HartChapter6solutions.doc

CHAPTER 6 SOLUTIONS 5/17/10

6-1)  Po

= Vo Io = Vo Is ;

h =

 Po  P s

=

Vo Io Vs I s

Ps =

= Vs I s

V o V s

6-2)  I o =

 P  V o

=

100 30

= 3.33 A.

a ) P s = Vs Io = (100)(3.33) = 333 W .; h  =

 P o  P   s

=

100 333

= 30 %

b) PQ = VCE Io = (70)(3.33) = 233 W .  

1 yr.=87 r.=8760 60 Hr.; Hr.; W = (233 (233)( )(87 8760) 60)=2 =204 044 4 kW-H kW-Hr, r, c ) e.g., @10 cents/kW-Hr,

cst = !204.40/yr.

6-3) a ) Vo = Vs D = (100)(0.6) = 60 V .   b) Vo,rms = Vm D = (100) 0.6 = 77.5 V (s ee "#$&'e 2-4) c) P =

V o2,rms

77.52

= = 600 W . 10  R es'ts $re nt *e&en*ent *e&en*ent n +reency +reency.. d ) es'ts

6-4)

a ) Vo = Vs D = ( 24)(0.65) = 15.6 V .  

15.6 = 1.56 A. 10  R V  1 5 .6 1 (1 - 0.65) Di L = o (1 - D )T = = 2.18 A. -6 25(10) 100, 000  L

b) I L = I R =

V o

=

2.18 = 2.65 A. 2 2 2.18 Di = I L -  L = 1.56 = 0.47 A. 2 2

 I L ,$# = I L +  I L ,n

Di L

= 1 .5 6 +

c ) DV o = or 

Vo (1 - D)

8 LCf  DV o

V o

2

15.6 5.6(1 - 0.65) 65)

=

8(25)(10)-6 (15)(10) -6 (100, 000)2

= 0.182

= 1.17%

6-5) a ) Vo = Vs D =  V .   b) I L = 1.8 A.; DiL = 2.4 A.  I L ,$# = I L +  I L ,n = I L DV o

c)

V o

Di L

2 Di L 2

= 3.0 A. = 0.6 A.

= 0.44%

6-6) a) D =

V o V  s

= 0.5

b) I L = I R =

 P o V o

=

125 25

 I L ,$# = 6.25 A. �  L = c) D

V o Vo

C=

V o Di L

= 5 A. Di L

2

= 1.25; D iL = 2.5 A.=

(1 - D)T =

= 5% = .005 =

1 - D

�DV  � 2 8� o �  Lf  V  �o �

=

25 2.5

(1 - .5)

1 100, 000

V o  L

(1- D )T 

= 50

m H .

1- D 8 LC f 2   1 - .5 8(.005 8(.005)( )(50) 50)((10)-6 (100 100,, 000)2

= 25

m F .

6-7) a) D =

V o V  s

=

1.5 = 0.25 6 2

1.5 = = 0.5 A. b) average  I L = I R = 3  R V o

rms  I L ,rms

�0.5625 / 2 � = 0.5 + � � = 0.526 A. 3 � � 2

Di L = 0.5625

1 - .25 �1 1 - D � �1 � = 1.5 � +  peak  I L ,$# = Vo � + � �= 0.781 A. -6 2 3 2(5)(10) (400,000)  R Lf  � � � �

�1 1 - D �  I L ,n = V o � �= 0.21  A. 2  R Lf  � � c ) P s = Po � Vs I s = Vo I R � Is =

Vo I R V  s

=

1.5(0.5) = 0.125 A. 6

d ) I D ,$# = I L,$# = 0.781 A.  I D = I o - I s = 0.5 - 0.125 = 0.375 A.

