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NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 1
Analysis and Design of CMOS
Analog Building Blocks
Márcio Cherem Schneider
Universidade Federal de Santa Catarina
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 2
Contents1. The intrinsic gain stage
2. The source-coupled pair
3. The two-transistor current mirror
4.A self-biased current source
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 3
Summary of main design equations
21 1S
m ft
Ig i
n
20/ 2, , , SH ox t T EI C n n V V
/S SHI I W L A EV V L
D F R S f rI I I I i i
Saturation
/md ds D Ag g I V
Technology parameters
Size- and bias-related transistor parameters
0.35 um CMOS technology
70 nA
25 nA SHN
SHP
I
I
1 3DSsat t fV i
( )( ) ( )1 1 1 ln 1 1P S D
f r f rt
V Vi i
UICM
0G TP
V VV
n
Saturation voltage
Forward and reverse currents
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks
From UICM we find the dc voltage VTH at the input:
4
THE INTRINSIC GAIN STAGE - 1
M1,M2 in saturation
Class A amplifier:
SR->SR+.
Vmax
Vmin
maximum output swing
VDSsat1
VDSsat2
VDD
VDD
vo
viVTH
vo=vi
Av
L B DI I I DI
BI
viVDD0
LI
1 11
; BD B F f
S
II I I i
I
011 1
1
1 2 ln 1 1TH Tf f
t
V Vi i
n
1 21 2
B Bds ds
A A
I Ig g
V V 1 1
021 d
m mV
o sds
g gA
g g g
1 2
1 1+
1
A A AV V V
1 2 1 2 , ,A AV V L L01 1
2
1 1A
Vt f
VA
n i
VDD
VI
M1
+
IB
CL
ID
IL
M2
~3 if0
|AV0|dB
Low-frequency gain versus inversion level
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 5
VO
VDD
VI
M+
IB
CL
ID
IL
CLgogmvgvi
+
vg vo
1o m i oV m
i i o L
v G v ZA g
v v g sC
V-I converter (transconductor) followed by an I-V converter
(output impedance)
m mG g is the transconductance
oZ is the output impedance
|AV|dB
ub0
-20 dB/dec
|AV0|
0
1
1 // ; /
V Vb
b o L u m L
A As
g C g C
Voltage gain vs frequency
THE INTRINSIC GAIN STAGE - 2
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 6
VO
VDD
VI
M1
+
IB
CL
ID
IL
CLgogmvgvi
+
vg vo
0
1
1E
Vt
V LA
n ECF
minD WI m tI I g n / 1 1 / 2D WI WI fECF I I I i
1
2m
ox t
gW
L C ECF
Power-area tradeoff
How long can L be?
Sizing and biasing: W, L, IB
ECFCIN and transit time are both proportional to L2 (for constant W/L)!
THE INTRINSIC GAIN STAGE - 3
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 7
VO
VDD
VI
M1
+
IB
CL
ID
IL
2 2 14 4 1ch F m c
ms msox
i K g fkTg kTg
f WLC f f
2chi
Bias-dependent factor
Thermal 1/fMOST noise model
2F
c Tt
Kf f
nq
Corner frequency
2 1/ 21
3 1 1fi
1/2 (WI) 2/3 (SI)
2000T
cf
f 0.35 um CMOS technology
2 /chi f
cf f
Noise current generator
Input-referred noise model
2 2
2
21n ch
m
be i
f g f
i
2ne
Noiseless MOST
- +
THE INTRINSIC GAIN STAGE - 4
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 8
VSS
IT
+vG1
-
M1 M2
I1 I2
+vG2
-
First order analysis: Ideal current source M1 & M2 in saturation I1 & I2 independent of drain voltage;
1 2
1 2
1 2 0S S S
r r
n n n
I I I
i i
1 2
1 2
1 2
T
OD
G G id
I I I
I I I
V V V
1 1 2 2
/ /
/ / t T S od OD S
S S
i I I i I I
i I I i I I
Normalization
THE SOURCE-COUPLED PAIR -1
1 12 2
ln 1 1 1 12 2
id t od t od
t
t od t od
V i i i i
n
i i i i
1 2 1 2 t odi i i i i i
0 84 12-4-8-12
1
it=1000100
10<1
I1/IT
I2/IT
id
t
V
n
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 9
VSS
IT
+vG1
-
M1 M2
I1 I2
+vG2
-
02 01 2 1; T T T S S SV V V I I I
2ST
G OS Tm S
IIV V V
g I
Offset voltage VOS = VG =VG2- VG1 such that
ID= I2- I1=0
Simple model
0( , )f G T Si function V V V
0S mD
G TD S D
I gIV V
I I I
The differential input voltage at the input required for ID =0 is
THE SOURCE-COUPLED PAIR - 2
D S f rI I i i ir =0 (sat)
0
D Dm
T G
dI dIg
dV dV
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 10
