Willy Sansen KULeuven, ESAT-MICAS Leuven, Belgium
59
Willy Sansen 10-05 041 Noise performance of elementary transistor stages Willy Sansen KULeuven, ESAT-MICAS Leuven, Belgium [email protected]
Transcript of Willy Sansen KULeuven, ESAT-MICAS Leuven, Belgium
Will
y Sa
nsen
10-0
5 0
41
Noi
se p
erfo
rman
ce
of e
lem
enta
ry tr
ansi
stor
stag
es
Will
y Sa
nsen
KU
Leuv
en, E
SAT-
MIC
AS
Leuv
en, B
elgi
umw
illy.
sans
en@
esat
.kul
euve
n.be
Will
y Sa
nsen
10-0
5 0
42
SNR
and
SN
DR
v OU
T
v IN
0.1
% d
isto
rtio
n
1 %
dis
tort
ion
0.1%
SN
DR
SNR
00
Will
y Sa
nsen
10-0
5 0
43
Tab
le o
f con
tent
s
�D
efin
ition
s of
noi
se�
Noi
se o
f an
ampl
ifier
�N
oise
of a
follo
wer
�N
oise
of a
cas
code
�N
oise
of a
cur
rent
mirr
or�
Noi
se o
f a d
iffer
entia
l pai
r�
Cap
aciti
ve n
oise
mat
chin
g
Will
y Sa
nsen
10-0
5 0
44
Noi
se v
ersu
s tim
e
t t
v N v N2
v N2
is th
e av
erag
e no
ise
pow
er
Ref
. Van
der
Ziel
(Pre
ntic
e H
all 1
954,
Wile
y 19
86),
Ott
(Wile
y 19
88)
Will
y Sa
nsen
10-0
5 0
45
Noi
se v
ersu
s fre
quen
cy
v N2
f
dvN
2Noi
se d
ensi
ty V
2 /H
z
whi
te n
oise
1/f n
oise
f 1df
f 2
v 12
=
v N2
=
�dv N
2df
=
(f2-
f 1) d
v N2
f 1
f 2V R
MS
Inte
grat
ed n
oise
V RM
S/�H
z
Will
y Sa
nsen
10-0
5 0
46
Noi
se o
f a r
esis
tor
is th
erm
al n
oise
RdvR
2
Rdi
R2
dvR
2 =
4kT
R d
f
is
whi
te
for R
= 1
k����
dvR
2=
4 nV
RM
S/
Hz
depe
nds
on T
, not
on
I R
at T
= 3
00 K
or 2
7oC
diR
2 =
=
d
f i
s w
hite
dvR
2
R2
4kT R
Will
y Sa
nsen
10-0
5 0
47
Inte
grat
ed N
oise
of R
esis
tor
-1
v out
dvR
s2
v in
RS
CL
BW
f
A
dvR
s2=
4kT
RS
dfB
W =
1��
RSC
L
�v R
s2=
dvR
s2
1 +
(f/ B
W) 2
0
�
Will
y Sa
nsen
10-0
5 0
48
Inte
grat
ed N
oise
of R
esis
tor
-2
BW
� 2B
Wn
f
A
�v R
s2=
dvR
s2
1 +
(f/ B
W) 2
0
�
BW
�dx
1 +
x 2
0
�� 2
==
v Rs2
=kT C
LC
L =
1pF
vR
s= 6
5 �V
RM
S
v Rs2
=4k
T R
SBW
� 2df
Will
y Sa
nsen
10-0
5 0
49
Noi
se d
ensi
ty v
s int
egra
ted
nois
e
BW
BW
n
f
A
�v R
s2=
dvR
s2
1 +
(f/ B
W) 2
0
�=
kT CL
dvR
s2=
4kT
RS
df
Noi
se d
ensi
ty (
V2/H
z) ~
RS
(or 1
/gm
)
Inte
grat
ed n
oise
(VR
MS)
~ 1
/CL
Will
y Sa
nsen
10-0
5 0
410
A r
esis
tor
also
has
1/f
nois
e
RdvR
f2dv
Rf2
= V R
2
for R
= 1
k���w
ith 2
0 �
‘s o
f 50 ����
and
1 �m
wid
e an
d V R
= 0.
