EEE 241EEE 241 ANALOG ELECTRONICS 1

L t 10&11Lecture 10&11

DR NORLAILI MOHD NOH

CE with Emitter Degeneration

ioib

CCV

CR

To determine Ri :

rοrπ v1g vm 1β io b=

io

vi vo

ib

Rc

+

CR

oV

C

B

E+

V

bI cI

(n)

(p)

(n)

RE ve

KCL at E:

−E

−iV

ER

( )

o e eob b o Eo e o ee C e Co b

v v vi i r Ri R v i R vv v1 i r rR R

+ +

++ +

=

= =

β

β

−

− −−( )

( )

o b o oE Eoe e Co b o oE

r rR Ri Rv v1 i r rR+ + +=

β

β

2( ) oo o eb oE C

r1 1i 1 i vrR R+ +⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟

⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

= β −

rοrπ v1g vm 1β i

io

v

ib

rοrπ 1 β io b=vi voRc

RE ve

KCL at C:o eo e Co o ob bo o

i R vv vi i ir r+ += =β β − −−

( )

b bo o

oSince KCL at E gives then,o o eb oE C

r rr1 1i 1 i vrR R+ +

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟

⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦⎡ ⎤⎛ ⎞

= β −

( )( ) oo e eCb oE Coo e ob bo oE C

r1 11 i v R vrR Rr1 11 i v ir rR R

+ ++ + +

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⎡ ⎤⎛ ⎞ ⎜ ⎟⎢ ⎥⎢ ⎥ ⎝ ⎠⎜ ⎟ ⎣ ⎦

⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

=β

β β− − −

−

( )or1+β ( )

( ) ( )

o o o oo o eC Cb o o oo oE EC C C C

o o

r r r1 1 1 1 11 R i R vr r rR r R R R R r Rr r1 1 1 1 11 1 i

+ + + + +

+ + + + + +

⎧ ⎫⎡ ⎤ ⎛ ⎞ ⎛ ⎞⎪ ⎪⎢ ⎥ ⎜ ⎟ ⎜ ⎟⎨ ⎬⎢ ⎥ ⎜ ⎟ ⎜ ⎟⎪ ⎪⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎩ ⎭

⎧ ⎫⎡ ⎤ ⎛ ⎞ ⎛ ⎞⎪ ⎪⎢ ⎥ ⎜ ⎟ ⎜ ⎟

=β β

β β β

− −

3

( ) ( )o oo o o eb o o oE EC C

r r1 1 1 1 11 1 i vr r rR R R R+ + + + + +⎪ ⎪⎢ ⎥ ⎜ ⎟ ⎜ ⎟⎨ ⎬⎢ ⎥ ⎜ ⎟ ⎜ ⎟⎪ ⎪⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎩ ⎭

=β β β− −

( ) ( )o oo o o eb o o oE EC C

r r1 1 1 1 11 1 i vr r rR R R R+ + + + + +⎧ ⎫⎡ ⎤ ⎛ ⎞ ⎛ ⎞⎪ ⎪⎢ ⎥ ⎜ ⎟ ⎜ ⎟⎨ ⎬⎢ ⎥ ⎜ ⎟ ⎜ ⎟⎪ ⎪⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎩ ⎭

=β β β− −

( ) ooCe bo

r1+ +1Rv ir 1 1+ +R R R R

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥

=β

ioib

E EC CR R R R⎢ ⎥⎢ ⎥⎣ ⎦

rοrπ v1g vm 1β io b=

o

vi vo

b

Rc

KVL of the input loop:-vi + v1 + ve = 0.Thus, -vi + ibrπ + ve = 0

RE ve( ) ooC

i b bo

r1+ +1Rv r i + ir 1 1+ +

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥

= π

β

( )E EC C

ooCi

+ +R R R Rr1+ +1v RR r + enough

⎢ ⎥⎢ ⎥⎣ ⎦

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥= =

β←

4

Cii ob

E EC C

R r + enoughi r 1 1+ +R R R R

⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

= = π ←

( ) or1+ +1⎡ ⎤⎢ ⎥β( ) oo

Ci o

E EC C

1+ +1RR r + r 1 1+ +R R R R

⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

= π

β

( )C C

ooE CC

o EC

rR R 1+ 1+ Rr +r +R +R

⎣ ⎦

⎡ ⎤⎢ ⎥⎣ ⎦= π

β

( ) ( )

