Cascode current mirror

CMOS Analog Design Using
All-Region MOSFET Modeling
Chapter 5
Current mirrors
CMOS Analog Design Using All-Region MOSFET
Modeling
1
The basic current mirror
First-order analysis
VDD
VOUT
IIN
IOUT
M1
M2
M1=M2
W
I D  I S i f  ir   G (VG ,VS )  G (VG ,VD ) 
L
Both M1 & M2 in saturation
G(VG ,VD )  0
1:1
Since M1 & M2 are identical with same
gate, source and bulk voltages:
M1: iv converter
M2: vi converter
I OUT  I IN
CMOS Analog Design Using All-Region MOSFET
Modeling
2
Gain-of-two current mirror
VDD
VDD
IIN
IOUT
IIN
W/L
W/L
VDD
IIN
IOUT
W/L
W/L
W/L
1:2
W/L
IOUT
2W/L
W/L
1:2
1/2:1
Why not?
CMOS Analog Design Using All-Region MOSFET
Modeling
3
Error due to difference in drain voltages
I D  I S f VG  VT ,VS 1  VD  VD  VDsat
VDD
iout I S f VG  VT ,VS 1   vout 

iin
I S f VG  VT ,VS 1   vin 
iin
iout
M1
+
v
-
+
-
M2
vout
iout  iin
v v
   vout  vin   out in
iin
VA
1:1
ID
-VA
VD
The linear variation of the drain current
with the drain voltage is a crude
approximation. =1/VA , VA is the Early
voltage, roughly proportional to the
channel length.
CMOS Analog Design Using All-Region MOSFET
Modeling
4
Error due to mismatch - 1
I D  I S f VG  VT ,VS 1  VD  VD  VDsat
VDD
iin
iout
M1
+
vin
-
+
v =v
- out in
M2
1:1
Error due to  mismatch is negligible.
The mismatch can be calculated
either using Pelgrom’s model

2 
2
  I D  2  2  AVT 0  

 AISH  

2
ID
WL 
n

 t  



2

1 if 1 


or
N oi
N *2
 AVT 0 


n

 t 
2
 I2
D
I D2
 1 if
2  N oi 1

ln 
 *2
WL  N i f  ir  1  ir
CMOS Analog Design Using All-Region MOSFET
Modeling


2
  AISH 


5
2





Error due to mismatch - 2
Dependence of current matching on inversion level in linear and saturation regions
(|VDS| = 20 mV and |VDS| = 2 V, respectively, where VDS is the drain-to-source
voltage) for the large, medium-size, and small PMOS transistor arrays.
CMOS Analog Design Using All-Region MOSFET
Modeling
6
Frequency response
ii
io
ii
gi
C3
vo
M1
+
v
-
M2
io
vi
i2
gm1+
gds1
C1
gm2vi
gds2
C2
+
vo
1:A
C1  Cgs1  Cgb1  Cgs 2  Cgb 2  Cdb1
C1  1  A   Cgs1  Cgb1   Cdb1
I out
A
s

 
I in
1 s

C1
1 A

g mg1 2 fT
1. Model is valid as long as 1<<1;
2. C3 introduces a finite zero in the
transfer function;
3. Yin
vout  0
 g m1  s  C1  C3 
Yout  g ds 2  s  C2  Cdb 2 
CMOS Analog Design Using All-Region MOSFET
Modeling
7
Noise analysis
ii2
ac model (capacitive
effects not accounted for)
ii
io2
iout
i12
M1
M2
i1
2
2
i
1:A
g mg1 
g ds1
+
v
-
g mg 2 v
i2
ii, i1, i2  noise sources associated with input
signal source, M1, and M2, respectively.
Superposition
gm2
io   ii  i1 
 i2
g m1
&
uncorrelated noise sources