1 V
dvR
f2=
16
nVR
MS/
Hz
at 1
Hz
df fis
1/f
KF R
R�
AR
KF R
Si�
2 1
0 -2
1Sc
m2
KF R
poly
� 10
KF R
Si
V R+ -
Ref
. Van
dam
me,
ESS
DER
C ‘0
4
Will
y Sa
nsen
10-0
5 0
411
Noi
se o
f a d
iode
is sh
ot n
oise
I D
diD
2
diD
2 =
2q I D
df
is
whi
te
depe
nds
on I D
, not
on
T
for I
D=
50 �
Adi
D2
= 4
pAR
MS/
Hz
q =
1.6
10-1
9C
Will
y Sa
nsen
10-0
5 0
412
A d
iode
als
o ha
s 1/f
nois
e
diD
f2 =
I D
For a
dio
de o
f AD
= 5
x 2
�m
= 1
0 �m
2an
d I D
= 0.
1 m
A
diD
f2=
1 nA
RM
S/
Hz
at 1
Hz
df fis
1/f
KF D A
D
KF D
� 10
-21
Acm
2
I D
diD
f2
Will
y Sa
nsen
10-0
5 0
413
Noi
se o
f a M
OST
r DS
g mv G
S
v GS
+ -
v out
+ -
v in+ -
diD
S2
dvG
2 =
4kT
RG
df
dvG
2R
G
diD
S2 =
d
f = 4
kT
gm
dfR
CH
4kT
2 3R
ef. V
an d
erZi
el, P
rent
ice
Hal
l 195
4, W
iley
1986
.
Will
y Sa
nsen
10-0
5 0
414
MO
ST: e
quiv
alen
t inp
ut n
oise
: w
hite
dvie
q2 =
4kT
(Ref
f) d
f
R
eff=
+ R
G
r DS
g mv G
S
v GS
+ -
v in+ -dvie
q2R
G
v out
+ -
Hi F
req.
: di
ieq2
= (C
GS
)2dv
ieq2
is c
orre
late
d
g m2/3
Will
y Sa
nsen
10-0
5 0
415
Poly
Gat
e re
sist
ance
rG
in a
MO
ST
Will
y Sa
nsen
10-0
5 0
416
Subs
trat
e re
sist
ance
s rB
in a
MO
ST Ref
. Cha
ng, K
luw
er19
91
Will
y Sa
nsen
10-0
5 0
417
Noi
se b
y th
e B
ulk
resi
stan
ce
r DS
g mv G
S
v GS+ -
g mbv
BS
v BS
+ -
v inG+ -dvrG
2R
G
v inB
=0
+ -
dvrB
2R
B
r DS
g mv G
S
v GS+ -
v in+ -dvie
q2R
Gdv
ieq2
= 4
kT (R
eff)
df
Ref
f=
+ R
G+
RB
(n-1
)2g m2/
3
(n-1
) = C
D/C
ox=
g mb/
g m
Will
y Sa
nsen
10-0
5 0
418
Noi
se b
y th
e So
urce
res
ista
nce
r DS
g mv G
S
v GS+ -
v in
+ -dvie
q2R
G
dvie
q2 =
4kT
(Ref
f) df
Ref
f=
+ R
G+
RS
+ R
B(n
-1)2
g m2/3
RS
Noi
se o
f RS
= no
ise
RG
Will
y Sa
nsen
10-0
5 0
419
Noi
se b
y So
urce
res
isto
r R
i out
diM
2
diou
t2
Rdi
R2
v in g m
R >
> 1
i out
=v i
n R
diM
2 =
4kT
2/3
g m d
fdi
outM
2 = (g
mR
)2di
M2
diR
2 =
df
4kT R
diou
tR2
= di
R2
diou
t2 =
4kT R
(
+
1 )
df �
2/3
g mR
4kT R
df
dvin
2 =
4kT
R d
f
Will
y Sa
nsen
10-0
5 0
420
MO
ST: e
quiv
alen
t inp
ut n
oise
: E
xerc
ise
dvie
q2 �
4kT
(
) d
f
r DS
g mv G
S
v GS
+ -