o EC

Co oE oR1+ R +r1+r +

r +R +R

⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦= π

ββ

o ECr +R +R

5

( ) ( )Co oE o

i

R1+ R +r1+R r + +R +R

⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦= π

ββ

( ) [ ]

i o EC (in the case of ), then o o oEC

o oE o Ei

r +R +RIf r R and r R r

1+ R rR r + r + 1+ R⎛ ⎞⎜ ⎟

→∞

= =π π

>> >>β β

( )

o Ei oC oo

o

R r + r + 1+ Rr

R +r1+For a finite r 1

⎜ ⎟⎝ ⎠

= =π π β

β <,oo ECo i

For a finite r 1. r +R +R

Hence, a finite r will reduce the R when com

<

.oioi

pared to the R when rvFor a CE without degeneration R = r

→∞

= β

.

oi .i mi

i

For a CE without degeneration, R = r giThus, a CE with degeneration will increase the R Normally the R for a CE with emitter degeneration is taken as r + 1+

=

⎛ ⎞⎜

= πβ

β R⎟

6

oiNormally, the R for a CE with emitter degeneration is taken as r + 1+⎜⎝ ⎠π β ER⎟

To determine Gm :

r v1g vm 1

ioib

T d trοrπ v1 β io b=vi voRc

RE ve

Transconductance,

om

i

iG v v 0

==

iib

io

e eob b

v 0

At node E,v vi i rR+ +

=

β =

rοrπ v1g vm 1β io b=

io

vi 0vo =

ib

( )

ob b oEeio e

oE

rRv v 1 11 vr rR+ +

π

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

β

β−

=

RE ve( )

( )o

E

o ie1 v

v

r

+1+1 1+ +π

⎝ ⎠

β=

⎡ ⎤β⎢ ⎥

7

E or + +

R r rππ ⎢ ⎥

⎣ ⎦

( )o i

At node C,1 v+β

⎡ ⎤

( )( )o

o ie1 v

v+

1+1 1β

=⎡ ⎤β⎢ ⎥( )o

E oo o b

r

i i

1+1 1+ +R r r

+ ππ

β

⎡ ⎤β⎢ ⎥⎣ ⎦ = ioib

( )o

E or

1 1+ +R r rπ

π⎡ ⎤β⎢ ⎥⎣ ⎦

( )( )o

o o bo

o i

r1 v+

1+1 1

β

β

⎡ ⎤βrοrπ v1

g vm 1β io b=vi 0vo =

( )o

E oo

o

r

i r

1 1+ +R r r

+ ππ

⎡ ⎤β⎢ ⎥⎣ ⎦

RE ve eib

v vi rπ

−=

( ) ( )v o oii i

1 v 11 v+ +

⎧ ⎫ ⎧ ⎫⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪− −⎨ ⎬ ⎨ ⎬

β β

⎡ ⎤ ⎡ ⎤( ) ( )v

o o

E o E o

i i

o o

1 v

r r1+ 1+1 1 1 1+ + + +

R r r R r rπ ππ π

⎨ ⎬ ⎨ ⎬⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎩ ⎭ ⎩ ⎭β β

⎡ ⎤ ⎡ ⎤β β⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦= =

8

o or rπ πβ β

⎧ ⎫⎪ ⎪

( )( )

( )( )oo

oo ii

11 v 1 v++1+1+ 1 11 1 + ++ +

⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪

ββ⎡ ⎤β⎡ ⎤β⎢ ⎥⎢ ⎥

( ) ( )oo

E oE oo o

o

rr

i r r

+ ++ +R r rR r r

+ ππππ

π

⎪ ⎪⎪ ⎪⎪ ⎪⎩ ⎭

⎧ ⎫

β

β⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦ =

( )( )

( )( )

o o ii

1 1 v1 v+ +

⎧ ⎫⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪−⎨ ⎬

β β⎡ ⎤ ⎡ ⎤( ) ( )o o

E o E o

i

o o

r r

i rr

1+ 1+1 1 1 1+ + + +R r r R r rπ π

π π

⎨ ⎬⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎩ ⎭= −β

⎡ ⎤β ⎡ ⎤β⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

o oorrπ

β

9

⎧ ⎫⎧ ⎫⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪( )

