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3. Fundamental MOS Configurations and
Discrete MOS Amplifiers
ECE 102, Winter 2011, F. Najmabadi
Reading: Sedra & Smith: Secs. 5.6 & 5.7
Voltage Amplifier Model
Voltage Amplifier Model
Input Resistance: Ri = vi/iiOpen-loop gain: Avo = vo/vi with no loadOutput resistance: Ro (resistance seen between
output terminals with vi= 0 )
We focus on Unilateral amplifiers (i.e., Ri is independent of Load)
sigi
i
S
i
RRR
vv
+=
oL
Lvov
in
o
RRRAA
vv
+⋅==
oL
Lvo
sigi
i
S
out
RRRA
RRR
vv
+⋅⋅
+=
Rsig
Cascaded Amplifiers
91.0100k1M
1M
1
11 =+
=+
=sigi
i
S
i
RRR
vv
9.91k100k
100k10
11
11,
1
21 =
+⋅=
+⋅==
oL
Lvo
i
iv RR
RAvvA100k 2121 === iLio RRvv
9.901k10k
10k100
22
22,
2
32 =
+⋅=
+⋅==
oL
Lvo
i
iv RR
RAvvA10k 3232 === iLio RRvv
909.010100
1001
33
33,
33 =
+⋅=
+⋅==
oL
Lvo
i
Lv RR
RAvvA
8183211
=⋅⋅== vvvi
Lv AAA
vvA 74491.0 x 8181 ==⋅=
s
iv
s
L
vvA
vv
MOS Fundamental Configurations
MOS fundamental amplifier configurations
Common-Source Common-Gate Common-Drain
Since PMOS has the same signal model, configurations and results are exactly the same
Common Source Configuration
Small Signal Circuit:
Small Signal Circuit with MOS SSM
Common Source Configuration (Gain)
)||(
)||||(
)||||(
Domvo
LDomin
ov
LDogsmo
RrgA
RRrgvvA
RRrvgv
−=
−==
−=
Small Signal Circuit with MOS SSM
Relevant circuit forGain calculation
Common Source Configuration (Ri)
∞==
=
i
ii
i
ivR
i 0
Small Signal Circuit with MOS SSM
Relevant circuit forRi calculation
Common Source Configuration (Ro)
Doo RrR ||=Current source becomes open circuit
Small Signal Circuit with MOS SSM
Relevant circuit forRo calculation (set vi = 0)
Common Source with Source Resistor
∞==⇒=i
iii i
vRi 0Input Resistance
Small Signal Circuit:
Small Signal Circuit with MOS SSM
Common Source with Source Resistor (Gain*)
* Text book ignore ro
oDSm
Dmvo
oLDSm
LDmv
LDSomo
LDom
i
ov
rRRgRgA
rRRRgRRgA
RRRrgrRRrg
vvA
/1
/)||(1)||(
)||()1()||(
++−=
++−≈
+++−==
0)(||
0)(
=−+−
+
=−−−
+
−=
Simo
So
LD
o
Simo
oS
S
S
Sigs
vvgr
vvRR
v
vvgr
vvRv
vvv
Node voltage method:
Node vs
Node vo
Relevant circuit forGain calculation
Common Source with Source Resistor (Ro*)
* Text book ignore ro
DSomoo RRrgrR ||])1([ ++=
Somo
x
S
s
Smo
xS
S
S
Sgs
Rrgrv
Rv
vgr
vvRv
vv
)1(
0)(
++=
=−−−
+
−=
Node voltage method:
Node vs
set vi = 0 Attach ix and compute vx
D
x
Somo
x
o
xx
D
x
S
Sx
Rv
Rrgrv
Rvi
Rv
Rviii
+++
==
+=+=
)1(
21
2121 ||111 :Noting
RRRR=+
Common Gate Configuration
Small Signal Circuit:
Small Signal Circuit with MOS SSM
Common Gate Configuration (Gain*)
)||()||||(
)||||(1
Domvo
LDomv
LDoo
om
i
ov
RrgARRrgA
RRrr
rgvvA
≈≈
+==
io
om
LDo
o
imo
io
LD
o
igs
vr
rgRRr
v
vgr
vvRR
vvv
+=
=−+−
+
−=
1||||
0)(||
Node voltage method:
Node vo
Relevant circuit forGain calculation
Common Gate Configuration (Ri and Ro*)
om
LD
mi
om
LDo
i
ii
rgRR
gR
rgRRr
ivR
||11
||
+≈
++
==
)||()1(
)||()(
LDoiomi
LDiogsmii
RRrirgvRRirvgiv
+=+
++=KVL:
* Text book ignore ro
Doo RrR ||=
Current source becomes open circuit
Output Resistance (set vi = 0)
Input Resistance
Common Drain Configuration (Source Follower)
11
)||(1)||(
≈+
=
+=
om
omvo
Lom
Lomv
rgrgA
RrgRrgA
Note: This circuit needs a load as it is really a current amplifier.
