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Advanced Analog Building Blocks
Current mirrors
Albert Comerma (PI)(comerma@physi.uni-heidelberg.de)
Course web
SoSe 2017
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Introduction: CMOS transistors
• Several possibilities for representation of transistors.
NMOS
Saturation (VDS > VGS − VTH):
ID = µCox2
WL
(VGS − VT )2 (1 + λVDS)
gm ≈√
2µCoxWLID
PMOS
Saturation (VSD > VSG − |VTH |):
ID = µCox2
WL
(VSG − |VT |)2 (1 + λVSD)
gm ≈√
2µCoxWL|ID |
• For simplicity usually only one type of circuits are depictedeven if both implementations are posible.
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 1 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Introduction: Diode connected transistor
Drain and Gateconnected NMOS
Always on saturation!VDS = VGS → VDS > VGS − VT
ID = µCox2
WL
(VGS − VT )2 (1 + λVDS)
DIODE CONNECTED
For any given ID , the VGS = VDS
will adapt to permit the current flow.
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 2 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Introduction: Use of current mirrors
Several applications:
• Biasing of circuits.
• Current amplification
• Active loads.
• Current-mode signal processing.
Best current mirror;
• High output impedance (ideally ∞).
• Rail-to-rail output swing (from VDD to GND).
Current mirrors performance is strongly dependent ontransistor matching!!Good layout techniques needed.
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 3 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Simple current mirrorWilson current mirrorCascode current mirror
Simple current mirror: Same VGS transistors circuit
Assuming saturation;
IM1 = µCox2
WL
(VG − VT )2 (1 + λVD1)
IM2 = µCox2
WL
(VG − VT )2 (1 + λVD2)
IM2IM1
=W2L2W1L1
1+λVD21+λVD1
For same L:
The ratio of IM2IM1
is given by W2W1
Early effect cancelled for VD2 = VD1
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 4 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Simple current mirrorWilson current mirrorCascode current mirror
Simple current mirror: circuit operation
M1 connected as a diode;
IM1 = µCox2
WL
(VG − VT )2 (1 + λVG )
IM2 = µCox2
WL
(VG − VT )2 (1 + λVD)
IM2IM1
=W2L2W1L1
1+λVD1+λVG
Output swing:VD,min = VDsat
Current is copied ”mirrored”:
The ratio of IM2IM1
is given by W2W1
(for same L)Early effect cancelled for VD = VG (same L desired)
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 5 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Simple current mirrorWilson current mirrorCascode current mirror
Simple current mirror: output impedance
• The output resistance (ro) depends only on M2 outputtransistor.
• vgs = 0 since gate voltage is DC.
• ro = rds value depends on current and geometry of transistor.
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 6 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Simple current mirrorWilson current mirrorCascode current mirror
Wilson current mirror: circuit operation
Same principle of operation;
VGS1 = VGS2 → IM1 ≈ IM2
IoutIref
=W2L2W1L1
1+λVDS21+λVDS1
VDS1 = VDS2 + VGS3 → error
IoutIref
=W2L2W1L1
1+λVDS2
1+λ(VDS2+VGS3)
Output swing:Vout,min = VGS2 + VDSsat3
Vout,min > VTh + 2VDSsat
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 7 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Simple current mirrorWilson current mirrorCascode current mirror
Wilson current mirror: output impedance
• RL (Iref current generator impedance) must be large.
vg2 = vs3 = ixgm2
vg3 = −gm1vg2rT → rT = RL//rds1
rout = vxix
= 1gm2
+ rds3
[1 + gm3
gm2+ gm3
gm2gm1rT
]rout ≈ rds3
gm3gm2gm1rT ≈ rds3
gm3gm2gm1rds1
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 8 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Simple current mirrorWilson current mirrorCascode current mirror
Wilson current mirror: improved
Same principle of operation;
VDS1 = VDS2 + VGS3 − VGS4
VDS1 = VDS2 if VGS3 = VGS4
IoutIref
=W2L2W1L1
1+λVDS2
1+λ(VDS1)
IoutIref
=W2L2W1L1
No error introduced
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 9 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Simple current mirrorWilson current mirrorCascode current mirror
Wilson current mirror: improved output impedance
vg3 = −gm1vg2r′T
RLgm41+RLgm4
r ′T = rds1//(RL + 1
gm4
)rout ≈ rds3
gm3gm2gm1r
′T
RLgm41+RLgm4
≈ rds3gm3gm2gm1rds1
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 10 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Simple current mirrorWilson current mirrorCascode current mirror
Cascode current mirror: circuit operation
Principle of operation;
VDS1 = VDS2 + VGS3 − VGS4
VDS1 = VDS2 if VGS3 = VGS4
IoutIref
=W2L2W1L1
1+λVDS2
1+λ(VDS1)
IoutIref
=W2L2W1L1
Output swing:Vout,min = VGS1 +VGS4 −VGS3 +VDSsat3
Vout,min = VGS2 + VDSsat3
Vout,min > VTh + 2VDSsat
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 11 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Simple current mirrorWilson current mirrorCascode current mirror
Cascode current mirror: output resistance
ix = gm3vgs3 + vx−vs3rds3
ix = vs3rds2
vx = (ix − gm3(−vs3)) rds3 + ix rds2
rout = vxix
= ix rds3+gm3vs3rds3+ix rds2ix
rout = rds2 + rds3 + rds3gm3rds2 ≈ rds3gm3rds2
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 12 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Basic current mirrors comparison
Type Complexity Output impedance Output swing (V0,min)
Simple low 3 rds 7 VDSsat 3
Wilson1 medium 3 rds3gm3gm2
gm1rds1 3 VTh + 2VDSsat 3
W. Improved high 7 rds3gm3gm2
gm1rds1 3 VTh + 2VDSsat 3
Cascode high 7 rds3gm3rds2 3 VTh + 2VDSsat 3
1Introduces an error in current copy, not desirable.