( )( )

( )o o

o o1 11

r r

+ +1+ 1+1 1 1 1+ + + +

R r r R r rπ π

⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪

β β⎡ ⎤β ⎡ ⎤β⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦E o E o

o o ioi vrr

R r r R r rπ π

π

⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎩ ⎭ −⎨ ⎬⎪ ⎪⎪ ⎪⎪ ⎪

β⎢ ⎥

⎣ ⎦ ⎣ ⎦=

⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪

( ) ( )1 1+

⎪ ⎪⎪ ⎪⎩ ⎭

⎧ ⎫⎪ ⎪⎪ ⎪⎪ ⎪β β( )

( )( )

o

o o1 11

r ri

+ +1+1 1 1+ +

R r rπ π

⎪ ⎪⎪ ⎪−⎨ ⎬⎪ ⎪⎪ ⎪⎪ ⎪

β β⎡ ⎤β⎢ ⎥⎣ ⎦

( )o1+1+ +R r r

⎡ ⎤β⎢ ⎥⎣ ⎦ h

10

E oom o

i

iG v rR r rπ

π

⎪ ⎪⎪ ⎪⎩ ⎭ −β ⎣ ⎦= = E o

orR r rπ⎣ ⎦ enough→

ER1⎡ ⎤E

o om

m

m E

gG

1+g R +

1r

1 11⎛ ⎞⎜ ⎟⎜ ⎟

⎡ ⎤−⎢ ⎥β⎣ ⎦=+

m o om E1 g R 1

g r⎜ ⎟⎜ ⎟⎝ ⎠

+β

P i ll β 1 R d 1Practically, βo >> 1, ro >> RE and gmro >> 1

mgG =mm E

G 1+g R=

This expression is often used to calculate the transconductance of the CE with emitterpdegeneration amplifier. Practically, Gm_CE_emitter degen < Gm_CE as Gm_CE = gm .

11

To determine Ro :

tvR R //R ′= =rοrπ v1

g vm 1β io b=

io

0vi =vt

ib

R to c o

ti

R R //Ri v 0= =

=π β io b= vtRc

RE veRo

itRo′

i1

( )E

e1r // Ro1

v = vv = i π

−− ( )

( )E

E

o1r // Ro m o m o1 1

et t1 1 1

vi =i g v =i g i

v i r v =0, v i r v =0

π

⎡ ⎤π⎢ ⎥⎣ ⎦+

+ + +ο ο

−− ∴ − −

( ) ( )( ) ( )

m E E

m E E

1 g r // R r // Ro ot

t 1 g r // R r // Roo

v i r i =0vR = = ri

π π

π π

+ + +⎡ ⎤ ο⎣ ⎦

+ +⎡ ⎤ ο⎣ ⎦

−

′

12

( ) ( )m E E

o

1 g r // R r // Ro c o cR =R //R =R // r⎧ ⎫π π⎨ ⎬

⎩ ⎭+ +⎡ ⎤ ο⎣ ⎦

′∴ enough→

( ) ( )

( ) ( )

m E E

E m E

t 1 g r // R r // Rot

r // R 1 g r // R

vR = = rir

π π

π π

+ +⎡ ⎤ ο⎣ ⎦

<< +⎡ ⎤ ο⎣ ⎦

′

( ) ( )

( )

E m E

Em E m

E

r // R 1 g r // R

r R1 g r // R 1 go r +R

r

R = r = r

π π

ππ

π

<< +⎡ ⎤ ο⎣ ⎦⎡ ⎤+ +⎡ ⎤ ο ο⎢ ⎥⎣ ⎦ ⎣ ⎦

⎡ ⎤⎡ ⎤ ⎡ ⎤

′

( )m E m E m E

E m EE

g R g R g R1 1 1o 1 R g Rr +R 1 1r r

R = r = r = rπ

π π ο

⎡ ⎤⎡ ⎤ ⎡ ⎤⎢ ⎥⎢ ⎥ ⎢ ⎥

+ + +ο ο ο⎢ ⎥⎢ ⎥ ⎢ ⎥+ +⎢ ⎥⎢ ⎥ ⎢ ⎥

β⎣ ⎦ ⎣ ⎦ ⎣ ⎦

′

m1 gm oEIf g R , R =π π οβ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

+ο′<<β E

m E

R

// 1 g Ro c

rR =R r

⎡ ⎤ ο⎣ ⎦+⎡ ⎤ ο⎣ ⎦

m E

m E

g R1 1m oE g RIf g R , R = r = rο

⎡ ⎤⎢ ⎥

+ +β⎡ ⎤ο ο ο⎢ ⎥ ⎣ ⎦⎢ ⎥

β⎣ ⎦

′>>β

m E.

