2.5 0.4 ()8.33 0.4 () ()0.6 ()36 0 - NTUT Solutions... · Microelectronics: Circuit Analysis and...

Microelectronics: Circuit Analysis and Design, 4th edition Chapter 4 By D. A. Neamen Problem Solutions ______________________________________________________________________________________

Chapter 4 4.1

(a) (i) DQn

m IL

Wkg ⎟

⎠⎞

⎜⎝⎛′=

22

( ) 5.25.021.025.0 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

(ii) ( )22 TNGSQn

DQ VVL

WkI −⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 4.24.05.221.05.0 2 =⇒−⎟⎠⎞

⎜⎝⎛= GSQGSQ VV V

(b) (i) ( ) 33.815.021.025.0 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

(ii) ( )( ) 0.14.033.821.015.0 2 =⇒−⎟⎠⎞


______________________________________________________________________________________ 4.2

(a) (i) DQp

m IL

Wkg ⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

22

( ) 12015.0204.022.1 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

(ii) ( )22 TPSGQ

pDQ VV

LWk

I +⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 85.06.0120204.015.0 2 =⇒−⎟

⎠⎞

⎜⎝⎛= SGQSGQ VV V

(b) (i) ( ) 3650.0204.022.1 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

(ii) ( )( ) 43.16.036204.050.0 2 =⇒−⎟

⎠⎞


______________________________________________________________________________________ 4.3

( ) ( )( )( )

[ ] [ ]( )( )

2

11

2 2

11 101 3.4

1 3.0 1 53.4 1 5 3.0 1 103.4 3.0 3 10 3.4 5 0.0308

5 12.5 k0.4

D n GS TN DS

DSD

D DS

DSo

D

I K V V V

VII V

VrI

λλλ

λ λλ λλ λ

= − +

++= ⇒ =

+ +

+ = +− = ⋅ − ⋅ ⇒ =

Δ= = = Ω

Δ ______________________________________________________________________________________

Microelectronics: Circuit Analysis and Design, 4th edition Chapter 4 By D. A. Neamen Problem Solutions ______________________________________________________________________________________ 4.4

( ) ( )

0

0

1

1 1 0.833 mA0.012 100

D

D D

rI

I Ir

λ

λ

=

= = ⇒ =

______________________________________________________________________________________ 4.5

(a) ( ) ( DSTNGSnD VVVKI λ+−= 12 ) ( )DSDOD VII λ+= 1

Then ( )( )λ

λ5.113.31

250.0258.0

++

=

Or ( ) 01826.03.315.11032.1 =⇒+=+ λλλ V 1−

( )( )[ ] 2433.05.101826.01250.0 =⇒+= DODO II mA

( )( ) 2252433.001826.0

11===

DOo I

rλ

kΩ

(b) ( ) ( )( )[ ] 2655.0501826.012433.0 =+=DI mA ______________________________________________________________________________________ 4.6 (a)

(i) ( )( )1 1 1000 K

0.02 0.05oD

rIλ

= = =

(ii) ( )( )1 100 K

0.02 0.5or = =

(b)

(i)

1 0.001 mA 1.0 A1000

DSD

o

VIr

μΔ

Δ = = = =

1.0 2%50

D

D

IIΔ

= ⇒

(ii)

1 0.01 10 A100

10 2%500

DSD

o

D

D

VI

rI

I

μΔ

Δ = = = ⇒

Δ= ⇒

______________________________________________________________________________________ 4.7

( )( )

1.0 mA1 1 100 K

0.01 1

D

oD

I

rIλ

=

= = =

______________________________________________________________________________________


(a) DSQDDQDD VRIV +=

mA ( ) 36.05.153.3 =⇒+= DQDQ II

( )22 TNGSQn

DQ VVL

WkI −⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 824.04.04021.036.0 2 =⇒−⎟⎠⎞


(b) ( ) 24021.0

2=⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

LWk

K nn mA/V 2

( )( ) 697.136.0222 === DQnm IKg mA/V

( )( ) 1.11136.0025.0

11===

DQo I

rλ

kΩ

( ) ( )( ) 12.851.111697.1 −=−=−= Dom RrgAυ ______________________________________________________________________________________ 4.9

(a) Dm RgA −=υ

mA/V ( ) 38.0108.3 =⇒−=− mm gg

DQnm IKg 2= DQn I

LWk

⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

22

( ) 02.612.021.0238.0 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

(b) mA/V ( ) 50.0105 =⇒−=− mm gg

( ) 4.1012.021.0250.0 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

______________________________________________________________________________________ 4.10

(a) DSQDDQDD VRIV +=

k ( ) 435.05 =⇒+= DD RR Ω

( )22 TNGSQn

DQ VVL

WkI −⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( ) 7.346.02.1208.05.0 2 =⎟

⎠⎞

⎜⎝⎛⇒−⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

(b) ( )( ) 666.15.07.34208.02

22 =⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′= DQ

nm I

LWk

g mA/V

( )( ) 3.1335.0015.0

11===

DQo I

rλ

kΩ

(c) ( ) ( )( ) 47.643.133666.1 −=−=−= Dom RrgAυ ______________________________________________________________________________________


[ ]

[ ]

22 2

2

22

sin sin

1sin 1 cos 22

So 1 cos 22

2ω ω

ω ω

ω

⎡ ⎤= =⎣ ⎦

= −

= −

n gs n gs n gs

n gsn gs

K v K V t K V

t t

K VK v t

t

( )

( )

2

cos 22Ratio of signal at 2 to that at :

2 s

The coefficient of this expression is then:4

n gs

n GSQ TN gs

gs

GSQ TN

K Vt

inK V V V

V

V V

ωω ω

tω

⋅

− ⋅

−

______________________________________________________________________________________ 4.12

( )( )( )( )

0.014

So 0.01 4 3 1 0.08 V

=−

= − ⇒ =

gs

GSQ TN

gs gs

VV V

V V

______________________________________________________________________________________ 4.13

(a) ( ) 66.03.324060

60

21

2 =⎟⎠⎞

⎜⎝⎛

+=⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛+

= DDGS VRR

RV V

( ) ( )( ) 270.04.066.08021.0

222 =−⎟

⎠⎞

⎜⎝⎛=−⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′= TNGS

nDQ VV

LWk

I mA

( )( ) 14.18270.03.3 =−=−= DDQDDDSQ RIVV V

(b) ( )( ) 078.2270.08021.02

22 =⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′= DQ

nm I

LWk

g mA/V

( )( ) 18527.002.0

11===

DQo I

rλ

kΩ

(c) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

+−=

SiDom RRR

RRRrgA

21

21υ

We find 668.78185 ==Do Rr kΩ

482406021 ==RR kΩ

So ( )( ) 3.15248

48668.7078.2 −=⎟⎠⎞

⎜⎝⎛

+−=υA

______________________________________________________________________________________ 4.14

( )( )0 ||

10 100 || 5 2.1 mA/Vv m D

m m

A g r Rg g

= −− = − ⇒ =

______________________________________________________________________________________


(a) ( ) 1875.25225175

175

21

2 =⎟⎠⎞

⎜⎝⎛

+=⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛+

= DDG VRR

RV V

( )21875.2 TNGSSnGSSDGS VVRKVRIV −+=+=

( )( )( )64.06.1111875.2 2 +−+= GSGSGS VVV

or V 58.105475.16.02 =⇒=−− GSGSGS VVV

mA ( ) ( )( ) 608.08.058.11 22 =−=−= TNGSnDQ VVKI ( ) ( )( ) 96.141608.05 =+−=+−= DSDQDDDSQ RRIVV V

(b) Sm

Dm

RgRg

A+−

=1υ

( )( ) 56.1608.012 ==mg mA/V

( )( )( )( ) 44.2

156.11456.1

−=+−

=υA

(c) ( ) ( )( )

( )( ) ( )LDLD

Sm

LDm RRRR

RgRRg

A 6094.0156.11

56.11

−=+

−=

+

−=υ

( )( ) ( )( ) 0.36094.044.275.0 =⇒−=− LDLD RRRR kΩ

1234 =⇒= LL RR kΩ ______________________________________________________________________________________ 4.16

(a) ( )DSDQDDDSQ RRIVV +−=

( )( ) 5.32125 =+⇒+−= DSDS RRRR kΩ k , then k 5.0=SR Ω 3=DR Ω

( )2TNGSQnDQ VVKI −=

V ( ) 355.22.15.12 2 =⇒−= GSQGSQ VV ( )( ) 355.35.02355.2 =+=+= SDQGSQG RIVV V

DDinDDG VRR

VRR

RV ⋅⋅=⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛+

=121

2 1

( )( ) 894122501355.3 11

=⇒= RR

kΩ

347250894 2221 =⇒== RRRR kΩ

(b) ( )( ) 464.325.12 ==mg mA/V

( ) ( )( )