6-8)  I o = I L =  D =

V o V  s

 P o V o

=

=

25 = 1.25 A. 30

20 = 0.667 30

 I L ,n = (0.25)(1.25) = 0.31 A. = I L -

Di L

2 Di L = ( I L - I L ,n )2 = (1.25 - 0.31)2 = 1.88 A. Di L =

 L =

V o

 L V o

Di L

(1 - D )T  (1 - D)

1 20 1 = = 8 ( 1 - .667 ) 40000 f  1.88

m H 

6-)  Ln =  D =

(1 - D) R

V o V  s

2 f  20 20 = 0.4; Dn = = 0.33 50 60

; D$# =

 I L = I R =

 P o V o

; I R ,n =

75 20

= 3.75 A.; I R ,$# =

202

V o

125 20

6.25 A.

202

= 5.33 W; Rn = = 3.20 W ; R$# = 75 125  P  (1 - Dn ) R$# (1 - .33)(5.33) = = 17.76 m H   Ln = 2 f  2(100, 000)

 R =

6-10)

(1 - D )( R)

 Ln =

2 f 

f = 200 kHz 

=5 

Vs, V

D

I, A.

R, Ω

Lmin, µH

10

0.5

0.5

10

12.5

10

0.5

1.0

5

0.5

10

6.25 16.7 (rst c$se,  = 1/3,  = 10)

1.0

5

8.33

15 15

1/3 1/3

 L =

 Ln

6-11)

"#$&'e *esgn

(1 - Dn ) R$# 2 f 

�- 1 � 1 (10) � � 3 � = 16.67 m H  =� 2(200 k )

 D =

V o

=

V  s

15 48

= 0.3125

 Let f = 100 kHz ( for eamp!e) V  �  Let Di L = 40% of I L = 0.40 � o  R �  L =

C=

15 � � � �= 0.40 �8 �= 0.75 A � � �

( V s - Vo ) D ( 48 - 15 ) 0.3125 = = 137.5 m H  ( Di L ) f  ( 0.75) 100,000 1 - D

�DV  � 8 L � o �f  �V o �

=

1 - 0.3125 8 ( 150 ) 10 -6 (0.005)100,000

= 12.5

m F 

ter $'es +  $n*  $re $'* + te n*ctr crrent s cntns t $rgn.

6-12) ($se* n te e#$&'e *esgn n 6-11)

$#, stc = s = 48  $#, **e = s = 48  9$#, stc = 9$# = 1.5 : 0.75/2 = 1.875  9$g, stc = 9rs, stc =

 9 

=

s 1

15 ( 1.875 ) 48

= 0.586

<

 ( t) * t = 1.06  (nerc$''y) < � 2 

0

9$#,**e = 9$# = 1.875  9$g,**e =9- 9$g,stc = 1.875  0.586 = 1.28  <

9rs,**e =

6-13) "#$&'e *esgn

1  2 ( t) * t = 1.56  ( nerc$''y) < <

�

 D =

V o V  s

 Let f

C

=

15 24

=

0.625

400 kHz ( for eamp!e)

=

 Let Di L  L =

=

=

40% of I L

= 0.40

( 2 ) = 0.8 A

( V s - Vo ) D ( 24 - 15) 0.625 = = 17.6 m H  ( Di L ) f   ( 0.8) 400,000 1 -  D

�DV  8 L � o �V o

1 - 0.625

=

� 8 ( 17.6 ) 10-6 (0.01)400,000 �f   �

= 1.67 m F 

6-14) "#$&'e *esgn  D =

V o V  s

=

12 18

= 0.667

 Let f = 200 kHz ( for eamp!e)  I L = Io =

 P o Vo

=

10W  12V 

= 0.833 A

 Let Di L = 40% of I L = 0.40 ( 0.833 ) = 0.333 A  L =

C=

( V s - Vo ) D ( 18 - 12 ) 0.667 = = 60 m H  ( Di L ) f  ( 0.333) 200,000 1 - D

�DV  � 8 L � o �f  �V o �

=

1 - 0.667 = 3.5 m F  0.1 � -6 � 8 ( 60 ) 10 � � 200, 000 �12 �

ter $'es +  $n*  $re $'* + te n*ctr crrent s cntns t $rgn.

6-15) " = 1 � V 1 = 30.27

>sng $c crct $n$'yss, Vo1 0.06 V o

=

0.06 20

=

=

0.048 V

=

2(0.048) = 0.06 V p - p

0.48% DV o

>sng ". 6 -16,

V o

=

0.46%

<e t&t 't$ge s $n'y te *c ter $n* te +rst $c ter.

