Albert Comerma (PI) · Simple current mirror Wilson current mirror Cascode current mirror Simple current mirror: output impedance The output resistance (r o) depends only on M 2 output

Advanced Analog Building Blocks

Current mirrors

Albert Comerma (PI)([email protected])

Course web

SoSe 2017

http://www.kip.uni-heidelberg.de/~shen/Advanced_Analog_Building_Blocks/

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©[email protected] Advanced Analog Building Blocks: Current mirrors 1 / 24


ComparisonOther


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.



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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.



ComparisonOther


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



ComparisonOther



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)



ComparisonOther



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.



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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



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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



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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



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Wilson current mirror: improved output impedance

vg3 = −gm1vg2r′T

RLgm41+RLgm4

r ′T = rds1//(RL + 1

gm4

)rout ≈ rds3

gm3gm2gm1r

′T

RLgm41+RLgm4

≈ rds3gm3gm2gm1rds1



ComparisonOther



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



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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



ComparisonOther


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.



ComparisonOther


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!!).



ComparisonOther



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



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Widar current mirror

• Current copy does not need to have a linear response.


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.



ComparisonOther


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



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High-swing Cascode


• The voltage increase shifts VDS1

enough to bias M3 withoutoperating M2 out of saturation.

• The change results in more swingat the output



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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).



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Regulated cascode


• VD is kept constant.

• Vb reference needed.Vc = A(Vb − VDS2)



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Regulated cascode: output resistance

OUTPUT IMPEDANCE

rout = rds3 + rds2 (1 + (1 + A)gm3rds3)



ComparisonOther



Regulated cascode: implementation

Possible implementation

Output impedance;A ≈ gm3rds3

rout ≈ rds1gm2rds2gm3rds3

• Low threshold on M3 increases outputswing (low VT transistor may help).



ComparisonOther


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).



ComparisonOther


Layout considerationsSchematic considerations

Schematic considerations

• Same dimensions transistors are desirable.

• Replicate constant size transistors.


Documents

Albert Comerma (PI) · Simple current mirror Wilson current mirror Cascode current mirror Simple current mirror: output impedance The output resistance (r o) depends only on M 2 output