( )( ) 93.25.0464.31

103464.31

−=+

−=

+

−=

Sm

LDm

RgRRg

Aυ

______________________________________________________________________________________ 4.17

(a) From Problem 4.16; kΩ , kΩ , 5.0=SR 3=DR kΩ , kΩ 8941 =R 3472 =R


(b) ( )( ) 464.325.12 ==mg mA/V

( ) ( )( ) 99.7103464.3 −=−=−= LDm RRgAυ ______________________________________________________________________________________ 4.18 (a)

15 2 7.5 Kv m D

D D

A g RR R

= −− = − ⇒ =

(b)

( )( )( )

12 7.5

5 11 2

m Dv

m S

SS

g RAg R

RR

−=

+

−− = ⇒ =

+ K

______________________________________________________________________________________ 4.19

(a) 1m D

vm S

g RA

g R−

=+

(1) ( )8

1 1m D

m

g Rg

−− =

+

(2) 16 m Dg R− = −

Then

( )168 1

1 116 K

mm

D

gg

R

= ⇒ =+

=

mA/V

(b)

( )( )( )1 16

101 1

0.6 K

vS

S

AR

R

−= − =

+

=

______________________________________________________________________________________ 4.20

(a) ( )22 TNGSQn

QDQ VVL

WkII −⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′==

( )( ) 247.18.05021.05.0 2 =⇒−⎟⎠⎞


( ) ( )( ) 25.3247.165.05 =+−=−−−= +GSQDDQDSQ VRIVV V

(b) ( )( ) 236.25.05021.02

22 =⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′= DQ

nm I

LWk

g mA/V

( )( ) 1005.002.0

11===

DQo I

rλ

kΩ

( ) ( )( ) 7.126100236.2 −=−=−= Dom RrgAυ


(c) ( ) ( )( ) 86.9206100236.2 −=−=−= LDom RRrgAυ

(d) ( ) ( )( ) 51.666100236.2 −=−=−= LDom RRrgAυ ______________________________________________________________________________________ 4.21

(a) ( ) ( DSDQDSQ RRIV + )−−−= 55 ( )( ) 451.0105.5 =+⇒+−= DSDS RRRR kΩ


( ) ( )( ) 143.18.085.01.0 2 =⇒−= GSQGSQ VV V 5=+ SDGS RIV

( ) 6.3851.0143.1 =⇒=+ SS RR kΩ k43.6=⇒ DR Ω

(b) ( )( ) 583.01.085.022 === DQnm IKg mA/V

( )( ) 5001.002.0

11===

DQo I

rλ

kΩ

(c) ( ) ( )( ) 19.34050043.6583.0 −=−=−= LoDm RrRgAυ ______________________________________________________________________________________ 4.22

(a) ( )DSDQDDDSQ RRIVV +−=

( )( ) 6.25.03.32 =+⇒+−= DSDS RRRR kΩ


V ( )( ) 3.08.025.0 2 −=⇒−−= GSQGSQ VV 0=+ SDQGSQ RIV k( ) 6.005.03.0 =⇒=+− SS RR Ω k2=⇒ DR Ω

(b) ( )( ) 25.0222 === DQnm IKg mA/V

( ) ( )( )

( )( ) 52.16.021

10221

−=+

−=

+

−=

Sm

LDm

RgRRg

Aυ

______________________________________________________________________________________ 4.23

(a) and SDQDSQDDQDD RIVRIV ++= 0=+ SDQGS RIV

Then ( ) GSDSQTNGSDnDD VVVVRKV −+−= 2

( )( )( ) GSGS VV −++= 5.28.0225 2

Which yields , 006.04.54 2 =++ GSGS VV 0112.0−=⇒ GSV V

and mA ( ) 244.18.00112.02 2 =+−=DQI ( )( ) ( ) Ω≅Ω=⇒++= 999.8244.15.22244.15 SS RR


(b) ( )( ) 155.3244.1222 === DQnm IKg mA/V

( ) ( )( )

( )( ) 07.3009.0155.3122155.3

1−=

+

−=

+

−=

Sm

LDm

RgRRg

Aυ

______________________________________________________________________________________ 4.24 a.

( )5 55 6 10

DQ S SDQ DQ D

DQ S DQ

I R V I RI R I

= + + −= + + − 5

1.

410

5

DQS

S SDQ DQ D SGQ

IR

V V I R V

=+

= + − =

2. ( )1 10DQ SI V+ = GQ

3. ( )22DQ p SGQI K V= −

4Choose 10 k 0.20 mA20S DQR I= Ω ⇒ = =

2 2

1 (0.2)(10) 3 V0.20 (3 2) 0.20 /

SGQ

P P

VK K mA

= + == − ⇒ = V

b.

( )( )( )( )

( ) ( )( )

20.20 3 2 0.20 mA

2 2 0.2 0.2 0.4 /

|| 0.4 10 ||10 2.0

DQ

m P DQ

v m D L v

I

g K I mA V

A g R R A

= − =

= = =

= − = − ⇒ = −

c.

2 2

4Choose 20 k 0.133 mA30

1 (0.133)(10) 2.33 V0.133 (2.33 2) 1.22 /

2 (1.22)(0.133) 0.806 mA/V(0.806)(10 10) 4.03

S DQ

SGQ

p p

m

v v

R I

VK K mA V

gA A

= Ω⇒ = =

= + == − ⇒ =

= == − ⇒ = −

A larger gain can be achieved. ______________________________________________________________________________________

Microelectronics: Circuit Analysis and Design, 4th edition Chapter 4 By D. A. Neamen Problem Solutions ______________________________________________________________________________________ 4.25 (a)

( )( )

( )

2

20.25 0.8 0.5

1.059 V3 1.059 7.76 K

0.251.059 1.5 0.441 V

0.441 310.2 K

0.25

DQ p SGQ TP

SGQ

SGQ

S S

D S SDQ

D D

I K V V

V

V

R R

V V V

R R

= +

= −

=−

= ⇒ =

= − = − = −

− − −= ⇒ =

(b)

( )( )( )

( )( )2 2 0.8 0.25 0.8944 mA/V

0.8944 10.2 || 21.50

v m D L

m p DQ

v

v

A g R R

g K I

AA

= −

= = =

= −= −

(c)

( ) ( )|| 0.25 10.2 || 2 0.418So 0.836 peak-to-peak

O D L

O

V I R RV

Δ = Δ = =Δ =

______________________________________________________________________________________


( )

( )( )

( )

( )

( )( )

2

2

2

2

2.2 2 6 0.202 /

6 0.202 2.8 2.65

188 10 1.33 k 1.33

6

1

12.21

11 2.2 1.33

2.21 2.93 2.21

3.93 2.2

DQ n GSQ TN

m n DQ

n n

TN TN

DSQ DQ S D

S D S D

m D Lv

m S

D

D

D

DD

D

I K V V

g K I

K K mA V

V V V

V I R R

R R R R

g R RA

g R

RR

RRRR

= −

=

= ⇒ =

= − ⇒ = −

= − +1 −

+ = = Ω⇒ = −

= −+

⎛ ⎞⋅− ⎜ ⎟+⎝ ⎠− =

+ −

+ − =+

−( )( )

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

( )( )

2

2

2

11 1

22

2

1 2.23.93 1.73 2.2 2.22.2 0.47 3.93 0

0.47 0.47 4 2.2 3.931.23 k , 0.10 k

2 2.22.8 6 0.1 3.4 V

1 1 100 18 3.4 529 k

529 100 123 k529

D D D

D D D

D D

D D

G GS S

G in DD

R R RR R R

R R

R R

V V V

V R V RR RR RR

+ =+ − =+ − =

− + += ⇒ = Ω

= + = + =

= ⋅ ⋅ = = ⇒ = Ω

= ⇒ = Ω+

SR = Ω

______________________________________________________________________________________ 4.27

(a) 9−+== DDQSDQSGQS RIVVV

( ) ( )( ) 44945 2 −+=−+= TPSGQpDQSGQ VVKIV

( ) 444.14.28 2 −+−= SGQSGQSGQ VVV

Or V 071.2052.72.208 2 =⇒=+− SGQSGQSGQ VVV

( ) ( ) 518.12.1071.22 22 =−=+== TPSGQpQDQ VVKII mA

(b) ( )( ) 485.3518.1222 === DQpm IKg mA/V

( )( ) 22518.103.0

11===

DQo I

rλ

kΩ

( ) ( )( ) 8.11224485.3 −=−=−= oDm rRgAυ

(c) ( ) ( )( ) 29.88224485.3 −=−=−= LoDm RrRgAυ ______________________________________________________________________________________


