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# Monthly Archives: June 2016

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## Waveguide Questions for GATE EC

1) Which is the dominant mode in TM?
a) $TM_{10}$
b) $TM_{21}$
c) $TM_{01}$
d) $TM_{11}$

2) Dominant mode in Waveguides usually refers to ?

a) $TE_{10}$
b) $TM_{10}$
c) $TM_{01}$
d) $TM_{11}$

3) The cut-off wavelength of rectangular waveguide was measured to be 8 cm and 4.8 cm when excited in $TE_{10}$ and $TE_{11}$ modes respectively. Determine the dimensions of a waveguide

a= ______
b= ______

4) A rectangular waveguide has dimensions a=2.5 cm and b=1 cm. A microwave signal at a frequency if 8.6 GHz is to be propagated through this waveguide.Which of the following mode can exist in rectangular waveguide?

a) $TE_{10}$
b) $TM_{10}$
c) $TM_{01}$
d) $TM_{11}$

5) The modes in a rectangular waveguide are denoted by $TE_{mn}$/$TM_{mn}$ where m and n are the Eigen
numbers along the larger and smaller dimensions of the waveguide respectively. Which one of
the following statements is TRUE?

a) The mode $TM_{10}$ of the waveguide does not exist
b) The mode $TE_{10}$ of the waveguide does not exist
c) The $TE_{10}$ and $TM_{10}$ the modes both exist and have the same cut – off frequencies
d) The $TM_{10}$ and $TM_{01}$ the modes both exist and have the same cut – off frequencies

6) If $\lambda_c$ is the cut off wavelength of a rectangular waveguide and $\lambda_o$ is a free space wavelength. Then the condition for wave propagation is

a) $\lambda_c$ > $\lambda_o$
b) $\lambda_c$ < $\lambda_o$
c) $\lambda_c$ = $\lambda_o$
d) $\lambda_c$ = 0

7)

TE(02) means the wave exists only in the Y direction. So look out for Electric field lines which are originating or ending at Y axis. In this case, options A and C are eliminated. Now we are left with option b and d.

Here as you can see, TE(02) means n=2 (Mode is 2) . So the E field equation will be of the following form

$E_y$= K $sin(\frac{2\pi y}{b})$

Y axis range is from 0 to b.

At

y=0 and y=b, value of sin is 0.

At y=b/4,  value of sin is 1

At y=3b/4, value of sin is -1

So, the correct answer is option “d” , where E field lines are pointing towards positive x axis below b/2 and towards negative x axis above b/2

…………………………………………………………………………………………………….
Answer Keys

1-d, 2-a ,3 => a=4, b=3 ,4-a,5-a, 7-d

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## Lead – Lag compensator previous GATE questions

GATE EC-2012

The transfer function of  a compensator is given by  $G_c(s)$=$\frac{s+a}{s+b}$

1.  $G_c(s)$ is a lead compensator if

A) a=1, b=2     B) a=3,b=2       C) a=-3 b=-1        d) a=3, b=1

2. The phase of the above lead compensator is maximum at

a)  $\sqrt{3}$              b) $\sqrt{2}$          c) $\sqrt{6}$    d) $\sqrt{1/3}$

3) The open loop transfer function of a plant is given as G(s)=$\frac{1}{s^2-1}$. If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

a) 10 $\frac{s-1}{s+2}$                                b) 10 $\frac{s-1}{s+2}$

c) 10 $\frac{s+2}{s+10}$                                       d) 2 $\frac{s+2}{s+10}$

4) The transfer function of a phase lead compensator is given by $G_c(s)$= $\frac{1+3Ts}{1+Ts}$ where T>0 . The maximum phase shift produced by such compensator is(in degrees)

a) 90             b) 30          c) 45            d) 60