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Analog Integrated CircuitsFundamental Building Blocks
Faculty of Electronics Telecommunications and Information Technology
Fundamental Building BlocksElementary amplifier stages
Information Technology
Gabor CsipkesBases of Electronics Department
Outline
basic one stage amplifier configurations
common source amplifiers – principles of operation, parameters
output voltage range output voltage range low frequency gain bandwidth, unity-gain bandwidth frequency response
the one transistor common source amplifier with resistive load
the one transistor common source amplifier with diode load
high gain common source amplfiers
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 2
high gain common source amplfiers
current source load
cascode and symmetrical cascode
folded cascode
Basic one stage amplifier configurations
configurations and their specific usage depend on transistor connections
typically use a single input transistor
CS CD CG
common source → voltage or transconductance amplifier → always inverting, typically drives capacitive loads, the only configuration providing gain
CS CD CG
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 3
typically drives capacitive loads, the only configuration providing gain
common drain → voltage follower, power (current) amplifier → non-inverting, used to drive loads with low resistive component
common gate → current buffer and impedance adapter
Common source amplifiers - principles
input transistor → voltage to current conversion → Gm
load circuit → current to voltage conversion → Rout
the general small signal model is always the same, only Rout may be different
0out
m outin
VA G RV
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 4
parameters: output voltage range, low frequency gain, output resistance, frequency response, bandwidth, unity-gain bandwidth, pole-zero configuration
Common source amplifiers – resistive load
most simple form → passive resistance as load, NMOS and PMOS inputs possible
operating point found by matching the current through M and R → intersection of the transistor output characteristic with the load line
the transistor needs appropriate bias (saturation) → DC voltages at the input and the output
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 5
Common source amplifiers – resistive load
the output voltage range defined by the saturation condition of the transistor → → Vout >VGS-VTh
the evolution of Vout is defined by the transfer characteristic of M
2C W 2
2ox
in Th out DDC WI V V V V I R
L
negative quadratic variation
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 6
Common source amplifiers – resistive load
the small signal low frequency model → replace the transistor with its small signal equivalent
calculate the DC gain A0 as the ratio of Vout to Vin
no parasitic capacitances
substrate transconductance gmb neglected for simplicity
0out outm in
DS
V Vg Vr R
KCL at the output node:
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 7
DSr R
0 ||1 1m out
out mm DS m out
in G RDS
V gA g r R G RV
r R
Common source amplifiers – resistive load
the small signal high frequency model → replace the transistor with its small signal equivalent and consider capacitances
calculate the frequency dependent gain A(s) as the ratio of Vout to Vin
consider the non-ideal input source resistance R and the input capacitance C consider the non-ideal input source resistance RS and the input capacitance Cin
KCL at the input and at the output nodes:
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 8
1
21
1
in GSin GS GS out
S
out outGS out m GS
out
V V sC V sC V VR
V sR CsC V V g V
R
KCL at the input and at the output nodes:
1
2
in GS
GD
DB L L
C CC CC C C C
Common source amplifiers – resistive load
1
21 1 1
1( )
1
m outm
out L S m out out S L in
Cg R sg
A ss R C C R g R C s R R C C C
Dominant pole approximation → two poles and one right half plane zero (Miller effect)
0
11
21
12 1
1
2
m out
pout S m L
pL m S
S
A g R
fR R g C C
f C g R CRC C C
Dominant pole approximation → two poles and one right half plane zero (Miller effect)
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 9
1
1
0 11
2
2 1
SL in
mzp
mp
S m L
C C Cgf
CgGBW A f
R g C C
Common source amplifiers – resistive load
the simplified small signal high frequency model → no RS considered
11( )
1
m outm
Cg R sg
A ssR C C
one pole and one right half plane zero (Miller effect)
11 out LsR C C
0
11
2
m out
pout L
m
A g R
fR C
gf
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 10
12
2
mzp
m
L
fC
gGBWC
The dominant pole approximation
helps in finding the poles a second order transfer function
22
1 1 1( )11 11 1 1
A ssa s bs s ss
1 2 1 2 1 2
1 1 1p p p p p p
s
assume that ωp1<<ωp2
1 2
1 1
p p 2 2
1 1 2
1 1( )11
p p p
A ss s sa s b
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 11
pole frequencies found by identifying coefficients of s
1 21 1;
2 2p paf f
a b where a and b depend on
circuit parameters
The Miller effect
appears when the input and the output of an inverting amplifier are shunted with a capacitance → the shunt capacitance is reflected back to the input and forward to the output
11M in M outaI sC a V sC V
a
1 1;
1in outV VI sC a I sC
1 2
1 1;in outV VI sC I sC
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 12
This interpretation of the Miller effect is correct only if no input source resistance RS is present !
