# Lecture 22 - Multistage Amplifiers (II) DC Voltage and Current ...

Electronics - Devices

Oct 7, 2013 (4 years and 9 months ago)

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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-1
Lecture 22 - Multistage Ampliﬁers (II)
DC Voltage and Current Sources
May 1,2003
Contents:
1.DC voltage sources
2.DC current sources and sinks
Howe and Sodini,Ch.9,§§9.4
Announcements:
Athena Oﬃce Hours:Thurs 5/1:8:30-9:30 PM,Sunday
5/4:7-9 PM,Athena Cluster 38-370
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-2
Key questions
• How does one synthesize voltage and current sources?
• How can this be done in an economic way?
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-3
1.DC voltage sources
✷ Features of voltage source:
• A well controlled voltage
• voltage does not depend on current drawn fromsource
(low internal resistance).
I-V characteristics of ideal voltage source:
I
VV
S
0
0
Equivalent circuit model of voltage source:
V
s
R
S
+
-
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-4
✷ Consider MOSFET in ”diode conﬁguration”:
V
DS
V
GS
I
D
+
+

V
DS
I
D
V
GS
V
T
V
GS
=V
T
0
0
I-V characteristics:
I
D
=
W
2L
µC
ox
(V
GS
−V
T
)
2
=
W
2L
µC
ox
(V
DS
−V
T
)
2
Beyond threshold,MOSFETlooks like ”diode” with quadratic
I-V characteristics.
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-5
✷ How does one synthesize a voltage source with this?
Assume a current source is available.
i
OUT
V
DD
i
D
I
REF
+

v
OUT
v
OUT
i
OUT
-I
REF
V
T
0
V
GS
= V
DS
takes value needed to sink current:
I
D
= I
REF
+i
OUT
=
W
2L
µC
ox
(v
OUT
−V
T
)
2
Then:
i
OUT
=
W
2L
µC
ox
(v
OUT
−V
T
)
2
−I
REF
Solving for v
OUT
:
v
OUT
= V
T
+
￿
￿
￿￿￿￿￿
I
REF
+i
OUT
W
2L
µC
ox
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-6
v
OUT
is function of I
REF
and W/L of MOSFET:
• I
REF
↑ ⇒ v
OUT

• W/L ↑ ⇒ v
OUT

W/L
V
T
V
T
v
OUT
v
OUT
i
OUT
i
OUT
I
REF
I
REF
I
REF1
I
REF2
✷ Small-signal view of voltage source:
+
+
-
-
v
gs
v
t
i
t
g
m
v
gs
r
o
D
G
S
R
out
=
1
g
m
//r
o
￿
1
g
m
R
out
is small (good!).
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-7
✷ PMOS voltage source:
V
D
D
+

i
OUT
V
OUT
I
REF
Same operation and characteristics as NMOS voltage source.
PMOS needs to be bigger to attain same R
out
.
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-8
2.DC current sources and sinks
✷ Features of current source:
• A well controlled current,
• supplied current does not depend on voltage across
(high internal resistance)
I-V characteristics of ideal current source:
I
I
s
V
0
0
Equivalent circuit model of current source:
I
s
R
S
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-9
✷ Connect voltage source to another MOSFET:
V
DD
I
REF
i
OUT
M
1
M
2
+

V
REF
+

v
OUT
I
OUT
￿
1
2

W
L

2
µC
ox
(V
REF
−V
T
)
2
I
REF
￿
1
2

W
L

1
µC
ox
(V
REF
−V
T
)
2
Then:
I
OUT
= I
REF
￿
W
L
￿
2
￿
W
L
￿
1
I
OUT
scales with I
REF
by W/L ratios of two MOSFETs
(current mirror circuit).
Well ”matched” transistors important.
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-10
• Small-signal view of current source:
+
+
-
-
v
gs2
v
t
i
t
g
m2
v
gs2
r
o2
g
m1
R
out
= r
o2
I-V characteristics of NMOS current source:
1/r
o2
i
OUT
v
OUT
(W/L)
2
(W/L)
1
I
REF
V
DS
SAT2
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-11
✷ PMOS current source
• NMOS current source sinks current to ground.
• PMOS current source sources current from positive
supply.
PMOS current mirror:
V
DD
I
REF
M
1
i
OUT
M
2
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-12
✷ Multiple current sources
Since there is no DC gate current in MOSFET,can tie
up multiple current mirrors to single current source:
V
DD
I
REF
M
R
M
1
M
2
M
3
i
OUT1
i
OUT2
i
OUT3
I
OUTn
= I
REF
￿
W
L
￿
n
￿
W
L
￿
R
Similar idea with NMOS current sinks:
V
DD
I
REF
i
OUT1
M
R
M
1
+

V
REF
i
OUT2
M
2
i
OUT3
M
3
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-13
✷ Multiple current sources and sinks
Often,in a given circuit,we need current sources and
sinks.Can build them all out of a single current source:
I
REF
M
R
V
DD
M
1
M
2
M
4
M
3
i
OUT1
i
OUT2
i
OUT4
I
OUT1
= I
REF
￿
W
L
￿
1
￿
W
L
￿
R
I
OUT2
= I
REF
￿
W
L
￿
2
￿
W
L
￿
R
I
OUT4
= I
OUT1
￿
W
L
￿
4
￿
W
L
￿
3
= I
REF
￿
W
L
￿
4
￿
W
L
￿
1
￿
W
L
￿
3
￿
W
L
￿
R
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-14
✷ Generating I
REF
:
Simple circuit:
V
DD
R
V
OUT
I
REF
+

I
REF
=
V
DD
−V
OUT
R
V
OUT
= V
T
+
￿
￿
￿￿
I
REF
W
2L
µC
ox
For large W/L,V
OUT
→ V
T
:
I
REF
￿
V
DD
−V
T
R
– I
REF
set by value of resistor.
– V
DD
also aﬀects I
REF
.
– V
T
and Rare function of temperature ⇒ I
REF
(T).
In real world,more sophisticated circuits used to generate
I
REF
that are V
DD
and T independent.
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-15
✷ Can now understand more complex circuits.
Examples:
+2.5 V
2.5 V
I
REF
V
BIAS
v
s
R
S
M
1
M
2
M
3
v
OUT
+

+

+

Amp stages:
What does it do?
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-16
2.5 V
2.5 V
I
REF
M
1
M
2
M
3
R
L
R
S
V
s
V
BIAS
+

+

+

v
OUT
Amp stages:
What does it do?
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-17
+2.5 V
2.5 V
i
OUT
V
BIAS
I
REF
v
s
R
S
R
L
Q
1
M
3
M
2
+

+

Amp stages:
What does it do?
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-18
 3 V
+3 V
M
1
M
2
M
2B
M
4
M
3
v
OUT
i
OUT
+

V
BIAS
v
s
R
S
R
L
6 k
+

+

Amp stages:
What does it do?
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-19
V
BIAS
v
s
R
S
+

+

I
REF
M
2
M
6
M
5
M
4
M
3
Q
1
Q
2
v
OUT

+
2.5 V
+2.5 V
Amp stages:
What does it do?
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 22-20
Key conclusions
• Voltage source easily synthesized from current source
using MOSFET in diode conﬁguration.
• Current source easily synthesized from current source
using current mirror circuit.
• Multiple current sources and sinks with diﬀerent mag-
nitudes of current can be synthesized from a single
current source.
• Voltage and current sources rely on availability of well
”matched” transistors in IC technology.