( )( )

( )

2

20.5 0.25 0.8

0.614 10 0.614 18.8 K

0.50.614 3 2.386 V

2.386 1015.2 K

0.5

DQ p SGQ TP

SGQ

SGQ S

S S

D S SDQ

D D

I K V V

V

V V V

R R

V V V

R R

= +

= +

= =−

= ⇒ =

= − = − = −

− − −= ⇒ =

(b)

( )( )( )( )

2 2 0.25 0.5 0.7071 mA/V

0.7071 15.210.7

v m D

m p DQ

v

v

A g R

g K I

AA

= −

= = =

= −

= −

______________________________________________________________________________________ 4.29

( )( )

( )( )10 20 1 10 k

v m D L

DSQ DD DQ S D

S D S D

A g R R

V V I R RR R R R

= −

= − += − + ⇒ + = Ω

Let 8 k , 2 kD SR R= Ω = Ω

( )20810 mgA −=−=υ

mA/V75.1=mg ( ) 766.0122 =⇒== nnDQn KKIK mA/V 2

( )( )( ) ( )

( )( )

2 2

11 1

22

2

1 2 2 V

1 0.766 2 3.14 V3.14 2 5.14

1 1 200 20 5.14 778 k

778 200 269 k778

S DQ S

DQ n GS TN GS GS

G GS S

G in DD

V I R

I K V V V VV V V

V R V RR RR RR

= = =

= − ⇒ = − ⇒ == + = + =

= ⋅ ⋅ ⇒ = ⇒ = Ω

= ⇒ = Ω+

______________________________________________________________________________________ 4.30

(a) ( )( )( )( ) 998.0

100511005

1=

+=

+=

om

om

rgrg

Aυ

Ω≅⇒=== 2001002.0100511

oom

o Rrg

R


(b) ( )( )Som

Som

RrgRrg

A+

=1υ

We have 762.45100 ==So Rr kΩ

( )( )( )( ) 960.0

762.451762.45

=+

=υA

______________________________________________________________________________________ 4.31

( )( )1

0.98 491

m L ov

m L o

m om o

m o

g R rA

g R r

g rg r

g r

=+

= ⇒ =+

( )( )

( )( )

( )( )( )( )

Also 0.491

1

0.49

49 1 490.491 49 1 50

L om

m L o L o

m L o L om

L o

m L o

L o m L o

o o

R rgg R r R r

g R r R rgR r

g R rR r g R r

r r

⎛ ⎞⎜ ⎟+⎝ ⎠= =

+ ⎛ ⎞+ ⎜ ⎟+⎝ ⎠

=+ +

= =+ + +

50 K

0.98 mA/Vo

m

r

g

=

=

______________________________________________________________________________________ 4.32 (a)

( )( )( )( )2 25

1 1 2 250.981 1 25 0.5 || 25

20.49 K

m ov

m o

v

o om

o

g rA

g rA

R rg

R

= =+ +

=

= = =

=

(b)

( )( )

( )( )

( )( )

|| 2 25 || 2 2 1.8521 || 1 2 25 || 2 1 2 1.8520.787

m o Lv

m o L

v

g r RA

g r RA

= = =+ + +

=

______________________________________________________________________________________


(a) ( ) 15.010

5.10=

−−=DQI mA

( )22 TNGSQn

DQ VVL

WkI −⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 594.04.08021.015.0 2 =⇒−⎟⎠⎞


(b) ( )( ) 549.115.08021.02

22 =⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′= DQ

nm I

LWk

g mA/V

( )( ) 33315.002.0

11===

DQo I

rλ

kΩ

We find 708.910333 ==So Rr kΩ

Then ( )( )

( )( )( )( ) 938.0

708.9549.11708.9549.1

1=

+=

+=

Som

Som

RrgRrg

Aυ

(c) 708.96456.010333549.111

=== Som

o Rrg

R

or Ω= 605oR______________________________________________________________________________________ 4.34

(a) 5.25.0

25.15.2=

−=

−=

S

DSQDDDQ R

VVI mA

(b) Sm

Sm

RgRg

A+

=1υ

( )( ) 33.11

5.015.0

85.0 =⇒+

= mm

m gg

gmA/V

DQn

m IL

Wkg ⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

22

( ) 2575.221.0233.11 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

(c) ( )22 TNGSQn

DQ VVL

WkI −⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 041.16.025721.05.2 2 =⇒−⎟⎠⎞


291.225.1041.1 =+=+= OGSQIQ VVV V ______________________________________________________________________________________


(a) ( ) 15.25.2 =⇒=⇒= QQDDQ IIVIP mA

(b) om

o rg

R 1=

( )( ) 50102.0

11===

DQo I

rλ

kΩ

So 98.15015.0 =⇒= mm

gg

mA/V

DQn

m IL

Wkg ⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

22

( ) 6.19121.0298.1 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

(c) ( )( )( )( ) 990.0

5098.115098.1

1=

+=

+=

om

om

rgrg

Aυ

(d) ( )( ) 472.4110021.02 =⎟⎠⎞

⎜⎝⎛=mg mA/V

Ω=⇒=== 223502236.050472.411

oom

o Rrg

R

______________________________________________________________________________________ 4.36

(a) ( ) 917.210850350

350

21

2 =⎟⎠⎞

⎜⎝⎛

+=⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛+

= DDG VRR

RV V

GSGQSDQ VVRI ++=10

Now ( ) 6.180204.0

2=⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

LWk

K pp mA/V 2

So ( )( )( ) 917.22.146.110 2 ++−= SGQSGQ VV

We find V 084.20133.236.144.6 2 =⇒=+− SGQSGQSGQ VVV

mA ( ) 25.12.1084.26.1 2 =−=DQI V ( )( ) 5425.110 =−=SDQV

(b) ( )( ) 828.225.16.122 === DQpm IKg mA/V

( )( ) 1625.105.0

11===

DQo I

rλ

kΩ

778.14416 ==LSo RRr kΩ

( )( )

( )( )( )( ) 834.0

778.1828.21778.1828.2

1=

+=

+=

LSom

LSom

RRrg

RRrgAυ

(c) ( ) 2085.0834.0411

==⋅=⋅==i

o

Li

o

o

o

i

og R

iiA

υυ

υυ

υυmA/V


(d) 2.33536.0164828.211

=== oSm

o rRg

R

Ω= 318oR______________________________________________________________________________________ 4.37

(a) (i) ( ) 12021.0

2=⎟

⎠⎞

⎜⎝⎛=⋅

′=

LWk

K nn mA/V 2

( )( ) 472.45122 === DQnm IKg mA/V

( )( ) 10502.0

11===

DQo I

rλ

kΩ

857.2410 ==Lo Rr k Ω

( )( )Lom

Lom

RrgRrg

A+

=1υ

( )( )( )( ) 927.0

857.2472.41857.2472.4

=+

=

(ii) 10472.411

== om

o rg

R

Ω= 219oR

(b) (i) ( )( ) 828.2212 ==mg mA/V

( )( ) 25202.0

1==or kΩ

448.3425 ==Lo Rr k Ω

( )( )( )( ) 907.0

448.3828.21448.3828.2

=+

=υA

(ii) 25828.211

== om

o rg

R

Ω= 349oR______________________________________________________________________________________ 4.38 a.

