6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 25-1
Lecture 25 - Frequency Response of
Amplifiers (III)
Other Amplifier Stages
December 8, 2005
Contents:
1. Frequency response of common-drain amplifier
2. Cascode amplifier
Reading assignment:
Howe and Sodini, Ch. 9, §9.3.3; Ch. 10, §§10.5, 10.7
Announcement:
Final exam: December 19, 1:30-4:30 PM, duPont; open
book, calculator required; entire subject under examination but emphasis on lectures #19-26.
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 25-2
Key questions
• Do all amplifier stages suffer from the Miller effect?
• Is there something unique about the common drain
stage in terms of frequency response?
• Can we make a transconductance amplifier with a
large bandwidth?
Lecture 25-3
6.012 - Microelectronic Devices and Circuits - Fall 2005
1. Frequency response of common-drain amplifier
VDD
signal source
RS
+
vs
iSUP
VGG
VSS
Features:
• voltage gain 1
• high input resistance
• low output resistance
• ⇒ good voltage buffer
vOUT
signal
load
RL
Lecture 25-4
6.012 - Microelectronic Devices and Circuits - Fall 2005
High-frequency small-signal model:
Cgd
G
D
+
vgs
S
RS
gmbvbs
gmvgs
ro
-
vbs
+
vs
-
Cgs
Cdb
Csb
+
+
B
roc
RL
vout
-
vbs=0
Cgs
+ vgs -
RS
+
vs
-
+
gmvgs
Cgd
Cdb
ro//roc//RL=RL' vout
-
Av,LF
gmRL
=
≤1
1 + gmRL
Lecture 25-5
6.012 - Microelectronic Devices and Circuits - Fall 2005
Compute bandwidth by open-circuit time constant technique:
1. shut-off all independent sources,
2. compute Thevenin resistance RT i seen by each Ci with
all other C’s open,
3. compute open-circuit time constant for Ci as
τi = RT iCi
4. conservative estimate of bandwidth:
ωH 1
Στi
2 First, short vs:
Cgs
+ vgs -
RS
Cgd
+
gmvgs
Cdb
RL'
vout
-
Lecture 25-6
6.012 - Microelectronic Devices and Circuits - Fall 2005
2 Time constant associated with Cgs:
1
v
it + t -
2
+
+ vgs -
gmvgs
RS
RL'
vout
-
node 1:
it −
vt + vout
=0
RS
node 2:
vout
gm vgs − it − = 0
RL
also
vgs = vt
Solve for vout in 1 and plug into 2:
Lecture 25-7
6.012 - Microelectronic Devices and Circuits - Fall 2005
vt
RS + RL
= =
it 1 + gm R
L
RT gs
Time constant:
RS + RL
τgs = Cgs
1 + gm R
L
2 Time constant associated with Cgd :
+ vgs +
it
RS
+
vt
-
gmvgs
RL'
vout
-
RT gd = RS
τgd = Cgd RS
Lecture 25-8
6.012 - Microelectronic Devices and Circuits - Fall 2005
2 Time constant associated with Cdb :
+ vgs -
it
gmvgs
RS
RL'
it
gm
RT db
RL'
+
vt
-
1
R
L
= //R
L
=
gm
1 + gmRL
RL
τdb = Cdb
1 + gmRL
Notice:
RT db = Rout //RL
+
vt
-
Lecture 25-9
6.012 - Microelectronic Devices and Circuits - Fall 2005
2 Bandwidth:
1
1
ωH =
τgs + τgd + τdb Cgs RS +RL + Cgd RS + Cdb RL 1+gm R
1+gmR
L
L
2 If back is not connected to source:
VDD
signal source
RS
VSS
+
vs
iSUP
vOUT
-
VGG
VSS
signal
load
RL
Lecture 25-10
6.012 - Microelectronic Devices and Circuits - Fall 2005
Small-signal equivalent circuit:
Cgd
G
D
+
vgs
RS
Cgs
gmvgs
gmbvbs
ro
-
S
+
vs
-
vbs
Cdb
+
roc
Csb
RL
vout
-
+
B
Cgs
+ vgs -
RS
+
vs
-
gmvgs
Cgd
+
-
gmbvbs
vbs
Csb
ro//roc//RL=RL' vout
+
-
Cgs
+
vs
-
+
+ vgs -
RS
Cgd
gmvgs
Csb
RL'//(1/gmb)=RL'' vout
-
Av,LF =
gm RL”
1 + gm RL”
Lecture 25-11
6.012 - Microelectronic Devices and Circuits - Fall 2005
Csb shows up at same location as Cdb before, then bandwidth is:
ωH 1
RS +RL”
RL ”
Cgs 1+g
+
C
R
+
C
gd
S
sb
1+gm RL”
m RL ”
Simplify:
• CD amp is about driving low RL from high RS ⇒
RS RL”, and
ωH 1
RS ( 1+gCmgsRL” + Cgd ) + Csb 1+gRmLR” L”
• CD stage operates as voltage buffer with Av,LF 1 ⇒ gm RL” 1, and
ωH 1
Cgd RS + Cgmsb
Since Cgd and 1/gm are small, if RS is not too high, ωH
can be rather high (approach ωT ).
