6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 19-1
Lecture 19 - Transistor Amplifiers (I)
Common-Source Amplifier
November 15, 2005
Contents:
1. Amplifier fundamentals
2. Common-source amplifier
3. Common-source amplifier with current-source supply
Reading assignment:
Howe and Sodini, Ch. 8, §§8.1-8.6
Announcements:
Quiz 2: 11/16, 7:30-9:30 PM,
open book, must bring calculator; lectures #10-18.
Quiz 2 TA Review Session: 11/15, 7:30-9:30 PM,
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 19-2
Key questions
• What are the key figures of merit of an amplifier?
• How can one make a voltage amplifier with a single
MOSFET and a resistor?
• How can this amplifier be improved?
Lecture 19-3
6.012 - Microelectronic Devices and Circuits - Fall 2005
1. Amplifier fundamentals
Goal of amplifiers: signal amplification.
vOUT
+V
+
output
signal
+
vIN
RL
vOUT
-
-
vIN
-V
input signal
Features of amplifier:
• Output signal is faithful replica of input signal but
amplified in magnitude.
• Active device is at the heart of amplifier.
• Need linear transfer characteristics for distortion
not to be introduced.
Lecture 19-4
6.012 - Microelectronic Devices and Circuits - Fall 2005
Signal could be represented by current or voltage
⇒ four broad types of amplifiers:
RS
vs
voltage
amplifier
+
−
is
+
−
transconductance
amplifier
RS
transresistance
amplifier
RL
RL
iout
is
+
vout
−
iout
RS
vs
RL
RS
current
amplifier
RL
+
vout
−
Lecture 19-5
6.012 - Microelectronic Devices and Circuits - Fall 2005
More realistic transfer characteristics:
vOUT
output
signal
Q
vIN
input signal
• Transfer characteristics linear over limited range of
voltages: amplifier saturation.
• Amplifier saturation limits signal swing.
• Signal swing also depends on choice of bias point, Q
(also called quiescent point or operating point).
Other features desired in amplifiers:
• Low power consumption.
• Wide frequency response [will discuss in a few days].
• Robust to process and temperature variations.
• Inexpensive: must minimize use of unusual components, must be small (in Si area)
Lecture 19-6
6.012 - Microelectronic Devices and Circuits - Fall 2005
2. Common-Source Amplifier
Consider the following circuit:
V+=VDD
RD
iR
signal source
RS
iD
+
vOUT
vs
VGG
signal
load
RL
V-=VSS
Consider it first unloaded by RL. How does it work?
• VGG, RD and W/L of MOSFET selected to bias transistor in saturation and obtain desired output bias
point (i.e. VOU T = 0).
• vGS ↑ ⇒ iD ↑ ⇒ iR ↑ ⇒ vout ↓
• Av = vvout
< 0; output out of phase from input, but if
s
amplifier well designed, |Av | > 1.
[watch notation: vOU T (t) = VOU T + vout(t)]
Lecture 19-7
6.012 - Microelectronic Devices and Circuits - Fall 2005
Load line view of amplifier:
load line
IR=ID
VDD-VSS
VGG-VSS=VDD-VSS
RD
VGG-VSS
VGG-VSS=VT
0
VSS
VDD
VOUT
Transfer characteristics of amplifier:
VOUT
VDD
VSS
0
VT
VDD-VSS VGG-VSS
Want:
• Bias point calculation;
• small-signal gain;
• limits to signal swing
• frequency response [in a few days]
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 19-8
2 Bias point: choice of VGG, W/L, and RD to keep
transistor in saturation and to get proper quiescent VOU T .
Assume MOSFET is in saturation:
ID =
W
µnCox (VGG − VSS − VT )2
2L
VDD − VOU T
IR =
RD
If we select VOU T = 0:
VDD
W
2
ID = IR =
µnCox (VGG − VSS − VT ) =
2L
RD
Then:
VGG =
�
�
�
�
�
�
�
2VDD
+ VSS + VT
W
RD L µnCox
Lecture 19-9
6.012 - Microelectronic Devices and Circuits - Fall 2005
2 Small-signal voltage gain: draw small-signal equivalent circuit model:
RD
+
vin
vgs
-
D
G
+
+
gmvgs
ro
vout
-
- S
+
+
vin
gmvin
-
ro//RD
vout
-
vout = −gm vin(ro//RD )
unloaded
Then unlo
aded voltage gain:
Avo =
vout
= −gm (ro//RD )
vin
Lecture 19-10
6.012 - Microelectronic Devices and Circuits - Fall 2005
2 Signal swing:
VDD
RD
signal source
+
RS
vOUT
vs
VGG
-
VSS
• Upswing: limited by transistor going into cut-off:
vout,max = VDD
• Downswing: limited by MOSFET entering linear regime:
VDS,sat = VGS − VT
or
vout,min − VSS = VGG − VSS − VT
Then:
vout,min = VGG − VT
Lecture 19-11
6.012 - Microelectronic Devices and Circuits - Fall 2005
2 Effect of input/output loading:
VDD
RD
iR
iL
signal source
iD
RS
+
vOUT
vs
VGG
RL
-
VSS
• Bias point not affected because selected VOU T = 0.
