Chapter 3 Problem Solutions 3.1

210 0.08 0.333 mA/V2 1.2 2n

nkWK

L′⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞= = =⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠⎝ ⎠

For 0.1 VDSV = ⇒ Non Sat Bias Region (a) 0 0GS DV I= ⇒ =

(b) ( )( ) ( )21 V 0.333 2 1 0.8 0.1 0.1 0.01 mAGS DV I ⎡ ⎤= = − − =⎣ ⎦

(c) ( )( ) ( )22 V 0.333 2 2 0.8 0.1 0.1 0.0767 mAGS DV I ⎡ ⎤= = − − =⎣ ⎦

(d) ( )( ) ( )23 V 0.333 2 3 0.8 0.1 0.1 0.143 mAGS DV I ⎡ ⎤= = − − =⎣ ⎦

3.2 All in Sat region

210 0.08 0.333 mA/V1.2 2nK ⎛ ⎞⎛ ⎞= =⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(a) 0DI =

(b) [ ]20.333 1 0.8 0.0133 mADI = − =

(c) [ ]20.333 2 0.8 0.480 mADI = − =

(d) [ ]20.333 3 0.8 1.61 mADI = − = 3.3 (a) Enhancement-mode (b) From Graph VT = 1.5 V Now

( )( )( )( )

2

2

2

2

0.03 2 1.5 0.25 0.12

0.15 3 1.5 2.25 0.0666

0.39 4 1.5 6.25 0.0624

0.77 5 1.5 12.25 0.0629

n n n

n n n

n n n

n n n

K K K

K K K

K K K

K K K

= − = ⇒ =

= − = =

= − = =

= − = =

From last three, 2(Avg) 0.0640 mA/VnK = (c) 2

2

(sat) 0.0640(3.5 1.5) (sat) 0.256 mA for 3.5 V(sat) 0.0640(4.5 1.5) (sat) 0.576 mA for 4.5 V

D D GS

D D GS

i i Vi i V

= − ⇒ = == − ⇒ = =

3.4 a.

( ) ( )0

0 2.5 2.5 GS

DS GS TN

VV sat V V V

== − = − − =

i.

( ) ( )( ) ( )2

0.5 V Biased in nonsaturation

1.1 2 0 ( 2.5) 0.5 0.5 2.48 mADS

D D

V

I I

= ⇒

⎡ ⎤= − − − ⇒ =⎣ ⎦

ii.

( ) ( )( )2

2.5 V Biased in saturation

1.1 0 2.5 6.88 mADS

D D

V

I I

= ⇒

= − − ⇒ =

iii. VDS = 5 V Same as (ii) 6.88 mADI⇒ = b. VGS = 2 V

( ) ( )sat 2 2.5 4.5 VDSV = − − = i.

( ) 2

0.5 V Nonsaturation

1.1 2(2 ( 2.5))(0.5) (0.5) 4.68 mADS

D D

V

I I

= ⇒

⎡ ⎤= − − − ⇒ =⎣ ⎦

ii.

( ) 2

2.5 V Nonsaturation

1.1 2(2 ( 2.5))(2.5) (2.5) 17.9 mADS

D D

V

I I

= ⇒

⎡ ⎤= − − − ⇒ =⎣ ⎦

iii.

( ) ( )( )2

5 V Saturation

1.1 2 2.5 22.3 mADS

D D

V

I I

= ⇒

= − − ⇒ =

3.5

( )0 2 2 DS GS TNV V V V> − = − − = Biased in the saturation region

( )

( )

2

2

20.0801.5 0 2 9.375

2

nD GS TN

k WI V VL

W WL L

′= ⋅ −

⎛ ⎞⎛ ⎞= − − ⇒ =⎡ ⎤⎜ ⎟⎜ ⎟ ⎣ ⎦⎝ ⎠⎝ ⎠

3.6

( )( )( )14 10600 3.9 8.85 10 2.071 10n oxn n ox

ox ox ox

k Ct t t

μμ− −×∈ ×′ = = = =

(a) 500 A 241.4 A/Vnk μ′ = (b) 250 282.8 A/Vnk μ′ = (c) 100 2207 A/Vnk μ′ = (d) 50 2414 A/Vnk μ′ = (e) 25 2828 A/Vnk μ′ = 3.7 a.

( )( )

( )( )

148 2

80 0

8

2

3.9 8.85 107.67 10 F/cm

450 10

21 64650 7.67 102 40.399 /

ox oxox

x x

n oxn

n

Ct t

C WKL

K mA V

μ

−−

−

−

×∈ ∈= = ⇒ = ×

×

= ⋅

⎛ ⎞= × ⎜ ⎟⎝ ⎠

=

b.

( ) ( )( )2 2

3 V Saturation

0.399 3 0.8 1.93 mAGS DS

D n GS TN D

V V

I K V V I

= = ⇒

= − = − ⇒ =

3.8

( )

( )

2

2

2 20.081.25 2.5 1.2 23.1 m

1.25 2

nD GS TN

kI V Vω

ω ω μ

′⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎛ ⎞⎛ ⎞ − ⇒ =⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

3.9

( ) ( )14

80

8 2

3.9 8.85 10

400 108.63 10 F/cm

oxox

x

Ct

−

−

−

×∈= =

×= ×

( ) ( )( )

8

5

21 600 8.63 102 2.5

1.036 10

n oxn

n

C WKL

W

K W

μ

−

−

= ⋅

⎛ ⎞= × ⎜ ⎟⎝ ⎠

= ×

( )( ) ( )

2

23 51.2 10 1.036 10 5 1 7.24 mD n GS TNI K V V

W W μ− −

= −

× = × − ⇒ =

3.10 Biased in the saturation region in both cases.

( )2

2p

D SG TP

k WI V VL

′= ⋅ +

(1) ( )20.0400.225 32 TP

W VL

⎛ ⎞⎛ ⎞= +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(2) ( )20.0401.40 42 TP

W VL

⎛ ⎞⎛ ⎞= +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

Take ratio of (2) to (1): 2

2

(4 )1.40 6.2220.225 (3 )

46.222 2.49 2.33 3

TP

TP

TPTP

TP

VVV V VV

+= =++= = ⇒ = −+

Then ( )20.0400.225 3 2.33 25.12

W WL L

⎛ ⎞⎛ ⎞= − ⇒ =⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

3.11

( )5 V, 0 5 V

0.5 5 0.5 4.5 S G SG

TP SD SG TP

V V VV V V sat V V V

= = ⇒ == − ⇒ = + = − =

a.