( )( )

( )

( ) ( )

40.95

1 10.95 4 1 0.95 4.75 mA/V

122

4.75 2 0.030 4 47.0

mm Lv

m L m

m m

m n ox Q

gg RA

g R gg g

Wg C IL

W WL L

μ

= ⇒ =+ +

= − ⇒ =

⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

⎛ ⎞= ⇒⎜ ⎟⎝ ⎠

4

=

b. ( )( )

122

4.75 2 0.030 60 3.13 mA

m n ox Q

Q Q

Wg C IL

I I

μ⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

= ⇒ =

______________________________________________________________________________________


( )( )

( )

( )( )

( ) ( )

2

2

0

5 5 2 1 V 1 V5 1 5 1.2 k

5

2 2 5 5 10 /

1 1 20 k0.01 5

DQ n GS TN

GS GS S GS

SDQ S S

S

m n DQ

DQ

I K V V

V V V VV

I R RR

g K I mA V

rIλ

= −

= + ⇒ = − ⇒ = − =

− − += ⇒ = ⇒ = Ω

= = =

= = = Ω

( )( )

( )( )( )( )

0

01

10 20 1.2 20.878

1 10 20 1.2 2

m S Lv

m S L

v

g r R RA

g r R R

A

=+

= ⇒+

=

0 0

1 1|| || || 20 ||1.2 91.9 10S o

m

R r R Rg

= = ⇒ = Ω

______________________________________________________________________________________ 4.40

(a) ( )( ) ⇒=−=−= 05155SDQS RIV 0=GSV

( )22 TNGSQn

DQ VVL

WkI −⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )[ ] 252021.05 2 =⎟

⎠⎞

⎜⎝⎛⇒−−⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

(b) ( )( ) 552521.02 =⎟⎠⎞

⎜⎝⎛=mg mA/V

( )( ) 20501.0

11===

DQo I

rλ

k Ω

9524.0120 ==So Rr kΩ

( )( )

( )( )( )( ) 826.0

9524.0519524.05

1=

+=

+=

Som

Som

RrgRrg

Aυ

(c) Ω=⇒== 165120511

oSom

o RRrg

R

(d) 6452.02120 ==LSo RRr kΩ

( )( )

( )( )( )( ) 763.0

6452.0516452.05

1=

+=

+=

LSom

LSom

RRrg

RRrgAυ

______________________________________________________________________________________ 4.41

0

1S

m

R Rg

=

Output resistance determined primarily by gm


( )( )( )

( )

( )( )

( )( )

2

2

1Set 0.2 k 5 mA/V

2 5 2 4 1.56 mA

1.56 4 21.38 V, 1.38 V

1.38 54.09 k

1.565 4.09 2

0.8701 1 5 4.09 2

mm

m n DQ DQ DQ

DQ n GS TN

GS

GS S GS

S S

m S Lv v

m S L

gg

g K I I I

I K V V

VV V V

R R

g R RA A

g R R

= Ω⇒ =

= ⇒ = ⇒ =

= −

= += − = − =

− −= ⇒ = Ω

= = ⇒ =+ +

______________________________________________________________________________________ 4.42

(a) ( )( ) 14.1410522 === DQpm IKg mA/V

( )( ) 101001.0

11===

DQo I

rλ

k Ω

( )( )( )( ) 993.0

1014.1411014.14

1=

+=

+=

om

om

rgrg

Aυ

(b) Ω=⇒=== 2.701007072.01014.14

11oo

mo Rr

gR

(c) ( )( )Lom

Lom

RrgRrg

A+

=1υ

( )( )( )( )Lo

Lo

RrRr

14.14114.14

90.0+

= ( ) 6365.0=⇒ Lo Rr kΩ

Ω=⇒= 6806365.010 LL RR ______________________________________________________________________________________ 4.43

( )

0

0

0

1

min1

D DQS L

DQ S LDQ S L

S L

DQ S

S

L

i I vR R

I R Rv I R R

R RI R

vRR

−Δ = = ⋅Δ

⋅Δ = − ⋅ = −

+

= −+

( )( )( ) ( )

( )

( ) ( )

0

1

1

min 1

m S Lv

im S L

DQ S L m S Li

m S L

DQi m S L

m

g R R vA

vg R R

I R R g R Rv

g R R

Iv g R R

g

= =+

⎡ ⎤− +⎣ ⎦=

⎡ ⎤= − +⎣ ⎦

______________________________________________________________________________________


( )3 1.5 0.25 6 K

DD DSQ DQ S

S S

V V I RR R

= += + ⇒ =

( )( )

2

2

1.5 V

0.25 0.5 0.4

1.107 V

S

DQ n GSQ TN

GSQ

GSQ

V

I K V V

V

V

=

= −

= −

=

( )( )

2

1 2 1

1 21

1.107 1.5 2.607 V

1

12.607 300 3 345.2 K 2291 K

G GSQ S

G DD L DD

V V V

RV V R VR R R

R RR

= + + + =

⎛ ⎞= = − −⎜ ⎟+⎝ ⎠

= ⇒ = ⇒ =

(b)

( )( )

( )( )( )( )

( )

2 2 0.5 0.25 0.7071 m1

0.7071 60.809

1 0.7071 6

1 1 6 1.414 || 60.7071

1.14 K

m Sv m n DQ

m S

v v

o Sm

o

g RA g K I

g R

A A

R Rg

R

= = = =+

= ⇒ =+

= = =

=

A/V

______________________________________________________________________________________ 4.45

25.0

15.01==⇒== m

mi g

gR mA/V

DQn

m IL

Wkg ⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

22

( ) 8025.021.022 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

Dm RgA =υ

kΩ ( ) 10220 =⇒= DD RR______________________________________________________________________________________ 4.46

(a) 500== Do RR Ω(b) V 2.1=GSQV

( )( ) ( )

5.03.04.02.12.2

5.03.02.2 +−−=

+−=

−=

satVR

VVI DS

D

DSDDDQ

mA 2.2=DQI


(c) ( )2TNGSQnDQ VVKI −=

mA/V ( ) 438.34.02.12.2 2 =⇒−= nn KK 2

( )( ) 5.52.2438.322 === DQnm IKg mA/V

Ω=⇒== 1825.5

11i

mi R

gR

(d) ( )( ) 75.25.05.5 === Dm RgAυ

______________________________________________________________________________________ 4.47

( ) 48021.0

2=⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

LWk

K nn mA/V 2

( )( ) 828.25.0422 === DQnm IKg mA/V

( )( ) 3.114828.2 === Dm RgAυ

Ω=⇒=== 3423536.010828.2110110 i

mi R

gR

______________________________________________________________________________________ 4.48 a.

( )

( )( )( )

( ) ( )( )( )

( )( )( )( )

2

2

2

2

2

55

5 10 3 2 1

30 59 25 0

59 59 4 30 251.35 V

2 30

3 1.35 1 0.365 mA

10 0.365 5 10 4.53 V

GS DQ S

GSDQ n GS TN

S

GS GS GS

GS GS

GS GS

DQ DQ

DSQ DSQ

V I RV

I K V VR

V V V

V V

V V

I I

V V

+ =−

= = −

− = − +

− + =

± −= ⇒

= − ⇒ =

= − + ⇒ =

=

b.

( )( )

( ) ( )0 0

2 2 3 0.365 2.093 /

1 10 0.365

m n DQ m

DQ

g K I g mA V

r rIλ

= = ⇒ =

= = ⇒ = ∞

c. ( ) ( )( )2.093 5 4 4.65v m D L vA g R R A= = ⇒ =

______________________________________________________________________________________

Microelectronics: Circuit Analysis and Design, 4th edition Chapter 4 By D. A. Neamen Problem Solutions ______________________________________________________________________________________ 4.49 a.

( )( )( )

( )( )( )

2

20.75 0.5 1 2.225 V5 2.2255 3

0.7510

6 10 0.75 3.70 1.63 k

DQ p SG TP

SG SG

DQ S SG S S

SDQ DQ S D

D D

I K V V

V V

I R V R R

V I R RR R

= +

= − ⇒ =−

= + ⇒ = ⇒ =

= − += − + ⇒ = Ω

.70 kΩ

b.

( )( )

1

2 2 0.5 0.75 1.225 /

1 0.816 k1.225

1.63 k

im

m p DQ

i i

o D o

Rg

g K I mA V

R R

R R R

=

= = =

= ⇒ = Ω

= ⇒ = Ω

c.