m E

g R1 1o g RR = r = r

ο

ο

β⎣ ⎦⎡ ⎤⎢ ⎥

+ +β⎡ ⎤ο ο⎢ ⎥ ⎣ ⎦⎢ ⎥

′

13

m E

.

g R

//co_CE o_CEo_CE_degenR =R r R > R . ο

⎢ ⎥β⎣ ⎦

ο

CS with Source Degeneration

CS with S degeneration is not as typically implemented as the CE with E degeneration. The reasons are:

1. The transconductance of the MOS is far less than the transconductance of the BJT. When implementing S degeneration, the transconductance of the MOS ill b d d Thi diti i d i dMOS will be reduced. This condition is undesired.

2. With E degeneration, Ri in CE is increased. However, Ri →∞ in the case of CS even without degeneration. Hence, the need for the degeneration circuit is not crucialcircuit is not crucial.

CS with S degeneration is sometimes implemented to increase the Ro of the MOSthe MOS.

14

oiii DGDDVv

CS with Source Degeneration

iv

+

DRor ov

+

oI

DR

dIgsv

+i

ii

vR = =i ∞

−

−S

GD

S

iV

iI

oV+

+

d

dISR

m gsg V

S−

sv+

om

i oo

iG = v v 0KCL at S when v 0:

==iV

−− SRSsv

−

( )

os s

m gso s

s s

KCL at S when v 0:v vv r R

v vv v

g

g

= +

− = +i ( )m si o ss s

m m si o s

v v r R

v vv vr R

1 1

g

g g

⎛ ⎞

= +

= + +

oiii

v

+

or 0v

+DG

v

+

mm si o s1 1v v r Rg g⎛ ⎞

⎜ ⎟⎝ ⎠

= + +iv or

−

0ov =

−S

m gsg V

S

gsv

−

+

15

SRsv+

−

mm si o s1 1v v r Rg g⎛ ⎞

⎜ ⎟⎝ ⎠

= + + oiii+

DG

m ism

o s

vv1 1r R

g

g

⎝ ⎠

⎛ ⎞⎜ ⎟⎝ ⎠

=+ + iv

+

or

−

0ov =

m gsg Vgsv

+

−

om

i o

iG = v v 0KCL at D when v 0:

==

−S

SR

S

sv+

−os

m gs oo

gs si

KCL at D when v 0:vv ir

v v vg

−

=

= += Therefore,g i

m i

,

v1 1

g

g⎧ ⎫⎡ ⎤⎪ ⎪⎢ ⎥

⎡ ⎤⎢ ⎥⎢ ⎥⎛ ⎞⎢ ⎥⎜ ⎟+ +m

o sm i-m oi omo s

r Rvv ir1 1

r R

ggg

g

⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎨ ⎬⎢ ⎥⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎣ ⎦⎩ ⎭

⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

⎛ ⎞⎜ ⎟⎝ ⎠

+ += +

+ +

16

⎣ ⎦⎩ ⎭⎝ ⎠

m ivg⎡ ⎤⎢ ⎥⎢ ⎥m i

mo sm i-m oi o

1 1r Rvv ir1 1

g

ggg

g

⎧ ⎫⎡ ⎤⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎨ ⎬⎢ ⎥⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥