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 13 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Use examplesWildar current mirror
Use examples: bias distribution
• PACIFIC design biasdistribution.
• 4x3.85mm2 die size.
• Bias voltages distributedeverywhere.
• Long distances for biasing(drop in different supplyvoltages!!).
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 14 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Use examplesWildar current mirror
Use examples: binary weighted DAC
• Binary weighted DAC.
• n is the number of bits.
• Lower transistors justenable output.
• Iout,max = Iref .
• Other implementationsposible (cascode).
Vout = IoutR = Rn∑
i=1Inbn−1
bn is a digital signal which can be 0 or 1
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 15 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Use examplesWildar current mirror
Widar current mirror
• Current copy does not need to have a linear response.
Principle of operation;
VS2 = RIM2
IM1 = µCox2
WL
(VG − VT )2 (1 + λVG )
IM2 = µCox2
WL
(VG − VS2 − VT )2 (1 + λVD)
IM2 =
1−
√1+2R
√2µCox
W2L2
IM1
2
2µCoxW1L1
R2
Useful for small currents generation.
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 16 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Multiple stages CascodeHigh-swing CascodeHigh-swing CascodeRegulated Cascode
Multiple stages Cascode
More cascode stages can be stackedto increase ro .
Output impedance;
rout ≈ (rdsgm) (n − 1)rds
n→ number of stages
Saturation voltage increases to;
Vout,min = (n − 1)VTh + nVDSsat
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 17 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Multiple stages CascodeHigh-swing CascodeHigh-swing CascodeRegulated Cascode
High-swing Cascode
Principle of operation;
• The voltage increase shifts VDS1
enough to bias M3 withoutoperating M2 out of saturation.
• The change results in more swingat the output
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 18 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Multiple stages CascodeHigh-swing CascodeHigh-swing CascodeRegulated Cascode
High-swing Cascode
Possible implementationVoltage increase;∆V = VGS4 − VGS5
∆V =
√2k′
(L4W4
)Iref −
√2k′
(L5W5
)I5
∆V =
√2k′
(L4W4
)Iref
(1−
√L5W5
L6W6
L4W4
L1W1
)
• ∆V fixed by dimensions of M1,4,5,6.
• Output swing:Vout,min = VDS2 + VDS3 = 2VDSsat .
• Systematic error since VDS1 6= VDS2.
• Only for strong inversion conditions(which may not be the case).
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 19 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Multiple stages CascodeHigh-swing CascodeHigh-swing CascodeRegulated Cascode
Regulated cascode
Principle of operation;
• VD is kept constant.
• Vb reference needed.Vc = A(Vb − VDS2)
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 20 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Multiple stages CascodeHigh-swing CascodeHigh-swing CascodeRegulated Cascode
Regulated cascode: output resistance
OUTPUT IMPEDANCE
rout = rds3 + rds2 (1 + (1 + A)gm3rds3)
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 21 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Multiple stages CascodeHigh-swing CascodeHigh-swing CascodeRegulated Cascode
Regulated cascode: implementation
Possible implementation
Output impedance;A ≈ gm3rds3
rout ≈ rds1gm2rds2gm3rds3
• Low threshold on M3 increases outputswing (low VT transistor may help).
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 22 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Layout considerationsSchematic considerations
Layout considerations
• Fabrication process introduce variations in transistor size(dashed line).
• Area variation dependent on transistor size.
• Ideally use fixed transistor size for mirrors.
• Change number of transistors to obtain different sizes.
• Other layout techniques also usefull (common centroid).
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 23 / 24
IntroductionBasic current mirrors
ComparisonOther
Enhanced current mirrorsSome considerations
Layout considerationsSchematic considerations
Schematic considerations
• Same dimensions transistors are desirable.
• Replicate constant size transistors.
c©comerma@physi.uni-heidelberg.de Advanced Analog Building Blocks: Current mirrors 24 / 24
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