ee 2004 gate paper

18
! " #$! % !% &% ! !(&) $ & $ " & * & & $+ ε = , & !- ε = , . && !/- "/$$ #$ &!0 # & && *# * &"+& #!% " #! #! &#! $ &"*#1*" & 213 & " & 1 ’,4’#1 #5& & +5 & 6& 6 * 7 "007 $$7 &!7 + ) 8 ) "9 1) 9 1) && ) : Ω ! ε;$<&;+ ε;!<&;- ε;--× 1! =

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Page 1: Ee 2004 Gate Paper

!

" #$!%

!%

& %

! '!(&)

$&$" &* & & $+ε = , & !-ε = , .

&&

!/-

" /$$

#$

& !0

# &&&*#*&"+&

#!% " #! #! & #!

$ & "* #1 * "&213&

"

& 1

' ,4' #1 #5 &&

+5 & 6& 6*

7 " 007 $$7 & !7

+ )

8) " 91)

91) & &)

:

Ω

!

ε;$<&;+

ε;!<&;-

ε;--×1!=

Page 2: Ee 2004 Gate Paper

2

>

?

0 &*

8@ " ?&

A & 2

- *1&&

&&* " 1*

1* & 1*

/ & #1 & ,

& #1 & ) '1?1@

,)*&"

?1@1' " @1'1?

'1@1? & ?1@1'@1'1?

&*)1*

" &*1*

&*1*

& @1*

&#1*

" ,

& ,

! )#1*

2>? " 2?> ?2> & >?2

# (,&*&&"*

& "

& & "

Page 3: Ee 2004 Gate Paper

$ "&"*&"&&B"

C " 9 & (

& * * "*&

&* " DE*

ED* & *

+ &&

##' " ##' !' & '

0 *&&(

' " !#' $#' & 0#'

,ΩF#4

(

β;β;

04

F

1

14

!!,Ω

#4( 2

F

1

4

2 ;,Ω

4 ;##4

Page 4: Ee 2004 Gate Paper

- &",&"&

1&", " 1&",

1&", & 1&",

/ &

""1"

" "1"

"1"

&

! " & 11&

1")

" !1")

$1")

& -1")

! .*) G &

*1B G *

H " $H /H & -H

!! @& ( ) ( )!

# !

=

+ + 3

)

"

!

# &

2

2?

2I

@;6

@;6

@;6 2

2@

4@@

2A

F

1

4E

4

4!

Page 5: Ee 2004 Gate Paper

!# θ & &

& C 4=&=

( )( )

Θ"

! "

&

!$ '& &&"!4&

#'&&-4""+'""+-

4 " #$4 4 & 04

! & &"* &

& !Ω & Ω

*&&&"

$7

" !7

!7

& $7

!+ '1'Ω

*& Ω

" &

!0 '"B?J &"*"

1E E. (E.?J

""1&"1B"&

" "1B"&&"1B

&"&

"1B&"&&"1B

"&

& ""1&"1B&"&

!- 1!#4

1,&&8&8!

! 4

" 4

! 4

& 4

Ω!4

!'

K&

!#4=114

8!

!#4

8

Page 6: Ee 2004 Gate Paper

2

>

?

.

2

!/ * * )

'&12)&

*"*&&4"

Ω

" +Ω

& -Ω

# #1 1

*#11*11

4*)*$)*

$ " - ! & !$

@*!D,I

# &

! + '

" + ! '

$

#'

& '

#! (

!4

" !$4

#4

& $$4

3&4

2

4"

4";!±$4

+'

1+'

=!

F

1

+ΩΩ

+ΩI'

9 !'

Page 7: Ee 2004 Gate Paper

## (22"&2!ΩΩ&Ω*2

2!&2#Ω)1

! " ! ! & !!

#$ ( & A

= + # = − = + * (

I

FB

" LB-

FB-

& LB!

# (2Ω

" !

# & $

#+ ( *@"

&A&"

$0'

" -'

$'

& '

#0 &'

&&,!'

$' " 0#' !!$' & #'

2#

2!

2

"

2"

2@

2 "

I;∠4>2

> >

4 2

Ω

F1

!'

Ω

4

A

F1

!'!Ω

F1

Page 8: Ee 2004 Gate Paper

#- 6!1,"*

/ !

! +

>!!&>6,"*

! " $ 1$ & -

#/ *&#1

-&

0$&& " 0$&

!&& & !&

$ ' 1&" &

&&&"&*&

) " *)

*) & )

$ &-Ω'&

& ' *! 4 &

* & & #'"

$-7 " 07 /!7 & ---7

$! ' ,4' ##=!#4 1 &

"

,4'

" #,4'

00$,4'

& 0+0$,4'

$# & ,4' M$4 1> &"

! & 0 * & &*

!FB0 Ω " FB/! Ω

!FB!/$ Ω & 0!+FB!$ Ω

$$ ' 1 !# 4 $ 1 &

&&

D& ;+FB$Ω

'6*& ;-FB+Ω

4;##4.

.!

4

Page 9: Ee 2004 Gate Paper

)& & /H &

"&6*&"

0+-$% " -0!$% !+!+% & !--+%

$ #1>1& "&

" " * 0Ω &

"&B&

##4& & &B&#!4

*&K&&*"

+/-' " !/$' ##/+' & --!'

$+ '$4,5$>1&&&

$7)&

++. " /. //$0. & +!$0#.

$0 -H!1"=&

&

" # + & /

$- '-8@61&#!

+(6+5"!