⎢ ⎥⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

⎛ ⎞⎜ ⎟

+ += +

+ +

⎡ ⎤⎢ ⎥

mo sr Rg⎪ ⎪⎢ ⎥

⎪ ⎪⎢ ⎥⎣ ⎦⎩ ⎭⎜ ⎟⎝ ⎠

+ +

m i

mo sm i

v1 1r Rvv i

g

ggg

⎧ ⎫⎡ ⎤⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎨ ⎬

⎢ ⎥⎢ ⎥⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

+ +=i-m oi om

o s

v ir1 1

r R

ggg

⎪ ⎪⎢ ⎥⎨ ⎬⎢ ⎥⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎣ ⎦⎩ ⎭

⎧ ⎫⎧ ⎫⎡ ⎤⎪ ⎪⎪ ⎪⎢ ⎥

⎝ ⎠⎣ ⎦⎛ ⎞⎜ ⎟⎝ ⎠

− =+ +

m m-o mio mm o so s

i v 1 1 1 1 1r r Rr R

g gggg

⎪ ⎪⎪ ⎪⎢ ⎥⎪ ⎪⎪ ⎪⎢ ⎥⎪ ⎪ ⎪⎢ ⎥⎨ ⎨ ⎬ ⎬⎢ ⎥ ⎛ ⎞⎪ ⎪ ⎪⎢ ⎥ ⎜ ⎟⎪ ⎪ ⎪⎢ ⎥ ⎜ ⎟⎪ ⎪ ⎪⎢ ⎥ ⎝ ⎠⎣ ⎦⎩ ⎭⎩

⎛ ⎞⎜ ⎟⎝ ⎠

= −+ ++ +

⎪

⎪⎪⎪⎭

17

so s⎢ ⎥ ⎝ ⎠⎣ ⎦⎩ ⎭⎩ ⎝ ⎠ ⎭

m m-o mii v 1 1 1 1 1r

g gggg

⎧ ⎫⎧ ⎫⎡ ⎤⎪ ⎪⎪ ⎪⎢ ⎥⎪ ⎪⎪ ⎪⎢ ⎥⎪ ⎪⎪ ⎪⎢ ⎥⎨ ⎨ ⎬ ⎬⎢ ⎥ ⎛ ⎞⎪ ⎪ ⎪ ⎪⎢ ⎥ ⎜ ⎟⎪ ⎪ ⎪ ⎪⎢ ⎥

⎛ ⎞⎜ ⎟

= −+ ++ +

m m1 1r Rg g

⎧ ⎫⎧ ⎫⎡ ⎤⎪ ⎪⎪ ⎪⎢ ⎥⎪ ⎪⎪ ⎪⎢ ⎥⎪ ⎪⎪ ⎪⎢ ⎥

+ +

o mm o so sr r Rr R

gg ⎜ ⎟⎪ ⎪ ⎪ ⎪⎢ ⎥ ⎜ ⎟⎪ ⎪ ⎪ ⎪⎢ ⎥ ⎝ ⎠⎣ ⎦⎩ ⎭⎩ ⎭⎜ ⎟⎝ ⎠

+ ++ +

mo smo m m

o s o si

m

r R1 1 1 1i r R r Rm v

ggg gG

g

⎪ ⎪⎪ ⎪⎢ ⎥⎨ ⎬⎪ ⎪⎢ ⎥⎪ ⎪⎪ ⎪⎢ ⎥⎪ ⎪⎪ ⎪⎢ ⎥

⎨ ⎬⎪ ⎪⎢ ⎥⎣ ⎦⎩ ⎭⎪ ⎪⎪ ⎪⎪ ⎪

⎛ ⎞⎜ ⎟⎝ ⎠

− + + + += =

m

o m o s1 1r r R

1 1 1

gg

g g

⎪ ⎪⎛ ⎞⎪ ⎪⎜ ⎟⎪ ⎪⎜ ⎟⎪ ⎪⎝ ⎠⎩ ⎭

⎧ ⎧ ⎫⎪ ⎪ ⎪

−+ +

+ +⎫⎪m m

o s omm

o s

r R r m 1 1r R

g gG g

g

⎪ ⎪ ⎪⎪ ⎪ ⎪⎪ ⎪ ⎪⎨ ⎨ ⎬⎪ ⎪ ⎪⎪ ⎪ ⎪

⎪ ⎪⎩ ⎭⎩

− −+ +=

+ +

⎪⎪⎪⎬⎪⎪

⎪ ⎪⎭

msm ss mm

1R m R1 1 R 1R

gG ggg

⎧ ⎫⎡ ⎤⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎪ ⎪⎢ ⎥⎨ ⎬⎢ ⎥⎪ ⎪

⎢ ⎥⎪ ⎪⎢ ⎥⎪ ⎪

= =+ ++ +

18

oo s rr R gg⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭

mss m

m RR 1gG

g=

+ +s mo

mo s

s m

R 1r

If r >> R , m R 1

g

gGg

+ +

=+s m

ms

s m s

R 11If R is large, m R R

ggGg

+

= =

Without S degeneration, Gm = gm . This shows that with source degeneration, Gm has reduced. Gm_CS_degen < Gm_CS .

