : 1^{1}/_{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) TE_{10} ii) TE_{11} 
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 TE_{00}, TE_{01} and TE_{10} modes can't exist in a circular waveguide?  2 
Q2 
( a ) 
Derive the field expression for the TM_{mnp} modes in a rectangular cavity resonator. 
5 
( b ) 
For TE_{101} 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 EH 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 S_{12} and S_{21} 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 
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