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Analog Integrated CircuitsFundamental Building Blocks
Faculty of Electronics Telecommunications and Information Technology
Fundamental Building BlocksDifferential amplifiers
Information Technology
Gabor CsipkesBases of Electronics Department
Outline
differential and common mode signals – voltage balancing and virtual ground
a differential amplifier with resistive load
input and output voltage range input and output voltage range
the half circuit concept
small signal and low frequency model
small signal and high frequency model
frequency response
the differential amplifier with current source load
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 2
the differential amplifier with current mirror load
Differential and common mode signals
differential voltage (vin) → floating voltage between two ground referenced nodes
common mode voltage (VCM) → the component common to both Vinp and Vinm (average?)
2in
inp CMvV V
v
in inp inm
inp inm
v V VV V
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 3
2in
inm CMvV V
2
inp inmCM
V VV
In most cases VCM is the DC component of Vin → virtual ground.
Differential amplifiers
two common source amplifiers balanced around gound or virtual ground
input signal → differential and common mode components
the output can be either differential (symmetrical/balanced) or referenced to ground → special case: differential amplifier with current mirror loadspecial case: differential amplifier with current mirror load
operation often described through the equivalent half circuit (exceptions!!) → the circuit must be symmetrical
The load can be any type discussed for the elementary common source amplifiers
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 4
equivalent half circuits
Virtual ground
What is virtual ground? → playground balance/scale example
This point is not moving relative to ground in spite of the non-zero displacement but its
position is not zero → virtual ground
positive displacement
negative displacementrelative position to
ground not zero
position is not zero → virtual ground
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 5
the displacements are measured relative to the virtual ground instead of the proper ground
in terms of variations the virtual ground is no different from proper ground
in a circuit any potential not changing with the signal is virtual ground
Differential amplifier with resistive load
common source amplifier with resistive load as half circuit
bipolar version can also be used if the technology allows bipolar transistors
differential input and differential output
input common mode (VCMin) range and output voltage swing are both important
Virtual ground
Virtual ground
GSV
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 6
minoV
1,2 1,2 min
1,2 1,2 min
NMOS:
PMOS:CMin DSat Th o
CMin DD DSat Th o
V V V V
V V V V V
1,2 1,2
1,2 1,2
NMOS: ,
PMOS: 0,out S DSat DD
out S DSat
V V V V
V V V
Differential amplifier with resistive load
the small signal low frequency model – the large signal behavior given by the DC transfer function: only qualitative description here
outVinpV
inmV
1
1
2
02 2 ||
02 2 ||
m in out
DS D
m in out
g V Vr R
g V Vr R
opVomV
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 7
22 2 ||DS Dr R
1,2
0 1,22 ||2
outm
moutDS D
inRG
gVA r RV
DC transfer function
Differential amplifier with resistive load
the small signal high frequency model → replace transistors with their small signal equivalents and consider capacitances
calculate the frequency dependent voltage gain A(s) as the ratio of Vout to Vin
the differential input source resistance is neglected the differential input source resistance is neglected
1 2 1,2
2 2GDC C C
C C C C C
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 8
3 4 1,22 2L DB LC C C C C
1 1
13
12 2 2 || ||
in out m in out
DS D
sC V V g V V
r RsC
The analysis of one half circuit is sufficient → KCL at the output:
Differential amplifier with resistive load
the small signal high frequency model
1,200
1
1,2 3,4 1
11( )
1 || 1
zpm
DS D
sC AA sg
A s ss C C r R
1p
1,2 3,4 1
1 12 2 ||p
out DS D L
fR C C r R C
g
one pole and one right half plane zero caused by
the Miller effect
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 9
1
1,2
10
2
2
mzp
mp
L
gfC
gGBW A fC
Differential amplifier with current source load
common source amplifier with current source load as half circuit
bipolar version can also be used if the technology allows bipolar transistors
differential input and differential output, similar to the resistive load configuration
input common mode (VCMin) range and output voltage swing are both important
Virtual groundVirtual
ground
GSV
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 10
GSV
minoV
1,2 1,2 min
1,2 1,2 min
NMOS:
PMOS:CMin DSat Th o
CMin DD DSat Th o
V V V V