6-16) a ) rC = 0.5 W, DiL = 2.88 A = D iC  DVo,E$R = D iC rC  = 2.88(0.5) = 1.44 V . DV o

V o b)

=

1.44 = 8% 18

DV o

V o

�0.5%

DVo �DVo ,E$R = DiC rC

50(10)-6 rC  = C

6-17)

 

� rC =   

DV o DiC 

=

0.005(18) = 0.031 W 2.88

50(10) -6 50(10)-6 = = 1600 � C= 0.031 r C 

m F .

20 = 50 V . 1 - D 1 - .6 20 V  s b) I L = = = 10 A. 2 (1 - D ) R (1 - .6) 2 (12.5) V  s

a ) Vo =

V s

 I $# =

(1 - D )2 R V s

 I n = c)

=

2

(1 - D ) R

DVo

Vo

=

+

20 20(.6) / (200,000) Vs DT   = + = 13 A. 2L (1 - .6) 2 (12.5) 2(10)(10) -6

-

Vs DT   = 7.0 A. 2L

0.6 = 0.6% RCf   12.5(40)(10)-6 (200,000) D

d )  I D = I o =

V o  R

=

=

50 = 4.0 A. 12.5

6-18)

9n*ctr crrent (see "#$&'e 2-8) 2

 I L ,rms

2

�D I  / 2 � �4.61/ 2 � 2 10 = I + �  L = + � � � = 10.0 A. � 3 � � 3 � 2 L

$&$ctr crrent (*e+ne t=0 $t &e$k crrent)

1/2

10  s 25 s � 1 � � � 5 2 2 ( 4.61(10) 8.3) ( 4) =� + + t dt dt � = 4.7 A. � � -6 �� � � 25(10) � � 10  s �0 � � � m

 IC ,rms

m 

m 

6-1) Vo =

V s

1 - D

� D = 1-

V s V o

= 1-

5 = 0.667 15

V o2

152 = = W  R = 25 25 5 V  s  I L = = = 5 A. (1 - D) 2 R (1 - .667) 2 ()  I L ,n = 0.5(5) = 2.5 A. � DI L = 5 A. D I L =

V s DT  D I  L

=

5(.667) / 300 5

 From E%. 6 - 27, C =

= 2.22

 D

� V o � D �f   R � � V o �

m H 

=

0.667 = 24.7 (.01)(300,000)

m F .

6-20) "#$&'e *esgn  D = 1 -

 R =

V  s V o

V o2

=

 P 

 I L =

=1-

182 20

12 18

= 0.333

= 16.2 W

V  s 2

( 1 - D ) R

=

12 2

( 1 - .333) 16.2

= 1.67 A

 Let f = 200 kHz   Let Di L = 40% of I L = 0.4 ( 1.67 ) = 0.667 A  L =

V s D

( Di L )

( Ln C =

f 

=

12 ( 0.333 ) (0.667)200,000

= 30 m H 

for co"ti"&o&sc&rre"t = 6 m H )  D

�DV  �  R � o �f  �V o �

=

0.333 16.2 ( 0.005) 200,000

= 20.6 m F 

6-21) 'si"g C = 48

m F,

R = 50 W , to" = 0.6T =

0.6 = 24 m s 25000

vo (t ) = Vo ,$# e- t / RC  vo (24

m s )

= Vo ,$# e

Vo ,$# - vo (24 DV o

V o

m s)

= 0.01 = 1%

-24/?(50)(48)

= Vo ,$#  ( 0.005)

= DVo = Vo ,$# - 0.005Vo ,$# �0.01Vo,$# 

6-22)

6-23) a ) Vo

= -Vs

� D � � 0.6 � = -12 = - 18 V . � � 1 - D � 1 - 0.6 � � � � �

b) E%. 6 - 31 I L  I L,$#

=

 I L,-n

=

c)

DV o

Vo

V s D  R (1 - D)

2

V s D  R (1 - D) 2 =

D

=

=

=

-

V s D  R (1 - D) 2 Vs DT  

=

2L Vs DT   2L

=

=

12(.6) (10)(1 - .6) 2

4.5 +

  =

4.5 A.

12(.6) / 200,000 2(10)(10) -6

=

6.3 A.

2.7 A. 0.6

RCf   10(20   )(10)-6 (200, 000)

