Set 3: Fundamental Amplifier Configurations & Elementary R Forms
Transcript of Set 3: Fundamental Amplifier Configurations & Elementary R Forms
3. Fundamental amplifier configurations & Elementary R forms
Sedra & Smith Sec. 5.6
(S&S 5th Ed: Sec. 4.7)
ECE 102, Fall 2012, F. Najmabadi
Voltage Amplifier Model
F. Najmabadi, ECE102, Fall 2012 (2/23)
Input Resistance: Ri = vi/ii Voltage gain: Av = vo/vi with load Open-loop gain: Avo = vo/vi with no load Output resistance: Ro (resistance seen between output terminals with vi= 0 )
sigi
i
sig
i
RRR
vv
+=
oL
Lvov
i
o
RRRAA
vv
+⋅==
oL
Lvo
sigi
i
sig
o
RRRA
RRR
vv
+⋅⋅
+=
Fundamental MOS Amplifier Configurations
F. Najmabadi, ECE102, Fall 2012 (3/23)
We are considering only signal circuit here!
There are only FOUR single-transistor MOS Amplifier Configuration
Possible MOS amplifier configurations
F. Najmabadi, ECE102, Fall 2012 (4/23)
Same as Common Gate (vi does not change)
Common-Source Common-Gate Common-Drain
Common-Source with Rs Not Useful
PMOS configurations are the same as NMOS
F. Najmabadi, ECE102, Fall 2012 (5/23)
Common-Source Common-Gate Common-Drain
Since PMOS has the same signal model, configurations and results are exactly the same
Textbook includes RD in its analysis
F. Najmabadi, ECE102, Fall 2012 (6/23)
Small Signal Circuit for a Common Source Amplifier
Textbook is inconsistent. It includes RD for common source and common gate but does not include RS in common drain.
Note RD is parallel to RL.
To avoid confusion, I am using only one resistor, R’L, which is the equivalent of all resistors in the drain circuit (e.g., for the above circuit, R’L = R L || RD )
Textbook:
Lecture:
Common Source Configuration (Gain)
F. Najmabadi, ECE102, Fall 2012 (7/23)
Signal Circuit:
Small Signal Circuit with MOS SSM
omvo
Lomi
ov
Logsmo
rgA
RrgvvA
Rrvgv
−=
′−==
′−=
)||(
)||(
Relevant circuit for Gain calculation
By KCL
Common Source Configuration (Ri)
F. Najmabadi, ECE102, Fall 2012 (8/23)
0
∞==
=
i
ii
i
ivR
i
Small Signal Circuit with MOS SSM
Relevant circuit for Ri calculation
Common Source Configuration (Ro)
F. Najmabadi, ECE102, Fall 2012 (9/23)
oo rR = Current source becomes open circuit
Small Signal Circuit with MOS SSM
Relevant circuit for Ro calculation (set vi = 0)
Common Source with Source Resistor
F. Najmabadi, ECE102, Fall 2012 (10/23)
0 ∞==⇒=i
iii i
vRiInput Resistance
Signal Circuit:
Small Signal Circuit with MOS SSM
Common Source with Source Resistor (Gain*)
F. Najmabadi, ECE102, Fall 2012 (11/23) * Text book ignore ro
omvo
oLSm
Lmv
LSomo
Lom
i
ov
rgArRRg
RgA
RRrgrRrg
vvA
−=
′++′
−≈
′+++′
−==
/1
)1(
0)(
0)(
=−+−
+′
=−−−
+
−=
Simo
So
L
o
Simo
oS
S
S
Sigs
vvgr
vvRv
vvgr
vvRv
vvv
Node voltage method:
Node vS
Node vo
Relevant circuit for Gain calculation
Common Source with Source Resistor (Ro*)
F. Najmabadi, ECE102, Fall 2012 (12/23) * Text book ignore ro
)1( Somoo RrgrR ++=
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 vx and compute ix
Ro = vx /ix
Somo
x
S
Sx Rrgr
vRvi
)1( ++==
Somox
x
o Rrgrvi
R )1(11++
=≡
Common Gate Configuration
F. Najmabadi, ECE102, Fall 2012 (13/23)
Signal Circuit:
Small Signal Circuit with MOS SSM
Common Gate Configuration (Gain*)
F. Najmabadi, ECE102, Fall 2012 (14/23)
omvo
Lomv
Loo
om
i
ov
rgARrgA
Rrr
rgvvA
≈
′≈
′+==
)||(
)||(1
io
om
Lo
o
imo
io
L
o
igs
vr
rgRr
v
vgr
vvRv
vv
+=
′
=−+−
+′
−=
1||
0)(
Node voltage method:
Node vo
Common Gate Configuration (Ri and Ro*)
F. Najmabadi, ECE102, Fall 2012 (15/23)
om
L
mi
om
Lo
i
ii
rgR
gR
rgRr
ivR
′+≈
+′+
==
1
1
)()1(
)(
Loiomi
Liogsmii
RrirgvRirvgiv′+=+
′++=KVL:
* Text book ignore ro
oo rR =
Current source becomes open circuit
Output Resistance (set vi = 0)
Input Resistance
Common Drain Configuration (Source Follower)
F. Najmabadi, ECE102, Fall 2012 (16/23)
11
)||(1
)||(
≈+
=
′+′
=
om
omvo
Lom
Lomv
rgrgA
RrgRrgA
omLo
oim
oimo
o
L
o
oigs
vgRr
vvg
vvgrv
Rv
vvv
+′
=
=−−+′
−=
||
0)(
Node voltage method:
Node vo
Gain
Common Drain Configuration (Source Follower)
F. Najmabadi, ECE102, Fall 2012 (17/23)
m
x
o
xgsm
o
xx g
vrvvg
rvi
/1+=−=
Input Resistance
Output Resistance (set vi = 0)
1||1 m
om
o gr
gR ≈=
0=ii
∞==i
ii i
vR
MOS Fundamental Amplifier Configurations (PMOS circuits are identical)
F. Najmabadi, ECE102, Fall 2012 (18/23)
Common Source with RS oLSm
Lmv rRRg
RgA/1 ′++
′−=
Common Drain/Source Follower
)||(1)||(
Lom
Lomv Rrg
RrgA′+
′=
Common Source )||( Lomv RrgA ′−=
Common Gate )||( Lomv RrgA ′=
F. Najmabadi, ECE102, Fall 2012 (19/23)
Elementary R Forms
A Transistor can be configured to act as a resistor for small signals!
F. Najmabadi, ECE102, Fall 2012 (20/23)
oo rR =Set vi = 0, current source becomes open circuit
Ex: Output resistance of a CS Amplifier
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.
Notation: ro is the small-signal resistance between the point and ground
A Transistor can be configured to act as a resistor for small signals!
F. Najmabadi, ECE102, Fall 2012 (21/23)
But, MOS should be in saturation for small signal model to work! o Connection between MOS terminals are, therefore, made through ground for
signals. o In fact, one or two MOS terminals have to be connected to bias power supply
to ensure that MOS is in saturation (there is an exception, see next page)
Signal Circuit Real Circuit
A)
No Signal circuit MOS is NOT in saturation
B)
MOS Elementary R Forms (PMOS circuits are identical)
F. Najmabadi, ECE102, Fall 2012 (22/23)
∞
Input resistance of 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
Diode-connected Transistor Always in saturation! m
om g
rg
1||1≈
or
F. Najmabadi, ECE102, Fall 2012 (23/23)
Gain, input, and output resistances of MOS amplifiers can be found
using fundamental amplifiers configurations
and elementary R forms