7. Fundamental Transistor Amplifier
Configurations
Lecture notes: Sec. 5
Sedra & Smith (6th Ed): Sec. 5.4, 5.6 & 6.3-6.4
Sedra & Smith (5th Ed): Sec. 4.4, 4.6 & 5.3-5.4
ECE 65, Winter2013, F. Najmabadi
Issues in developing a transistor amplifier:
1. Find the iv characteristics of the elements for the signal (which
can be different than their characteristics equation for bias).
o This will lead to different circuit configurations for bias versus signal
2. Compute circuit response to the signal
o Focus on fundamental transistor amplifier configurations
3. How to establish a Bias point (bias is the state of the system
when there is no signal).
o Stable and robust bias point should be resilient to variations in
µnCox (W/L),Vt (or β for BJT) due to temperature and/or
manufacturing variability.
o Bias point details impact small signal response (e.g., gain of the
amplifier).
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (2/26)
What are amplifier parameters?
Voltage Gain of the Circuit : A =
vo
vsig
Voltage Gain of the Amplifier : Av =
Open - loop Gain : Avo =
Input Resistance : Ri =
vo
vi
vo
vi
RL → ∞
vi
ii
Output Resistance of Amplifier : Ro = −
vo
io
v →0
sig
Output resistance is the Thevenin
resistance between the output terminals!
 In general Ri depends on RL and Ro depends on Rsig
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (3/26)
Observations on the amplifier parameters
Overall Gain :
v
v v
Ri
A= o = i × o =
Av
vsig vsig vi Ri + Rsig
vi
Ri
=
vsig Ri + Rsig
 Value of Ri is important.
o For Ri >> Ri , vi ≈ vsig
o For Ri = Rsig , vi = 0.5 vsig
o For Ri << Rsig , vi ≈ 0
 Prefer “large” Ri
Av =
vo
RL
=
Avo
vi RL + Ro
 Avo is the maximum possible gain
of the amplifier.
 Value of Ro is important.
o For Ro << RL , Av ≈ Avo
o For Ro = RL , Av = 0.5 Avo
o For Ro >> RL , Av ≈ 0
 Prefer “small” Ro
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (4/26)
Some observation on
single-transistor amplifiers
1. As we will discuss, there are many ways to bias a transistor. Thus,
there are many practical single-transistor amplifier circuits.
o Fortunately, signal circuits always reduce to one of four
fundamental configuration .
2. We compute the voltage gain and input resistance of these four
fundamental configurations in the presence of an arbitrary load
RL. Then: Overall Gain :
Open - loop Gain :
A=
vo
v v
Ri
= i × o=
Av
vsig vsig vi Ri + Rsig
Avo = Av |RL → ∞
3. Ro is calculated in a real circuit (with Rsig & vsig) once load is
clearly identified.
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (5/26)
Fundamental Transistor Amplifier
Configurations
We are considering only signal circuit here!
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (6/26)
Possible BJT amplifier configurations
Common-Emitter
Common-Emitter with RE
Common-Base
Same as Common Base
(vi does not change)
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (7/26)
Common-Collector
Not Useful
PNP configurations are the same as those of NPN
(because of similar small-signal model)
Common-Emitter
Common-Base
Common-Collector
Common-Emitter
Common-Base
Common-Collector
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (8/26)
MOS fundamental configurations are analogous to BJTs
Common-Emitter
Common-Base
Common-Collector
Common-Source
Common-Gate
Common-Drain
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (9/26)
Common Emitter Configuration
Signal Circuit:
Signal Circuit with BJT SSM:
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (10/26)
o
o
ro and R’L are in parallel
vπ = v i
Common Emitter Configuration (Av & Ri)
By KCL
ii =
vi
v
⇒ Ri = i = rπ
rπ
ii
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (11/26)
vo = − g m vi (ro || RL′ )
Av =
vo
= − g m (ro || RL′ )
vi
Common Source Configuration
Signal Circuit:
Signal Circuit with MOS SSM:
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (12/26)
o
o
ro and R’L are in parallel
vgs = vi
Common Source Configuration (Av & Ri)
By KCL
ii = 0 ⇒ Ri =
vi
=∞
ii
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (13/26)
vo = − g m vi (ro || RL′ )
Av =
vo
= − g m (ro || RL′ )
vi
Common Source & Common Emitter
Configurations are “similar”
Signal Circuit
Signal Circuit with
transistor SSM
Av =
vo
= − g m (ro || RL′ )
vi
Ri = rπ
Similar formula if
we let rπ → ∞
Av =
vo
= − g m (ro || RL′ )
vi
Ri = ∞
Note that Av & Ri are independent of vsig & Rsig
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (14/26)
Common Emitter Configuration with RE
Signal Circuit:
Signal Circuit with BJT SSM:
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (15/26)
Common Emitter Configuration with RE (Av & Ri)
Node voltage method:
vπ = vi − ve
Node ve
ve ve − vi ve − vo
+
+
− g m (vi − ve ) = 0
RE
rπ
ro
Node vo
vo vo − ve
+
+ g m (vi − ve ) = 0
RL′
ro
Av =
vo
g m RL′
≈−
vi
1 + g m R E +( RL′ / ro )(1 + RE / rπ )
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (16/26)