=

0.015 = 1.5%

6-24)

9n*ctr crrent (see "#$&'e 2-8) 2

 I L, rms

=

2

�D I  / 2 � �3.6 / 2 � 2 I L2 + �  L � = 4.5 + � � = 4.62 A. 3 3 � � � �

$&$ctr crrent Ar cnenence, re*e+ne t = 0 $t te &e$k crrent. <e crrent s ten e#&resse* $s iC  ( t )

=

(

)

4.5 - 1.8 10 6 t A

= -1.8  A

for 2 m s < t < 5 m s

T 

 I rms

1 2 = i (t ) dt T 0

�

for 0 < t < 2 m s

T=

1 1 = = 5 ( 10-6 ) = 5m s f  200,000 1/2

5 s � 1 �2  s � � 2 2 -6 � � =� 4.5 -1.8 ( 10 ) dt + � (- 1.8) dt � � = 2.30 A. �� � � � 5(10)-6 � � � 2  s �0 � � � m

 I C ,rms

m 

m 

6-25) a ) Ar ". 6-48, D =  I L =

V s D  R (1 - D) 2

=

V o

=

V s + V o

24(.6) 10(1 - .6)2

36 24 + 36

= 0.6

=  A. � I L ,n = 0.4() = 3.6 A.

D I L = 2( - 3.6) = 10.8 A.

Ar ". 6-28,  L =

V s DT 

b) Ar ". 6-36, C =

D I  L

=

24(.6) = 13.3 m H  10.8(100,000)

 D

�DV  �  R � o �f  �V o �

=

0.6 10(0.005)(100,000)

= 120m F 

6-26) "#$&'e *esgn V o

>sng ". (6-48),  D =

>sng ". (6-4),

 R =

V o2  P 

=

502 75

=

V s + V o

 I L =

 P  V s D

=

50 40 + 50 75

40 ( 0.556 )

= 0.556

= 3.375 A.

= 33.3 W

ettng + = 100 kHB (*esgnerCs cce),  Ln =

( 1 - D )

2

R

2 f 

2

( 1 - 0.556 ) 33.3 = = 32. m H  2 ( 100, 000 )

se  $t 'e $st 25% '$rger t$n  n (41 m H).  cn &r$ctce s t se'ect  sc t$t D L = 40% + 9 L = 0.40 ( 3.375 ) = 1.35  A. >sng ". (6-45),  L =

V s D Di L f 

=

40 ( 0.556 ) 1.35 ( 100, 000 )

>sng ". (6-54),

C =

= 165

m H 

 D

�DV  �  R � o �f  �V o �

=

0.556 33.3 ( 0.01) ( 100,000 )

= 16.7 m  F 

6-27) "#$&'e *esgn

V o

>sng ". (6-48),  D =

$n*  D =

15 18 + 15

>sng Ln =

V s + V o

, D=

15 12 + 15

= 0.556 +r te 12- srce,

= 0.455 +r te 18- srce.

( 1 - D )

2

R

2 f 

, te rst c$se s +r  = 0.455 +r te 18- srce. 2

ettng + = 100 kHB (*esgnerCs cce), Ln

( 1 - 0.455 ) 15 = = 22.3 m H  2 ( 100,000 )

se  $t 'e$st 25% '$rger t$n  n (28 m H). 'tern$te'y, $ cn &r$ctce s t se'ect  sc t$t D L = 40% + 9 L .  I !  =

V o2 V s RD

=

152 18 ( 15 ) ( 0.455 )

= 1.83 A

Di L = 0.40 ( 1.83) = 0.73 A. >sng ". (6-45),

 L =

V s D Di L f 

=

18 ( 0.455 ) 0.73 ( 100, 000 )

>sng ". (6-54),

C=

C  =

0.556 15 ( 0.01) ( 100, 000 )

= 112

mH

 D

�DV  �  R � o �f  �V o � = 37 m F 

(100

m H  ''

De +ne)

, s D$se  n  = 0.556, (12- srce)

6-28) >sng te e$tns V o

 D =

 R =

V s + V o V o2  P 

 Ln =  I  L =

C =

( 1 - D )

2

R

2 f 

 P  V s D  D

�DV  �  R � o �f  �V o �

 $n* sng + = 100 kHB (*esgnerEs cce), res'ts $re sn n te t$D'e.

