Analysis and Design of Analog Integrated Circuits Lecture ... · M.H. Perrott R th g v g A vv g i s...
Transcript of Analysis and Design of Analog Integrated Circuits Lecture ... · M.H. Perrott R th g v g A vv g i s...
M.H. Perrott
Analysis and Design of Analog Integrated CircuitsLecture 7
Differential Amplifiers
Michael H. PerrottFebruary 12, 2012
Copyright © 2012 by Michael H. PerrottAll rights reserved.
M.H. Perrott
Review Proposed Thevenin CMOS Transistor Model
RthgAvvgvg
isRths
Rthdisα
g
s
d
Proposed Small Signal Transistor Model
Av = 1
α = 1
RS
RG
RD
Rthd
Rths
Rthg
ID
Rthd= ro (1+gmRS)
Rthg= infinite
Rths=
1 + RD /ro
gm
Thevenin Resistances
Approximation(gmb << gm, gmro >> 1)
g
s
d
Rthd= ro (1+(gm+gmb)RS)+RS
Rthg= infinite
Exact
Rths= 1+RD /ro gm+gmb
1ro( )( )
Av = gm+gmbgmro
gm
ApproximationExact
α = 1+RD /Rthd
RD
RS
Rthd
Rths
Rthg
RG
-gmbvsvgs
vs
rogmvgs
Hybrid-π Model
g
s
d
1gm
gm 2μnCox(W/L)ID
2 2|ΦF| + VSB
γgmgmb
λID1ro
Key Small-Signal Parameters
qID nkT
(n-1)qID
nkT
Strong Inversion Weak Inversion
λID1
Parameter
(gmb<<gm, gmro>>1)
Note: gmb = 0if RS=0 or Vsb=0
(RD<< ro ) (RD<<Rthd
)
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M.H. Perrott
RthgAvvgvg
isRths
Rthdisα
g
s
d
Proposed Small Signal Transistor Model
Av = 1
α = 1
RS
RG
RD
Rthd
Rths
Rthg
ID
Rthd= ro (1+gmRS)
Rthg= infinite
Rths=
1 + RD /ro
gm
Thevenin Resistances
Approximation(gmb << gm, gmro >> 1)
g
s
d
Rthd= ro (1+(gm+gmb)RS)+RS
Rthg= infinite
Exact
Rths= 1+RD /ro gm+gmb
1ro( )( )
Av = gm+gmbgmro
gm
ApproximationExact
α = 1+RD /Rthd
1gm
(gmb<<gm, gmro>>1)
(RD<< ro ) (RD<<Rthd
)
Key Observations
For calculations focusing on signal flow from gate or source to the drain- Observe that current through Rd equals is
True since * Rthd/(Rd + Rthd) = 1 You can avoid doing calculations involving or Rthd
For calculations focusing on signal flow from the drain- Drain simply looks like impedance Rthd 3
M.H. Perrott
Basic Single-Stage Amplifiers and Current Mirrors
SourceM1
W1L
Vout
ZL
idVin
M1
W1L
Vout
ZL
id
iin
Source
M1
W1L
Vout
ZL
VinSource
SourceM1
W1L
Vout
ZL
idVin
ZS
Common Source Common Gate Source Follower
Common Sourcewith Source Degeneration
M1
W1L
iout
M2
W2L
iin
Current Mirror
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M.H. Perrott
Today We Will Look At Differential Amplifiers
SourceM1
W1L
Vout
ZL
idVin
M1
W1L
Vout
ZL
id
iin
Source
M1
W1L
Vout
ZL
VinSource
SourceM1
W1L
Vout
ZL
idVin
ZS
Common Source Common Gate Source Follower
Common Sourcewith Source Degeneration
M1
W1L
iout
M2
W2L
iin
Current Mirror
M1 M2Vin+ Vin-
Vo+Vo-
Ibias
ZL ZL
DifferentialAmplifier
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M.H. Perrott
Differential and Common Mode Signals
Consider positive and negative input terminal signals Vi
+ and Vi-
Define differential signal as: Define common mode signal as: We can create arbitrary Vi
+ and Vi- signals from
differential and common mode components:
This also applies to differential output signals:
Vc
Vd/2
-Vd/2
Vic = (V+in + V
−in )/2
Vid = V+in − V −in
V +in = Vic +1
2Vid V −in = Vic −
1
2Vid
V +o = Voc +1
2Vod V −o = Voc −
1
2Vod
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M.H. Perrott
Differential Amplifier
Useful for amplifying signals in the presence of noise- Common-mode noise is rejected
Useful for high speed digital circuits- Low voltage swing allows faster gate/buffer
performance
M4
M1 M2
M3
Ibias1Vin+
RL
Vin-
RL
Vo+Vo-
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M.H. Perrott
First Steps in Small Signal Modeling
Small signal analysis assumes linearity- Impact of M4 on amplifier is to simply present its drain
impedance to the diff pair transistors (M1 and M2)- Impact of Vin+ and Vin- can be evaluated separately and then added (i.e., superposition) By symmetry, we need only determine impact of Vin+
Calculation of Vin- impact directly follows
M4
M1 M2
M3
Ibias1Vin+
RL
Rthd4= ro4
Vin-
RL
Vo+Vo-
M1 M2Vin+
RL
Vin-
RL
Vo+Vo-
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M.H. Perrott
Calculate Impact of Vin+ using Thevenin Models
Analysis follows fairly easily, but there is a simpler way!