2
 gm2 
2
i  i i 

i

2
g
 m1 
2
o
2
i
2
1
gm2
A
g m1
Thermal & flicker noise
CMOS Analog Design Using All-Region MOSFET
Modeling
8
Current gain schemes - 1
VDD
Gain=A
Gain=1/(NM)
ii
io==Aii
io==ii/(NM)
......
ii
VDD
io==ii/A
ii
...
...
N
.....
.
......
M
Gain= 1/A
CMOS Analog Design Using All-Region MOSFET
Modeling
9
Current gain schemes - 2
I
R
I/4
I/2
2R
R
R
2R
R
I/16
I/8
2R
2R
R
CMOS Analog Design Using All-Region MOSFET
Modeling
10
Current gain schemes - 3
C. C. Enz and E. A. Vittoz, CMOS Low-Power Analog Circuit Design, Chapter 1.2 in Emerging
Technologies, R. Cavin and W. Liu (eds.), Tutorial for ISCAS 96.
CMOS Analog Design Using All-Region MOSFET
Modeling
11
Op-amp based current mirror
i
G1
-
G2
VCM
io    G2 / G1  i
+
Inverting
current mirror
VCM
VDD
i
M1
-
+
VDD
-
+
VCM
W / L 2
io  
i
W
/
L

1
CMOS Analog Design Using All-Region MOSFET
Modeling
M2
VCM
+
12
Cascode current mirror - 1
VDD
IIN
VOUT
Simple current mirror:
IOUT
Error  VOUT  VIN
VIN
dI OUT
dVOUT
Low output impedance large
M1
M2
1:1
Possible solution: Increase L 
Is frequency response acceptable?
t
fT 
2
2
2 L


1 if 1
CMOS Analog Design Using All-Region MOSFET
Modeling
13
Cascode current mirror - 2
Basic idea to improve the
performance of the simple current
mirror output voltage follows the
input voltage
Choosing VDVDSsat1 gives
maximum output swing
Active regulated cascode
current mirror
CMOS Analog Design Using All-Region MOSFET
Modeling
14
Cascode current mirror - 3
iout
VB
VDD
M3
iin
X
M1
+
v
-
M2
1:1
The cascode stage
vout
+
-
1. Voltage at node X is (almost) independent
of Vout (as long as M3 operates in saturation).
Output impedance (small-signal analysis):
iin  0  v  0
iout  g mg 2 v  g md 2 vx ; iout   g ms 3vx  g md 3vout
iout
g md 3
g
 g md 2
 g md 2 md 3
vout
g ms 3  g md 2
g ms 3
Output conductance
of a single transistor
Inverse of
voltage gain
2. VX  v and v depends on iin  error
3. What about VB?
CMOS Analog Design Using All-Region MOSFET
Modeling
15
Self-biased cascode current mirror - 1
iin
Suppose M1M2M3 M4
VDD
+
VCS
_
iout
M4
M3
Y
M1
1. First-order analysis: If M4 operates in
saturation, then VXVY and Iout Iin
X
+
v
-
1:1
M2
vout
+
-
2. The output conductance:
iin  0  v  0;
iout
g
 g md 2 md 3
vout
g ms 3
3. Note that VDD> VCS+VGS3+VGS1
VCS is the minimum voltage for proper
operation of the current source
4. Note that Vout> VGS1+VDS4,sat for
saturation of M4
5. SBCCM is not a low-voltage current
mirror
CMOS Analog Design Using All-Region MOSFET
Modeling
16
Self-biased cascode current mirror - 2
VDD
+
VCS
_
iin
iout
M4
M3
Y
X
vout
+
-
Example: 0.35 um CMOS technology,
VT0N=0.55V, n1.3, ISQN=70 nA, W=10
m, L=1 m
a) Iin=70 A, IS=70x10/1=700 nA
if=70/0.7=100
VP1
 1  i f  2  ln 1  i f  1  10.25
t


