EEE 241EEE 241 ANALOG ELECTRONICS 1 LtLecture …ee.eng.usm.my/eeacad/laili/241/L10_L11.pdf · EEE...
Transcript of EEE 241EEE 241 ANALOG ELECTRONICS 1 LtLecture …ee.eng.usm.my/eeacad/laili/241/L10_L11.pdf · EEE...
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⎟
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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