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10-1
CMOS (1)
10-2op amp
AVin+
Vin
Vout
Vout = A (Vin+ Vin )
+
A > 103
op amp
/
AM/FM
10-3
F
Vin+ Vout
1out inF
AV VA
Vin+=Vin-A
+ AVin-
op amp
in F outV V
Vout = A (Vin+ Vin )
1F
in inF
AV VA
inout
F
VV
in inV V
Vout
Vin+ Vin
VDD
00
A >> 1
< 1mV
10-4
Vin+
VinVout
2
1 2in out
RV VR R 1
2
1out inRV VR
in inV V
+
R1
R2
10-5
+Vref
10-6
I I
VTn+ 1 VTn+ 2
1 2= I R
2
21 2
1 2 2IR
VDD
M1 M2
R
10-7op amp
+
10-8op amp
Vin VoutVin+
CC
10-9
ISS
I1 I2 1 2SSI I I
12in T
IV V 22in T
IV V
in in inv V V
2 2 4
1,2 22 2 4SS SS in in
SS SS
I I v vII I
0
ISS
I1
I2
2 SSI 2 SSIvin
1 2
0in
md SSin v
I Ig I
v
VinVin+
10-10
ISS
I1
I1
I2Vin+ Vin
Vin+
Vin
iout=gmd (Vin+ Vin )
OTA (Operational Transconductance Amplifier)
1 2outi I I
4 2//O o oR r r
4 2//md o oA g r r
M1
M2
M4
M3 Vin+
Vin
A (Vin+ Vin )
Vout
4 2 4 2// //out o o out md o o in outV r r i g r r V V
4 2//out o oV r r md in outg V V
Ro
10-11
RI :RL :
vin
Avvin
vout
RI :RL :
Aiiin Rout
iin iout
Rin
Rin >> RIRout << RL
Rin << RIRout >> RL
RI :RL :
OTA
vin
gmvin
iout
Rin >> RIRout >> RL
Av= gm Rout
RI RL
Rout
Rout
10-12
Vin+ Vin
Vout
M1
M4
M2
M3
M5
VCM =(Vin++Vin-)/2
A B
A B A B
5 3,4
12 o m
Ar g
Vin+=Vin-
M1+M2
M5
M3+M4
Vout
VCM 3,4
12O
m
Rg
out DM in CM CMv A v A v
5 3,4
12CM
o m
Ar g
4 2//DM md o oA g r r
CMRR =
5 3,4 4 22 //DMo m md o o
CM
A r g g r rA
CMMR ~ 103 (60dB)0.1%
CMRR
10-13
0
stF s f t e dt1
2i st
if t F s e ds
i
Laplace Laplace
Fourier f(0)
F(j ), = 2 f f :
10-14RC
Cvin vout
1
1out
in
p
vH s sv1
p RC
0dB 20dB/dec
dB = 20 log10 (|H(j )|)p
0
-90
1 1p
jH j Re[H(j )]
Im[H(j )]
01
0Bode
R
10-15
Vin VoutVin+
C1
Vin+
Vin
A1 (Vin+ Vin )
Vout Vin
A2Vin
Vout
Vin+
Vin
V1C2
1 2
1 2
1 1
1 1A s A As s
out in inV A s V V
Vout
11 1
1
OR C 22 2
1
OR C
C1 C2
Ro1 Ro2
Ro1 Ro2
10-16
F
Vin Vout+ A
1out in
A sV V
L s
1 2
1 2
1 m
n
s r s r s rL s
s p s p s p
FL s A s s
L(s)
open loop poleclosed loop pole
closed loop pole Re(ri) < 0
10-17
1 2
1 2
1 m
n
s r s r s rL s
s p s p s p
open loop dr = 0close loop nr = 0
1out
in
A sVV L s
1 l r l rL j n n d dnl : r1, …, rmnr : r1, …, rmdl : p1, …, pmdr : p1, …, pm
0L s l r l rn n d d
1 2 r rL j n d
1 + L( j )
Re[L(j )]
Im[L(j )]
100
Re s
Im s
0
a
ab
b
1 1L s L s
10-18
L(j ) = [0, ]
-1
-1 0
Im[L(j )]
Re[L(j )]0
-1 0
Im[L(j )]
Re[L(j )]0
1 Arg[L(j )]= -180 |L(j )| < 1
2 |L(j )| = 1 Arg[L(j )] > -180
10-19
L(s) Bode
0dB
-180
0
Bode
c
Arg[L(j )]
20log10(|L(j )|)
10-20
Vin VoutVin+
0
1 2
1 1
AA ss s
0dB
-180
0Bode
1 21 2
c
1~ 2
0 1 2c A
1 2, c
10-21
0
1 2
1 1
AA ss s A0=1000, 1=1
-1 0 1 2 3 4
-4
-2
0
2
-1 0 1 2 3 4
-175
-150
-125
-100
-75
-50
-25
2=1
=3.6
2=10
=6.3
2=100
=18
2=1000
=5210 10 10 10 10 10
10
10
10
10
0.01 0.02 0.03 0.04 0.05
0.25
0.5
0.75
1
1.25
1.5
1.75
2
0.01 0.02 0.03 0.04 0.05
0.25
0.5
0.75
1
1.25
1.5
1.75
2
0.1 0.2 0.3 0.4 0.5
0.25
0.5
0.75
1
1.25
1.5
1.75
2
0.1 0.2 0.3 0.4 0.5
0.25
0.5
0.75
1
1.25
1.5
1.75
2
0.1 0.2 0.3 0.4 0.5
0.25
0.5
0.75
1
1.25
1.5
1.75
2
0.1 0.2 0.3 0.4 0.5
0.25
0.5
0.75
1
1.25
1.5
1.75
2
Vout
0
1
10
Vin2=1
0 1
2=102=100
2=1000
2=1
2=102=100
2=1000
60
10-22
VinVin+
C1 C2
CC Vin+
Vin
V1 Vout
CC
Vout
2 21 2
2 2 1 2 1 1 2 1 2 1 21 1C O
C O C O C O O
A C R sA s AC C R C A C R s C C C C C R R s
out in inV A s V V
0
1 2
1
1 1
z
s
As s
2
2z
C O
AC R 1
2 1
1
C OA C R2
21 2
1 2 2OC
AC CC C RC
C1 C2
Ro1 Ro2
10-23
12
12 z
pole zero
2
2z
C O
AC R
12 1
1
C OA C R2
21 2
1 2 2OC
AC CC C RC
11 1
1
OC R 22 2
1
OC R
1 2 ,C z
0 1C A 1 1
2
90 tan tanC C
z
60
210 , 2.2Z C C
C
C
10-24nulling resistance
VinVin+
C1 C2
CCVout
RC
12 z
2
2z
C O
AC R
2
2 2z
C O C
AC R A R
A2 < 0
2
2 6
1OC
m
RR
A g
M6
10-25
Vin VoutVin+
CCM1 M2
3 M4
M5
M6
M7
M
CL
2 1, L CC C C C
0.22C LC C6 10m mdg g
ISS1,2md SSg I
6 6 62mg I
GBW = gmd /2 CC
AV = gmd RO1 gm6 RO2
1 4 2//O o oR r r 2 6 7//O o oR r r
5 3,4 12 o m md OCMRR r g g RRO = RO2
op amp
0dB
-6dB/Oct
10-26op amp
(offset voltage)
(power-supply rejection ratio)
(common-mode input range)
(slew rate)
(settling time)
DDV
OUT
VPSRR AV
t
V
+Vin+= Vin-
+Vin
Vout
Vout SR = V/ tVin
Vout
t
tsettling time
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