v in+ -dvie
q2
v out
+ -
g m2/3
dvie
q2 �
?fo
r ID
S=
65 �
A
Will
y Sa
nsen
10-0
5 0
421
dvie
qf2
=
r DS
g mv G
S
v GS
+ -
v in+ -dvie
qf2
RG
WL
Cox
2
KF F
v out
+ -
df fpM
OST
KF F
� 1
0-32
C2 /
cm2
nMO
STK
F F �
4 1
0-31
C2 /
cm2
pJFE
TK
F F �
10-
33C
2 /cm
2
W &
L in
cm
; Cox
inF/
cm2
MO
ST: e
quiv
alen
t inp
ut n
oise
: 1/
f noi
se
Will
y Sa
nsen
10-0
5 0
422
Noi
se v
s cur
rent
: co
rner
freq
uenc
y
dvie
q2
ff c
hif c
lo
I DSl
ow
hite
noi
se ~
~
I DSh
i
Cor
ner f
requ
ency
~ g
m
1/f n
oise
~
g m1WL
WL1
Will
y Sa
nsen
10-0
5 0
423
Noi
se v
s cur
rent
: ex
erci
se f c
dvie
q2
ff c
hif c
lo
I DSl
ow
hite
noi
se ~
I DSh
i
1/f n
oise
g m1
Ex. :
fc?
For I
DS
= 65
�A
; K
’ n=
60 �
A/V
2an
d L
= 1 �m
(0.3
5 �m
pro
cess
)f c
� 37
0 kH
z
Will
y Sa
nsen
10-0
5 0
424
Noi
se se
en a
t the
Bul
k
dvie
q2dv
ieqb
2
dvie
q2 =
4kT
(
) d
f
dvie
qf2
=
WL
Cox
2
KF F
df f
g m2/3
n-1
= g mg m
b
dvie
qb2
= 4
kT (
)
df
dvie
qfb2
=
WL
Cox
2
KF F
df f
2/3
g m g mb2
g m2
g mb2
Will
y Sa
nsen
10-0
5 0
425
Noi
se o
f a B
ipol
ar tr
ansi
stor
r og m
v BE
+vB
E
-
v out
+ -
v in+ -
diC
2
dvB
2 =
4kT
r Bdf
dvB
2r B
diB
2 =
2q
I Bdf
diC
2 =
2q
I Cdf
diB
f2 =
A
EB
KF B
I Bdf f
KF B
� 1
0-21
Acm
2
r �di
B2
C E
Ref
. Van
der
Ziel
(Pre
ntic
e H
all 1
954)
Will
y Sa
nsen
10-0
5 0
426
Bip
olar
tran
s.: e
quiv
alen
t inp
ut n
oise
dvie
q2 =
4kT
(Ref
f) d
f
R
eff=
+ R
B +
RE
r og m
v BE
v out
+ -
g m1/2
diie
q2 =
di B
2 =
2q
I Bdf
+ v B
E
-
v in+ -dv
ieq2
RB
r �di
ieq2
Will
y Sa
nsen
10-0
5 0
427
Tab
le o
f con
tent
s
�D
efin
ition
s of
noi
se�
Noi
se o
f an
ampl
ifier
�N
oise
of a
follo
wer
�N
oise
of a
cas
code
�N
oise
of a
cur
rent
mirr
or
�N
oise
of a
diff
eren
tial p
air
�C
apac
itive
noi
se m
atch
ing
Will
y Sa
nsen
10-0
5 0
428
Noi
se o
f an
ampl
ifier
with
act
ive
load
v out
M1M2
v in
CL
dv22
dv12
dvB
2
+
If d
v B2
is
negl
igib
le :
diou
t2 =
g m12
dv12
+ g m
22 dv
22
dvie
q2 =
dv12
+dv
22 ()2
g m1
g m2
dvie
q2 =
dv12
(1 +
)
g m1
g m2
Smal
l gm
2: s
mal
l (W
/L) 2
or l
arge
(V G
S-V
T ) 2
dvie
q2
V B
Will
y Sa
