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Analog Integrated Circuits
Fundamental Building Blocks
Current mirrors
Faculty of Electronics
Telecommunications and
Information Technology
Gabor Csipkes
Bases of Electronics Department
Outline
 current source biasing – voltage sources
 MOS transistor current mirrors




fundamental current mirror
cascode current mirror
low swing cascode current mirror
unbalanced and symmetrical Wilson current mirrors
 bipolar transistor current mirrors
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fundamental current mirror
fundamental current mirror with β compensation
fundamental current mirror with resistive emitter degeneration
cascode current mirror
unbalanced and symmetrical Wilson current mirrors
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
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Current mirrors – principles of operation
 integrated current sources with transistors need bias voltages → voltage sources
1
gm
Rin
Rout
1: n
Is this a voltage
source?
Current mirror
 key parameters to consider:
 input resistance → must be as small as possible → current input
 output resistance → must be as large as possible → current output
 minimum required output voltage
 required input voltage
 current gain → precision imposed by the application
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
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The fundamental MOS current mirror
NMOS
PMOS
Vin  VDSat1  VTh
Vo min  VDSat 2
Small signal model
Vin
1
Rin 

I in g m1
I out  2 VGS  VTh 2 1  VDS 2 
 current gain: n 

I in
1 VGS  VTh1 1  VDS 1 
 Δβ – geometry mismatch
 ΔVTh – threshold voltage mismatch
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
Rout
n
Vout

 rDS 2
I out
1  Vout
1  Vin
 2VTh
n  1

2  VDSat
4
The MOS cascode current mirror
NMOS
PMOS
Vin  VDSat 3  VTh 3  VDSat1  VTh1
f VBS 3 
Vo min  VDSat 4  VDSat 2  VTh 2 (!)
Rin 
1
1

g m1 g m 3
Rout  rDS 2  rDS 4   g m 4  g mb 4  rDS 2 rDS 4
Small signal
model
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
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The MOS cascode current mirror
 the VGS voltages of M3 and M4 balance the
fundamental mirror M1-M2 → n is accurately
defined
Vin  Vout
VDS 1
 VDS 1  VDS 2
VDS 2
The current gain is very close to
unity even when the inputoutput voltage imbalance ΔV is
significant
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
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The MOS low swing cascode current mirror
 the cascode current mirror is not optimal in terms of Vomin → the gate voltage of M4
must be decreased by VTh
1
VG 4
Vo min  2VDSat
2
VG 4
VDS 1  VDS 2
4
3
VDS1  VDS 2  VR
R
triode region
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
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The MOS low swing cascode current mirror
NMOS
PMOS
Vin  VDSat1  VTh1
Vo min  VDSat 4  VDSat 2
Rin 
1
g m1
Rout  rDS 2  rDS 4   g m 4  g mb 4  rDS 2 rDS 4
Small signal
model
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
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The Wilson current mirror
NMOS
PMOS
Vin  VDSat 3  VTh 3  VDSat 2  VTh 2
Vo min  VDSat 3  VDSat 2  VTh 2
Rin 
Rout 
Small signal
model
g m 2  g m3
g m1 g m 3
g m1 g m 3rDS 1rDS 3
gm 2
Vin and Vout create voltage imbalance
between VDS1 and VDS2
Accuracy issues for the current gain n
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
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The balanced Wilson current mirror
NMOS
PMOS
Vin  VDSat 3  VTh 3  VDSat 2  VTh 2
Vo min  VDSat 3  VDSat 2  VTh 2
Rin 
Rout 
g m 2  g m3
g m1 g m 3
g m1 g m 3rDS 1rDS 3
gm 2
Small signal
model
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
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The fundamental bipolar current mirror
NPN
PNP
Vin  VBE1
Vo min  VCE 2
1
Rin 
g m1
Rout  rCE 2
 current gain:
n
I S 2  VCE 2  VCE1 
1 

I S1 
VCE1  VEA 
1 I S 2  VCE 2  VCE1 
1 
1 

  I S1  VCE1  VEA 
 ΔV – input-output voltage imbalance
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
IS 2 
V 
n
1 

I S 1  Vin  VEA 
n
IS 2 

I S1   2
11
The fundamental current mirror with β compensation
NPN
PNP
Vin  VBE1  VBE 3
Vo min  VCE 2
1
Rin 
g m1
Rout  rCE 2
 current gain → β replaced by β (β+1) → n much closer to the ideal value when the
input and the output are balanced in voltage
IS 2 
V 
n
1 

I S 1  Vin  VEA 
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
I S 2     1
n

I S 1     1  2
12
The degenerated fundamental current mirror
NPN
PNP
Vin  VBE1  I in R1 Vo min  VCE 2  I out R2
 current gain:
1
Rin  R1 
g m1
VBE1  I in R1  VBE 2  I out R2
 remember to adjust the emitter areas of Q1 and Q2
proportionally with the current in each branch !!!
Rout  rCE 2  R2  g m 2 rCE 2 R2
n
R1
R2
A2 I S 2 R1


n
A1 I S1 R2
 n is still affected by the finite β and by ΔV
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
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The bipolar cascode current mirror
NPN
PNP
Vin  VBE1  VBE 3 Vo min  VCE 4  VBE 2
1
1
Rin 

g m1 g m 3
 current gain → β influences the accuracy while the
fundamental mirror Q1-Q2 is balanced by the cascode
transistors Q3-Q4
Analog Integrated Circuits – Fundamental building blocks – Current mirrors
Rout 
g m 4 rCE 4 rCE 2 rBE 4
 gm 2 
rBE 4  rCE 2  1 

g
m1 

IS 2
2
n
 2
I S1   4  2
14
The bipolar Wilson current mirror
asymmetrical
Vo min  VCE 4  VBE 2 Vin  VBE1  VBE 3
rBE 3  g m 2  g m 3 
Rin 
g m 2  g m1 g m 3 rBE 3
g m1 g m 3rCE1rCE 3 
Rout 
balanced
 current gain → β influences the accuracy
while the fundamental mirror Q1-Q2 is
balanced by the cascode transistors Q3-Q4
rCE1
rBE 3
I S 2  2  2
n
 2
I S1   4  2
 rCE1 
rCE1
g m 2 1 

g
 m1
r
rBE 3
BE 3 

Analog Integrated Circuits – Fundamental building blocks – Current mirrors
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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 – Current mirrors
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