( )2

0 5 V Biased in saturation

2 5 0.5 40.5 mAD SD

D D

V V

I I

= ⇒ = ⇒

= − ⇒ =

b.

( )( ) ( )2

2 V 3 V Nonsaturation

2 2 5 0.5 3 3 36 mAD SD

D D

V V

I I

= ⇒ = ⇒

⎡ ⎤= − − ⇒ =⎣ ⎦

c.

( )( ) ( )2

4 V 1 V Nonsaturation

2 2 5 0.5 1 1 16 mAD SD

D D

V V

I I

= ⇒ = ⇒

⎡ ⎤= − − ⇒ =⎣ ⎦

d. 5 V 0 0D SD DV V I= ⇒ = ⇒ = 3.12 (a) Enhancement-mode (b) From Graph VTP = + 0.5 V

( )( )( )( )

2

2

2

2

2

0.45 2 0.5 2.25 0.20

1.25 3 0.5 6.25 0.20

2.45 4 0.5 12.25 0.20

4.10 5 0.5 20.25 0.202Avg 0.20 mA/V

p p p

p p

p p

p p

p

k K K

k K

k K

k KK

= − = ⇒ =

= − =

= − =

= − ==

(c) 2

2

(sat) 0.20 (3.5 0.5) 1.8 mA(sat) 0.20 (4.5 0.5) 3.2 mA

D

D

ii

= − == − =

3.13 ( )SD SG TPV sat V V= +

(a) ( ) ( )1 2 1 SD SDV sat V sat V= − + ⇒ =

(b) ( ) ( )0 2 2 SD SDV sat V sat V= + ⇒ =

(c) ( ) ( )1 2 3 SD SDV sat V sat V= + ⇒ =

( ) ( ) 22

2 2p p

D SG TP SD

k kW WI V V V satL L

′ ′= ⋅ + = ⋅ ⋅ ⎡ ⎤⎣ ⎦

(a) ( )( )20.040 6 1 0.12 2D DI I mA⎛ ⎞= ⇒ =⎜ ⎟

⎝ ⎠

(b) ( )( )20.040 6 2 0.48 2D DI I mA⎛ ⎞= ⇒ =⎜ ⎟

⎝ ⎠

(c) ( )( )20.040 6 3 1.08 2D DI I mA⎛ ⎞= ⇒ =⎜ ⎟

⎝ ⎠

3.14

(sat) 3 0 8 2 2 VSD SG TPV V V . .= + = − =

215 0 04 0 25 mA/V1 2 2P

.K ..

⎛ ⎞⎛ ⎞= =⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

a) VSD = 0.2 Non Sat ( )( ) ( )20 25 2 3 0 8 0 2 0 2 0 21 mADI . . . . .⎡ ⎤= − − =⎣ ⎦

b) VSD = 1.2 V Non Sat ( )( ) ( )20 25 2 3 0 8 1 2 1 2 0 96 mADI . . . . .⎡ ⎤= − − =⎣ ⎦

c) VSD = 2.2 V Sat 20 25(3 0 8) 1 21 mADI . . .= − = d) VSD = 3.2 V Sat ID = 1.21 mA e) VSD = 4.2 V Sat ID = 1.21 mA 3.15

( )( )( )14 11

0 0 0

250 3 9 8 85 10 8 629 10p oxp p ox

x x x

. . .k Ct t t

μμ

− −×∈ ×′ = = = =

(a) 2500Å 17 3 A/Vox pt k . μ′= ⇒ =

(b) 2250Å 34 5 A/Vpk . μ′⇒ =

(c) 2100Å 86 3 A/Vpk . μ′⇒ =

(d) 250Å 173 A/Vpk μ′⇒ =

(e) 225Å 345 A/Vpk μ′⇒ = 3.16

( )( )

( ) ( )( )( ) ( )( )

148 2

80

8 2

8 2

3.9 8.85 106.90 10 F/cm

500 10

675 6.90 10 46.6 A/V

375 6.90 10 25.9 A/V

oxox

x

n n ox

p p ox

Ct

k C

k C

μ μ

μ μ

−−

−

−

−

×∈= = = ×

×

′ = = × ⇒

′ = = × ⇒

PMOS:

( )

( )

( )

2

2

2

2

0.02590.8 5 0.6 3.192

4 m 12.8 m

0.0259 3.19 41.3 A/V2

pD SG TP

p

p p

p

p p n

k WI V VL

W WL L

L W

K K K

μ μ

μ

′ ⎛ ⎞= +⎜ ⎟⎝ ⎠

⎛ ⎞⎛ ⎞ ⎛ ⎞= − ⇒ =⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠

= ⇒ =

⎛ ⎞= ⇒ = =⎜ ⎟⎝ ⎠

Want Kn = Kp

41.32 2

46.6 41.3 1.7724 m 7.09 m

pn

N p

N N

N

kk W WL L

W WL L

L Wμ μ

′′ ⎛ ⎞ ⎛ ⎞= =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⎛ ⎞⎛ ⎞ ⎛ ⎞= ⇒ =⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠

= ⇒ =

3.17

( )( )

( )( )( )( )

( )( )

( )

2

0 0

2

0 0

2 V, 0.2 2 1.2 0.128 mA1 1 781 k

0.01 0.128

4 V, 0.2 4 1.2 1.57 mA1 63.7 k

0.01 1.571 1 100 V

0.01

GS D

D

GS D

A A

V I

r rI

V I

r r

V V

λ

λ

= = − =

= = ⇒ = Ω

= = − =

= ⇒ = Ω

= = ⇒ =

3.18

( )( ) ( )( )

( )( )

( ) ( ) ( )

2 2

10

0

0.080 4 3 0.8 0.16 3 0.8 0.774 2

1 1 1 (max) 0.00646200 0.774

1 1min min 155 max 0.00646

D D

D D

A A

I I mA

r VI r I

V V V

λ λλ

λ

−

⎛ ⎞= − = − ⇒ =⎜ ⎟⎝ ⎠

= ⇒ = = ⇒ =

= = ⇒ =

3.19

( ) ( )

( )