1M MI sC a I sC
1
2
11
M M
M M
C C a aCaC C C
a
Common source amplifiers – diode load
the passive load resistance swapped with a MOS transistor in diode connection
the operating point is found by matching the currents through M1 and M2 → intersection of the M1 output characteristic with the M2 transfer characteristic
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 13
211
1
222
2
12
| |2
n oxD in Thn out
p oxD DD out Thp
C WI V V VL
C WI V V V
L
output characteristic → I=ID1=f (Vout)
transfer characteristic → I=ID2=f (Vout)
Common source amplifiers – diode load
the output voltage range is defined by the voltage drops across M1 and M2
M2 is always saturated (VSG=VSD), the output voltage cannot swing above VDD-VDSat2-|VThp|
M1 requires at least VDSat1 for saturation → Vout>VDSat1
In practice:
small Vin → M1 in subthreshold region → ID1 slowly increases with Vin causing a subthreshold voltage drop on M2 → Voutsuffers a near linear decrease
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 14
large Vin → M2 delivers increasing current until velocity saturation → Voutcannot reach VDSat1 because its variation stops
Common source amplifiers – diode load
the small signal low frequency model → replace the transistors with their small signal equivalent models
calculate the DC gain A0 as the ratio of Vout to Vin
no parasitic capacitances no parasitic capacitances
substrate transconductance gmb neglected for simplicity
1 1 2 21 2
0||out
m GS m GSDS DS
Vg V g Vr r
KCL at the output node:
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 15
0 1 1 2 12 2
1 1|| ||m
out
outm DS DS m m out
in m mGR
VA g r r g G RV g g
The gain approximately unity if gm1=gm2 → typical voltage buffer !
Common source amplifiers – diode load
the small signal high frequency model → replace the transistors with their small signal equivalents and consider capacitances
calculate the frequency dependent gain A(s) as the ratio of Vout to Vin
the input source resistance R is neglected the input source resistance RS is neglected
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 16
2
1 1
1
in
out outin out m GS
outV
V sR CsC V V g V
R
KCL at the output node:1 1
2 1 2 2
GD
DB DB GS L
C CC C C C C
Common source amplifiers – diode load
the small signal high frequency model
10
1
1 2
11( )
1 1
m outzpmout
in out
sC Ag R sgVA s sV sR C C
one pole and one right half plane zero (Miller effect) 1 2 1in out
p
10
2
21 2
m
m
mp
L
gAggf
C
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 17
1
1
2
2
L
mzp
Cgf
C
Common source amplifiers – current source load
the diode load swapped with a simple MOS current source
the operating point is found by matching the currents through M1 and M2 → intersection of the transistor output characteristics
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 18
211
1
222 2
2
12
12
n oxD in Thn out
p oxD DD G out
C WI V V VL
C WI V V V
L
output characteristic → I=ID1=f (Vout)
output characteristic → I=ID2=f (Vout)
Common source amplifiers – current source load
the output voltage range is defined by the voltage drops across M1 and M2
both transistors must be biased in saturation
for larger input voltages the relatively high gain may cause clipping (distortion) at the output → both the input and the output voltage ranges are limitedoutput → both the input and the output voltage ranges are limited
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 19
min
max
out DSat
out DD DSat
V VV V V
Common source amplifiers – current source load
the small signal low frequency model → replace the transistors with their small signal equivalent models
calculate the DC gain A0 as the ratio of Vout to Vin
no parasitic capacitances no parasitic capacitances
substrate transconductance gmb neglected for simplicity
1 1 2 21 2
0||out
m GS m GSDS DS
Vg V g Vr r
KCL at the output node:
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 20
0 1 1 2||m out
outm DS DS m out
in G R
VA g r r G RV
High gain, typically larger than 20dB.