VY  1.3t 10.25  0.550  0.883 V
VP 3  VY
 1  100  2  ln 1  100  1 
t


VG 3  1.3t 10.25  0.883  0.550  2.03 V
M2
M1
1:1
b) What’s the minimum Vout to
keep M4 in saturation
c) What’s VG3 in a) if VSB3=0?
d) Exercise: Repeat a), b),
and c) for Iin=70 nA
CMOS Analog Design Using All-Region MOSFET
Modeling
17
Low-voltage cascode current mirror - 1
Saturation of M3:
iout
VB
VDD
M3
iin
X
M2
M1
1:Ai
vout
+
-
VDS 3  VDS 3, sat
Vout  VX  VDS 3, sat
To maximize the output voltage swing
 minimize VX  VX= VDS2,sat + V 
VB should be designed accordingly.
Error due to different VDS for M1 & M2
CMOS Analog Design Using All-Region MOSFET
Modeling
18
Low-voltage cascode current mirror - 2
VDD
IB
Iout
Iin
M3
UICM applied to M3, find VG3 such that (I) is
satisfied
M4
X
M2 on the edge of saturation
V  t
(I) VS 3  VDS 2  VDSsat 2  V
VDSsat  t ( 1  i f  3)
UICM applied to M4, find if4 such that VG3 is
obtained
Find a set IB4 & S4 for the value found for if4
M2
M1
1:Ai
CMOS Analog Design Using All-Region MOSFET
Modeling
19
Low-voltage cascode current mirror - 3
VDD
VDD
IB
IB5
M5
VP5  t  1  i f 5  2  ln

M1

1  i f 5 1 

VP 4  VS 4  t  1  i f 4  2  ln

VO
M3

IO
M2
+
VDS
2
_
Symmetric low-voltage cascode
current mirror

1  i f 4 1 

(II)
V  t
VS 4  VDS 2  VDSsat 2  V
M4

(I)
VDSsat  t ( 1  i f  3)
(I)=(II)
 1  i f 5  1  ln


 1 if 4  3      1 if 4

 
I in  I B  iin
CMOS Analog Design Using All-Region MOSFET
Modeling

 1  ln 
1 i f 5 1  

if 4 

1 i f 4 1 

IB
IS 4
20
Experimental results - 1
2 m CMOS technology
VT0N0.55 V
CMOS Analog Design Using All-Region MOSFET
Modeling
21
Experimental results - 2
CMOS Analog Design Using All-Region MOSFET
Modeling
22
Class-AB current mirror
VDD
VDD
IB
M3
VDD
M6
M8
M1
II
VBias
M4
IO
M2
IB
M5
CMOS Analog Design Using All-Region MOSFET
Modeling
M7
23
Appendix: current mirror distortion - 1
Distortion in CM is mainly generated by VT (doping fluctuations)
mismatch and dependence of the current on the output voltage
VDD
IB1
IIN
M1
I
VT 0
I B
I I
2
 B 2 B1  S 
IB
IS
 I B 2  I B1 
1  i f  1 nt


2


IB2+IOUT
I S
I I
 S 2 S1
IS
 I S 2  I S1 


2


M2
if 
VP1  VP 2
t
Simple MOS current mirror and symbols
used to analyze distortion. Drain voltages
of M1 and M2 assumed to be equal.

VT 0  VT 02  VT 01
IB
IS
VT 0
I I
I I
 1  B1 IN  1  B 2 OUT
nt
I S1
IS 2




I B1  I IN
I B 2  I OUT
 ln  1 
 1  ln  1 
 1
I
I
S1
S2




CMOS Analog Design Using All-Region MOSFET
Modeling
24
Appendix: current mirror distortion - 2
dI OUT
dI IN
 1
0
d 2 I OUT
2
dI IN
d 3 I OUT
3
dI IN
I S
1 VT 0

1
IS
1  i f nt
0
VT 0
2nt I S
0
3 VT 0

4 nt I S2


1
1 if


I MO 2
I M VT 0
HD2 

IM
8I S nt
3
1
1 if

5
HD3 
I MO 3
IM

1
1 if
2
1  I M  VT 0
 

32  I S  nt
CMOS Analog Design Using All-Region MOSFET
Modeling


3
1
1 if

25
5