Solutions Manual for Power Electronics Circuits Devices and Applications 4th Edition by Rashid

Prob 2.1

−6 t := 5⋅ 10 rr ( a) Eq. (2.10)

di_dt := 80⋅ 10

6

6

QRR  := 0.5⋅  0.5 ⋅ di_dt⋅  di_dt⋅ trr 2 ( b)

3

QRR ⋅10 = 1 × 10

μC

Eq. (2-11)

IRR := 2⋅ QRR ⋅di_dt

IRR = 400

A

Prob 2.2 t

−6 := 5⋅ 10

rr

t

s

6 A

:= 800⋅ 10

I fall_rate

SF := 0.5

s

rr

−6 −

ta := 1 + SF

ta = 3.333 × 10

t := SF ⋅ t  b a

t = 1.667 × 10 b

I

RR

:= I

⋅t

3

fall_rate a

IRR = 2.667 × 10

Using Eq. (2-7), ( a)

1 QRR := 2

⋅t ⋅ t + t

⋅ I

(

1

Q RR := 2

fall_rate a

⋅I ⋅ t + RR 

(a

)(

 tb

a

 b

)

6

3

QRR ⋅10 = 6.667 × 10

μC

6

)

QRR ⋅10 = 6.667 × 10

μC

Using Eq. (2-6), ( b)

I

RR

:= I

3

3

⋅t

fall_rate a

IRR = 2.667 × 10

Page #2-1

Prob 2.3

−6

:= 5⋅ 10

t

SF := 0.5

rr rr

ta = 3.333 × 10

ta := 1 + SF

t =  1.667 × 10 b

t := SF ⋅ t  b a 1

−6 −

− 12

m := 2 ⋅ta⋅trr

m = 8.333 × 10

QRR ( x) := m⋅ x Plot of the charge storage verus di/dt

0.008

0.006

QRR  (x)   (x) 0.004

0.002

0

8

2 .10

4 .10

8

6 .10

8

x di/dt

Chapter 2-Diodes Circuits Page #2-2

8 .10

8

1 .10

9

IRR (x) (x) := ta⋅x Plot of the charge storage verus di/dt 4000

3000 e g a r to

IRR  (x)  (x) s e

2000 g r a h C

1000

0 1 .10

2 .10 3 .10 4 .10 5 .10

x di/dt

8 .10 9 . 10

−3

VT := 25.8⋅ 10

Prob 2.5

VD2 := 1.6

VD1 := 1.2

Using Eq. (2-3), ( a)

6 .10 7 .10

η :=

D2

−

ID2 := 1500

ID1 := 100

D1

η = 5.725

D2 VT⋅ln D1

x :=

( b)

D1

x = 8.124

η⋅VT

Using Eq. (2-3),

I I := S

D1

D1

x

e

= 1.2

VT⋅η⋅ln

IS Chapter 2-Diodes Circuits Page #2-3

I = 0.03 S

1 . 10

Prob 2-7 VD1 := 2200

VD2 := 2200

−3

I := 20⋅ 10 S1 ( a)

I

I := 35 ⋅ 10 S2

3

R 1 := 100⋅ 10

−3

V

D1

IR1 = 0.022

R1 := R  1

Using Eq. (2-13),

( b)