Common source amplifiers – current source load
the small signal high frequency model → replace the transistors with their small signal equivalents and consider capacitances
calculate the frequency dependent gain A(s) as the ratio of Vout to Vin
the input source resistance R is neglected the input source resistance RS is neglected
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 21
2
1 1
1
in
out outin out m GS
outV
V sR CsC V V g V
R
KCL at the output node:1 1
2 1 2 2
GD
DB DB GS L
C CC C C C C
Common source amplifiers – current source load
the small signal high frequency model
10
1
1 2
11( )
1 1
m outzpmout
in out
sC Ag R sgVA s sV sR C C
one pole and one right half plane zero (Miller effect)
1p
0 1 1 2
1 2
1
||1
2 ||
m DS DS
pDS DS L
m
A g r r
fr r C
gf
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 22
1
1
1
2
2
mzp
m
L
gfCgGBW
C
Common source amplifiers – cascode input
the load is still a single MOS transistor current source, but the input stage is cascoded
the operating point is found by matching the currents → intersection of M1-M2 current source with the M3 output characteristics
Recall transistor biasing in the cascode input stage
Recall transistor biasing in the cascode current source and carefully consider voltage budget !
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 23
Common source amplifiers – cascode input
the output voltage range is defined by the voltage drops across M1, M2 and M3
all transistors must be biased in saturation
for larger input voltages the relatively high gain may cause clipping (distortion) at the output → both the input and the output voltage ranges are limitedoutput → both the input and the output voltage ranges are limited
min
max
2out DSat
out DD DSat
V VV V V
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 24
maxout DD DSat
Common source amplifiers – cascode input
the small signal low frequency model → replace the transistors with their small signal equivalent models
calculate the DC gain A0 as the ratio of Vout to Vin
no parasitic capacitances no parasitic capacitances
substrate transconductance gmb neglected for simplicity
22 2
2 3
2 22 2 1 1
2 1
0out S outm GS
DS DS
out S Sm GS m GS
DS DS
V V Vg Vr r
V V Vg V g Vr r
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 25
2 1DS DSr r
3 2 2 1
0 13 2 2 1
m
out
DS m DS DSm m out
DS m DS DSGR
r g r rA g G Rr g r r
Common source amplifiers – cascode input
the small signal high frequency model → replace the transistors with their small signal equivalents, consider capacitances and calculate the frequency dependent gain A(s)as the ratio of Vout to Vin
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 26
3 322 2
2 3
2 1 221 2 2 2 1 1
2 1
10
1
out DSout Sm GS
DS DS
S DSout Sin S m GS m GS
DS DS
V sr CV Vg Vr r
V sr CV VsC V V g V g Vr r
Common source amplifiers – cascode input
101 3
1
2 3 3 1 23 3
2 1 2
11( )
1 1 1
m DSzpm
DSDS
m p p
sC Ag r sg
A sr C C C s ss r C s
g
two poles and one right half plane zero (Miller effect)
use the dominant 1 2p p
0 1 3
13
22
1 2
1 12 2
2
m DS
pds L out L
mp
A g r
fr C R C
gfC C
use the dominant pole approximation
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 27
1 2
1
1
1
2
2
2
mzp
m
L
C Cgf
CgGBW
C
Common source amplifiers – symmetrical cascode
a cascode input stage loaded with another cascode current source
the operating point is found by matching the currents → intersection of the two current source output characteristics
Recall transistor biasing in the Recall transistor biasing in the cascode current source and carefully consider voltage budget !
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 28
Common source amplifiers – symmetrical cascode
the output voltage range is defined by the lowest allowed voltage drops across the two cascode current sources → all transistors must be biased in saturation
the nearly vertical slope suggests very high gain
even for small input voltages the very high gain may cause clipping (distortion) at the even for small input voltages the very high gain may cause clipping (distortion) at the output → both the input and the output voltage ranges are limited
min 2out DSatV V
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 29
max 2out DD DSatV V V
Common source amplifiers – symmetrical cascode
the small signal low frequency model → replace the transistors with their small signal equivalent models
calculate the DC gain A0 as the ratio of Vout to Vin
similar calculations as for the cascode input amplifier, but r is replaced with R similar calculations as for the cascode input amplifier, but rDS3 is replaced with Rp
22 2
2
2 22 2 1 1
0out S outm GS
DS p
out S Sm GS m GS
V V Vg Vr R
V V Vg V g Vr r
3 3 4p m DS DSR g r r
R
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 30
2 2 1 12 1
m GS m GSDS DS
g V g Vr r
0 1 2 2 1 3 3 4||m out
m m DS DS m DS DS m outG R
A g g r r g r r G R
pR
The gain is typically larger than 60dB due to Rout !