omLo
oim
oimo
o
L
o
oigs
vgRr
vvg
vvgrv
Rv
vvv
+=
=−−+
−=
||
0)(
Node voltage method:
Node vs
Gain
Common Drain Configuration (Source Follower)
m
x
o
xgsm
o
xx g
vrvvg
rvi
/1+=−=
Input Resistance
Output Resistance (set vi = 0)
mo
mo g
rg
R 1||1≈=
0=ii
∞==i
ii i
vR
Summary of MOS Amp. Fundamental Forms(PMOS circuits are identical)
Common Source with RS
oLDSm
LDmv rRRRg
RRgA/)||(1
)||(++
−=
Common Drain/Source Follower
)||(1)||(
Lom
Lomv Rrg
RrgA+
=
Common Source
)||||( LDomv RRrgA −=
Common Gate
)||||( LDomv RRrgA =
Transistor can be configured to act as a resistor for small signals!
Doo RrR ||=Set vi = 0, current source becomes open circuit
Ex: Output resistance of a CS Amplifier
Do Rr ||
or
If we connect any two terminals of a MOS, we get a two-terminal device.o For Small Signals, this two terminal device can be replaced with its
Thevenin equivalent circuit.o As there is NO independent sources present, the Thevenin
equivalent circuit is reduced to a resistor.
Transistor can be configured to act as a resistor for small signals!
But, MOS should be in saturation for small signal model to work!o Connection between MOS terminals are, therefore, made through
ground for small signals.o In fact, one or both MOS terminals have to be connected to bias power
supplies to ensure that MOS is in saturation
Notation: ro is the small-signal resistance between the point and ground
Small Signal CircuitReal Circuit
A)
No Small Signal circuitMOS is NOT in saturation
B)
Elementary Configuration for MOS resistance(PMOS circuits are identical)
∞
Input resistanceof CS Amp
Above configurations are for Small Signal. Typically one or both grounds are connected to bias voltage sources to ensure that MOS is in saturation!
Output resistance of CS Amp with Rs
)1()1(Rgr
RRgr
mo
mo
+≈++
Input resistance of CG Amp
ommom
o
rgR
grgRr
+≈++ 1
1
or Diode-connectedTransistorAlways in saturation!m
om g
rg
1||1≈
Gain, input and output resistances of MOS amplifiers can be found
usingthe fundamental amplifiers and
elementary R configurations
Discrete MOS Amplifiers(Analysis using the fundamental Amplifiers
and elementary R configurations)
Stable Bias circuits for discrete MOS amplifiers
Drain Feedback
Will Discuss later
Identical small-signal circuit if
21 || RRRG =
One power supply
DSGGS IRVV −=
Two power supplies
DSSSGS IRVV −=
We will do analysis for this configuration
Signal is typically coupled to discreteamplifiers via coupling capacitors
We assume that the small signals of interest are at sufficiently high frequencies, such that the (large) capacitors can be approximated as shorts.o A lower cut-off frequency for Amplifier
These capacitors can be added at input, output, and between amplifier stages.
These capacitor can also be used to “by-pass” resistors needed for bias but not for small-signal.
Discrete CS Amplifier
Real Circuit
Test book uses current source for biasing(not a practical discrete circuit)
Fundamental CS form
Derivation of small-signal circuit for Discrete CS Amplifier
Real Circuit
Short capsZero bias supplies
Rearrange
Discrete CS Amplifier
)||||( LDomv RRrgA −=
Fundamental CS form
Elementary R Configuration
Gi RR =
∞
Elementary R Configuration
Doo RrR ||=
or
Discrete CS Amplifier with RS
Real Circuit
Small Signal Circuit
Discrete CS Amplifier with RS
Fundamental CS form with RS
∞
Elementary R Configuration
Gi RR =
∞
Elementary R Configuration
DSmoo RRgrR ||)]1([ +=)1( smo Rgr +
oLDSm
LDmv rRRRg
RRgA/)||(1
)||(++
≈
Discrete CG Amplifier
Real Circuit
Small Signal Circuit
Discrete CG Amplifier
Fundamental CSGform
Doo RrR ||=
Elementary R Configuration
Elementary R Configuration
om
LD
mom
LDo
rgRR
grgRRr ||1
1||
+≈++
++
=om
LDoSi rg
RRrRR1
|| ||
)||||( LDomv RRrgA =
Discrete CD Amplifier (Source Follower)
Real Circuit
Small Signal Circuit
Discrete CD Amplifier (Source Follower)
Fundamental CD form
Gi RR =
Elementary R Configuration
∞
Elementary R Configuration
Sm
o Rg
R ||1=
mg/1
mg/1
)||||(1)||||(
LSom
LSomv RRrg
RRrgA+
=
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