nsen
10-0
5 0
429
1/f N
oise
of a
mpl
ifier
with
act
ive
load
v out
M1
M2
v in
CL
dv2f
2
dv1f
2
dvB
2
+
If dv
B2
is
negl
igib
le :
dvif2
= dv
1f2
+dv
2f2 (
)2
g m
1
g m2
dvif2
= dv
1f2
[1 +
(
)2
()2
]
dvif2
has
min
imum
at
g m1
g m2
dv1f
dv2f
dvif2
= dv
1f2
[1 +
(
)2]
KF 1
KF 2
L 2L 1K
’ 1
K’ 2
L 1op
t= L
2�
10 L
2th
en d
v if2
= 2
dv1f
2
KF 2
KF 1
K’ 2
K’ 1
V B
Will
y Sa
nsen
10-0
5 0
430
Noi
se fi
gure
of a
n am
plifi
er
v in+ -
dvS2
RS di
ieq2dv
ieq2
v out
+ -
AR
in=
�
NF
=
=
1 +
NS
+ N
A
NS
NA
NS
NF
= 1
+ 4k
T R
S df
dvie
q2+
RS2
diie
q2Vo
ltage
driv
e N
F ~
Cur
rent
driv
e N
F ~
RS1 RS
Will
y Sa
nsen
10-0
5 0
431
Res
istiv
e no
ise
mat
chin
g
RS
NF
NS
NA
Rso
pt
=
100
r B=
100 �
Rso
pt=
dvie
q2
diie
q2
g m=
3.8
mS
Will
y Sa
nsen
10-0
5 0
432
Tab
le o
f con
tent
s
�D
efin
ition
s of
noi
se�
Noi
se o
f an
ampl
ifier
�N
oise
of a
follo
wer
�N
oise
of a
cas
code
�N
oise
of a
cur
rent
mirr
or�
Noi
se o
f a d
iffer
entia
l pai
r�
Cap
aciti
ve n
oise
mat
chin
g
Will
y Sa
nsen
10-0
5 0
433
Noi
se o
f an
emitt
er fo
llow
er
i CE
v INRS
diie
2dv
ie2
v OU
T
CL
RT
A
dvA
2
diA
2I T
dvie
q2
dvie
q2 =
dvie
2 +
dvA
2 +
(RS
-)2
diie
2 +
dvS2
diT2
1 g m
diT2 +
di A
2
g m2
Will
y Sa
nsen
10-0
5 0
434
Tab
le o
f con
tent
s
�D
efin
ition
s of
noi
se�
Noi
se o
f an
ampl
ifier
�N
oise
of a
follo
wer
�N
oise
of a
cas
code
�N
oise
of a
cur
rent
mirr
or�
Noi
se o
f a d
iffer
entia
l pai
r�
Cap
aciti
ve n
oise
mat
chin
g
Will
y Sa
nsen
10-0
5 0
435
Noi
se o
f a c
asco
deam
plifi
er
I B
+v o
ut
v in
M1
M2
dv22
dv12
dvie
q2
dvie
q2 =
dv12
+ dv
221
(gm
1 r o
1)2
�dv
12
Will
y Sa
nsen
10-0
5 0
436
Inpu
t ref
erre
d no
ise
of a
cas
code
RL
+
v out
v in
i SR
Si N
v out
RL
g mr D
SRS
g mr D
S
v out i S
= g m
r DSR
S
v in i S
= R
S
v out i N
= r D
S
g mR
S
1 g m
g mr D
S>>
1
Will
y Sa
nsen
10-0
5 0
437
Noi
se g
ains
in a
cas
code
RL
+
v out
v in
i SR
Si N
A
RL
r DS
g mr D
S
v out
=v i
n
i Seq i N
=g m
RS
1
i Nv o
ut=
g mr D
Sv i
ni S
RL RS
Cas
code
nois
e i N
is
only
neg
ligib
le i
f RS
is la
rge
!!!