Common source amplifiers – symmetrical cascode
the small signal high frequency model → replace the transistors with their small signal equivalents, consider capacitances and calculate the frequency dependent gain A(s)as the ratio of Vout to Vin
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 31
322 2
2
2 1 221 2 2 2 1 1
2 1
10
1
out pout Sm GS
DS p
S DSout Sin S m GS m GS
DS DS
V sR CV Vg Vr R
V sr CV VsC V V g V g Vr r
Common source amplifiers – symmetrical cascode
101
1
2 3 1 23
2 1 2
11( )
1 1 1
m outzpm
outout
m p p
sC Ag R sg
A sR C C C s ss R C s
g
two poles and one right half plane zero (Miller effect)
use the dominant pole approximation1 2p p
0 1 2 2 1 3 3 4
1
22
||
12
2
out
m m DS DS m DS DS
R
pout L
mp
A g g r r g r r
fR C
gfC C
pole approximation
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 32
1 2
1
1
1
2
2
2
mzp
m
L
C Cgf
CgGBW
C
Common source amplifiers – folded cascode
similar to the classical cascode input configuration but the input stage is folded → useful in low voltage applications
the operating point is found by matching the currents → intersection of the two current source output characteristics
Recall transistor biasing in the cascode current source and carefully consider voltage budget !
folded cascode input stage
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 33
Common source amplifiers – folded cascode
the output voltage range is defined by the transistor biasing requirements → all transistors must be biased in saturation
the input and output voltage ranges are similar with the cascode input case
min
max 2out DSat
out DD DSat
V VV V V
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 34
Common source amplifiers – folded cascode
the small signal low frequency model → replace the transistors with their small signal equivalent models
calculate the DC gain A0 as the ratio of Vout to Vin
M is an auxiliary source → g V also eliminated from the small signal model M4 is an auxiliary source → gm4VGS4 also eliminated from the small signal model
22 2
2 3
2 22 2 1 1
2 1 4
0
||
out S outm GS
DS DS
out S Sm GS m GS
DS DS DS
V V Vg Vr r
V V Vg V g Vr r r
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 35
2 1 4||DS DS DSr r r
3 2 2 1 40 1
3 2 2 1 4
||||
m
out
DS m DS DS DSm m out
DS m DS DS DSGR
r g r r rA g G R
r g r r r
Common source amplifiers – folded cascode
the small signal high frequency model → replace the transistors with their small signal equivalents, consider capacitances and calculate the frequency dependent gain A(s)as the ratio of Vout to Vin
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 36
3 322 2
2 3
2 1 4 221 2 2 2 1 1
2 1 4
10
1 ||||
out DSout Sm GS
DS DS
S DS DSout Sin S m GS m GS
DS DS DS
V sr CV Vg Vr r
V s r r CV VsC V V g V g Vr r r
Common source amplifiers – folded cascode
101 3
1
2 3 3 1 23 3
2 1 2
11( )
1 1 1
m DSzpm
DSDS
m p p
sC Ag r sg
A sr C C C s ss r C s
g
two poles and one right half plane zero (Miller effect)
use the dominant pole approximation1 2p p
0 1 3
13
22
1 2
12
2
m DS
pDS L
mp
A g r
fr C
gfC C
pole approximation
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 37
1
1
1
2
2
mzp
m
L
gfCgGBW
C
Bibliography
P.E. Allen, D.R. Holberg, CMOS Analog Circuit Design, Oxford University Press, 2002
B. Razavi, Design of Analog CMOS Integrated Circuits, McGraw-Hill, 2002
D. Johns, K. Martin, Analog Integrated Circuit Design, Wiley, 1996
P.R.Gray, P.J.Hurst, S.H.Lewis, R.G, Meyer, Analysis and Design of Analog Integrated Circuits, Wiley,2009
R.J. Baker, CMOS Circuit Design, Layout and Simulation, 3rd edition, IEEE Press, 2010
Analog Integrated Circuits – Fundamental building blocks – Elementary Amplifiers 38