1. Add the two node equations to get
ve in terms of vo and vi
2. Substitute for ve in Node vo
equation to find vo and gain
3. Compute ii in terms of node
voltages. Then Ri = vi/ii
4. Lengthy calculations (See Notes).
Ri ≈ rπ +
g m rπ RE
1 + ( RL′ / ro )(1 + RE / rπ )
Common Source Configuration with RS (Av & Ri)
Signal Circuit
Av =
vo
g m RL′
≈−
1 + g m R E +( RL′ / ro )(1 + RE / rπ )
vi
Ri ≈ rπ +
Av =
g m rπ RE
1 + ( RL′ / ro )(1 + RE / rπ )
Ri = ∞
Let
rπ → ∞
RE → RS
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (17/26)
vo
g m RL′
≈−
vi
1 + g m R S + ( RL′ / ro )
Common Base Configuration (Gain)
Signal Circuit:
Node voltage method:
vπ = −vi
Node vo
Signal Circuit with BJT SSM:
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 =
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (18/26)
Common Base Configuration (Ri)
Define Rx =
KCL:
ii =
vi
v v
vi
+ ix = i + i =
rπ Rx rπ || Rx
rπ
Ri =
By KCL
vi
ix
vi
= rπ || Rx
ii
KVL: vi = (ix +g m vπ )ro + ix RL′
vπ = −vi
vi (1 + g m ro ) = ix (ro + RL′ )
Rx =
vi
r + R′
= o
ix 1 + g m ro
Ri = rπ || Rx = rπ ||
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (19/26)
ro + RL′
1 + g m ro
Common Gate Configuration (Av & Ri)
Signal Circuit
vo
≈ g m (ro || RL′ )
vi
r + RL′
Ri = rπ || o
1 + g m ro
vo
≈ g m (ro || RL′ )
vi
r + RL′
Ri = o
1 + g m ro
Av =
Av =
Let rπ → ∞
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (20/26)
Common Collector Configuration
(Emitter Follower)
Signal Circuit:
Node voltage method:
vπ = vi − vo
Node vo
vo vo − vi vo
+
+ − g m (vi − vo ) = 0
RL′
rπ
ro


vo
1 
1 
vo = g m 1 +
vi ≈ g m vi
+ 1 +
ro || RL′  g m rπ 
 g m rπ 
g m rπ = β >> 1
Signal Circuit with BJT SSM:
Av =
ii =
vo
g m (ro || RL′ )
=
vi 1 + g m (ro || RL′ )
vi − vo vi
= × (1 − Av )
rπ
rπ
Ri =
vi
r
= π
ii 1 − Av
Ri = rπ + g m rπ (ro || RL′ ) = rπ + β (ro || RL′ )
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (21/26)
Common Drain Configuration (Source Follower)
Signal Circuit
v
g (r || R′ )
Av = o = m o L
vi 1 + g m (ro || RL′ )
Ri = g m rπ (ro || RL′ ) = β (ro || RL′ )
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (22/26)
Let rπ → ∞
vo
g m (ro || RL′ )
Av = =
vi 1 + g m (ro || RL′ )
Ri = ∞
BJT Basic Amplifier Configurations
(PNP circuits are identical)
Common Emitter
Common Base
Av = − g m (ro || RL′ ), Ri = rπ
ro + RL′
Av = g m (ro || RL′ ), Ri = rπ ||
1 + g m ro
Common Emitter with RE
Av ≈ −
g m RL′
1 + g m R E +( RL′ / ro )(1 + RE / rπ )
Ri ≈ rπ +
g m rπ RE
1 + ( RL′ / ro )(1 + RE / rπ )
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (23/26)
Common Collector/
Emitter Follower
g m (ro || RL′ )
Av =
1 + g m (ro || RL′ )
Ri = rπ + β (ro || RL′ )
MOS Basic Amplifier Configurations
(PMOS circuits are identical)
Common Source
Av = − g m (ro || RL′ ), Ri = ∞
Common Source with RS
g m RL′
Av = −
, Ri = ∞
1 + g m R S + RL′ / ro
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (24/26)
Common Gate
ro + RL′
Av = g m (ro || RL′ ), Ri =
1 + g m ro
Common Drain/Source Follower
g m (ro || RL′ )
Av =
, Ri = ∞
1 + g m (ro || RL′ )
Observations of Transistor Amplifiers (1)
 Common-Emitter has a high gain of Av = − g m (ro || RL′ ) and a
“medium” Ri = rπ (several k).
o Minus sign in the gain reflects a 180o phase shift in the output.
 Common-Base also has a high gain of Av ≈ g m (ro || RL′ ) but a “low”
Ri (several hundred Ω) which significantly affects the overall
circuit gain.
 Common-Source has a high gain of Av = − g m (ro || RL′ ) (but lower
than the BJT analog, CE amplifier). It has an infinite Ri.
 Common-Gate also has a high gain of Av ≈ g m (ro || RL′ ) but a “low”
Ri (several hundred Ω).
CE and CS configurations are the main gain cells in ICs.
CB and CG configurations have superior high-frequency response
(discussed in ECE102).
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (25/26)
Observations of Transistor Amplifiers (2)
 Common-Emitter with RE has a much lower gain compared to a
CE amplifier (i.e., no RE ) but has a much larger Ri .
o Amplifier gain is also much less sensitive to BJT parameters
(i.e., β).
o It is used primarily in discrete circuits because it does not need
a by-pass capacitor (will be discussed later).
 Common-Source with RS has a much lower gain compared to a CS
amplifier (i.e., no RS ). It has an infinite Ri .
 Common-Collector (emitter follower) and Common-Drain (source
follower) configurations have a gain ≤ 1 . They have a large Ri
(infinite for CD) and a low Ro (as we will see later). They are
usually configured to get a gain close to 1 and used either as a
“buffer” or as a “current amplifier” to drive a load.
F. Najmabadi, ECE65, Winter 2013, Fundamental Amp Configuration (26/26)
*Buffers are discussed later in the context
of multi-stage amplifiers