6. Discrete MOS Amplifiers
Reading: Sedra & Smith Sec. 5.8
(S&S 5th Ed: Sec. 4.7)
ECE 102, Fall 2011, F. Najmabadi
In this set, we discuss how to use
MOS Fundamental Amplifier Configurations
and Elementary R Forms
to find the response of discrete MOS amplifiers
(First, a few observations)
Stable Bias circuits for discrete MOS amplifiers
One power supply
VGS = VG − RS I D
Two power supplies
Drain Feedback
VGS = VSS − RS I D
Will Discuss later
Identical small-signal circuit if
RG = R1 || R2
We will do analysis
for this configuration
Signal is typically coupled to discrete amplifiers
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.
 Note: In general, one should NOT assume
that all capacitors are short. We will see
the impact of various capacitors later when
we discuss frequency response of amplifiers
(until then, we assume all caps. are short)
Real Circuit
Test book uses current source for biasing
(not a practical discrete circuit)
The analysis method introduced here,
however, apply to any discrete bias case.
The best way to identify the type of amplifier
is to follow the signal
Common Source
Common Gate
Input at the GATE
Output at the DRAIN
Input at the SOURCE
Output at the DRAIN
Common Source with RS
Common Drain/Source Follower
Input at the GATE
Output at the DRAIN
Input at the GATE
Output at the SOURCE
Analysis Steps
Note: We should solve the complete circuit (i.e., include vsig,
Rsig , RL in our analysis).
 Compute Bias point.
o All capacitors are open circuits
o Compute gm and ro
 Draw signal circuit (with MOS intact).
o Low-frequency Caps are short, high-frequency Caps are open
(discussed later)
 Indentify fundamental amplifier configuration and compute
proper amplifier gain (vo/vi) and the circuit gain (vo/vsig)
 Use elementary R forms to find Ri and Ro
o In general Ri will depend on RL and Ro depends on Rsig
Discrete Common-source Amplifier
 This is a common-source amplifier (input at the gate and output at
the drain).
 Bias calculations are NOT done here as we have done that before.
vi
Ri
=
 Note
(this is true for ALL circuits)
v sig R i + R sig
Derivation of small-signal circuit
for Discrete CS Amplifier
Real Circuit
Rearrange
Short caps
Zero bias supplies
Discrete CS Amplifier (Gain)
 Signal input at the gate
 Signal output at the drain
 No RS
RL′ = RD || RL
Fundamental CS form
vo
= − g m (ro || RD || RL )
vi
vo
Ri
vo
=
×
vsig R i + R sig vi
Discrete CS Amplifier (Ri)
 Replace transistor with its equivalent resistance
 Looking into the gate
R =∞
R
Elementary R Configuration
R =∞
Ri = RG
Discrete CS Amplifier (Ro)




Set vsig = 0
Replace transistor with its equivalent resistance
Since ig = 0, Rsig and RG can be removed (vg = 0)
Looking into the drain
R
R = ro
Elementary R Configuration
R = ro
Ro = RD || ro
Discrete CS Amplifier with RS
Real Circuit
Small Signal Circuit
Short caps
Zero bias supplies
Discrete CS Amplifier with RS (Gain)
 Signal input at the gate
 Signal output at the drain
 RS !
RL′ = RD || RL
Fundamental CS form with RS
vo
g m ( RD || RL )
=−
vi
1 + g m R S + ( RD || RL ) / ro
vo
Ri
v
=
× o
vsig R i + R sig vi
Discrete CS Amplifier with RS (Ri)
 Replace transistor with its equivalent resistance
 Looking into the gate
R =∞
R
Elementary R Configuration
R =∞
Ri = RG
Discrete CS Amplifier with RS (Ro)




Set vsig = 0
Replace transistor with its equivalent resistance
Since ig = 0, Rsig and RG can be removed (vg = 0)
Looking into the drain
R
R = ro (1 +g m RS ) + RS
= RS
Elementary R Configuration
R
R = ro (1 +g m RS ) + RS
Ro = RD || [ro (1 +g m RS ) + RS ]
Discrete CG Amplifier
Real Circuit
Small Signal Circuit
Short caps
Zero bias supplies
Discrete CG Amplifier (Gain)
 Signal input at the source
 Signal output at the drain
RL′ = RD || RL
Fundamental CG form
vo
= + g m (ro || RD || RL )
vi
vo
Ri
vo
=
×
vsig R i + R sig vi
Discrete CG Amplifier (Ri)
 Replace transistor with its equivalent resistance
 Looking into the source
= RD || RL
R=
R
r + ( RD || RL )
R= o
1 + g m ro
ro + ( RD || RL )
1 + g m ro
Elementary R Configuration
 ro + ( RD || RL ) 
Ri = RS || 

+
1
g
r
m o


Discrete CG Amplifier (Ro)
 Set vsig = 0
 Replace transistor with its equivalent resistance
 Looking into the drain
R = ro [1 +g m ( RS || Rsig )] + RS || Rsig
R
= RS || Rsig
Elementary R Configuration
R
ro [1 +g m ( RS || Rsig )] + RS || Rsig
Ro = RD || {ro [1 +g m ( RS || Rsig )] + RS || Rsig }
Discrete CD Amplifier (Source Follower)
Real Circuit
Small Signal Circuit
Short caps
Zero bias supplies
Discrete CD Amplifier (Gain)
 Signal input at the gate
 Signal output at the source
RL′ = RS || RL
Fundamental CS form
vo
g m (ro || RS || RL )
=
vi 1 + g m (ro || RS || RL )
vo
Ri
vo
=
×
vsig R i + R sig vi
Discrete CD Amplifier (Ri)
 Replace transistor with its equivalent resistance
 Looking into the gate
R =∞
R
Elementary R Configuration
R =∞
Ri = RG
Discrete CD Amplifier (Ro)




Set vsig = 0
Replace transistor with its equivalent resistance
Since ig = 0, Rsig and RG can be removed (vg = 0)
Looking into the source
R
1
1
|| ro ≈
gm
gm
Elementary R Configuration
R
Ro = RS ||
1
gm