2 2

2 0.8 2 2 0.35

2.5 0.837 2 0.35 10.4

TN TNO f SB f

TN f SB

SB SB

V V V

V V

V V V

γ φ φ

φ

⎡ ⎤= + + −⎣ ⎦⎡ ⎤Δ = = + −⎣ ⎦

+ = + ⇒ =

3.20

( ) ( )[ ]

2 2

0.75 0.6 2 0.37 3 2 0.37

0.75 0.6 1.934 0.8601.39 V

(sat) 2.5 1.39 1.11 V

TN TNo f SB f

TN

DS

V V r V

VV

φ φ⎡ ⎤= + + −⎣ ⎦⎡ ⎤= + + −⎣ ⎦

= + −== − =

(a) ( ) ( )20.08Sat Region 15 2.5 1.392

0.739 mA

D

D

I

I

⎛ ⎞= −⎜ ⎟⎝ ⎠

=

(b) ( ) ( )( ) ( )20.08Non-Sat 15 2 2.5 1.39 0.25 0.252

0.296 mA

D

D

I

I

⎛ ⎞ ⎡ ⎤= − −⎜ ⎟ ⎣ ⎦⎝ ⎠=

3.21 a.

( )( )6 80 6 10 275 10

16.5 VG ox x

G

V t

V

−= = × ×

=

%

b. 16.5 5.5 V3G GV V= ⇒ =

3.22 Want ( )( ) ( )6

0 03 24 6 10G ox x xV t t= = = ×% 5

0 1.2 10 cm 1200 Angstromsxt −= × = 3.23

( )2

1 2

18 10 3.6 V18 32G DD

RV V

R R⎛ ⎞ ⎛ ⎞= = =⎜ ⎟ ⎜ ⎟+ +⎝ ⎠⎝ ⎠

Assume transistor biased in saturation region

( )

( )( )( )

2

2

2

3.6 0.5 2 0.81.6 0.64

S G GSD n GS TN

S S

GS GS

GS GS

V V VI K V VR R

V VV V

−= = = −

− = −= − +

( ) ( )

( )( )( )

( )

2

2

0.6 2.96 0

0.6 0.6 4 2.962.046 V

23.6 2.046 0.777 mA

2

10 0.777 4 2 5.34 V

sat

GS GS

GS GS

G GSD D

S

DS DD D D S

DS

DS DS

V V

V V

V VI IR

V V I R RV

V V

− − =

± += ⇒ =

− −= = ⇒ =

= − += − + ⇒ =

>

3.24

(a)

(b)

4

1.67

4 5

ID(mA)

VDS(V)

Q-pt

Q-pt

(a) 4 V (sat) 4 0 8 3 2 VGS DSV V . .= = − =

( )2If Sat 0.25 4 0.8 2.561.44

D

DS

IV

= − == ×

Non-Sat ( )

( )( ) ( )

( )

2

2

2

2

4 2

4 0.25 1 2 4 0.8

4 2.6 0.250.25 2.6 4 0

2.6 6.76 4 1.88 V2 0.25

4 1.88 2.12 mA1

D D DS n D GS T DS DS DS

DS DS DS

DS DS

DS DS

DS

D

I R V K R V V V V V

V V V

V VV V

V

I

⎡ ⎤= + = − − +⎣ ⎦⎡ ⎤= − − +⎣ ⎦

= −− + =

± −= =

−= =

(b) Non-Sat region ( )

( )( ) ( )

2

2

2

5 2

5 0.25 3 2 5 0.8

5 7.3 0.75

D D DS n D GS T DS DS DS

DS DS DS

DS DS

I R V K R V V V V V

V V V

V V

⎡ ⎤= + = − − +⎣ ⎦⎡ ⎤= − − +⎣ ⎦

= −

( )

20.75 7.3 5 0

7.3 53.29 152 0.75

0.741 V5 0.741 1.42 mA

3

DS DS

DS

DS

D

V V

V

V

I

− + =

± −=

=−= =

3.25

(a)

(b)

ID(mA)

2.92

1.25

3.5 5 VSD(V)

Q-pt

(a) ( )3.5 sat 3.5 0.8 2.7 VSG DD SDV V V= = = − =

( )( )2If biased in Sat region, 0.2 3.5 0.81.46 mA

DI = −=

( )( )3.5 1.46 1.2 1.75 VSDV = − = × Biased in Non-Sat Region.

( )( )( ) ( )

( )( ) ( )( ) ( )

2

2

2

2

2

3.5 2

3.5 0.2 1.2 2 3.5 0.8

3.5 1.296 0.24 0.24 2.296 3.5 0

2.296 5.272 3.36 use sign 1.90 V2 0.24

0.2 2 3.5 0.8 1.9 1.9

SD D D SD p D SG TP SD SD

SD SD SD

SD SD SD

SD SD

SD SD

D

V I R V K R V V V V

V V V

V V VV V

V V

I

⎡ ⎤= + = + + −⎣ ⎦⎡ ⎤= + − −⎣ ⎦

= + −− + =

+ ± −= − =

⎡ ⎤= − − =⎣ ⎦ [ ]0.2 10.26 3.61

3.5 1.90 1.33 mA1.2

1.33 mA

D

D

I

I

−

−= =

=

(b) ( )5 V sat 5 0.8 4.2 VSG DD SDV V V= = = − =

If Sat Region ( )( )20.2 5 0.8 3.53 mA, 0D SDI V= − = < Non-Sat Region.

( )( )( ) ( )

( )

2

2

2

2

5 2

5 0.2 4 2 5 0.8

5 6.72 0.8 0.8 7.72 5 0

7.72 59.598 16 use sign 0.698 V2 0.8

5 0.698 1.08 mA4

SD p D SG TP SD SD

SD SD SD

SD SD SD

SD SD

SD SD

D D

V K R V V V V

V V V

V V VV V

V V

I I

⎡ ⎤= + + −⎣ ⎦⎡ ⎤= + − −⎣ ⎦

= + −− + =

± −= − =

−= ⇒ =

3.26

( )210 SD p SG TP

S

VI K V V

R−

= = +

Assume transistor biased in saturation region

( )

( )

2

1 2

20 10

22 20 10 4.67 V8 22

G

G

RVR R

V

⎛ ⎞= −⎜ ⎟+⎝ ⎠⎛ ⎞= − ⇒ =⎜ ⎟+⎝ ⎠

( ) ( )( )( )( )

( ) ( )( )( )