E

o o

R1m r and m_CS_degen m_CE_degen 1 1s 1m E

g1G G

R 1+g R +⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟

⎡ ⎤−⎢ ⎥β⎣ ⎦=+

=

m o om E g r

,o E E1m 1 o

g

If r R and R >> 1, thengG

⎜ ⎟⎜ ⎟⎝ ⎠β

⎡ ⎤⎣ ⎦= = =

>>

β

19

( )o o

om_CE_degen 11 1 oE1 1m E E

G R +g R + R +⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⎣ ⎦= = =

β β

ββ

m CS degen s1G

R=

( )1 o

m_CE_degen 11 o EE1E

G RR +R +⎛ ⎞⎜ ⎟⎜ ⎟

= = ≈

β

β 1β

_ _ g sR

if βo >> 1

oE ⎜ ⎟

⎝ ⎠β

oiii DG ti

tovR = i

o

0iv =

DRor tv+

DG

gsv

+

ti

t

ot i

i v 0= −

S

SR

m gsg V

S−

sv+

t

′SRsv− oR ′

oR

20

t tv v′t t,o o ot i i

v vR = R =i iv 0 v 0

v vgs s

= =

=−oiii DG ti

st

v vgs s

KCL at node D:v vi vg +

−=−

0iv =

DRor tv+

−m gsg Vgsv

+

−

ti

o m s o

st sm gs o

i v rKCL at node S:

v v vv r R

g

g

+

−+

=

=

S

SR

S

sv+

− oR ′oR

g o sst sm s o s

s s t

r Rv v vv r R

vv vv

g

g

−− +

+ +

=

= s tvvi vg +s s tm s o osts

m o

v r rRvv

1 1 rrR

g

g⎛ ⎞⎜ ⎟⎜ ⎟

+ +

+ +

=

=

s to m s o o

m ot

i v r r1r 1 vr

g

g⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟

⎝ ⎠⎢ ⎥⎢ ⎥⎛ ⎞

+

+

=− −

− −=

21

m oos rR g⎜ ⎟⎝ ⎠

tom oos

vr1 1 rrR g⎢ ⎥⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦

++ +

s tvvi vg +=− − s to m s o o

m ot

i v r r1r 1 vr1 1

g

g⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟

⎝ ⎠⎢ ⎥⎢ ⎥⎛ ⎞

+

+

=

− −= to

m oos1 1to 1 1 1 1

r1 1 rrRvR i

g⎢ ⎥⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦

+ +

⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞′ = = =

m m mo o s o

om o m o

s o s o

1 1 1 1o1r r R r

1 1 1 1rr rR r R r

ig g g

g g

⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞− − − − + + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠+⎢ ⎥ ⎢ ⎥⎛ ⎞ ⎛ ⎞⎢ ⎥ ⎢ ⎥+ + + +⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦s o s oR r R r

1oR

⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦′ = 1

o o s m s1

1R

r r R Rg⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥

= = + +

( )

s

m o s m os o s o

1R1 1 1 1r R r

R r R r

R r 1 R R

g g

g

⎢ ⎥ ⎢ ⎥⎛ ⎞ ⎛ ⎞⎢ ⎥ ⎢ ⎥+ + + +⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦

′ + +

22

( )o o s m sR r 1 R Rg= + +

( )o o s m sR r 1 R Rg′ = + +

If Rs↑, will also ↑.

F th CE ith E d ti

oR ′

( )

For the CE with E degeneration: .1oR = rο+β⎡ ⎤ ο⎣ ⎦

′

h h ill b li i d i i l f ( β )R ′Even though RE →∞, will be limited to its maximum value of ro(1+ βo).oR

23