EE40 Lec 20
MOS Circuits
Reading: Chap. 12 of Hambley
Supplement reading on MOS Circuits
http://www.inst.eecs.berkeley.edu/~ee40/fa09/handouts/EE40_MOS_Circuit.pdf
EE40 Fall 2009
Slide 1
Prof. Cheung
OUTLINE
–Bias circuits
–Small-signal equivalent circuits
–Examples:
Common source amplifier
Source follower
Common gate amplifier
–Digital Gates
–CMOS
EE40 Fall 2009
Slide 2
Prof. Cheung
Bias Circuits
• Use load line to find Quiescent operating point.
• Remember no current flow through the gate.
Fixed-plus Self-Bias CKT
VDD
VDD
RD
RD
R1
VG+vin
R2
EE40 Fall 2009
Slide 3
RS
Prof. Cheung
Steps for MOSFET Circuit Analysis
• 1) Look at DC case to find Q point
– Use load line technique
– All capacitors are open circuit, Inductors are
short circuit
– Determine Q-point, get gm and rd for small
signal AC model
• 2) AC Small signal analysis
– DC source is ac ground (because there is no
AC signal variation).
– All capacitors are approximated as short
circuit (unless otherwise specified).
EE40 Fall 2009
Slide 4
Prof. Cheung
Example: Common Source Amplifier
VDD
RD
C
R1
C
+
v(t)
-
EE40 Fall 2009
+
vin
-
RL
VG
R2
Slide 5
RS
+
vo
-
C
Prof. Cheung
Step 1: find Q point
VG  VDD
R2
R1  R2
VDD
Not connected
for DC component
VGS  VG  I D RS
VDD  I D ( RD  RS )  VDS
RD
C
R1
C
+
v(t)
-
+
vin
-
VG
R2
VDS
RS
RL
+
vo
-
C
Not connected
for DC component
EE40 Fall 2009
Slide 6
Prof. Cheung
Load line to determine Q Point by graphical method
Loadline to determine VGSQ
VG  VGS
ID 
RS
ID 
VDD  VDS
R0  RS
ID 
VGSQ
VG  VGS
RS
Loadline to determine VDSQ
ID 
VDD  VDS
R0  RS
From load lines, we get ID  and hence gm and rd
EE40 Fall 2009
Slide 7
Prof. Cheung
Load line to determine Q Point by analytical method
Solve VGSQ assume saturation region first
I DQ
VG  VGSQ

RS
I DQ  K ( VGSQ  V t ) 2
IDQ is known, then solve VDSQ
VDD  I DQ ( R D  R S )  VDSQ
Check VDSQ value is consistent with saturation region ( i.e. VDS> VGSQ-Vt)
From load lines, we get ID  and hence gm and rd
EE40 Fall 2009
Slide 8
Prof. Cheung
Determination of gm and rd graphically
Example: Q point is known to be VGS=2.5V, VDS=6V
1
i D (2.9  2.3)mA


 0.05  10 3 Siemens
rd vDS
(14  2)V
or
EE40 Fall 2009
Slide 9
rd  20k
Prof. Cheung
Determination of gm and rd by Analytical Models
In Saturation Region
i D  K ( v GS  Vt ) 2
i D
gm 
 2K ( v GS  Vt )  2 K i DQ
v GS
KP W
2 L
  channel mod ulation factor
K
i D
1 / rd 
   i DQ
v DS
In Triode Region
i D  K[2( v GS  Vt ) v DS  v 2 DS ]
gm 
i D
 2Kv DSQ
v GS
1 / rd 
i D
 K[2( v GSQ  Vt )  2 v DSQ ]
v DS
EE40 Fall 2009
Slide 10
Prof. Cheung
Small Signal Model
Inverting
vg  vin , vs  0  vgs  vin
For output impedance Rout:
1. Turn off all independent
sources.
2. Take away load impedance
RL
RL RD
vo 
( g m vgs )
RL  RD
vo
RL RD
Av 
  gm
vin
RL  RD
vin  0, vgs  0, g m vgs  0
vin
R1 R2
Rin 

iin R1  R2
EE40 Fall 2009
Rout
Slide 11
rd RD

rd  RD
Prof. Cheung
Example: Source Follower
VDD
R1
C
+
v(t)
-
EE40 Fall 2009
+
vin
-
VG
R2
Slide 12
C
RS
RL
+
vo
-
Prof. Cheung
Step 1: find Q point
VG  VDD
R2
R1  R2
VDD
VGS  VG  I D RS
VDD  I D RS  VDS
R1
C
+
v(t)
-
EE40 Fall 2009
+
vin
-
VG
R2
Slide 13
C
RS
RL
+
vo
-
Prof. Cheung
Small Signal Model
Non-inverting,
Voltage Gain <1
Rin high
Current gain can be high
RL 
1
rd 1  RS 1  RL 1
vgs  vin  vo
vo  g m vgs RL
vin  vgs (1  g m RL )
vo
g m RL
Av 

vin 1  g m RL
v
RR
Rin  in  1 2
iin R1  R2
EE40 Fall 2009
For output impedance Rout:
1. Turn off all independent sources.
2. Take away RL
3. Add Vx and find ix
vx  vs , vg  0, vgs  vx
Rs 

rd Rs
v
, ix  x  g m (vx )  vx Rs1  g m
rd  Rs
Rs
Rout 
1
g m  rd 1  Rs 1
Slide 14
Rout is small
Prof. Cheung