2

2

2

2

10 4.67 1 0.5 2

5.33 0.5 4 4

0.5 3.33 0

1 1 4 0.5 3.333.77 V

2 0.5

S G SG

SG SG

SG SG SG

SG SG

SG SG

V V V

V V

V V V

V V

V V

= +

− + = −

− = − +

− − =

± += ⇒ =

( )

( )( )( )

10 4.67 3.773.12 mA

0.52020 3.12 0.5 2 12.2 V

D D

SD D S D

SD

I I

V I R RV

− += ⇒ =

= − += − + ⇒ =

( )satSD SDV V>

3.27

0,G SG SV V V= = Assume saturation region

( )( )( )

( )( )( )

2

2

0.4

0.4 0.2 0.8

0.4 0.8 2.21 V0.2

5 0.4 5 5 3 V2.21 3 5.21 V

D p SG TP

S

S S

D D D

SD S D SD

I K V V

V

V V

V I RV V V V

= = +

= −

= + ⇒ =

= − = − = −= − = − − ⇒ =

( )satSD SDV V>

3.28

DD DQ D DSQ DQ SV I R V I R= + +

(1) ( )10 5 5DQ GSI V= + + and ( )2

2n

DQ GS TNk WI V V

L′⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

or (2) ( )20.060 1.22DQ GS

WI VL

⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

Let 2.5 GSV V=

Then from (1), ( )10 5 5 2.5 0.5 DQ DI I mA= + + ⇒ =

Then from (2), ( )20.0600.5 2.5 1.2 9.862

W WL L

⎛ ⎞⎛ ⎞= − ⇒ =⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

2.5 5 0.5

GSDQ S GS S S

DQ

VI R V R R k

I= ⇒ = = ⇒ = Ω

( ) ( )1 2

10 0.5 0.05 0.025 RI mAR R

= = =+

Then 1 210 400

0.025R R k+ = = Ω

( ) ( ) ( )2 21 2

1 2

2 10 2 2.5 200 400DD GS

R RV V R R kR R

⎛ ⎞ ⎛ ⎞= ⇒ = ⇒ = = Ω⎜ ⎟ ⎜ ⎟+ ⎝ ⎠⎝ ⎠

3.29

( )

( )

27525 0.9375 mA/V2

6 10 5 2 V6 14

n

G

K

V

⎛ ⎞= ⇒⎜ ⎟⎝ ⎠

⎛ ⎞= − = −⎜ ⎟+⎝ ⎠

( ) ( ) ( )

( )( )( )( )

2

2

2

5

2 5 0.9375 0.5 1

3 0.469 2 1

G GSD n GS TN

S

GS GS

GS GS GS

V VI K V V

R

V V

V V V

− − −= = −

− − + = −

− = − +

( )( )

( )( )

2

2

0.469 0.0625 2.53 0

0.0625 0.003906 4.746 2.26 V2 0.469

0.9375 2.26 1 1.49 mA

10 1.49 1.7 7.47 V

GS GS

GS GS

D D

DS DS

V V

V V

I I

V V

+ − =

− ± += ⇒ =

= − ⇒ =

= − ⇒ =

3.30 20 DQ S SDQ DQ DI R V I R= + + (1) 20 10SG DQ DV I R= + +

( )2

2p

DQ SG TP

k WI V VL

′⎛ ⎞⎛ ⎞= +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(2) ( )20.040 22DQ SG

WI VL

⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

For example, let 0.8 and 4 DQ SGI mA V V= =

Then ( )20.0400.8 4 2 102

W WL L

⎛ ⎞⎛ ⎞= − ⇒ =⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

( )0.8 4 5 DQ S SG S SI R V R R k= ⇒ = ⇒ = Ω

From (1) ( )20 4 10 0.8 7.5 D DR R k= + + ⇒ = Ω

( )( ) 1 21 2

20 0.8 0.1 250 RI R R kR R

= = ⇒ + = Ω+

( ) ( )( )1

1 2

20 2 2 4SGR

VR R

⎛ ⎞= =⎜ ⎟+⎝ ⎠

( )11 220 8 100 , 150

250R R k R k= ⇒ = Ω = Ω

3.31 (a) (i) ( )

( )

250 500 1.2 1.516

5 1.516 6.516 Q GS GS

DS DS

I V V V

V V V

= = − ⇒ =

= − − =⇒ =

(ii) ( )( )( )

21 0.5 1.2 2.61

5 2.61 7.61 Q GS GS

DS DS

I V V V

V V V

= = − ⇒ =

= − − ⇒ =

(b) (i) Same as (a) 1.516 GS DSV V V= =

(ii) 2.61 GS DSV V V= = 3.32

( )( )( )

( )( )

2

20.25 0.2 0.6

0.25 0.6 1.72 V 1.72 V0.2

9 0.25 24 3 V

D n GS TN

GS

GS GS S

D D

I K V V

V

V V V

V V

= −

= −

= + ⇒ = ⇒ = −

= − ⇒ =

3.33 (a)

ID(mA)

1.0

0.5

0.808

3.81 10 VDS(V)

Q-pt

( )( )

2

5 1 8 K0.50.5 0.25 1.4 2.81 V2.81 5

4.38 K0.5

D D

DQ GS GS

S S

R R

I V V

R R

−= ⇒ =

= = − ⇒ =− − −

= ⇒ =

(b) Let 8.2 K, 4.3 KD SR R= =

( ) ( )

( )

( )( )( )( )

2

2

2

2

5Now 0.25 1.4

4.35 1.075 2.8 1.96

1.075 2.01 2.89 0

2.01 4.04 12.427 2.82 V2 1.075

0.25 2.82 1.4 0.504 mA10 0.504 8.2 4.3 3.70 V

GSD GS

GS GS GS

GS GS

GS GS

D D

DS DS

VI V

V V V

V V

V V

I IV V

− − −= = −

− = − +

− − =

± += ⇒ =

= − ⇒ == − + ⇒ =

(c) If 4.3 10% 4.73 KSR = + =

( )

( )( )( )

2

2

2

5 1.18 2.8 1.96

1.18 2.31 2.68 0

2.31 5.336 12.65 2.78 V2 1.18

0.25 2.78 1.4 0.476 mA

GS GS GS

GS GS

GS

D D

V V V

V V

V

I I

− = − +

− − =

± += =

= − ⇒ =

If 4.3 10% 3.87 KsR = − =

( )( )

( )( )( )