[ ]

( )( )( ) ( )

0

0

0 0

0 0 0

1/

1.63 3.701.63 2 3.70 0.816

0.368 1.84sin

1.84 2 sin 3.68sin mV

SDi

D L S m

i

i

L

RRi iR R R g

i i

i i i t A

v i R t v t

ω μ

ω ω

⎛ ⎞⎛ ⎞= ⋅⎜ ⎟⎜ ⎟⎜ ⎟+ +⎝ ⎠⎝ ⎠⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟+ +⎝ ⎠⎝ ⎠

= = =

= = ⇒ =

______________________________________________________________________________________ 4.50

(a) ( )( ) GSDSO VsatVV −+= 25.0 15.025.04.025.0 −=+−=−+−= GSTNGSO VVVV V

( ) 975.02

15.08.1=

−−=DR k Ω

(b) Dm RgA =υ

mA/V ( ) 154.6975.06 =⇒= mm gg

DQn

m IL

Wkg ⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

22

( ) 7.94221.02154.6 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

LW

LW

(c) ( )22 TNGSQn

DQ VVL

WkI −⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 05.14.07.9421.02 2 =⇒−⎟⎠⎞


______________________________________________________________________________________


(a) ( )2TNGSQnQDQ VVKII −==

V ( ) 307.16.042 2 =⇒−= GSQGSQ VV 193.2307.15.3 =−=−= GSQDSQD VVV V

554.02

193.23.3=

−=DR k Ω

(b) ( )( ) 657.52422 === DQnm IKg mA/V

Ω=⇒== 177657.511

im

i Rg

R

(c) ( ) ( )( ) 75.24554.0657.5 === LDm RRgAυ ______________________________________________________________________________________ 4.52

(a) ( )2TPSGQpDQ VVKI +=

V ( ) 493.18.05.22.1 2 =⇒−= SGQSGQ VV

51.12.1

493.13.3=

−=

−=

+

DQ

SGQS I

VVR kΩ

( ) ( ) 49.151.12.16.636.6 =⇒+−=⇒+−= DDDSDQSDQ RRRRIV kΩ

(b) ( )( ) 464.32.15.222 === DQpm IKg mA/V

( ) ( )( ) 76.3449.1464.3 === LDm RRgAυ ______________________________________________________________________________________ 4.53

(a) ( )( ) 5===

L

D

L

D

LWLW

KK

Aυ

So 25=⎟⎠⎞

⎜⎝⎛

DLW

From Example 4.11,

( ) ( )( ) 05.151

516.06.03.3=

+++−

=GSDtυ V

825.06.02

6.005.1=+

−=GSDQυ V

(b) ( ) ( )( )22 6.0825.02521.0

2−⎟

⎠⎞

⎜⎝⎛=−⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′= TNGSDQ

D

nDQ VV

LWk

I

mA 0633.0=DQI Now DLDD II =

( ) ( )22TNGSLQ

LTNGSDQ

D

VVL

WVVL

W−⎟

⎠⎞

⎜⎝⎛=−⎟

⎠⎞

⎜⎝⎛

( ) TNODDTNGSDQ VVVVV −−=−125

( ) 6.03.36.0825.05 −−=− OV Or V 575.1== ODSDQ VV

______________________________________________________________________________________


(a) Neglect λ in dc analysis. Transition points: For point B, 2.48.05 =−=−= TNLDDOtB VVV V For point A, DLDD II =

( ) ( 22TNLGSLQnLTNDGSDQnD VVKVVK −=− )

( )( ) ( ) ( )[ ]22 8.002.06.02.1 −−=−GSDQV

So ( ) 9266.06.08.02.12.0

=+=GSDQV V

Then 3266.06.09266.0 =−=−= TNDGSDQOtA VVV V For point A: V, 3266.0=OtAV 9266.0=GSDQV V For point B: V, 2.4=OtBV 9266.0=GSDQV V

(b) V, 9266.0=GSDQV

2633.23266.02

3266.02.4=+

−=DSDQV V

(c) ( ) ( )( ) 128.06.09266.02.1 22 =−=−= TNDGSDQnDDQ VVKI mA

(d) ( )oLoDmD rrgA −=υ

( )( ) 6.390128.002.0

11====

DQoLoD I

rrλ

kΩ

( )( ) 7838.0128.02.122 === DQnDmD IKg mA/V

( )( ) 1536.3906.3907838.0 −=−=υA ______________________________________________________________________________________ 4.55

(a) V 6.0=TNV

( )2TNDSnD VVKI −=

mA/V ( ) 6173.06.05.15.0 2 =⇒−= nn KK 2

( )TNDSnDS

D VVKdVdI

r−== 21

Then ( ) ( )( ) Ω=⇒−

=−

= 9006.05.16173.02

12

1 rVVK

rTNDSn

(b) mA ( )( ) 56.36.036173.0 2 =−=DI

( )( ) Ω=⇒−

= 3376.036173.02

1 rr

______________________________________________________________________________________


( ) ( ) ( )( )

( ) (( )

)

22

2 2

20

0 0

0.5 0 1

0.5

0.5 0.030 10 1

0.5 9 4.92 V0.030

DQ nD GS TND

DQ

DQ nL GSL TNL nL DD O TNL

I K V V

I mA

I K V V K V V V

V

V V

= − = − −

=

= − = − −

= − −

= − ⇒ =

b.

( ) ( )

( )

( )

( )( )

2 2

//

500 4.0830

DD DL

nD i TND nL DD o TNL

nDi TND DD o TNL

nL

nDo DD TNL i TND

nL

o nD Dv

i nL L

v v

I I

K V V K V V V

K V V V V VK

KV V V V V

K

W LdV KA

dV K W L

A A

=

− = − −

− = − −

= − − −

= = − = −

= − ⇒ = −

______________________________________________________________________________________ 4.57 (a)

( ) (( )( )

( )( )( )

)2 2

2

2

2

0.1 4 1 0.9

0.9 1 1 1.95 V1.95 4 5.95 V

DQ L GSL TNL L DSL TNL

D

DQ D GSD TND

GSD GSD

GG GSD DSL GG

I K V V K V V

I mA

I K V V

V VV V V V

= − = −

= − =

= −

= − ⇒ == + = + ⇒ =

b.

( ) ( )

( )

( )

2 2

1

/ 11 / 1 /

DD DL

D GSD TND L GSL TNL

DGG i o TND o TNL

L

D Do GG i TND

L L

D Lov v

i

TNL

D L L

I I

K V V K V V

K V V V V V VK

K KV V V VK K

K KdVA AdV D

V

K K K

=

− = −

+ − − = −

⎛ ⎞+ = + − +⎜ ⎟⎜ ⎟

⎝ ⎠

= = ⇒ =+ + K

Microelectronics: Circuit Analysis and Design, 4th edition Chapter 4 By D. A. Neamen Problem Solutions ______________________________________________________________________________________ (c) From Problem 4.55.

( )

( )( )( )( )

( )( )

( )( )( )( )

12

1 1.67 2 0.1 4 1

2 2 1 0.9 1.90 /

|| 1.90 1.67 || 40.691

1 || 1 1.90 1.67 || 4

LDL DSL TNL

m D DQ

m LD Lv v

m LD L

RK V V

k

g K I mA V

g R RA A

g R R

=−

= = Ω−

= = =

= = ⇒ =+ +

L

______________________________________________________________________________________ 4.58 a. From Problem 4.57.

( )( )

( )( )( )( )

|| 1.90 1.67 ||101 || 1 1.90 1.67 ||100.731

m LD Lv

m LD L

v

g R RA

g R RA

= =+ +

=

b.

0

0

1 1 1.67 0.526 ||1.671.90

0.40 k

LDm

R Rg

R

= = =

= Ω

______________________________________________________________________________________ 4.59

(a) ( )oLoDmD rrgA −=υ

( )( ) 1005.002.0

11===

DQDoD I

rλ

kΩ

( )( ) 505.004.0

11===

DQLoL I

rλ

kΩ

33.3350100 ==oLoD rr kΩ Then ( ) 20.133.3340 =⇒−=− mDmD gg mA/V

( )DQD

nmD I

LWk

g ⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

22

( ) 4.145.021.0220.1 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

DD LW

LW

(b) ( )22 TPSGQ

L

pDQ VV

LWk

I +⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 107.14.050204.05.0 2 =⇒−⎟

⎠⎞


BSGQ VVV −= +

V 393.15.2107.1 =⇒−= BB VV


(c) ( )22 TNGSDQ

D

nDQ VV

LWk

I −⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 233.14.04.1421.05.0 2 =⇒−⎟⎠⎞

⎜⎝⎛= GSDQGSDQ VV V

______________________________________________________________________________________ 4.60

(a) (i) ( )( ) 10025.004.0

11===

DQDoD I

rλ

kΩ

( )( ) 20025.002.0

11===

DQLoL I

rλ

kΩ

67.66200100 ==oLoD rr k Ω

( )oLoDmD rrgA −=υ ( )⇒−=− 67.6625 mDg 375.0=mDg mA/V

DQD

pmD I

LWk

g ⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

22

( ) 03.725.0204.02375.0 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

DD LW

LW

(ii) ( )2

2 TNBL

nDQ VV

LWk

I −⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 107.14.01021.025.0 2 =⇒−⎟⎠⎞

⎜⎝⎛= BB VV V

(iii) ( )22 TPSGDQ

D

pDQ VV

LWk

I +⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 933.16.003.7204.025.0 2 =⇒−⎟