V V V V V
1,2 1,2 3,4
3,4 1,2 1,2
NMOS: ,
PMOS: ,out S DSat DD DSat
out DSat S DSat
V V V V V
V V V V
Differential amplifier with current source load
the small signal low frequency model
outVinpV inmV
1
1 3
2
02 2 ||
02 2 ||
m in out
DS DS
m in out
g V Vr r
g V Vr r
opVomV
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 11
2 42 2 ||DS DSr r
1,2
0 1,2 3,42 ||2
outm
moutDS DS
inRG
gVA r rV
DC transfer function
Differential amplifier with current source load
the small signal high frequency model → replace transistors with their small signal equivalents and consider capacitances
calculate the frequency dependent voltage gain A(s) as the ratio of Vout to Vin
the differential input source resistance is neglected the differential input source resistance is neglected
1 2 1,2
2 2GDC C C
C C C C C C C
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 12
3 4 1,2 3,4 3,42 2L DB DB GD LC C C C C C C
1 1
1 33
12 2 2 || ||
in out m in out
DS DS
sC V V g V V
r rsC
The analysis of one half circuit is sufficient → KCL at the output:
Differential amplifier with current source load
the small signal high frequency model
1,200
1
1,2 3,4 1,2 3,4
11( )
1 || 1
zpm
DS DS
sC AA sg
A s ss C C r r
1,2 3,4 1,2 3,4
1 12 2 ||p
out DS DS L
fR C C r r C
g
one pole and one right half plane zero caused by
the Miller effect
1p
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 13
1
1,2
10
2
2
mzp
mp
L
gfC
gGBW A fC
Differential amplifier with current mirror load
no equivalent half circuit due to the current mirror load
differential input and single ended output
input common mode (VCMin) range and output voltage swing are both important
Virtual groundVirtual
ground
GSV
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 14
minoV
1,2 1,2 min
1,2 1,2 min
NMOS:
PMOS:CMin DSat Th o
CMin DD DSat Th o
V V V V
V V V V V
1,2 1,2 3,4
3,4 1,2 1,2
NMOS: ,
PMOS: ,out S DSat DD DSat
out DSat S DSat
V V V V V
V V V V
Differential amplifier with current mirror load
the small signal low frequency model
MOS diode
V1 2
inGS
VV
From the schematic:
1 1 4 31 3
1 1 0m GS G mDS DS
g V V gr r
2 3 1 41 3
0
1 1
1 12
m m m mDS DS
g g g gr r
A
inpVinmV
4GV2
4 4
2in
GS
GS G
VV
V V
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 15
1 3
2 2 4 42 4
1 1 0
DS DS
m GS out m GSDS DS
g V V g Vr r
2 4
1 12DS DSr r
Eliminate VG4 and solve for Vout/Vin
0 1 2 4||m out
m DS DSG R
A g r r
1 2
3 4
1 2
3 4
m m
m m
DS DS
DS DS
g gg gr rr r
Differential amplifier with current mirror load
the DC transfer function → single ended output
the slope in the linear region is A0 → the same order of magnitude as the gain of the configuration with current source load
the unloaded DC output voltage defined by the diode in the current mirror → V -V the unloaded DC output voltage defined by the diode in the current mirror → VDD-VSG3
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 16
Differential amplifier with current mirror load
the small signal high frequency model → replace transistors with their small signal equivalents and consider capacitances
calculate the frequency dependent voltage gain A(s) as the ratio of Vout to Vin
the differential input source resistance is neglected the differential input source resistance is neglected
4GV
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 17
1 2 1,2
3 1 3 3 4
4 2 4
5 4
GD
DB DB GS GS
L DB DB L
GD
C C CC C C C CC C C C CC C
No half circuit analysis due to the current mirror that actively
influences the signal !!
Differential amplifier with current mirror load
analysis of A(s) → consider the circuit as a whole and add capacitances to the small signal low frequency model
Kirchhoff's current law at the output and at the gate of M4
1 1g V V
eliminate VG4 and solve for Vout/Vin → rigorous solution is rather complicated
the demonstration shows that C has little influence on A(s) → it can be neglected
14 3 3 5 4 1 4
1 3
24 4 4 2 5 4
2 4
1 12 2
1 12 2
m in inG m G out G
DS DS
m in inm G out out G out
DS DS
g V VV g sC sC V V sC Vr r
g V Vg V V sC sC V sC V Vr r
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 18
the demonstration shows that C5 has little influence on A(s) → it can be neglected
A(s) will have the form:31
01 3
2
1 12
( )1
m m
CCA s sg g
A sas bs
Differential amplifier with current mirror load
the small signal high frequency model → use the dominant pole approximation on A(s)
0 1 1( )
1 1
zp zn
s sAA s
s s
where a and b are coefficients dependent on the small signal parameters
11
12 2
mp
out L L
gf GBWR C C
one pole and one right half plane zero caused by the Miller effect + a pole-left half plane
zero pair introduced by the mirror load
1 2
1 1p p
Analog Integrated Circuits – Fundamental building blocks – Differential amplifiers 19
3 12
3 1
3
3
;2 222
m mp zp
mzn
g gf fC C
gfC
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 – Differential amplifiers 20