2

2

2

5 0.9675 2.8 1.96

0.9675 1.71 3.10 0

1.71 2.924 12.0 2.88 V2 0.9675

0.25 2.88 1.4 0.548 mA

GS GS GS

GS GS

GS

D

V V V

V V

V

I

− = − +

− − =

± += =

= − =

3.34

( )

( )

( ) ( )

2

2

9 2.5 0.1 65

2

0.0250.1 2.5 1.5 82

DD SD DQ

pDQ SG TP

V V I RR R k

k WI V VL

W WL L

= += + ⇒ = Ω

′⎛ ⎞⎛ ⎞= +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

⎛ ⎞⎛ ⎞= − ⇒ =⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

Then for 4 , 32 L m W mμ μ= =

3.35

( )

( )( )

( )

( )

( )

( )

1 21 2

2

2

2

1 2

22 1

5 2 2.51.25

10 1.25 0.1 80

1.251.25 0.5 1.5 1.50.5

0.0811

2.5 0.0811 2.42

10 5

2.42 10 5 59.4 ,80

DQ S SDQ DQ

DQ

R

DQ p SG TP

SG SG

SG

G S SG

G

I R V II mA

I R R kR R

I K V V

V V

V V

V V V V

RVR R

R R k R

= + = +=

= = ⇒ + = Ω+

= +

= + ⇒ − =

=

= − = − =

⎛ ⎞= −⎜ ⎟+⎝ ⎠

⎛ ⎞= − ⇒ = Ω⎜ ⎟⎝ ⎠

20.6 k= Ω

3.36 (a)

5 VSD(V)

ID(mA)

0.429

Q-pt

( )

( )

( ) ( )

( )

2

2

5 5 2 12 K0.25

2

0.0350.25 15 1.2 2.18 V2

5 2.18 11.3 K0.25

2.18 2 4.18 V

DD D

DQ

pD SG TP

SG SG

S S

SD

VR R

I

kWI V VL

V V

R R

V

− − −= = ⇒ =

′⎛ ⎞⎛ ⎞= +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

⎛ ⎞= − ⇒ =⎜ ⎟⎝ ⎠

−= ⇒ =

= − − =

(b)

( ) ( )

( )

2

2

2

2

35 5% 36.75 A/V50.0367515 1.2

2 11.3

3.11 2.4 1.44 5

3.11 6.46 0.522 0

p

SGD SG

SG SG SG

SG SG

kV

I V

V V V

V V

μ′ = + =−⎛ ⎞= − =⎜ ⎟

⎝ ⎠

− + = −

− − =

( )

( )( )

6.46 41.73 6.49 2.155 V2 3.11

5 2.155 0.252 mA11.3

10 0.252 12 11.3 4.13 V

SG

D

SD

V

I

V

± += =

−= =

= − + =

( ) ( )

( )

( )

( )( )

2

2

2

2

35 5% 33.25 A/V50.0332515 1.2

2 11.3

2.82 2.4 1.44 5

2.82 5.77 0.939 0

5.77 33.29 10.59 2.198 V2 2.82

5 2.198 0.248 mA11.3

10 0.248 12 11.3 4.22 V

p

SGD SG

SG SG SG

SG SG

SG

D

SD

kV

I V

V V V

V V

V

I

V

μ′ = − =−⎛ ⎞= − =⎜ ⎟

⎝ ⎠

− + = −

− − =

± += =

−= =

= − + =

3.37

( )

( ) ( )

( )

( )( )

2 2

G

2

1 2

1 2

11

22

2

10 6 105 0.8 k

5 3 1.75

5 1.75 3.04 V V 3.043

10 5 3.04

|| 80 k1 80 10 5 3.04 408 k

408 80 99.5 k408

SDD D

D D

D P SG TP SG

SG

G

in

VI R

R R

I K V V V

V

RVR R

R R R

RR

R RR

− − − − += ⇒ = ⇒ = Ω

= + ⇒ = −

= + = ⇒ = −

⎛ ⎞= − = −⎜ ⎟+⎝ ⎠= = Ω

⋅ = − ⇒ = Ω

= ⇒ = Ω+

3.38

(a) ( )

( )

21

22

60 4 120 A/V2

60 1 30 A/V2

n

n

K

K

μ

μ

⎛ ⎞= =⎜ ⎟⎝ ⎠⎛ ⎞= =⎜ ⎟⎝ ⎠

For 1 ,Iv V= M1 Sat. region, M2 Non-sat region.

( )( ) ( ) ( )2 1

2 230 2 5 5 120 1 0.8D D

TNL O O

I I

V v v

=

⎡ ⎤− − − − = −⎣ ⎦

We find 2 6.4 7.16 0 4.955 O O Ov v v V− + = ⇒ =

(b) For 3 ,Iv V= M1 Non-sat region, M2 Sat. region. 2 1D DI I=

( ) ( )2 230 1.8 120 2 3 0.8 O Ov v⎡ ⎤− − = − −⎡ ⎤⎣ ⎦ ⎣ ⎦

We find 24 17.6 3.24 0 0.193 O O Ov v v V− + = ⇒ =

(c) For 5 ,Iv V= biasing same as (b)

( ) ( )2 230 1.8 120 2 5 0.8 O Ov v⎡ ⎤− − = − −⎡ ⎤⎣ ⎦ ⎣ ⎦

We find 24 33.6 3.24 0 0.0976 O O Ov v v V− + = ⇒ = 3.39 For 5 ,Iv V= M1 Non-sat region, M2 Sat. region.

( ) ( )

( )( ) ( ) ( ) ( )

1 2

221 1 1 1 2 2

1 2

22

1

22 2

2 5 0.8 0.15 0.15 1 0 2

D D

n nGS TN DS DS GS TN

I Ik kW WV V V V V V

L LWL

=′ ′⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞⎡ ⎤− − = −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎣ ⎦⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎡ ⎤− − = − −⎡ ⎤⎜ ⎟ ⎣ ⎦⎣ ⎦⎝ ⎠

1

which yields 3.23WL

⎛ ⎞ =⎜ ⎟⎝ ⎠

3.40 a. M1 and M2 in saturation

( ) ( )

( )( )( )

2 21 1 1 2 2 2

1 2 1 2 1 2 0

2

, 2.5 V, 2.5 V

15 40 2.5 0.8 1.73 mA

n GS TN n GS TN

n n TN TN GS GS

D D

K V V K V VK K V V V V V

I I

− = −= = ⇒ = = =

= − ⇒ =

b.

