5. Fundamental amplifier forms &
Elementary R configurations
Reading: Sedra & Smith Sec. 5.6
(S&S 5th Ed: Sec. 4.7)
ECE 102, Fall 2011, F. Najmabadi
Fundamental MOS Amplifier Forms
We are considering only signal circuit here!
Voltage Amplifier Model
Input Resistance:
Voltage gain:
Open-loop gain:
Output resistance:
Ri = vi/ii
Av = vo/vi with load
Avo = vo/vi with no load
Ro (resistance seen between
output terminals with vi= 0 )
vi
Ri
=
vsig Ri + Rsig
vo
RL
= Av = Avo ⋅
vin
RL + Ro
vo
Ri
RL
=
⋅ Avo ⋅
vsig Ri + Rsig
RL + Ro
Possible MOS amplifier configurations
Common-Source
Common-Gate
Common-Source with Rs
Same as Common Gate
(vi does not change)
Common-Drain
Not Useful
PMOS configurations are the same as NMOS
Common-Source
Common-Gate
Common-Drain
Since PMOS has the same signal model, configurations and results are exactly the same
Textbook includes RD in the fundamental
configurations
Small Signal Circuit for a Common Source Amplifier
Textbook:
 Textbook is inconsistent. It
includes RD for common source
and common gate but does not
include RS in common drain.
Lecture:
 Note RD is parallel to RL.
 To avoid confusion, I am using
only one resistor, R’L.
Common Source Configuration (Gain)
Signal Circuit:
vo = − g m v gs (ro || RL′ )
Av =
vo
= − g m (ro || RL′ )
vin
Avo = − g m ro
Small Signal Circuit
with MOS SSM
Relevant circuit for
Gain calculation
By KCL
Common Source Configuration (Ri)
Small Signal Circuit
with MOS SSM
Relevant circuit for
Ri calculation
ii = 0
Ri =
vi
=∞
ii
Common Source Configuration (Ro)
Small Signal Circuit
with MOS SSM
Relevant circuit for
Ro calculation (set vi = 0)
Current source becomes open circuit
Ro = ro
Common Source with Source Resistor
Small Signal Circuit:
Small Signal Circuit
with MOS SSM
Input Resistance
ii = 0 ⇒ Ri =
vi
=∞
ii
Common Source with Source Resistor (Gain*)
Relevant circuit for
Gain calculation
Node voltage method:
v gs = vi − vS
Node vS
vS vS − vo
+
− g m (vi − vS ) = 0
RS
ro
Node vo
vo vo − vS
+
+ g m (vi − vS ) = 0
RL′
ro
* Text book ignore ro
vo
g m ro RL′
=−
vi
ro + (1 + g m ro ) R S + RL′
g m RL′
Av ≈ −
1 + g m R S + RL′ / ro
Av =
Avo = − g m ro
Common Source with Source Resistor (Ro*)
 set vi = 0
 Attach vx and compute ix
 Ro = vx /ix
Node voltage method:
v gs = −vS
Node vS
vS vS − v x
+
− g m ( −vS ) = 0
RS
ro
vS
vx
=
RS
ro + (1 + g m ro ) RS
ix =
vS
vx
=
RS ro + (1 + g m ro ) RS
* Text book ignore ro
i
1
1
≡ x =
Ro v x ro + (1 + g m ro ) RS
Ro = ro + (1 + g m ro ) RS
Common Gate Configuration
Small Signal Circuit:
Small Signal Circuit
with MOS SSM
Common Gate Configuration (Gain*)
Node voltage method:
v gs = −vi
Node vo
vo vo − vi
+
+ g m (−vi ) = 0
′
RL
ro
vo
1 + g m ro
vi
=
ro || RL′
ro
vo 1 + g m ro
=
(ro || RL′ )
vi
ro
Av ≈ g m (ro || RL′ )
Av =
Avo ≈ g m ro
Common Gate Configuration (Ri and Ro*)
Input Resistance
KVL: vi = (ii +g m v gs )ro + ii RL′
vi (1 + g m ro ) = ii (ro + RL′ )
vi ro + RL′
Ri = =
ii 1 + g m ro
1
R′
+ L
Ri ≈
g m g m ro
Output Resistance (set vi = 0)
Current source becomes open circuit
Ro = ro
* Text book ignore ro
Common Drain Configuration (Source Follower)
Gain
Node voltage method:
v gs = vi − vo
Node vo
vo vo
+ − g m (vi − vo ) = 0
RL′ ro
g m vi =
vo
+ g m vo
′
ro || RL
g m (ro || RL′ )
Av =
1 + g m (ro || RL′ )
Avo =
g m ro
≈1
1 + g m ro
Common Drain Configuration (Source Follower)
Input Resistance
ii = 0
Ri =
vi
=∞
ii
Output Resistance (set vi = 0)
ix =
vx
v
v
− g m v gs = x + x
ro
ro 1 / g m
Ro =
1
1
|| ro ≈
gm
gm
MOS Amplifier Fundamental Configurations
(PMOS circuits are identical)
Common Source
Common Gate
Av = − g m (ro || RL′ )
Av = g m (ro || RL′ )
Common Source with RS
Common Drain/Source Follower
g m RL′
Av = −
1 + g m R S + RL′ / ro
Av =
g m (ro || RL′ )
1 + g m (ro || RL′ )
Elementary R Configurations
Transistor can be configured to act as a resistor
for small signals!
Ex: Output resistance of a CS Amplifier
ro
Set vi = 0, current source becomes open circuit
Ro = ro
Notation:
ro is the small-signal resistance
between the point and ground
 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
Real Circuit
Small Signal Circuit
A)
B)
No Small Signal circuit
MOS is NOT in saturation
Elementary Configurations for MOS resistance
(PMOS circuits are identical)
ro (1 +g m R ) + R
∞
≈ ro (1 +g m R )
ro +R
1
R
≈
+
1 + g m ro g m
g m ro
Output resistance
of CS Amp with Rs
ro
Input resistance
of CG Amp
1
1
|| ro ≈
gm
gm
Input resistance
of CS Amp
Diode-connected
Transistor
Always in saturation!
Above configurations are for Small Signal. Typically one or both grounds
are connected to bias voltage sources to ensure that MOS is in saturation!
Gain, input, and output resistances of
MOS amplifiers can be found
using
the fundamental amplifiers and
elementary R configurations