⎠⎞

⎜⎝⎛= SGDQSGDQ VV V

(b) (i) ( )( ) 2501.004.0

11===

DQDoD I

rλ

kΩ

( )( ) 5001.002.0

11===

DQLoL I

rλ

kΩ

7.166500250 ==oLoD rr kΩ

( )oLoDmD rrgA −=υ ( ) 15.07.16625 =⇒−=− mDmD gg mA/V

DQD

pmD I

LWk

g ⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

22

( ) 81.21.0204.0215.0 =⎟

⎠⎞

⎜⎝⎛⇒⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

DD LW

LW


(ii) ( )2

2 TNBL

nDQ VV

LWk

I −⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 874.04.01021.01.0 2 =⇒−⎟⎠⎞

⎜⎝⎛= BB VV V

(iii) ( )22 TPSGDQ

D

pDQ VV

LWk

I +⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 934.16.081.2204.01.0 2 =⇒−⎟

⎠⎞

⎜⎝⎛= SGDQSGDQ VV V

______________________________________________________________________________________ 4.61

( )

( ) ( )

21

1 1 1

85 50 2.125 mA/V2

2 2 2.125 0.1 0.9220

n

m n D

K

g K I

⎛ ⎞= ⇒⎜ ⎟⎝ ⎠

= = =

( ) ( )

( )( )

11 1

22 2

1 1 200 K0.05 0.1

1 1 133.3 K0.075 0.1

oD

oD

rI

rI

λ

λ

= = =

= = =

( ) ( )( )1 1 2|| 0.922 200 ||133.373.7

v m o o

v

A g r rA

= − = −= −

______________________________________________________________________________________ 4.62

( )

( )( )

21

1 1 1

40 50 1.0 mA/V2 2

2 2 1 0.1 0.6325 mA/V

pp

m p D

k wKL

g K I

′ ⎛ ⎞ ⎛ ⎞= = ⇒⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

= = =

( )( )

( )( )

11 1

22 2

1 1 133.3 K0.075 0.1

1 1 200 K0.05 0.1

oD

oD

rI

rI

λ

λ

= = =

= = =

( ) ( )( )1 1 2 0.6325 133.3 || 200

50.6v m o o

v

A g r r

A

= − = −

= −

______________________________________________________________________________________ 4.63

(a) DLDD II =

( ) ( 22TNLGSLnLTNDGSDnD VVKVVK −=− )

( ) 4.04.05.0

2−=−− OOI VVV

4.038.02 −=− OI VV

( )4.031

32

⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛= IO VV


)

For V, V 8.0=IV 4.0=OV For V, V 5.2=IV 533.1=OV

(b) ( ) ( )( 22 4.05.0 −=−= OTNLGSLnLD VVVKI

( ) ( ) ( )22

533.0325.04.04.0

31

325.0 ⎥

⎦

⎤⎢⎣

⎡−⎟

⎠⎞

⎜⎝⎛=⎥

⎦

⎤⎢⎣

⎡−⎟

⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛= IID VVI

For V, ; For 8.0=IV 0=DI 5.2=IV V, 642.0=DI mA (c) From (a), voltage gain = constant = 2/3 = 0.667

______________________________________________________________________________________ 4.64

(a) ( ) ( ) 1.14.015.2 =−−=+= TPSGSD VVsatV V

( ) ( ) 4.11.15.2max =−=−=⇒−= ++ satVVVVVV SDOOSD V

(b) ( ) ( )( ) 121.04.015.25204.0

222 =−−⎟

⎠⎞

⎜⎝⎛=+⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′= TPSGL

L

pD VV

LWk

I mA

(c) ( )2

2 TPSGDD

pD VV

LWk

I +⎟⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′=

( )( ) 748.04.050204.0121.0 2 =⇒−⎟

⎠⎞

⎜⎝⎛= SGDSGD VV V

(d) ( )( ) 6957.0121.050204.02

22 =⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ′= D

D

pmD I

LWk

g mA/V

( )( ) 6.330121.0025.0

11====

DoLoD I

rrλ

kΩ

( )( )

( )( )( )( ) 9914.0

3.1656957.013.1656957.0

1=

+=

+=

oLoDmD

oLoDmD

rrgrrg

Aυ

______________________________________________________________________________________ 4.65

(a) ( )2TNGSDQnDQ VVKI −=

V ( ) 307.16.021 2 =⇒−= GSDQGSDQ VV

( )2TPSGLQpDQ VVKI +=

V ( ) 014.26.05.01 2 =⇒−= SGLQSGLQ VV V 286.1014.23.3 =−=OV ( ) 593.2307.1286.1 =−−=−= SODSDQ VVV V (b) ld II = omLimD VgVg =

p

n

mL

mD

i

o

KK

gg

VV

A ===υ

(c) 25.0

2==υA

______________________________________________________________________________________


( )

( )( )

( )( )

( ) ( )

21

1 1 1

11 1

22 2

85 50 2.125 mA/V2

2 2 2.125 0.1 0.922 mA/V

1 1 200 K0.05 0.1

1 1 133.3 K0.075 0.1

n

m n D

oD

oD

K

g K I

rI

rI

λ

λ

⎛ ⎞= ⇒⎜ ⎟⎝ ⎠

= = =

= = =

= = =

(b)

( ) ( )( )( )( )

11

11

1

11 1 2

1 1 1.085 K0.922

1.085 0.9560.050 1.085 0.050

0.956 0.922 200 133.3

70.5

im

igs i i

i

gsv m o o

i

v

Rg

RV V V

RV

A g r rV

A

= = =

⎛ ⎞ ⎛ ⎞= − = − = −⎜ ⎟ ⎜ ⎟+ +⎝ ⎠⎝ ⎠

= − ⋅ = +

=

iV

(c) 1

1 10.05 0.05 1.135 K0.922i i

m

R Rg

= + = + ⇒ =

(d) 1 2 200 133.7 80 Ko o o oR r r R≈ = ⇒ ≈ ______________________________________________________________________________________ 4.67 (a)

( )( )( )( )

( )( )

1 1

2 2

1 2

2 2 2 0.1 0.8944 mA/V

2 2 2 0.1 0.8944 mA/V

1 1 100 K0.1 0.1

m n D

m p D

o oD

g K I

g K I

r rIλ

= = =

= = =

= = = =

(b) The small-signal equivalent circuit

(1)

2 21 2 2

1 2

0sg sg om i m sg

o o

V Vg V g V

r r−

+ + + =V

Microelectronics: Circuit Analysis and Design, 4th edition Chapter 4 By D. A. Neamen Problem Solutions ______________________________________________________________________________________ (2)

( )

22 2

2

2 22 2

2 2

1 1 1

1 1 1 0.8944 0.0331750 100 100

o sgom sg

o o

o sg mo o o

o sg sg o

V VVg V

r r

V V gr r r

V V V V

−+ =

⎛ ⎞ ⎛ ⎞+ = +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠⎛ ⎞ ⎛ ⎞+ = + ⇒ =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(1)

( )

( )

1 2 21 2 2

1 1

1 10.8944 0.03317 0.8944100 100 100

0.8944 0.01 0.03033

44

om i sg m

o o o

oi o

i o

o

i

Vg V V g

r r r

VV V

V VVV

⎛ ⎞+ + + =⎜ ⎟

⎝ ⎠⎛ ⎞+ + +⎜ ⎟⎝ ⎠

= −

= −

=

(c) For output resistance, set 0.iV =

(1)

22 2

2

x sgxm sg x

o o

V VVg V I

r r−

+ = +

(2)

2 22 2

1 2

0sg sg xm sg

o o

V Vg V

r r−

+ +V

=

(2)

( )

2 21 2 2

2

2

1 1

1 10.8944100 100 100

0.010936

xsg m

o o o

xsg

sg x

VV g

r r r

VV

V V

⎛ ⎞+ + =⎜ ⎟

⎝ ⎠⎛ ⎞+ + =⎜ ⎟⎝ ⎠=

(1)

( )

( )

2 22 2

1 1 1

1 1 10.010936 0.894450 100 1000.03 0.0098905

49.7 K

x x sg mo o o

x x x

x x

xo

x

I V V gr r r

I V V

I VV

RI

⎛ ⎞ ⎛ ⎞= + − +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠⎛ ⎞ ⎛= + − +⎜ ⎟ ⎜⎝ ⎠ ⎝

= −

= =

⎞⎟⎠

______________________________________________________________________________________


(a) ( )21111 TNGSQnDQ VVKI −=

V ( ) 6.16.02.02.0 12

1 =⇒−= GSQGSQ VV

( )22222 TPSGQpDQ VVKI +=

V ( ) 307.16.00.15.0 22

2 =⇒−= SGQSGQ VV

32.06.0

1 ==SR kΩ

V 6.226.01 =+=DV

122.0

6.251 =

−=DR k Ω

V 2.26.06.16.011 =+=+= GSQG VV

( ) ( ) ( )(540015152.21121

21 R

RRRR

RV inG =⋅⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛+

== )