1 21 2

GS GSW W V VL L

⎛ ⎞ ⎛ ⎞> ⇒ <⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

( ) ( ) ( )

( ) ( )

2 21 2

2 1

1 1

1 1

40 0.8 15 0.85

1.633 0.8 5 0.82.633 5.506 2.09 V

GS GS

GS GS

GS GS

GS GS

V VV V

V VV V

− = −= −

− = − −= ⇒ =

2 0 12.91 V, 2.91 VGS GSV V V= = =

( )( )( )215 15 2.91 0.8 1.0 mAD DI I= − ⇒ = 3.41 (a)

( )

( )

( )

1 3

2

3

3

2 2 2 1

2

2 2

1 2

2

1 1

2.5 V0.060.5 2.5 1.2

2

9.86

6 V 6 2.5 3.5 V0.060.5 3.5 1.2 3.15

210 10 6 4 V

0.060.5 4 1.2 2.2

GS

D

GS

GS

V VWIL

WL

V V V VW WL L

V VW WL L

= =

⎛ ⎞ ⎛ ⎞= = −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⎛ ⎞ =⎜ ⎟⎝ ⎠

= ⇒ = − = − =

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= − ⇒ =⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

= − = − =

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= − ⇒ =⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

13

(b) 2

12

2 3

0.06 5% 0.063 mA/V0.6 5% 0.057 mA/V

n

n n

kk k

′ = + =′ ′= = − =

For M3: ( ) ( )21

0.0579.86 1.22DI V⎛ ⎞= −⎜ ⎟

⎝ ⎠

For M2: ( ) ( )22 1

0.0573.15 1.22DI V V⎛ ⎞= − −⎜ ⎟

⎝ ⎠

For M1: ( ) ( )22

0.0632.13 10 1.22DI V⎛ ⎞= − −⎜ ⎟

⎝ ⎠

( ) ( ) ( )2 2 21 2 1 20.281 1.2 0.0898 1.2 0.0671 8.8V V V V− = − − = −

Take square root. ( ) ( ) ( )1 2 1 2

(1) 0.830 0.300 0.276 (2) 0.559 0.300 2.641 2 2 1

0.530 1.2 0.300 1.2 0.259 8.8V V V V

V V V V= + = +

− = − − = −

From (2) 2 10.537 4.72V V⇒ = + Substitute into (1)

[ ]1 1 1

1

0.830 0.300 0.537 4.72 0.276 0.161 1.692.53 VV V V

V= + + = +

=

( )2

2

Then0.537 2.53 4.726.08 V

VV

= +=

3.42 ML in saturation MD in nonsaturation

( ) ( )

( )( ) ( )( ) ( )

[ ]

2 2

2 2

2

1 5 0.1 0.8 2 5 0.8 0.1 0.1

16.81 0.83

20.3

GSL TNL GSD TND DSD DSDL D

D

D

D

W WV V V V V VL L

WL

WL

WL

⎛ ⎞ ⎛ ⎞ ⎡ ⎤− = − −⎜ ⎟ ⎜ ⎟ ⎣ ⎦⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎡ ⎤− − = − −⎜ ⎟ ⎣ ⎦⎝ ⎠

⎛ ⎞= ⎜ ⎟⎝ ⎠

⎛ ⎞ =⎜ ⎟⎝ ⎠

3.43 ML in saturation MD in nonsaturation

( ) ( )

( )( ) ( )( ) ( )

[ ]

2 2

2 2

2

1 1.8 2 5 0.8 0.05 0.05

3.24 0.4175

7.76

GSL TNL GSD TND DSD DSDL D

D

D

D

W WV V V V V VL L

WL

WL

WL

⎛ ⎞ ⎛ ⎞ ⎡ ⎤− = − −⎜ ⎟ ⎜ ⎟ ⎣ ⎦⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎡ ⎤= − −⎜ ⎟ ⎣ ⎦⎝ ⎠

⎛ ⎞= ⎜ ⎟⎝ ⎠

⎛ ⎞ =⎜ ⎟⎝ ⎠

3.44

0 5 0.1 0.49 mA10

DDD

D

V VI

R− −= = =

Transistor biased in nonsaturation

( ) ( )( ) ( )2

0.49

0.015 2 4.2 0.8 0.1 0.1

0.49 0.01005 48.8

DIWL

W WL L

=

⎛ ⎞ ⎡ ⎤= − −⎜ ⎟ ⎣ ⎦⎝ ⎠⎛ ⎞= ⇒ =⎜ ⎟⎝ ⎠

3.45

( )

( )

( )

2

2

55 12 1.6 0.2 267

20.04012 5 0.8 34

2

D D DS

D D

nD GS TN

I R V VR R

k WI V VL

W WL L

= + += + + ⇒ = Ω

′⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

⎛ ⎞⎛ ⎞= − ⇒ =⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

γ

3.46

( )

( )

( )

2

2

55 0.15 15 1.6 217

2

0.02015 5 0.8 852

SD D D

D D

pD SG TP

V I R VR R

k WI V VL

W WL L

= + += + + ⇒ = Ω

′⎛ ⎞⎛ ⎞= +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

⎛ ⎞⎛ ⎞= − ⇒ =⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

γ

3.47 (a)

( )( )

( ) ( )( ) ( )

2

2

1 2

0.0602 22

5 0.2 2 0.030 2 5 0.8 0.2 0.220

0.24 0.0984 2.44

DD OGS TN O O

D

V V W V V V VR L

WL

W W WL L L

− ⎛ ⎞⎛ ⎞ ⎡ ⎤= − −⎜ ⎟⎜ ⎟ ⎣ ⎦⎝ ⎠⎝ ⎠− ⎛ ⎞ ⎡ ⎤= − −⎜ ⎟ ⎣ ⎦⎝ ⎠

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= ⇒ = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

(b)

( ) ( )

( )

2

2

2

5 0.062.44 2 5 0.820 2

5 12.30 1.4641.464 13.30 5 0

13.30 176.89 29.282 1.464

0.393 V

OO O

O O O

O O

O

O

V V V

V V VV V

V

V

− ⎛ ⎞ ⎡ ⎤= − −⎜ ⎟ ⎣ ⎦⎝ ⎠− = −

− + =

± −=

=

3.48

( )

( )( )

( )

211

1

221

2

2

2 2 1

3 2

2

sat20.080.1 0.5 10

2200 20100

nQ GS TN

nQ DS

kWI V VL

kWI VL

W W WL L L

W WL L

′⎛ ⎞⎛ ⎞= −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠′⎛ ⎞⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= ⇒ = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞⎛ ⎞= =⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠

M1 & M2 matched.