&&

/+4 " /!4 #-$4 & 0+-4

$/ '$4,4'-&1&*

*!Ω&"&

&!,5&-,5*/,5

&-&&

!!/' " +!$' !!/' & #+--'

' D5 #1 >1& * &

!,4-&&&"

#$#,' " 0/,' !#!,' & !0#+,'

'-,4&=,&

+-=, ( &"*D5

!$D5 " $D5 !-D5 & !++D5

Page 10: Ee 2004 Gate Paper

! ',46N39I&"&

! =, ( & N39I $! −× &"5=,

" #0 #0- & -/

# ' , & ,' , $ ,4

&!Ω&

1&)&","

!,4 " +,4 !,4 & !/,4

$ & #1 !!,4 &&

';8;/#+FB+;/#+ /-

?;##FB#-;$! 0+$Ω

@;1-FB/$ ×1+Ω

(& &D5!!,4/

&&&&"

##!#,4 " !!,4 !#0-,4 & !$+#,4

' I ; $# O) !!FB0 P &

*QNR*""&

"4 6*6*

"&"*R / = R

& !/ = &"4*

"

// " /0# /+# & /

+ ' #1 & D4' ,4 &

", & 6 "1 /7 ′′ = !+7 ′ = & *

;#7 &&&1

" ",& &*","

$$$,' " !!!,' ##/,' & #-$,'

Page 11: Ee 2004 Gate Paper

0 ' #1

1&& &QR

&

&

)

QR"

0- #− " 0-/

+##/ & #−

- 'D4'#1"1&!!,4G

>1&&&*&&)

! & = = = &&&&

*& &"1&"

!- " #### +++0 & -#

/ '$1D4'!!,4"1 &&1

-A&&*&

"*$7. & )D."

!- " - -$- & /

+ '*&"&&!&*

(&&")&

+ " ! + & !$

+ '&&&8

-'

" '

'

& 1#'

+! &

A2(.

" -#,Ω

& !,Ω

"

=

- =

(@;

48!8

-4

β;

,S

4@@

@;α 4

2@

4A

@;α

,S,S

@;α

Page 12: Ee 2004 Gate Paper

F$4

'2

4;14

+# 2 9DEA ""&

!!Ω " $0Ω +-Ω & !Ω

+$ (;"&ω)

&= " &= &= & &=

+

=

F,Ω

" 1,Ω

FDΩ

& 1DΩ

++ & ? 6 ( ) ( ) = + + "

+ " '8F?

( ) ( ) + + & +

2!

F

1

2;!,Ω

(6

F

1

2;,Ω

2#;DΩ

2!;,Ω

46

Page 13: Ee 2004 Gate Paper

?# '# ?!'! ? '? '

>

+0 '&" # ! # !

>;"

" &

+- &&&,@"

"

&

92;

@3;

E=9

@3C

J

C

@3C

Page 14: Ee 2004 Gate Paper

4E

,S

F4

4;

!S

(;!'

2 @ F

F

F

F

+/ ( A

4@I ;4 4E3

!4

" #4

!4

& 4

0 ( 6& " *,A'2E'3

A'2D4'$

A(23@

J. A(

'3

T

T

T

D$'

2*

J1A(

$ " - # & +

0 ) # !$ + − + + = " 1

"

" &

0! ",&( )( )

)

!

!

+ "

!

!

+ +

!

+ + &

!

+ +

Page 15: Ee 2004 Gate Paper

0# "&*N;'N

N&&'*6"*

!

!

=

)

1!&F! " 1B!&FB! 1!&1! & F!&1!

0$ ",&&*"*

C&9 *&0&&&)*ω&=*)

!&#

" !&!

!&#

& !&!

0 &&&1&&*"*

( ) +! - −= ≥

&*1*)

" ! &

0+ ( * 6 ; ( &*1

* "

( ) $

!

− " ( ) $

!

+ ( ) $ − & ( ) $ +

00 *&",*

( )!

+=

QR$H)

$ " $$ -$ & $

2

( )!

+@

F9

F

1

+

* 6

Page 16: Ee 2004 Gate Paper

0- '@2E"&,Ω

"&"9&&"

##4

" $#04

$$4

& 4

0/ '&&&&!

*(&&6&*!')

!%. " %. %. & %.

- '&'1 &'!4 $$'1=

&*"6&

#0=,5 " #+=,5 =,5 & /+=,5

- '&1)!$%.&

!H'&%=&

!%=& " $-%=&

!%=& & $+%=&

-! ' 1 & & " 2 & > $ 4

*#1$1*)2>?'

&*&-&

10/5

" 1/05

F/05

& F0/5

-# '"*@&*&*

'*"&Ω1

!"*&&*

$+H " -$H /$+H & 0$H

:

,Ω 9

,Ω@2E9"

4

,

2

>

?

.

5

Ω

-

Page 17: Ee 2004 Gate Paper

-$ 6@"-#&&

" $%5" !!5" & 5"

- 'DEAI&'&E.

DEAI Ω E.

DEAI

##-5

" 5

05

& #-5

-+

&,&&

#/+-5

" !/5

0/#5

& -5

-0 4& &*

A-&*&&&&8&&*

+' " +$' -' & '

-- &A &A!

6*&A&$4+'A!&$4#

' & !'&&*

,A

' " !' #' & $'

'

ω

π #π!π

!# ! ω α;$

π

2;Ω

A

8 Ω4

A

!%!'!4

8

A!

!%

Page 18: Ee 2004 Gate Paper

-/ ' 11& & *6&&

&",4='

*!Ω,

!#41#HK&&&"

##/ " #/ #++ & #-+

/ '" && & $. &&

) & & & &

$-,! " +$,!

/+,! & !-,!

F!.

)

A&

1

F