• Signal swing:
– Upswing limited by resistive divider:
RL
vout,max = VDD
RL + RD
– Downswing not affected by loading
• Voltage gain:
– input loading (RS ): no effect because gate does
not draw current;
– output loading (RL ): RL detracts from voltage
gain because it draws current.
|Av | = gm(ro //RD //RL) < gm (ro //RD )
Lecture 19-12
6.012 - Microelectronic Devices and Circuits - Fall 2005
2 Generic view of loading effect on small-signal operation:
Two-port network view of small-signal equivalent circuit
model of voltage amplifier:
Rin is input resistance
Rout is output resistance
Avo is unloaded voltage gain
RS
Rout
+
+
vs
+
+
vin
-
Rin
-
input
loading
-
Avovin
RL
vout
-
unloaded circuit
output
loading
Voltage divider at input:
s
vin = Rin Rinv+R
S
Voltage divider at output:
vin
vout = RL RAoutvo+R
L
Loaded voltage gain:
vout
Rin
RL
=
Avo
Av =
vs
Rin + RS
RL + Rout
Lecture 19-13
6.012 - Microelectronic Devices and Circuits - Fall 2005
• Calculation of input resistance, Rin:
- load amplifier with RL
- apply test voltage (or current) at input, measure test
current (or voltage)
For common-source amplifier:
it
+
+
vt
-
vgs
gmvgs
ro//RD
-
vt
it = 0 ⇒ Rin = = ∞
it
No effect of loading at input.
RL
Lecture 19-14
6.012 - Microelectronic Devices and Circuits - Fall 2005
• Calculation of output resistance, Rout :
- load amplifier at input with RS
- apply test voltage (or current) at output, measure
test current (or voltage)
For common-source amplifier:
it
+
RS
+
vgs
gmvgs
ro//RD
-
vgs = 0 ⇒ gm vgs = 0 ⇒ vt = it(ro //RD )
Rout
vt
= = ro//RD
it
-
vt
Lecture 19-15
6.012 - Microelectronic Devices and Circuits - Fall 2005
Two-port network view of common-source amplifier:
RS
Rout
+
+
vs
+
vin
-
-
input
loading
+
Rin
-
Avovin
unloaded circuit
RL
vout
-
output
loading
vout
vs
Rin
RL
RL
=
Avo
= −gm(ro //RD )
Rin + RS
RL + Rout
RL + ro //RD
Av =
Or:
Av = −gm (ro //RD //RL )
Lecture 19-16
6.012 - Microelectronic Devices and Circuits - Fall 2005
2 Design issues of common-source amplifier (unloaded):
Examine bias dependence:
|Avo | = gm(ro //RD ) gm RD
Rewrite |Avo | in the following way:
�
�
�
�
�
�
W
VDD
VDD
√
∝
|Avo | gmRD = 2 µnCox ID
L
ID
ID
Then, to get high |Avo |:
⇒ VDD ↑
⇒ ID ↓
Both approaches imply ⇒ RD =
VDD
ID
↑
Consequences of high RD :
• large RD consumes a lot of Si real state
• large RD eventually compromises frequency response
Also, it would be nice not to use any resistors at all!
⇒ Need better circuit.
Lecture 19-17
6.012 - Microelectronic Devices and Circuits - Fall 2005
3. Common-source amplifier with current-source
supply
VDD
iSUP
signal source
iD
RS
signal
load
+
RL
vOUT
vs
VGG
-
VSS
Loadline view:
load line
iSUP=ID
VGG-VSS=VDD-VSS
ISUP
VGG-VSS
VGG-VSS=VT
0
VSS
VDD
VOUT
Lecture 19-18
6.012 - Microelectronic Devices and Circuits - Fall 2005
Current source characterized by high output resistance:
roc.
Then, unloaded voltage gain of common-source stage:
|Avo | = gm (ro //roc )
significantly higher than amplifier with resistive supply.
Can implement current source supply by means of pchannel MOSFET:
VDD
VB
iSUP
signal source
iD
RS
+
vOUT
vs
VGG
VSS
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 19-19
• Relationship between circuit figures of merit and device
parameters
Remember:
�
�
�
�
�
�
gm = 2
W
µnCox ID
L
1
L
ro ∝
λnID ID
Then:
Circuit Parameters
Device ∗
|Avo |
Rin Rout
Parameters gm (ro//roc ) ∞ ro//roc
ISU P ↑
↓
↓
W ↑
-
↑
µnCox ↑
-
↑
L↑
↑
↑
∗
adjustments are made to VGG so
none of the other parameters change
CS amp with current supply source is good voltage amplifier (Rin high and |Av | high), but Rout high too ⇒
voltage gain degraded if RL ro//roc .
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 19-20
Key conclusions
• Figures of merit of an amplifier:
– gain
– signal swing
– power consumption
– frequency response
– robustness to process and temperature variations
• Common-source amplifier with resistive supply: trade-
off between gain and cost and frequency response.
• Trade-off resolved by using common-source amplifier
with current source supply.
• Two-port network computation of voltage gain, input
resistance and output resistance of amplifier.