( ) ( )21

1

1

0.08Then 0.1 10 0.252

0.75 V0.75 2 1.25 V

2.5 1.25 12.5 K0.1

GS

GS

D

D D

V

VV

R R

⎛ ⎞= −⎜ ⎟⎝ ⎠

== − + =

−= ⇒ =

3.49 (a)

( )( )

( )

( )

2

2

2

2

2

sat2

0.040.25 0.8 19.52

100 19.5 7.81250

pQ SDB

B

B B A

KQ

C BQ

kWI VL

W W WL L L

IW WL I L

′⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= ⇒ = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞=⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⎛ ⎞= =⎜ ⎟⎝ ⎠

( )

( ) ( )

22

2

2

0.040.25 19.5 0.52

1.30 V

pQ SGA TP

A

SGA

SGA

kWI V VL

V

V

′⎛ ⎞⎛ ⎞= +⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

⎛ ⎞= −⎜ ⎟⎝ ⎠

=

(b)

( )1.3 4 2.7 V

2.7 59.2 K

0.25

DA

D D

V

R R

= − = −− − −

= ⇒ =

3.50

( )( )

( )

( )

( ) ( )

22

2

2

2 2 1

21

1

21

1 1

sat20.060.4 0.5 53.3

2

20.060.4 53.3 0.75

21.25 V 1.25 4 2.75 V5 2.75 5.625 K

0.4

nQ DS

nQ GS TN

GS

GS D

D D

kWI VLW W WL L L

kWI V VL

V

V V

R R

′⎛ ⎞⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= ⇒ = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

′⎛ ⎞⎛ ⎞= −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎛ ⎞= −⎜ ⎟⎝ ⎠

= = − + =−= ⇒ =

3.51

( )satDS GS PV V V= −

So ( )sat , DS DS P D DSSV V V I I> = − =

3.52

( ) ( )sat 3 satDS GS P GS DSV V V V V= − = + =

a. 0 6 mAGS D DSSV I I= ⇒ = =

b. 2 211 6 1 2.67 mA

3GS

D DSS DP

VI I I

V⎛ ⎞ −⎛ ⎞= − = − ⇒ =⎜ ⎟ ⎜ ⎟−⎝ ⎠⎝ ⎠

c. 226 1 0.667 mA

3D DI I−⎛ ⎞= − ⇒ =⎜ ⎟−⎝ ⎠

d. 0DI =

3.53 2

2

2

2

2

2

1

12.8 1

30.30 1

112.8 9.33

0.30 31

113.055

31

1 9.1651 3.055

8.165 2.055 3.97 V

12.8 1 0.563.97

GSD DSS

P

DSSP

DSSP

P

P

P

P

P P

PP

DSS DSS

VI IV

IV

IV

V

V

V

V

V V

VV

I I

⎛ ⎞= −⎜ ⎟

⎝ ⎠

⎛ ⎞= −⎜ ⎟

⎝ ⎠

⎛ ⎞= −⎜ ⎟

⎝ ⎠

⎛ ⎞−⎜ ⎟

⎝ ⎠= =⎛ ⎞

−⎜ ⎟⎝ ⎠

⎛ ⎞−⎜ ⎟

⎝ ⎠ =⎛ ⎞

−⎜ ⎟⎝ ⎠

− = −

= ⇒ =

⎛ ⎞= − =⎜ ⎟⎝ ⎠

( )0 5.0 mADSSI⇒ =

3.54

, S GS SD S DDV V V V V= − = − Want ( )satSD SD P GSV V V V≥ = −

S DD P GS GS DD P GS DD PV V V V V V V V V V− ≥ − − − ≥ − ⇒ ≤ −

So 2.5 VDDV ≤ − 2

2

2 1

2 6 1 1.06 V 1.06 V2.5

GSD DSS

P

GSGS S

VI IV

V V V

⎛ ⎞= = −⎜ ⎟

⎝ ⎠

⎛ ⎞= − ⇒ = ⇒ = −⎜ ⎟⎝ ⎠

3.55

( )( )( )

2

2

2

18.5 0.35

86.2 0.5

D n GS TN

n TN

n TN

I K V V

K V

K V

= −

= −

= −

( )( )

( )

2

2

2 2

Then

0.3518.5 0.2146 0.221 86.2 0.50

18.5 0.35 0.221 1.11 /

TNTN

TN

n n

VV V

V

K K mA V

−= = ⇒ =

−

= − ⇒ =

3.56

( )( )

2

2 2250 0.75 0.24 0.961 /D GS TNI K V V

K K mA V

= −

= − ⇒ =

3.57

( ) ( )( )( )

( )( )

2

2

2

2

2

2

1

10 15 0.2

22 15 25

2 9 2 025 52 45 50 0

45 45 4 2 501.17 V

2 21.17 5.85 mA0.2

20 5.85 2 8.3 V

GS S GSD DSS

P S S

GS GS

GS GSGS

GS GS

GS GS

GS GS

GSD D

S

D

DS D S

V V VI IV R R

V V

V V V

V V

V V

V V

VI IR

VV V V

⎛ ⎞= − = = −⎜ ⎟

⎝ ⎠

⎛ ⎞− = −⎜ ⎟−⎝ ⎠⎛ ⎞

+ + = −⎜ ⎟⎝ ⎠

+ + =

+ + =

− ± −= ⇒ = −

= − = ⇒ =

= − == − 8.3 1.17 7.13 VDSV= − ⇒ =

3.58

( )2

8 10 2 V 5 0.4 k

1

DS DD S

S S D S S S

GSD DSS

P

V V VV V I R R R

VI IV

= −= − ⇒ = = = ⇒ = Ω

⎛ ⎞= −⎜ ⎟

⎝ ⎠

2

2

15 1 Let 10 mA

15 10 1 3.41 V

DSS DSSP

PP

I IV

VV

⎛ ⎞−= − =⎜ ⎟⎝ ⎠

⎛ ⎞−= − ⇒ = −⎜ ⎟⎝ ⎠

( )( )