Will
y Sa
nsen
10-0
5 0
438
Noi
se o
f a fo
lded
cas
code
dv22
dvie
q2
dvie
q2 =
dv12
+ dv
22
+ d
v 32
1(g
m1
r o1)
2
I B1
v out
v in
M1
M2
CL
+
I B2
M3
dv32
dv12
dvB
2
(gm
3)2
(gm
1)2
Smal
l gm
3:
(W/L
) 3(V
GS-
V T) 3
If dv
B2
is n
eglig
ible
:
Will
y Sa
nsen
10-0
5 0
439
Noi
se o
f a c
asco
dew
ith li
near
M1
I B
+
v out
v in
M1
linea
r
M2
dv22
dv12
dvie
q2
(Ron
1+
) d
f
V DS1
Av
= �
1g m
2 r o
2
Ron
1=
1
1(V
GS1
-VT)
2/3
g m2
I DS1
= 1
V DS1
(VG
S1-V
T)
�1
= V D
S1
V GS1
-VT
�1
< 0.
5
4kT
�12
dvie
q2=
Will
y Sa
nsen
10-0
5 0
440
Smal
l-sig
nal m
odel
of a
cas
code
with
line
ar M
1
r o2
g m2v
2
v 2+ - v in
dv22
v out + -
+dv
ieq2
Ron
1
g m1v
in
CL
-
Ron
1=
1
1(V
GS1
-VT)
I DS1
= 1
V DS1
(VG
S1-V
T)
dv12
dv12
=4k
T R
on1
�12
v out
/ dv 2
= g
m2
r o2
(Ron
1+
) d
f2/
3g m
2
4kT
�12
dvie
q2=
dv22
=4k
T 2/
3g m
2v o
ut/ d
v 1= �
1g m
2 r o
2
Will
y Sa
nsen
10-0
5 0
441
Tab
le o
f con
tent
s
�D
efin
ition
s of
noi
se�
Noi
se o
f an
ampl
ifier
�N
oise
of a
follo
wer
�N
oise
of a
cas
code
�N
oise
of a
cur
rent
mirr
or�
Noi
se o
f a d
iffer
entia
l pai
r�
Cap
aciti
ve n
oise
mat
chin
g
Will
y Sa
nsen
10-0
5 0
442
Noi
se o
f a c
urre
nt m
irro
r
1 : B
i ini o
ut
M1
M2
di22
di12
diin
2
diou
t2
diou
t2 =
di22
+ B
2(d
i in2
+ di
12 )
Smal
l gm
:
(W/L
)
(VG
S-V T
)
4kT
g m2
df2 3
=
Will
y Sa
nsen
10-0
5 0
443
Noi
se o
f a c
urre
nt m
irro
r w
ith se
ries
R
i ini o
ut
M1
M2
di22
di12
diin
2
diou
t2di
out2
= di
22 + d
i R22
+
(di 1
2 + d
i R12 )
Smal
l gm
:
(W/L
)
(VG
S-V T
)
RR
1R
2di
R12
diR
22
(R1)
2
(R2)
2
Will
y Sa
nsen
10-0
5 0
444
Noi
se o
f a c
urre
nt m
irro
r w
ith se
ries
R R1=
R2
diou
t2
RR
M
M
diou
t2=
8kT
R2
diou
t2=
4kTg
m2
(gm
2R2)
2
4 3
1/g m
4kT(
)g
m2d
f4 3
Bilo
tti, J
SSC
Dec
75,
516
-524
df
df
Will
y Sa
nsen
10-0
5 0
445
Cur
rent
mir
ror
with
seri
es R
I out
M2di
outR
2di
outR
2 =
diou
t2 Smal
l gm
:
(W/L
)
(VG
S-V T
)
V G
R
M1
V G+ -
I out
diou
t2 (VG
S-V T
)(V
GS-
V T)
(W/L
)(W
/L)
Sam
e I o
ut&
sam
e V G
:
Will
y Sa
nsen
10-0
5 0
446
Noi
se in
bip
olar
cur
rent
mir
ror
1 : B
i ini o
ut
M1
M2
M3 R
Noi
se a
dded
by
M3
:
diou
tM32
= 2q
I C3
df
Noi
se a
dded
by
R :
Bot
h ar
e di
vide
d by
32
to b
e ad
ded
to th
e ou
tput
and
are
thus
neg
ligib
le !