ro4
M1 M2Vin+
RL RL
Vo+Vo-
Rthg1Av1vg1vg1
is1
Rths1
Rthd11is1α
M1
RL
Vo-
Rths2is2 Rthd2
is2
α2
RL
Vo+
ro4
M2
Common GateGeneral Model
Vin+
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M.H. Perrott
Method 2 of Differential Amplifier Analysis
Partition input signals into common-mode and differential components
By superposition, we can add the results to determine the overall impact of the input signals
ro4
M1 M2Vin+
RL
Vin-
RL
Vo+Vo-
ro4
M1 M2
RL RL
Vo+Vo-
Vic
Vid2
-Vid2
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M.H. Perrott
Differential Analysis
Key observations- Inputs are equal in magnitude but opposite in sign to each
other- By linearity and symmetry, is1 must equal -is2 This implies iR is zero, so that voltage drop across ro4 is zero
The sources of M1 and M2 are therefore at incremental ground and decoupled from each other!
Analysis can now be done on identical “half-circuits”
M1 M2
Vid
R1 R2
Vo+Vo-2
-Vid2
M1 M2
Vid
RL RL
Vo+Vo-2
-Vid2
ro4
is1
iR
is2
is1= is2iR = 0
M1 M2
Vid
R1 R2
Vo+Vo-2
-Vid2
What is the differential DC gain?11
M.H. Perrott
Common Mode Analysis
Key observations- Inputs are equal to each other- By linearity and symmetry, is1 must equal is2
This implies iR = 2is1 = 2is2- We can view ro4 as two parallel resistors that have equal current running through them
Analysis can also be done on two identical half-circuits
ro4
M1 M2Vic
RL RL
Vo+Vo- Vic
is1
iR
is2
is1= is2iR = 2is1= 2is2
2ro4
M1 M2Vic
RL RL
Vo+Vo- Vic
is1
2ro4
is2idiff = 0
M1 M2Vic
RL RL
Vo+Vo- Vic
2ro42ro4
What is the common mode DC gain?12
M.H. Perrott
Useful Metric for Differential Amplifiers: CMRR
Common Mode Rejection Ratio (CMRR)- Define: avd: differential gain, avc: common mode gain
- CMRR corresponds to ratio of differential to common mode gain and is related to received signal-to-noise ratio
Vinput VodVid=VsigVnoise
Vod = avdVsig + avcVnoise
⇒ Signal
Noise=
µavdavc
¶µVsigVnoise
¶= CMRR
µVsigVnoise
¶
CMRR =
µavdavc
¶
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M.H. Perrott
Another Useful Metric for Differential Amplifiers: PSRR
Power Supply Rejection Ratio (PSRR)- avd: differential gain- avp+: positive power supply gain- avp-: negative power supply gain
Vinput VodVid=VsigVnoise
Vsup+
Vsup-
PSRR+ =
µavdavp+
¶PSRR− =
µavdavp−
¶
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M.H. Perrott
Example: Calculate CMRR and PSRR
First determine avd, avc, avp+, and avp-
Then calculate CMRR and PSRR- Note that CMRR and PSRR are often expressed in dB
Example: CMRR = 20log(avd/avc)
ro4
M1 M2Vin+
RL
Vin-
RL
Vo+Vo-
ro4
M1 M2
RL RL
Vo+Vo-
Vic
Vid2
-Vid2
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M.H. Perrott
Common Mode Voltage Range of Differential Amplifier
While keeping all devices in saturation:- What is the maximum common mode output range?
Assume Vid = 0- What is the maximum common mode input range?
Assume Vod = 0
M4
M1 M2
M3
Ibias
RL
Vin-
RL
Vo+Vo-Id1 Id2
VTH+ΔV2
Vin+
VTH+ΔV1 Iss
ΔV4
ΔV1 ΔV2
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M.H. Perrott
Large Signal Behavior of Differential Mode Operation
Note: above analysis assumes strong inversion
M4
M1 M2
M3
Ibias
Vid = Vin+-Vin-
RL
Vin-
RL
Vo+Vo-
Id1 Id2
Iss
-Iss
Iod = Id1-Id2
VTH+ΔV2
Vin+
VTH+ΔV1
Vid = Vin+-Vin-= (VTH+ΔV1) - (VTH+ΔV2) = ΔV1-ΔV2
Id1where k =
μnCoxW2Lk
Iss
Id2
kVid =
Iss+Iod/2k
Iss-Iod/2k
Vid =
square and solve for Iod
where Iod = Id1-Id2
2Iss
k-Vid
2Iod = KVid for Vid <Iss
k
Iss
k
Iss
k
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