2

1 2 1

11

22

2

1 2 1 V

1

11 500 10 5 M

5 0.5 0.556 M5

G GS S

G DD in DD

V V V

RV V R VR R R

RR

R RR

= + = − + =

⎛ ⎞= = ⋅ ⋅⎜ ⎟+⎝ ⎠

= ⇒ = Ω

= ⇒ = Ω+

3.59

2

2

1

5 8 1 0.838 V4

GSD DSS

P

GSGS

VI I

V

VV

⎛ ⎞= −⎜ ⎟

⎝ ⎠

⎛ ⎞= − ⇒ =⎜ ⎟⎝ ⎠

( )( ) ( )20 5 0.5 2 7.5 V

SD DD D S D

SD

V V I R RV

= − += − + ⇒ =

( ) ( )

2

1 2 1

20 5 0.5 17.5 V17.5 0.838 18.3 V

1

S

G S GS

G DD in DD

VV V V

RV V R V

R R R

= − == + = + =

⎛ ⎞= = ⋅ ⋅⎜ ⎟+⎝ ⎠

( ) ( ) 11

22

2

118.3 100 20 109 k

109100 1.21 M

109

RR

RR

R

= ⇒ = Ω

= ⇒ = Ω+

3.60

( )( )( )( )( )

( )

2

2

2

1 2

22 1

1

5 7 1 0.465 V3

6 12 5 0.3 0.9 k

12 5 0.3 10.5 V10.5 0.465 10.965 V

10.965 12 91.4 k 8.6 k100

GSD DSS

P

GSGS

SD DD D S D

D D

S

G S GS

G DD

VI IV

V V

V V I R RR R

VV V V

RV VR R

R R R

⎛ ⎞= −⎜ ⎟

⎝ ⎠

⎛ ⎞= − ⇒ =⎜ ⎟⎝ ⎠

= − += − + ⇒ = Ω

= − == + = + =

⎛ ⎞= ⎜ ⎟+⎝ ⎠

⎛ ⎞= ⇒ = Ω ⇒ = Ω⎜ ⎟⎝ ⎠

3.61

( )

( )( ) ( )

2

1 2

2

2

2

60 20 6 V140 60

1

8 2 1 64

16 1 62 16

G DD G

GS S G GSD DSS

P S S

GSGS

GS GSGS

RV V VR R

V V V VI IV R R

V V

V V V

⎛ ⎞ ⎛ ⎞= = ⇒ =⎜ ⎟ ⎜ ⎟+ +⎝ ⎠⎝ ⎠

⎛ ⎞ −= − = =⎜ ⎟

⎝ ⎠

⎛ ⎞− = −⎜ ⎟⎜ ⎟−⎝ ⎠

⎛ ⎞+ + = −⎜ ⎟

⎝ ⎠

( ) ( )

( )( )

2

2

2

9 10 0

9 9 4 101.30

2

1.308 1 3.65 mA

4

GS GS

GS GS

D D

V V

V V

I I

+ + =

− ± −= ⇒ = −

⎛ ⎞−= − ⇒ =⎜ ⎟⎜ ⎟−⎝ ⎠

( )( )( )

( )( )

20 3.65 2 2.72.85 V

sat1.30 4

2.7 V (Yes)

DS DD D S D

DS

DS DS GS P

V V I R R

VV V V V

= − += − +=> = −= − − −=

3.62

( )( )5 12 0.5 1 4.67 mA

DS DD D S D

D D

V V I R RI I

= − += − + ⇒ =

( ) ( )

( )2

1 2

4.67 0.5 2.33 V

20 12 0.511 V450 20

S D S S

G DD G

V I R V

RV V V

R R

= = ⇒ =

⎛ ⎞ ⎛ ⎞= = ⇒ =⎜ ⎟ ⎜ ⎟+ +⎝ ⎠⎝ ⎠

( )

2

2

0.511 2.33 1.82 V

1

1.824.67 10 1 5.75 V

GS G S GS

GSD DSS

P

PP

V V V V

VI I

V

VV

= − = − ⇒ = −

⎛ ⎞= −⎜ ⎟

⎝ ⎠

−⎛ ⎞= − ⇒ = −⎜ ⎟⎜ ⎟

⎝ ⎠

3.63

2

1 , 0

4 mA

10 3 1.75 k4

GSD DSS GS

P

D DSS

DD DSD D

D

VI I VV

I I

V VR R

I

⎛ ⎞= − =⎜ ⎟

⎝ ⎠= =

− −= = ⇒ = Ω

3.64

( )

( )

1 2

2

2

2

1 2

22

1

10 20 1 10 k

20 200 k0.1

1

1 2 1 0.586 V2

10 0.586 10.586

10.586 20 106 k200

94 k

SD DD D S

S S

DD

GSD DSS

P

GSGS

G S GS

G DD

V V I RR R

VR RI

VI I

V

VV

V V V

RV VR R

R R

R

= −= − ⇒ = Ω

+ = = = Ω

⎛ ⎞= −⎜ ⎟

⎝ ⎠

⎛ ⎞= − ⇒ =⎜ ⎟⎝ ⎠

= + = + =

⎛ ⎞= ⎜ ⎟+⎝ ⎠

⎛ ⎞= ⇒ = Ω⎜ ⎟⎝ ⎠

= Ω

3.65

( )( )( )( )

( )( )( )

( )

2

2

2

1 2

22

1

2 3 0.040 10 15 k

40 250 0.20 0.60 V

0.60 0.040 10 1.0 V

1 3 50 k150100 k

DS DD D S D

D D

D GS TN

GS GS

G GS S

G DD

V V I R RR R

I K V V

V V

V V V

RV VR R

R R

R

= − += − + ⇒ = Ω

= −

= − ⇒ =

= + = + =

⎛ ⎞= ⎜ ⎟+⎝ ⎠⎛ ⎞= ⇒ = Ω⎜ ⎟⎝ ⎠= Ω

3.66 For ( )0.70 0.70

0.75 0.15 0.6O DS DS GS TNV V V V sat V V= ⇒ = > = −

− =

Biased in the saturation region

( ) ( )2 2 2

3 0.7 46 50

46 0.75 0.15 128 /

DD DSD D

D

D GS TN

V VI I A

R

I K V V K K A V

μ

μ

− −= = ⇒ =

= − ⇒ = − ⇒ =