diou
tR2
= 4k
T/R
df
Will
y Sa
nsen
10-0
5 0
447
Low
-noi
se c
urre
nt m
irro
r w
ith se
ries
R
I out
M2
diou
t22
1 M
OST
: di o
ut2
=
RM
1V G
1+ -
I out
diou
t12
Larg
e R
or V
G2
Sam
e I o
ut&
diff
eren
t VG
:
+ V G2
>VG
1
-
3 41 4
I out
diou
t2 =
diou
t12
+ di
out2
2 =
8kT 3
2Iou
t df
V GS-
V T
V G2-
V G1)
(V G
1-V T
9 161 4
+8k
T 32I
out d
fV G
1-V T
2 M
OST
s: V
G2 >V
G1
Will
y Sa
nsen
10-0
5 0
448
Tab
le o
f con
tent
s
�D
efin
ition
s of
noi
se�
Noi
se o
f an
ampl
ifier
�N
oise
of a
follo
wer
�N
oise
of a
cas
code
�N
oise
of a
cur
rent
mirr
or�
Noi
se o
f a d
iffer
entia
l pai
r�
Cap
aciti
ve n
oise
mat
chin
g
Will
y Sa
nsen
10-0
5 0
449
Noi
se o
f diff
eren
tial p
air
V DD V S
S
v OU
T
-
I B
RL
RL
+-
dv12
dv22
v OU
TA
dvie
q2
+ -+-
A+ -+-
v OU
T
M1
M2
+
dvie
q2 =
2 dv
12
Will
y Sa
nsen
10-0
5 0
450
Noi
se o
f diff
eren
tial p
air
with
act
ive
load
V DD
V SSv O
UT
CL
M1
M2
M3
M4
+-
I B
di12
di22
di42
di32
dvie
q2 =
=di
out2
g m12
dvie
q2 =
2dv 1
2 (1
+
)
g m12
2di 1
2 +2d
i 32
g m1
g m3
Smal
l gm
3:
(W/L
) 3
(VG
S-V T
) 3
Will
y Sa
nsen
10-0
5 0
451
Diff
eren
tial p
air
with
sour
ce r
esis
tors
I BR
RR
R
I B/2
I B/2
diou
t2 =
2 4k
T Rdf
dvin
2 =
2 (4
kT R
df)
g mR
>> 1
diB
2 is
neg
ligib
le
diou
t2 =
2 ( 4k
T Rdf
+ d
i B2
)
diB
2 =
4kT
2/3
gm
Bdf
dvin
2 =
2 (4
kT R
df)
(1 +
2/3
gm
BR
)
Will
y Sa
nsen
10-0
5 0
452
Noi
se o
f an
opam
p
v OU
TA
dvR
12
+-
dvie
q2=
dvR
12 +
dvR
22 (
) 2
+ dv
A2
(1 +
) 2 �
dv R
12 +
dvA
2
dvA
2
dvR
22R
2
dvie
q2
R1
dvie
q2=
�dv
out2
( )
2R
2
R1
R1
R2
dvou
t2 =
dv R
12 (
) 2
dvou
t2 =
dv R
22
R2
R1
R2
R1
dvou
t2 =
dv A
2 (1
+) 2
R
1
R2
Will
y Sa
nsen
10-0
5 0
453
Tab
le o
f con
tent
s
�D
efin
ition
s of
noi
se�
Noi
se o
f an
ampl
ifier
�N
oise
of a
follo
wer
�N
oise
of a
cas
code
�N
oise
of a
diff
eren
tial p
air
�N
oise
of a
cur
rent
mirr
or�
Cap
aciti
ve n
oise
mat
chin
g
Ref
.: Z.