Vs, (V)

P (W)

D

R (Ω)

Lmin (µH)

IL (A)

C (µF)

10 10 14 14

10 15 10 15

0.545 0.545 0.462 0.462

14.4 .6 14.4 .6

14. .

1.83 2.75 1.55 2.32

37.

!." 13.

56.8 32.1 48.1

<e $'e +  s'* De D$se* n s = 14  $n* F = 10 W, ere n = 20. GH. e'ect te $'e +  $t 'e$st 25% '$rger t$n n (26.1 GA). >sng $nter cn crtern + I = 40% + 9, $g$n +r 14  $n* 10 W,  = 104 GH. <e $'e +  s 56.8 GA +r te rst c$se + s = 10  $n* F = 10 W.

6-2)

� D � � 0.6 � = - 12 = - 18 V . Vo = -Vs � � � � 1 1 0.6  D � � � �  Po

 I L 2 =  I L1 =

-Vo

 P o V  s

Di L1 = Di L 2 =

=

=

Vo2 R -V o

=

27 = 1.5 A. 18

27 = 2.25 A. 12

V s D  Lf  V s D  L2 f 

12(.6)

=

200 ( 10)

-6

(250, 000)

= 0.14 A.

= 0.2 A.

6-30)  D =

1 1 = = 0.333 20 V  s 11-10 V o

 I L 2 = I o = 1 A.  I L1 =

�10 � (1) = 0.5 A. IL2 = � � V  s �20 �

V o

Di L1 = Di L 2 =

V s D  L1 f V s D  L2 f

� L1 =

Vs D Di L1 f 

� L2 =

=

Vs D Di L 2 f 

20(0.333) = 1.33 mH 0.10(.5)(100,000)

=

20(0.333) = 0.667 mH 0.10(1)(100,000)

   

6-31) "#$&'e *esgn V o V s

=-

D

1- D

=

-30

25

= -1.2

�  D = 0.5455

 Po 60 D==޳==2.0 A;  I L 2 ===� -Vo 30

iL 2

 P 60 2.4 A;  I L1 === s�D==޳== V s 25

iL1

0.4(2.0)

0.4(2.4)

0.4 A

L2

0.48 A

L1

Vs D

25( 0.5445)

DiL 2 f 

0.4 ( 100, 000 )

Vs D

25 ( 0.5445)

DiL1 f 

0.48 ( 100, 000 )

et + = 100 kHB (*esgnerCs cce). C2 �

1 - D

�DV o � 8 L2 f 2 � � �V o �

=

1 - 0.5455

( 0.01) 8 ( 341( 10 -6 ) ) (100,000 )

 VC1 = Vs - Vo = 25 - ( - 30 ) = 55 V

2

= 1.67

m F 

� D vC1 = 0.05   ( 55 ) = 2.75 V

2

>sng  = o2 / P = ( -30 ) / 60 = 15 W, 30 ( 0.5455) V D = = 3.7 C1 � o  Rf DvC 1 15 ( 100,000 ) 2.75

m F 

 

341 m F 

284 m F 

6-32) =

  + s

=

12 12 + 5

= 0.706

 2 122 9 1 = = = 7.2 s  5(4) D 1 =

s  1+ 

=

9 1,$# = 7.2 + 9 1,n = 7.2 9 2 =

(5)(0.706) 10(10)-6 (100,000) 3.53 2

= 3.53

= 8.6

3.53 = 5.44 2

 12 = = 3  4

D 1 =

s  2+ 

9 2, $# = 3 + 9 2,n = 3 -

=

(5)(0.706) 20(10)-6 (100,000)

1.765 = 3.88 2 1.765 2

= 2.12

= 1.765

6-33)  = 9 1 =

s 

=

1-   2 s 

D 1 =

=

s  1+ 

3.3(.7) 7.7 2 3.3(5)