IR2 :=

−3

IR2 = 7 × 10

IS1 + IR1 − IS2

V

D2

R  := 2

5

R 2 = 3.143 × 10

IR2 VD := 2.8

Prob 2.11 IT := 300

I1 = 150 I := 1

IT I2 = 150

2

I2 := I1

VD2 := 2.3

VD1 := 1.4

R 

−3

R 1 = 9.333 × 10

VD − V D1

1 := I1

R 2 :=

VD − V D2 I2

I := IT 1 2

Chapter 2-Diodes Circuits Page #2-4

−3

R 2 = 3.333 × 10

Prob 2-13

3

R 2 := 50 ⋅ 10

R 1 := 50⋅ 10

−

I := 20⋅ 10

3

3

VS := 10⋅ 10

−

I := 30⋅ 10

s1 Using Eq. (2-14),

s2

VS

I −I S1

V D2 :=

S2 + R 1

1 R 1

+

3

VD2 = 4.625 × 10

1 R 2

V D1 := V S − V D2

VD1 = 5.375 × 10

Prob 2-15

 p  Ip := 500

f := 500

−6

t1 := 100⋅ 10

1

3

T ⋅ 10 =  2

T := f

t

I I

AVG

:=

1

 p

T

⋅ sin ( 2⋅π⋅f  ⋅t) dt

I

AVG

= 3.895

0

t1

I

RMS

I

 peak

1⋅

:= I  p

sin ( 2⋅π⋅f ⋅t)  dt

T ⌡0

:= I

 p

Chapter 2-Diodes Circuits Page #2-5

I

= 20.08 RMS

 peak   Ipeak = 500

3

Prob 2-16

−6

t := 100⋅ 10

I := 120 f  :=  := 500 RMS 1

1

3

T ⋅ 10 = 2

T := f

3

RMS

I :=  p

I = 2.988 × 10  p

t1

⋅ sin ( 2⋅π⋅f ⋅t)  dt

1

T ⌡0 1⋅

:= I

I

 p

RMS

t

 p

:=

AVG

⌡

T

I I

⌠ t1

T

( sin ( 2⋅π⋅f  ⋅t))2 dt

= 120

I

0

RMS

1

sin ( 2⋅π⋅f ⋅t) dt

⋅

I

AVG

= 23.276

0

Prob 2-17 I := 100 AVG 1

f := 500

t := 100 ⋅ 10 1

−6

3

T ⋅ 10 = 2

T := f

AVG

 p  Ip := 1

T

⌠

t1 2⋅π⋅f ⋅t dt

sin

⋅

I p  p = 1.284 × 10

0

t

I I := AVG

 p

1

⋅

sin ( 2⋅π⋅f ⋅t) dt

T ⌡0

:= I

I RMS

4

 p

IAVG = 100 1⋅

⌠ t1

2

( sin ( 2⋅π⋅f  ⋅t))

dt

T ⌡0 Chapter 2-Diodes Circuits Page #2-6

I

RMS = 515.55

Prob 2-18

−6

t := 100⋅ 10 1 − t := 1⋅ 10 5

−6

−6

t := 200⋅ 10 2 f := 250

t := 400⋅ 10 3

:= 150

I

I := 100 b

a

(

)

(

)

IAVG := Ia⋅f ⋅t3 + I b  2⋅  I p  b⋅f ⋅  t5 − t4 + 2⋅  p − Ia ⋅f ⋅

( a)

−6

t := 800⋅ 10 4

I := 300 p

( t2 − t1) π

I

( b)

r1 :=

( I p  p − Ia)⋅ f ⋅

IAVG = 22.387

( t2 − t1)

Ir1 = 16.771

2 r2 := Ia⋅ f ⋅t3

Ir3 :=  I b  b⋅ f

⋅

Ir2 = 47.434

( t5 − t4)

Ir3 = 22.361

I := I 2 + I 2 + I 2 r1 r3 rms r2

Prob 2-19

−6

t := 100⋅ 10 1 − t := 1⋅ 10 5

−6

−6

t := 200⋅ 10 2 f := 250

Irms = 55.057

t := 400⋅ 10 3

:= 150

I a

(

)

(

I := 100 b

)

 2⋅  I p  b⋅f ⋅  t5 − t4 + 2⋅  p − Ia ⋅f ⋅ ( a) IAVG := Ia⋅f ⋅t3 + I b

( b)

I

r1 :=

( I p  p − Ia)⋅ f ⋅

rms

r1

π

IAVG = 20

Ir2 = 47.434

( t5 − t4)

Ir3 = 22.361

⋅

2+ I

:= I

( t2 − t1)

Ir1 = 0

r2 := Ia⋅ f ⋅t3

I

I := 150  p

( t2 − t1) 2

Ir3 :=  I b  b ⋅ f

−6

t := 800⋅ 10 4

2+ I

r2

2

r3

Chapter 2-Diodes Circuits Page #2-7

Irms = 52.44

Prob 2-20

−6

−6 t := 100 ⋅ 10 1 − t := 1⋅ 10 5

−6

t := 200⋅ 10 2 f := 250

t := 400⋅ 10 3

I := 150 a

t := 800⋅ 10 4

I := 100 b

−6

I := 150 p

Irms := 180

Ir2 := Ia⋅

Ir3 := I b  b⋅ f I := r1

Ir2 = 47.434

f ⋅ t3

⋅

2−I

I

2− I

rms

r2

2

Ir1 = 172.192

r3

r1

( a)

 p  Ip:= f⋅

( t2

r1

(  p

I

:= rms

a

−

3

)

 t1

I p = 1.69 × 10  p

+ Ia

2

I := I − I ⋅

( b)