Lecture 25-12
6.012 - Microelectronic Devices and Circuits - Fall 2005
2 What happened to the Miller effect in CD amp?
1
ωH RS ( 1+gCmgsRL” + Cgd ) + Csb 1+gRmLR” L”
Miller analysis of Cgs:
Cgs
gm RL”
1
) = Cgs
= Cgs(1−Av ) = Cgs(1−
1 + gmRL”
1 + gm RL”
agrees with above result.
Note, since Av → 1, Cgs
→ 0.
See in circuit:
iin
+
C
vin
-
+
+
-
Avvin
vout
-
CM = C(1 − Av )
bootstrapping
if Av 1 ⇒ CM 0: bootstrapping
Lecture 25-13
6.012 - Microelectronic Devices and Circuits - Fall 2005
2. Cascode amplifier
Common-source stage: excellent transconductance am
plifier, but bandwidth hurt by Miller effect.
What’s a circuit designer to do?
Consider CS-CG stage:
VDD
VDD
iSUP2
iSUP1
signal source
iOUT
RS
vOUT1
VG2
VSS
vs
signal
load
RL
iOUT1
VG1
IBIAS
VSS
VSS
How does this address the problem?
• Rin2 very small ⇒ iOU T 1 can change a lot with vOU T 1
changing little ⇒ small voltage gain in CS stage ⇒
no Miller effect ⇒ high bandwidth
• CG stage also has high bandwidth
Lecture 25-14
6.012 - Microelectronic Devices and Circuits - Fall 2005
Before analyzing CS-CG amp, notice that if we make
iSU P 1 = iSU P 2 = iSU P , amplifier drastically simplified:
VDD
VDD
iSUP
iSUP
signal source
iOUT
RS
VG2
vOUT1
VSS
vs
iOUT1
VG1
IBIAS
VSS
VSS
VDD
iSUP
iOUT
VG2
signal
source
VSS
RS
vs
VG1
VSS
signal
load
RL
signal
load
RL
Lecture 25-15
6.012 - Microelectronic Devices and Circuits - Fall 2005
VDD
iSUP
iOUT
VG2
signal
source
signal
load
VSS
RL
RS
vs
VG1
VSS
Small-signal equivalent circuit model:
(gm2+gmb2)vgs2
Cgd1
RS
+
+
vgs1
vs
-
Cgs1
gm1vgs1
Cdb1
ro1 vgs2
ro2
Cgs2+Csb2
Cgd2+Cdb2
roc//RL=RL'
-
+
Time constants associated with Cgs1 and Cgd2 +Cdb2 have
not changed.
Time constant associated with Cdb1 + Cgs2 + Csb2 small
(looking into Rin2 1/gm ).
Lecture 25-16
6.012 - Microelectronic Devices and Circuits - Fall 2005
Focus on time constant associated with Cgd1 :
+
+
RS
vgs1
vt
-
it
gm1vgs1
gm2+gmb2
-
From Lecture 24:
τgd1
1
gm1
=[
+ RS (1 +
)]Cgd1
gm2 + gmb2
gm2 + gmb2
If transistors identical (gm1 = gm2 ):
τgd1 2RS Cgd1
Much smaller than in single stage CS tansconductance
amp:
τgd = [Rout
+ RS (1 + gm Rout
)]Cgd
Cascode:
Casco
de: excellent transconductance amplifier with high
bandwidth.
6.012 - Microelectronic Devices and Circuits - Fall 2005
Lecture 25-17
Key conclusions
• Common-drain amplifier:
– Voltage gain 1, Miller effect nearly completely
eliminates impact of Cgs (bootstrapping)
– if RS is not too high, CD amp has high bandwidth
• Cascode amplifier:
– effective sharing of current source
– Miller effect minimized by reducing voltage gain of
CS stage as a result of low input impedance of CG
stage
– transconductance amplifier with high bandwidth