=

9 1,$# = 3.6 + 9 1,n = 3.6 9 2 =



D 1 =



=

s   2 + 

= 7.7

1 - .7

(3.3)(0.7) 4(10)-6 (300,000) 1.25 1.25 2

5

= 1.25

= 4.56

2

7.7

=

= 3.6

= 2.64

= 1.54

(3.3)(0.7) 10(10)-6 (300,000)

9 2,$# = 1.54 + 9 2,n = 1.54 D1 = D2 =

0.77

= 1.25

2 0.77 2

= 0.77

= 1.155

  + 

=

(7.7)(.7) 5(50)(10) -6 (300,000)

= 0.071

6-34) "$tn (6-6) +r te $er$ge 't$ge $crss te c$&$ctr 1 $&&'es 1 = s .

Wen te stc s c'se*, te 't$ge $crss 2 +r te nter$' < s  2 =  1

ssng t$t te 't$ge $crss 1 re$ns cnst$nt $t ts $er$ge $'e + s v L2 = VC1 = V s

(stc c'se*)

Wen te stc s &en n te nter$' (1 - )<, v L2 = -V o

(stc &en)

nce te $er$ge 't$ge $crss $n n*ctr s Ber +r &er*c &er$tn,

(

2, s c'se*

) ( < ) + ( 

s ( < )

- 

2, s &en

) ( 1 - ) < = 0

(1 - ) < = 0

res'tng n 

� � � 1-  � �

= s �

6-35) 9 1 = 9s = =

1 =

s

  + s

=

s  ( D 1 )+

9 2 = 9  = 2 =

 2

 

s  ( D 2 )+

=

62 (15)(2) 6

6 + 15

= 1.2

= 0.286

(15)(0.286)

=

0.4(1.2)250,000

=

=

6 2

= 35.7mH

= 3

(15)(0.286) 0.4(3)250,000

= 14.3mH

2 =  = 6 D2 = D =

  r  2 = 2+ 

1 = 2 = 28.6mA



�D �  �

� +  � �

=

0.286 = 28.6mA 2(.02)250,000

6-36) 

=

=

 + s 2.7

9 1 = 1 =

1

=

2.7 2.7 + 

= 0.231

= 2.7W

 2 s 

=

2.7 2 (2.7)

s 

( D 1 ) +

=

= 0.30

(0.231) 0.4(0.30)300,000

= 57.7mH

9 2 = 9  = 1 2 =

s 

( D 2 ) +

=

(0.231) 0.4(1)300,000

= 14.2mH

6-37) DiC = I L ,$# = 2.7 A. DV( , E$R = DiC rC  = (2.7)(0.6) = 1.62 V . DV ( ,E$R

V (

=

1.62 30

 

= 0.054 = 5.4%

Worst case  DV( = DV( ,C + DV( , E$R = 0.3 + 1.63 = 1.2 V . =  6.4% 6-38) $)itc* c!osed  v L

= Vs - VQ 

$)itc* ope" 

= V( - VD 

v L

avg (v L ) = 0  (Vs - VQ ) DT + (V( - VD )(1 - D) T =  0 \

V(

� D � � 1 - D � �

= VD - (Vs - VQ )  �

6-3) a ) Ln -

(1 - D) R 2 f

� R$# =

L2 f 

1- D

=

7.5(10)-6 (2)(40000) 1 - .375

= 12.5 W

b) Ar =20J, crrent s *scntns

� � � � � � 2 D 2(0.375) �= 48 � Vo = Vs � � 8 L � � 8(7.5)(10)-6 2 2 + +  D D � � �0.375 + (0.375) +  RT  � � 20/ 40000 � \ 18 �Vo �21.4 V . c) Lf n =

(1 - D) R 2

=

� � �= 21.4 V . � � �

(1 - 0.375)(20)

9ncre$se  Lf n  e. g., Ln

= 6.25 2 6.25 6.25 = = 157 m H or f n = = 64.1 kHz  40000 7.5 mH 

6-40) a ) R$#

2 Lf  2(120)(10)-6 (25000) = = = 62.5 W +r cntns crrent 0.6(1-).6)2  D(1 - D) 2

b) Ar =100J, tecrrent s *scntns

� 2 D 2 RT  � 1+ 1+ � �  L � � Vo = V s � � 2 � � � � � 2(.6) 2 (100) / 25000 � 1+ 1+ � � 120(10)-6 � �= 36 V . Vo = 12 � � 2 � � � � � � \ 30 �V o �36   for 25 �R �100 c ) Lf n = 4.8 � L >

4.8 25000

= 12

m H

or f >

4.8 120(10)-6

= 40 kHz.  