Ir3 = 22.361

( t5 − t4)

)

I r1

2

( t2 − t1) f⋅

Ir1 = 172.192

2

 + I 2+ I 2 r3 r2

(

Irms = 180

)

(

)

( t2 − t1)

IAVG := Ia⋅f ⋅t3 + I b  b⋅f ⋅ t5 − t4  + 2⋅ I p  p − Ia ⋅f ⋅

π

IAVG = 44.512

Chapter 2-Diodes Circuits Page #2-8

Prob 2-21

−6

−6 t := 100 ⋅ 10 1 − t := 1⋅ 10 5

t := 200 ⋅ 10 2 I f := 250

400 ⋅ 10 t := 400⋅ 3 := 150

−6

I := 100 b

a

−6

t := 800⋅ 10 4

I := 150 p

IAVG := 180 ( a) Iav1 = 15

Iav1 := Ia⋅f ⋅t3

I

av2

I

:= I ⋅f ⋅ t − t

av3

(5

 b

:= I

AVG

4

−I

)

Iav2 = 5

av1

−I

Iav3 = 160

av2

I

av3

 p  Ip := 2f ⋅

(

+ Ia

)

2 − t1

I p  p = 1.02 × 10

4

π

(

)

(

)

IAVG := Ia⋅f ⋅t3 +  b I b⋅f ⋅ t5 − t4  + 2⋅  p I p − Ia ⋅f ⋅

( t2 − t1) π IAVG = 180

( b)

I

r1 :=

( I p  p − Ia)⋅ f ⋅

( t2 − t1)

3

Ir1 = 1.124 × 10

2 Ir2 = 47.434

r2 := Ia⋅ f ⋅t3

Ir3 :=  I b  b⋅ f

⋅

( t5

−

 t4

)

I := I 2 + I 2 + I 2 r1 r3 rms r2

Chapter 2-Diodes Circuits Page #2-9

Ir3 = 22.361

3

Irms = 1.125 × 10

Prob 2-22 VS := 220

R := 4.7

−6

−6

C := 10⋅ 10

t := 2⋅ 10

−5

τ := R  ⋅ C

τ = 4.7 × 10

Using Eq. (2-20),

( a)

( b)

VS

 p  Ip := R

 p  Ip = 46.809

VO := VS W = 0.242

W := 0.5  0. 5⋅ C⋅  C ⋅ VO 2 Using Eq. (2-21),

−t τ ( c)

Vc = 9.165

V c := V S⋅ 1 − e

Prob 2-24 VS := 110

R := 4.7

L := 6.5⋅ 10

τ :=

−3

τ = 723.077

R  L Using Eq. (2-25), VS

( a)

ID

:=

R

( b)

ID = 23.404

IO := ID

W = 1.78

2

W := 0.5⋅ L⋅IO

4

Using Eq. (2-27),

( c)

di :=

di = 1.692 × 10

VS L

Chapter 2-Diodes Circuits Page #2-10

Prob 2-25 R := 4.7

VS := 220

τ :=

L := 6.5⋅ 10

R  L

−3

τ = 723.077

Using Eq. (2-25),

VS ID = 46.809

ID := R

( a) ( b)

IO := ID

W = 7.121

2

W := 0.5⋅ L⋅IO Using Eq. (2-27), di :=

( c)

VS

4

di = 3.385 × 10

L

Prob 2-29

−6

C := 10⋅ 10

VS := 110

L := 50⋅ 10

−6

Using Eq. (2-32),

( a)

I := V ⋅ C S L  p

t := π⋅ L ⋅ C 1 Using Eq. (2-35), ( b)

( c)

VC := 2⋅ VS

Chapter 2-Diodes Circuits Page #2-11

I = 49.193  p

t = 7.025 × 10 1

VC = 220

−5

Example 2.31

L :=  4 ⋅ 10

−3

C := 0.05⋅ 10

−6

Vs := 220

R

( a)