Or k and 9091 =R Ω 40021 == inRRR kΩ 7142 =⇒ R kΩ 907.3307.16.2212 =+=+= SGQDS VVV V

19.25.0907.35

2 =−

=SR kΩ

V 907.03907.3322 =−=−= SD VV

81.15.0

907.02 ==DR k Ω

(b) ( )( ) 4.02.02.022 111 === DQnm IKg mA/V

( )( ) 414.15.0122 222 === DQpm IKg mA/V

( )( ) 21212211 DDmmDmDm RRggRgRgA =−−=υ

( )( )( )( ) 3.1281.112414.14.0 ==υA______________________________________________________________________________________ 4.69

(a) ( )21111 TNGSnDQ VVKI −=

V ( ) 307.16.02.01.0 12

1 =⇒−= GSQGS VV


V ( ) 10.16.00.125.0 22

2 =⇒−= SGQSGQ VV ( )( ) 407.111.0307.11111 =+=+= SDQGSQG RIVV V

DDG VRR

RV ⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛+

=21

21 DDin VR

R⋅⋅=

1

1

( )( ) 5863.32501407.1 11

=⇒= RR

kΩ

25021 == inRRR kΩ k4362 =⇒ R Ω ( )( ) 3.12.111.01111 =+=+= DSQSDQD VRIV V

201.0

3.13.31 =

−=DR kΩ


V 4.21.13.1212 =+=+= SGQDS VVV

6.325.0

4.23.32 =

−=SR k Ω

V 6.08.14.2222 =−=−= SDQSD VVV

4.225.06.0

2 ==DR kΩ

(b) ( )( ) 2828.01.02.022 111 === DQnm IKg mA/V

( )( ) 0.125.0122 222 === DQpm IKg mA/V

( )( )( )( ) 6.134.2200.12828.02121 === DDmm RRggAυ ______________________________________________________________________________________ 4.70

( ) 4.020204.0

1 =⎟⎠⎞

⎜⎝⎛=pK mA/V 2

( ) 0.48021.0

2 =⎟⎠⎞

⎜⎝⎛=nK mA/V 2

(a) 61.06.0

1 ==SR k Ω

V 2.016.08.11 =−−=DV

( ) 201.0

8.12.01 =

−−=DR kΩ


V ( ) 90.04.04.01.0 12

1 =⇒−= SGQSGQ VV

( )2222 TNGSQnDQ VVKI −=

V ( ) 6739.04.043.0 22

2 =⇒−= GSQGSQ VV 3.09.06.08.16.08.1 11 =−−=−−= SGQG VV V

( ) 8.16.321

21 −⎟⎟

⎠

⎞⎜⎜⎝

⎛+

=RR

RVG

( )( ) 3438.16.320013.0 11

=⇒−= RR

kΩ

20021 =RR k kΩ 4802 =⇒ R Ω V 2.00.16.08.11 =−−=DV 4739.06739.02.0212 −=−=−= GSQDS VVV V

( ) 42.43.0

8.14739.02 =

−−−=SR kΩ

(b) ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+−

=22

22

11

11

11 Sm

Sm

Sm

Dm

RgRg

RgRg

Aυ

( )( ) 4.01.04.022 111 === DQpm IKg mA/V

( )( ) 191.23.0422 222 === DQnm IKg mA/V

( )( )( )( )

( )( )( )( ) 13.2

42.4191.2142.4191.2

64.01204.0

−=+

⋅+−

=υA


(c) Ω=⇒=== 41442.44564.042.4191.211

22

oSm

o RRg

R

______________________________________________________________________________________ 4.71 (a)

( )

( )( )( )

( ) ( )( )( )

211 1 1 1

2

21 1 1

21 1

2

1 1

10

10 4 10 4 4

40 159 150 0

159 159 4 40 1502.435 V

2 40

GSDQ n GS TN

S

GS GS GS

GS GS

GS GS

VI K V VR

V V V

V V

V V

−= = −

− = − +

− + =

± −= ⇒ =

( )( )( )( )

( )( )

21 1

1 1

2

2 2

4 2.435 2 0.757 mA

20 0.757 10 12.4 V

Also 0.757 mA

20 0.757 10 5 8.65 V

DQ DQ

DSQ DSQ

DQ

DSQ DSQ

I I

V V

I

V V

= − ⇒ =

= − ⇒ =

=

= − + ⇒ =

(b) ( )( )1 2 1 22 2 4 0.757 3.48 /m m DQ m mg g KI g g mA= = = ⇒ = = V

c.

( )( )( )( )

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

( )( ) ( )

0 2 2

2 1 1 2 2 1 2

1 2 1 2

2 2 2 1 2 1 2 1 2

2 2 2 1 2 1 2 1 2 1 1 2

1 1 22

2 1 2 1 1 2

1 20

1

m gs D L

gs m gs m gs S S

i gs gs gs i gs

gs m gs S S m i gs S S

gs m gs S S m gs S s m i S S

m i S Sgs

m S S m S S

m mv

i

V g V R R

V g V g V R R

V V V V V V

V g V R R g V V R R

V g V R R g V R R g V R R

g V R RV

g R R g R R

g gVA

V

= −

= − −

= − ⇒ = +

+ = − +

+ + = −

−=

+ +

= =( )( )

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

1 2

1 2 1 2

2

1

3.48 10 10 5 22.42

1 3.48 3.48 10 10

S S D L

m m S S

v v

R R R Rg g R R

A A

+ +

= ⇒ =+ +

______________________________________________________________________________________


( )( )( )

( )

( ) ( )

12

12

1 1

3 31 3

1 2 3

3 mA5 3 1.2 5 1.4 V

3 2 1 2.225 V2.225 1.4 0.825 V

5 0.825 5 82.5 k500

DQ

S DQ S

DQ GS TN

GS GS

G GS S

G

IV I R

I K V V

V VV V V

R RV R

R R R

== − = − = −

= −

= − ⇒ == + = − =

⎛ ⎞ ⎛ ⎞= ⇒ = ⇒ =⎜ ⎟ ⎜ ⎟+ + ⎝ ⎠⎝ ⎠Ω

( ) ( )

1 1 1

2 1

2 3 2 32

1 2 3

2 3 2

1.4 2.5 1.1 V1.1 2.225 3.325 V

5 3.325 5500

332.5 250 k

D S DSQ

G D GS

G

V V VV V V

R R R RVR R R

R R R

= + = − + == + = + =

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

1 1

2 1 2

500 250 82.5 167.5 k

1.1 2.5 3.6 V5 3.6 0.467 k

3

D D DSQ

D D

R R

V V V

R R

= − − ⇒ =

= + = + =−

= ⇒ = Ω

Ω

b.

( )( )( )( )

1

1 2 2 2 3 4.90 /

4.90 0.467 2.29

v m D

m n DQ

v v

A g R

g K I mA V

A A

= −

= = =

= − ⇒ = −

______________________________________________________________________________________ 4.73 a.

( )( )( )

( )( )

( )( )

1 12

1 12

1 1

1 1 1 3 3 3

1 1 1

2 1

2 3

2 3 2

2 1 2

10 5 2 10 0

5 4 1.5 2.618 V2.618 V 0.1 26.2 k

0 3.5 3.5V3.5 2.62 6.12V

0.161.2 k 35 k

S DQ S S

DQ GS TN

GS GS

G GS S

D S DSQ

G D GS

D D DSQ

V I R V

I K V V

V VV V V IR R R

V V VV V V

R RR R R

V V V

= − = − ⇒ =

= −

= − ⇒ == + = = = ⇒ =

= + = + == + = + =

= ++ = Ω⇒ = Ω

= + =

Ω

1 1

3.5 3.5 7.0 V10 7 0.6 k

510 6.12 38.8 k

0.1

D DR R

R R

+ =−

= ⇒ = Ω

−= ⇒ = Ω

Microelectronics: Circuit Analysis and Design, 4th edition Chapter 4 By D. A. Neamen Problem Solutions ______________________________________________________________________________________ b.

( )( )( )( )

1

1 2 2 4 5 8.944 /

8.944 0.6 5.37

v m D

m n DQ

v v

A g R

g K I mA V

A A

= −

= = =

= − ⇒ = −

______________________________________________________________________________________ 4.74 a.

( )

( )

( )

2

2

1

4 6 13

43 1 0.551 V6

6 10 4 1 k

GSDQ DSS

P

GS

GS GS

DSQ DD DQ D

D D

VI IV

V

V V

V V I RR R

⎛ ⎞= −⎜ ⎟

⎝ ⎠

⎛ ⎞= −⎜ ⎟⎜ ⎟−⎝ ⎠

⎡ ⎤= − − ⇒ = −⎢ ⎥

⎣ ⎦= −

= − ⇒ = Ω

b.