6-41) scntns crrent +r te Dck-Dst cnerter et < De te te t$t te stc s c'se* $n* 1< De te te t$t te stc s &en $n* te crrent n te n*ctr s &ste. Ar  $ 'ss'ess cnerter, te t&t &er s te s$e $s te n&t &er.  P s

= Vs I s = V s

 I $#  P  s =  P o

=

=

V s DT   L 2  s

V D 2T  2 L 2 o

V 

 R

V s2 D 2T 2 L V o V s

 I $# D � � 2 �

=  D

=

Vo2  R

RT  2L

6-42) Wen stces K1L $re c'se*, 1 $n* 2 $re cnnecte* n seres, e$c $ng s/2 'ts. Wen te K1L stces $re &ene* $n* te K2L stces $re c'se*,  = s + te srce &'s s/2 + 1, $kng  = 1.5s.

6-43)

20W

p(t) !r t"e M#$%&T

10W

0W (1.000m'405.19m) Average P = 405 mW -10W 0.990ms W(M1)

0.992ms AVG(W(M1))

0.994ms  

0.996ms Time

0.998ms

1.000ms

6-44) '$te te Dck cnerter + "#$&'e 6-1 sng F&ce. ($) >se $n *e$' stc $n* *e$' **e. eterne te t&t r&&'e 't$ge. &$re yr F&ce res'ts t te $n$'ytc res'ts n "#$&'e 6-1. (D) eterne te ste$*y-st$te t&t 't$ge $n* 't$ge r&&'e sng $ stc t $n n resst$nce + 2 J $n* te *e+$'t **e *e'

>sng n =0.01 +r te stc $n* n=0.01 +r te **e, te &-& r&&'e 't$ge s 3.83 . 3.83/20 = 0.46%, $greeng &recse'y t te $n$'ytc$' res'ts.

Wt n = 2 s, te &-& r&&'e s 0 , t $ re*ce* $er$ge $'e.

6-45)  Mte t$t +r e$c cnerter t&'gy, te $er$ge 't$ge $crss e$c n*ctr s Ber, $n* te $er$ge crrent n e$c c$&$ctr s Ber.

#$%& C'n*+*  +r "s. (6-) $n* (6-17)  = s 

$n*

9s

9 =



Ar te $er$ge* crct + Ag. 6.33D,

9  = 9 =  c $& = s

$n* $n*

�

9 s =  c

9 =

�

 = $&

9s 

 = s

#''s+ C'n*+*  +r "s. (6-27) $n* (6-28) t$t  =

s 1- 

9 = 9s ( 1 -  )

$n*

Ar te $er$ge* crct + Ag. 6.33c,

$& = s - 

$n*

9 = -c +  c = c (  - 1)

$& = -  $n*

�

9 s = - c

 =

�

s 1-  9 = 9 s (1-  )

#$%&-#''s+ C'n*+*  +r "s. (6-47) $n* (6-4) $n* &rece*ng e$tns t$t � �  = -s � $n* 9s = 9  � 1-  � � Ar te $er$ge* crct + Ag. 6.33*,

9  = c

$n*

�

9s =  c

$& = s - 

$n*

9 s = 9 

 = -$&

�  = -s � 1-  �

�

$& C'n*+*  +r "s. (6-5) $n* (6-61) t$t 9 1 9 2

=

 1- 

�  = - s � 1-  �

$n*

Ar te $er$ge* crct,

$& = s - 

$n*

$& = -

 c =  c + 9 2

$n*

9 1 =  c

�  = -s � 1-  �

� �

9 1 9 2

=

 1- 