α = 2 × 10

α := 2⋅ L

R := 160

4

Using Eq. (2-41),

ωo := ωr  :=  :=

1

ωo = 7.071 × 10

L ⋅ C ωo 2

− α2

 = 6.782  × 10 ωr  =

Vs

A2 := ω ⋅L r t := 1

( b)

vc( t) := e

4

4

A2 = 0.811

π

t ⋅10 1

ωr

− α⋅ t

(

⋅A2⋅sin ωr ⋅t

6

μs

= 46.32

)

Probl 2-32

−3

C := 0.5 ⋅ 10

L := 2⋅ 10

−6

Vs := 220

R

( a)

4

α = 4 × 10

α := 2⋅ L

R := 160

1

ωo :=

L ⋅ C

2

s1 := − α +

at t = 0

2

di := 0

α > ωo 4

s2 = −6.449 × 10

α − ωo 2

i := 0

4

s1 = −1.551 × 10

α − ωo 2

s2 := − α − at t = 0

ωo = 3.162 × 10

0 ≡ A1 + A2

Vs L

≡ A 1⋅s1 + A2⋅ s2

Chapter 2-Diodes Circuits Page #2-12

4

Vs

A1 := L

⋅

( s1 − s2)

A1 = 2.245

A2 := −A1

)

A2 = −2.245

− α⋅ t⋅

vc( t) := e

( s1⋅ t − es2⋅ t)

A1⋅ e

Probl 2-33

−3

L := 2⋅ 10

−6

Vs := 220

C := 0.05⋅ 10

R

( a)

α = 4 × 10

α := 2⋅ L

R := 16

3

1

ωo := ωr  :=  := A2

L ⋅ C ωo 2

− α2

vc( t) := e

:=

I O

4

A2 = 1.101

π

t ⋅10 = 31.441 1

ωr

− α⋅ t

(

⋅A2⋅sin ωr ⋅t

μs

) −3

VS := 110

Prob 2-34

5

 = 9.992 × 10 ωr  =

Vs := ω ⋅L r t := 1

( b)

ωo = 1 × 10

L := 1⋅ 10

VS ⋅t L 1

t1 := 100 ⋅ 10

I = 11 O 2

W := 0.5⋅ L⋅IO

Chapter 2-Diodes Circuits Page #2-13

W = 7.121

−6

Example 2.36 V := 220 s  N2

:= 450⋅ 10

L

−6

:= 100

 N  N1 := 10

m

2

−6

t := 50⋅ 10 1

a :=  N1 a = 10 Using Eq. (2-52),

( a)

v

:= V ⋅( 1 + a) D s

3

= 2.42 × 10

v D

Using Eq. (2-55),

Vs

( b)

Io := Lm ⋅t1

I ( c)

Io = 24.444

:= Io a o_peak

= 2.444

I o_peak

Using Eq. (2-58),

( d)

( e)

t2 :=

a⋅ Lm⋅Io

t2⋅10

Vs

W := 1 ⋅L ⋅I 2 m o

6

= 500 μs

W = 0.134

J

Example 2.37 V := 220 s  N2 a :=

250 ⋅ 10 := 250⋅

L

−6  N1 := 10

m a = 1

 N1 Using Eq. (2-52),

( a)

vD := Vs⋅( 1 + a)

vD = 440

Using Eq. (2-55),

( b)

Vs

Io := Lm ⋅t1

:= 10

 N

Io = 44

Chapter 2-Diodes Circuits Page #2-14

2

−

t := 50⋅ 10 1

:=

I ( c)

Io

o_peak

a

I

o_peak

= 44

Using Eq. (2-58), ( d)

t2 :=

a⋅ Lm⋅Io

μs

2

Vs

W := 1 ⋅L ⋅I 2 mo 2

( e)

6

t ⋅10 = 50

W = 0.242

J

Example 2.38 Lm :=  250⋅  250 ⋅ 10

Vs := 220

−6

 N1 := 10

 N

2 := 1000 t1 := 50⋅ 10− 6

 N2

a :=

a = 100

 N1 ( a)

( b)

I :=

Vs

o

Lm

( d)

a⋅ Lm⋅Io

1

Io = 44

1

( c)

t2 :=

vD = 2.222 × 10

⋅t

I := Io a o_peak

( e)

4

vD := Vs⋅( 1 + a)

Io_peak = 0.44

6

Vs

W := 2 ⋅Lm⋅Io

2

t2⋅10 = 5 × 10 W = 0.242

Chapter 2-Diodes Circuits Page #2-15

3 J

μs