Example: Common Gate Amplifier
VDD
RD
C
RL
VG
+
v(t)
-
+
vo
-
+ C
vin
RS
-VSS
EE40 Fall 2009
Slide 15
Prof. Cheung
Step 1: find Q point
VDD
VGS  0  I D RS  VSS
VDD  VSS  I D ( RD  RS )  VDS
RD
C
RL
VG
+
v(t)
-
+
vo
-
+ C
vin
RS
-VSS
EE40 Fall 2009
Slide 16
Prof. Cheung
Load line
The only difference in all three circuits are
the intercepts at the axes.
Again from load lines, we get ID  and
hence gm and rd
EE40 Fall 2009
Slide 17
Prof. Cheung
Small Signal Model
Non-inverting
RL 
1
RL 1  RD 1
vgs  vin
vo   g m vgs RL
Av 
vo
 g m RL
vin
iin  ( g m vgs 
vgs
Rs
)
For output impedance Rout:
1. Turn off all independent sources.
2. Take away RL
3. Add Vx and find ix
RRs
R 
R  Rs
v
ix  x  g m vgs
RD
vgs   g m vgs R , but g m R  1 vgs  0
v
1
Rin  in 
iin g m  Rs 1
EE40 Fall 2009
Rout  RD
Slide 18
Prof. Cheung
Logic Gates : Pull-Up and Pull-Down
PMOS or Resistor
NMOS or Resistor
EE40 Fall 2009
Slide 19
Prof. Cheung
Inverter = NOT Gate
Vin
Vout
Ideal Transfer Characteristics
Vout
V/2
EE40 Fall 2009
Slide 20
V
Vin
Prof. Cheung
NMOS Inverter: Resistor Pull-Up
VDD
Circuit:
Voltage-Transfer Characteristic
vOUT
RD
iD
A
iD
+
+
vIN
–
VDD
F
vDS = vOUT
vIN = VDD
–
0
VT
VDD
VDD/RD
increasing
vGS = vIN > VT
0
EE40 Fall 2009
vGS = vin  VT
Slide 21
VDD
vDS
A F
0 1
1 0
Prof. Cheung
vIN
NMOS NAND Gate
• Output is low only if both inputs are high
VDD
RD
F
A
Truth Table
A
0
0
1
1
B
EE40 Fall 2009
Slide 22
B
0
1
0
1
Prof. Cheung
F
1
1
1
0
NMOS NOR Gate
• Output is low if either input is high
VDD
RD
F
A
B
Truth Table
A
0
0
1
1
EE40 Fall 2009
Slide 23
B
0
1
0
1
Prof. Cheung
F
1
0
0
0
Disadvantages of NMOS Logic Gates
• Large values of RD are required in order
to
– achieve a low value of VLOW
– keep power consumption low
 Large resistors are needed, but these take
up a lot of space.
EE40 Fall 2009
Slide 24
Prof. Cheung
CMOS Inverter: Intuitive Perspective
SWITCH MODELS
CIRCUIT
VDD
G
VDD
VDD
S
Rp
D
VOUT
VIN
VOUT
D
G
EE40 Fall 2009
VOL = 0 V
Rn
S
Low static power consumption, since
one MOSFET is always off in steady state
VOUT
VIN = VDD
Slide 25
VOH = VDD
VIN = 0 V
Prof. Cheung
The CMOS Inverter: Current Flow
N: sat
P: sat
VOUT
N: off
P: lin
VDD
VDD
S
G
VOUT
I
A
D
G
C
N: sat
P: lin
D
VIN
B
D
E
N: lin
P: sat
S
N: lin
P: off
0
VDD
0
EE40 Fall 2009
i
Slide 26
VIN
Prof. Cheung
Power Dissipation: Direct-Path Current
VDD
VDD
vIN:
S
G
D
vIN
D
G
S
VT
0
Ipeak
vOUT
i
VDD-VT
i:
0
tsc
Energy consumed per switching period:
EE40 Fall 2009
Slide 27
time
Edp  t scVDD I peak
Prof. Cheung
CMOS NAND Gate
A
0
0
1
1
VDD
A
B
F
A
B
0
1
0
1
Notice that the
pull-up network is
related to the pulldown network by
DeMorgan’s
Theorem!
NMOS, Pull-down
PMOS, Pull-up
B
EE40 Fall 2009
Slide 28
Prof. Cheung
F
1
1
1
0
CMOS NOR Gate
A
0
0
1
1
VDD
A
B
F
Notice that the
pull-up network is
related to the pulldown network by
DeMorgan’s
Theorem!
NMOS, Pull-down
B
EE40 Fall 2009
B
0
1
0
1
PMOS, Pull-up
A
Slide 29
Prof. Cheung
F
1
0
0
0
Multiple Input NOR Gate
EE40 Fall 2009
Slide 30
Prof. Cheung
Features of CMOS Digital Circuits
• The output is always connected to VDD or GND
in steady state
 Full logic swing; large noise margins
 Logic levels are not dependent upon the relative
sizes of the devices (“ratioless”)
• There is no direct path between VDD and GND
in steady state
 no static power dissipation
EE40 Fall 2009
Slide 31
Prof. Cheung