Y.C
hang
, W.S
anse
n, L
ow-n
oise
wid
e-ba
nd a
mpl
ifier
s, K
luw
erA
P, 1
991
Will
y Sa
nsen
10-0
5 0
454
Cap
aciti
ve-s
ourc
e am
plifi
er
v out
v in
Ai in
Cf
Ca
Ca
Av
= C
f
Ca
I DS
CG
S=
kW
k�
2 fF
/�m
Wop
t?
ID
Sopt
? S
/Nop
tfo
r Vin
= 10
mV R
MS
?
Ca
= 5
pFC
f= 1
pF
Will
y Sa
nsen
10-0
5 0
455
Cap
aciti
ve n
oise
mat
chin
g -1
Cf
Ca
I DS
CG
S
Cf
Ca
dvie
q2
I DS
CG
S
dvi2 v G
S�
0
v out
v out
v iv out
=C
f+C
a+C
GS
Cf
v GS
� 0
v ieq
v out
=C
a Cf
No
Mill
er
with
CD
G !!
!
Will
y Sa
nsen
10-0
5 0
456
Cap
aciti
ve n
oise
mat
chin
g -2
v in
dvie
q2 =
Cf
Ca
dvie
q2
I DS
CG
S
dvi2
Ca2
(Cf+
Ca+
CG
S)2
dvie
q2 =
Ca2
(Cf +
Ca
+ kW
) 2
dvi2
=38k
Tg m1
df
g m=
2 K
’ nLW
(VG
S-V T
)
WL38k
T2
K’ n
(VG
S-V T
)1
Will
y Sa
nsen
10-0
5 0
457
Cap
aciti
ve n
oise
mat
chin
g -3
dvie
q2 =
Ca2
(Cf +
Ca
+ kW
) 2
WL38k
T2
K’ n
(VG
S-V T
)1
dvie
q2
Wop
tW
dvop
t2
Wop
t=
k
Cf +
Ca
g mC
GS
Noi
se m
atch
ing
whe
re
CG
S=
Cf +
Ca
Ope
ratin
g po
int
Will
y Sa
nsen
10-0
5 0
458
Cap
aciti
ve n
oise
mat
chin
g -4
dvie
q2
Wop
tW
dvop
t2
Wop
t=
k
Cf +
Ca
CG
Sopt
I DSo
pt,
g mop
t
dvop
t2 =
438k
Tg m
opt
df
BW
n=
B
W=
=
2�
2�A
vf T
4Av
1C
GSo
pt
g mop
tN
opt
S=
10 m
V RM
S
dvop
t2 B
Wn
Will
y Sa
nsen
10-0
5 0
459
Tab
le o
f con
tent
s
�D
efin
ition
s of
noi
se�
Noi
se o
f an
ampl
ifier
�N
oise
of a
follo
wer
�N
oise
of a
cas
code
�N
oise
of a
cur
rent
mirr
or�
Noi
se o
f a d
iffer
entia
l pai
r�
Cap
aciti
ve n
oise
mat
chin
g
