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6.002xCIRCUITS AND ELECTRONICS
Amplifiers –
Revisit Small Signal Trick
Reading: Amplifier small signal model -- Chapter 8 of A&L
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! MOSFET amp
! Saturation discipline — operateMOSFET only in saturation region
!
Large signal analysis1. Find vO vs v I under saturation discipline.2. Valid v I , vO ranges under saturation discipline.
ReviewV s
R L
vOv I i DS
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Large Signal Analysis ReviewReview
( ) L
T I
S O R
V v K V v
2
2
!
!=
“interesting” regio
Saturation discipl
corresponding
interesting
region for vO
2 Valid operating ranges
T I O V vv !=
T I O V vv !>
T I O V vv !
<
V g e 5.,.
V 1
V 1
V s
v I
vO
V T
V 2
1 vO vs v I
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Operating in the saturation region
I v
S V
T V
T I O V vv
!=
vO ( ) L
T I
S O R
V v K V v
2
2
!
!=
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But…
I v
S V
T V
T I O V vv !=
vO( )
L
T I
S O R
V v K V v
2
2
!
!=
Amp is no
How do wlinear am
V I
v A
V Iv A
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Small Signal Trick
T V
V SvO
v I
v
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Small Signal Trick
# Operate amp at V I , V O $ DC “bias”(possible choice: midpoint of valid input operating range)
# Superimpose small signal of interest on top of V I
# Response to small signal seems to be approximately linear
Remember“Boost and Shrink”
v I
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We use a DC bias V I to “boost” interesting inputsignal above V T (and in fact, well above V T )
Boost – Use DC Bias
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Let’s look at this in more detail —
I graphicallyII mathematicallyIII from a circuit viewpoint
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I Graphically interestiinput sign
v!
V
T I O V vv !=
vOV S
0 V T v I
v I
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Recall Small Signal Model Notationaka incremental modelaka linearized model
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Small Signal Model InputOutput
0 0
v I vO
t t
II M h i ll
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II Mathematically
…m
f
( )22
T I
L
S O V v K R
V v !!=
II M th ti ll
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II Mathematically
…m
f
( )22
T I
L
S O V v K R
V v !!=
Transconductance related to MOSFET parameters and V I
tt
s
M th ti ll
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Mathematically
( ) iT I Lo
vV V K Rv !!=
g m related to V I
In other words, our circuit behaves like a linear amplifier
for small signals
A th
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A
8
f
in
o
Another way( )2
2 T I
L
S O V v K R
V v !!=
S ll Si l D
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Small Signal Demointerestininput signa
+–+–
I v
S V
T V
T I O V vv !=
0
vi
V I
vO