VSS
IT
+vG1
-
M1 M2
I1 I2
+vG2
- 2 22 2
22ST
OS Tm S
IIV V
g I
2ST
G OS Tm S
IIV V V
g I
22 22
2; SVT IS
TS
IA AV
WL I WL
Pelgrom’s
model
22 2
2
2VT IST
OSm
A AIV
WL g WL
1 1
2 2fT D
tm m
iI In
g g
Uncorrelated VT & IS
Notes:
ISA A
0.35 um CMOS technology
5 10 mV m
1 2 % mVTA
A
THE SOURCE-COUPLED PAIR - 3
(I) (II)
(I) is dominant over (II) for
21 1 VT
ft IS
Ai
n A
575 for 32 mV
8 mV m, 2 % m
f t
VT
i n
A A
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 11
THE TWO-TRANSISTOR CURRENT MIRROR - 1VDD
ii
+vG
-
iovo
+-
M1 M2
1:1
M1: iv converterM2: vi converter
Basic principle VG1=VG2; VS1=VS2; vout>VDsat ioii
iD
vD
locus vD=vG
vG
vo
iD1
iD2
, 1 / D S G T S D A D DsatI I f V V V V V V V
o i o i o i
i i A E
i i v v v vi
i i V V L
Error due to difference in VD’s Error due to mismatch
00
0
1
D D DS T
D D S T
S mT
S D
I I II V
I I I V
I gV
I I
2 22 22
2 2
1D Sm mT VT IS
D D S D
I Ig gV A A
I I I WL I
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 12
1 1 1 2 2 1 2
1 1 1 1 2 1
gs gb gs gb db
gs gb db ovd
C C C C C C C
C A C C C C
1:A
1 1 20
2 2 20
o
i
i mv
o ds dbi
Y g s C C
Y g s C C
2mg v1
1
m
ds
g
g
ii
+v-
io
C1
C2
iiio
M1 M2
VDD
1
1
1
1 2o
i mg T
I CA As
I s g f
iin
io
M1 M2i1
i21:A
2
2 2 2 22 21 2
1 1
2 2 2 2 21 1
m mo in
m m
o in
g gi i i i A
g g
i A i i Ai
Uncorrelated noise sourcesNoise analysis
ac analysis
The effect of M1 on noise is A times greater than that of M2
THE TWO-TRANSISTOR CURRENT MIRROR - 2
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 13
Gain-of-two current mirrors
VDD
IIIO
1/2:1
W/L
W/L
W/L
VDD
II IO
1:2
W/L
W/LW/L
CURRENT MIRROR: GAIN SCHEMES
VDD
ii io==Aii
......
VDD
ii io==ii/A
......
Gain=A
Gain= 1/A
ii
io==ii/(NM)
.....
.
......N
M
Gain=1/(NM)
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 14
A SELF-BIASED CURRENT SOURCE – 1
21 2 2
1
11 1f f f
Si i i
S N
2
2 2
2
1 11 1 ln
1 1
fXf f
t f
iVi i
i
2 2
1 1 2( ) ( 1)
S f x
S f f x
I i NI
I i i N I
Applying UICM to both M1 & M2
2 1f ri i
Sat.
Triode
2 xI NI
SELF-CASCODE MOSFET (SCM)
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 15
V-I CHARACTERISTICS OF THE SCM
2
2 2
2
1 11 1 ln
1 1
ln
fXf f
t f
X t
iVi i
i
V
In WI:
2
1
11 1
S
S N
Sat.
Triode
I2=NIx
A SELF-BIASED CURRENT SOURCE – 2
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 16
VOLTAGE FOLLOWING (NMOS) CURRENT MIRROR (PMOS)1
9 ln( )ref S tV V JK
1 B. Gilbert, AICSP vol. 38, pp. 83-101, Feb. 2004
When both M8 & M9 operate in WI:
898 8
8
1 11 1 ln
1 1
fref Sf f
t f
JKiV VJKi i
i
A SELF-BIASED CURRENT SOURCE – 3
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 17
A self-biased current source
Vx
VFCMVx
A SELF-BIASED CURRENT SOURCE – 4
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 18
VFCM
A SBCS – 5: DESIGN
2
1
11 1 1 1 1 3
S
S N
1 30 11 30 1 10 ln 2.93
1 10 1X
t
V
M1 &M2 in MI: if2 = 10 S2= S1, N = 1
2
2 2
2
1 11 1 ln
1 1
fXf f
t f
iVi i
i
Let us choose
M3 &M4 in WI: if3(4) <<1
2.93ln 18.7X
t
Ve
4 4
3 3
118.7 1 1 8.85
1
S S
S S
Output current: Iref=10 nA
ISHn-channel100 nA, ISHp-channel40 nA
=1
=10 nA
2 2 2 2 110 nA 1 nA 0.01 S f SI i I S S Let us choose if3=0.187 4 3 4 3/ 1 2 / 0.01f fi i S S 4 4 4 410 nA 1 A 10S f SI i I S
43 1.13
8.85
SS
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 19
A SBCS – 6: DESIGN
S if ir
M1 0.01 10 0
M2 0.01 30 10
M3 1.13 0.187 0.01
M4 10 0.01 0
M8, M8(a) 1 0. 1 0
M9, M9(a) 1 0. 1 0
MP (all) 2.5 0.1 0
4 10S
VFCM
=1
=10 nA
2 1 0.0S
2.93X tV 2.93X tV 3 1.13S 1 1 0.0S
Summary
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 20
A SBCS – 7 : IOUT vs. VDD AT CONSTANT T
NAMITEC ColloquiumCampinas - 2010
Analysis and design of CMOS analog building blocks 21