( )( )

( )( )0 0

2 62 0.5511 1 3.2653 3

1 1 25 k0.01 4

DSS GSm m

P P

DQ

I Vg gV V

r rIλ

⎛ ⎞ −⎛ ⎞= − = − ⇒ =⎜ ⎟ ⎜ ⎟− −⎝ ⎠⎝ ⎠

= = ⇒ = Ω

mA/V

c. ( ) ( )( ) 14.3125265.3 −=⇒−=−= υυ ARrgA Dom ______________________________________________________________________________________


( )

( )

( )( )

( ) ( )

( ) ( ) ( )( )

1 22

2

1 2

2

2

2

2

2

0

1

1 0

2 0.1 0.25 1 0

20.7 1 0

2 2

0.175 1.7 0.7 0

1.7 1.7 4 0.175 0.70.4314 V

2 0.175

2

GS DQ S S

GSDQ DSS

P

GSGS DSS S S

P

GSGS

P

VGS GSGS

GS GS

GS GS

m

V I R R

VI IV

VV I R RV

VV

V

VV

V V

V V

g

+ + =

⎛ ⎞= −⎜ ⎟

⎝ ⎠

⎛ ⎞+ + − =⎜ ⎟

⎝ ⎠

⎛ ⎞+ + − =⎜ ⎟

⎝ ⎠⎛ ⎞⎜ ⎟+ − + =⎜ ⎟− −⎝ ⎠+ + =

− ± −= ⇒ =

=

−

( )

( ) ( )( )( )( )

( )( ) ( )

1

00 0

2 2 0.4311 1 1.569 mA/V2 2

1.569 8 43.62

1 1 1.569 0.1

/ 503.62 45.2/ 4

DSS GSm

P P

m D Lv v

m S

L Gi i

i i G i L

I V gV V

g R RA A

g R

v Ri v RA Ai v R v R

⎛ ⎞ −⎛ ⎞− = − ⇒ =⎜ ⎟ ⎜ ⎟− −⎝ ⎠⎝ ⎠− −

= = ⇒ = −+ +

⎛ ⎞= = = ⋅ = − ⇒ = −⎜ ⎟⎝ ⎠

______________________________________________________________________________________ 4.76

( )( )( )

( ) ( )

2

2

4 mA2

10 V2

10 20 4 2.5 k2 V 4 0.5 k , 2.0 k

1

44 8 1 4.2 1 1.23 V4.2 8

2 1.23

DSSDQ

DDDSQ

DSQ DD DQ S D

S D S D

S DQ S S S D

GSDQ DSS

P

GSGS GS

G S GS

G

II

VV

V V I R RR R R R

V I R R R R

VI IV

V V V

V V V

V

= =

= =

= − += − + ⇒ + = Ω= = = ⇒ = Ω = Ω

⎛ ⎞= −⎜ ⎟

⎝ ⎠

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

( ) ( )2 22 1

1 2

0.77 V 20 20 3.85 k , 96.2 K100

R R R RR R

⎛ ⎞ ⎛ ⎞= = = ⇒ = Ω =⎜ ⎟ ⎜ ⎟+ ⎝ ⎠⎝ ⎠Ω

______________________________________________________________________________________


( ) ( )

( )( )

2

2

2

1 2 1

11

5 mA2

12 6 V2 2

12 6 1.2 k5

1

55 10 1 5 1 1.464 V5 10

6 1.464 4.536 V

1

14.536 100 12 26

DSSDQ

DDDSQ

S S

GSDQ DSS

P

GSGS GS

G S GS

G DD in DD

II

VV

R R

VI IV

V V V

V V V

RV V R VR R R

RR

= =

= = =

−= ⇒ = Ω

⎛ ⎞= −⎜ ⎟

⎝ ⎠

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

⎛ ⎞= = ⋅ ⋅⎜ ⎟+⎝ ⎠

= ⇒ =

22

2

5 k

265 100 161 k265

R RR

Ω

= ⇒ = Ω+

b.

( )( )

( )( )( )( )

( )( )( )( )

0

0

0

0 0

2 102 1.461 1 2.83 mA/V5 5

1 1 20 k0.01 5

1

2.83 20 1.2 0.50.495

1 2.83 20 1.2 0.5

1 1 1.2 0.353 1.2 0.273 k2.83

DSS GSm m

P P

DQ

m s Lv

m S L

v v

Sm

I Vg g

V V

rI

g r R RA

g r R R

A A

R R Rg

λ

⎛ ⎞ −⎛ ⎞= − = − ⇒ =⎜ ⎟ ⎜ ⎟− −⎝ ⎠⎝ ⎠

= = = Ω

=+

= ⇒ =+

= = = ⇒ = Ω

______________________________________________________________________________________


( )

( )

( )( )

( )

( ) ( )( )( )

2

1 2

2

2

2

2

2

110 10 5.5 V110 90

101

10 5.5 2 5 11.75

4.5 10 1 1.143 0.3265

3.265 12.43 5.5 0

12.43 12.43 4 3.265 5.50.

2 3.265

G DD

G GS GSDQ DSS

S P

GSGS

GS GS GS

Gs GS

GS GS

RV VR R

V V VI I

R V

VV

V V V

V V

V V

⎛ ⎞ ⎛ ⎞= = =⎜ ⎟ ⎜ ⎟+ +⎝ ⎠⎝ ⎠

− − ⎛ ⎞= = −⎜ ⎟

⎝ ⎠

⎛ ⎞− + = −⎜ ⎟⎝ ⎠

+ = − +

− + =

± −= ⇒

( )

=

( )( )

2

511 V

0.5112 1 1.00 mA1.75

10 1.00 5 5.0 V

DQ DQ

SDQ SDQ

I I

V V

⎛ ⎞= − ⇒ =⎜ ⎟⎝ ⎠

= − ⇒ =

b.

( )

( )( )

( )( )( )( )

( )( )

( )

00

1 2

2 22 0.5111 1 1.618 mA/V1.75 1.75

1.618 5 100.844

1 1 1.618 5 10

//90 110 49.5 k

49.50.844 4.1810

DSS GSm m

P P

m S Lv v

m S L

L ii v

i i i L

i

i i

I Vg gV V

g R RA A

g R R

v Ri RA A

i v R RR R R

A A

⎛ ⎞ ⎛ ⎞= − = − ⇒ =⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

= = ⇒ =+ +

⎛ ⎞= = = ⋅⎜ ⎟

⎝ ⎠= = = Ω

⎛ ⎞= ⇒ =⎜ ⎟⎝ ⎠

c.

( )( )1.0 mA3.33 1.0 3.33 V

d

sd

ivΔ =

= = Maximum swing in output voltage = 6.66 V peak-to-peak ______________________________________________________________________________________


( )( )

( )

( )

2

2

1

44 8 1 4 1 1.17 V4 8

7.5 20 4 3.125 k2 82 1.171 1 2.83 mA/V

4 43.125

13 1

GSDQ DSS

P

GSGS GS

SDQ DD DQ S D

S D S D

DSS GSm m

P P

S D

m Dv

m S

m S

VI IV

V V V

V V I R RR R R R

I Vg gV V

R Rg RAg R

g R

⎛ ⎞= −⎜ ⎟

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

= − += − + ⇒ + = Ω

⎛ ⎞ ⎛ ⎞= − = − ⇒ =⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

= −−

=+

− + = −

( )( ) ( )

( )( )

( )2 22 1

1 2

3 1 2.83 3.125 2.83

9.844 2.83 0.9433 2.61 k 0.516 k

20 4 0.516 17.94 V17.94 1.17 16.77 V

20 335 k . 65 k400

m D

D D

D D D S

S S

G S GS

G DD

g RR R

R R R R

V VV V V

R RV V R RR R

+ − =⎡ ⎤⎣ ⎦− = ⇒ = Ω =

= − ⇒ == − = − =

⎛ ⎞ ⎛ ⎞= = ⇒ = Ω =⎜ ⎟ ⎜ ⎟+ ⎝ ⎠⎝ ⎠

Ω

Ω

______________________________________________________________________________________

2.5 0.4 ()8.33 0.4 () ()0.6 ()36 0 - NTUT Solutions... · Microelectronics: Circuit Analysis and...

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Transcript of 2.5 0.4 ()8.33 0.4 () ()0.6 ()36 0 - NTUT Solutions... · Microelectronics: Circuit Analysis and...