lecture 24 - frequency resp onse of amplifiers (i i) · lecture 24 - frequency resp onse of...
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-1
Lecture 24 - Frequency Resp onse of Amplifiers (I I)
Other Amplifier Stages
May 8, 2003
Contents:
1. Frequency resp onse of common-drain amplifier
2. Frequency resp onse of common-gate amplifier
Reading assignment:
Howe and So dini, Ch. 10, §§10.5-10.6
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-2
Key questions
• Do all amplifier stages suffer from the Miller effect?
• Is there something unique ab out the common-gate and common drain stages in terms of frequency resp onse?
• ⇒
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-3
1. Frequency resp onse of common-drain amplifier
VDD
signal source
vs
VGG
RS
vOUT iSUP
+
-
signal� load
RL
VSS
Features:
• voltage gain 1
• high input resistance
• low output resistance
go o d voltage buffer
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-4
High-frequency small-signal mo del:
G Cgd D
RS
+ vs -
B
S
+
-
vgs
+
-
vbs
+
-
vout
gmvgs ro
RL roc
Cgs
Csb
gmbvbs
Cdb
vbs=0
Cgs
+ RS
+
+ -vgs
gmvgs Cgd Cdb ro//roc//RL=RL' vout
vs --
g R m L A = ≤ 1 v,LF 1 + g R m L
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-5
Compute bandwidth by op en-circuit time constant technique:
1. shut-off all indep endent sources,
2. compute Thevenin resistance R seen by each C with Ti i
all other C ’s op en,
3. compute op en-circuit time constant for C as i
τ = R C i Ti i
4. conservative estimate of bandwidth:
1 ω H
Στ i
First, short v : s
Cgs
+
RS
+ -vgs
gmvgs Cgd Cdb RL' vout
-
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-6
Time constant asso ciated with C : gs
+ -vgs
gmvgs
1 2it + vt
+
RS RL' vout
-
no de 1:
v + v t out i − = 0 t
R S
no de 2:
v out g v − i − = 0 m gs t
R L
also
v = v gs t
Solve for v in 1 and plug into 2: out
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-7
v R + R t S LR = = Tgs i 1 + g R t m L
Time constant:
R + R S L τ = C gs gs 1 + g R m L
Time constant asso ciated with C : gd
-+ vgs
+
RS gmvgs +
-vt
it
RL' vout
-
R = R Tgd S
τ = C R gd gd S
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-8
Time constant asso ciated with C : db
-+ vgs it +
RS vt -
gmvgs RL'
it +
gm RL' vt -
1 R L R = //R = Tdb L g 1 + g R m m L
R L τ = C db db 1 + g R m L
Notice:
R = R //R Tdb out L
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-9
Bandwidth:
1 1 ωH
τgs + τdb =
Cgs R S +RL RL+ τgd
L+ Cgd RS + Cdb 1+g m R 1+g m RL
If back is not connected to source:
VDD
signal source
vs
VGG
RS
vOUT
VSS
iSUP
+
-
signal� load
RL
VSS
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-10
Small-signal equivalent circuit:
G Cgd D
RS
+ vs
-
S
+
-
vgs
+
-
vbs
gmvgs ro
+
-
vout roc
Cgs
Csb
gmbvbs
Cdb
RL
B
Cgs
+ RS
+
+ -vgs
+
-
vbs gmvgs gmbvbs Cgd Csb ro//roc//RL=RL' vout
vs --
Cgs
+ RS
+
+ -vgs
gmvgs Cgd Csb RL'//(1/gmb)=RL'' vout
vs --
g R ” m L A = v,LF
1 + g R ” m L
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-11
C shows up at same lo cation as C b efore, then bandsb db
width is:
1ωH
Cgs R +R R S L L + C R + C gd S sb R R L L
” ”1+g m ” 1+g m ”
Simplify:
• CD amp is ab out driving low R L from high R S ⇒RS RL ”, and
1ωH
RS C gs
1+g R L ”( + C ) + C gd sb R L ” ”m R L 1+g m
• CD stage op erates as voltage buffer with A v,LF
1 ⇒ g m RL ” 1, and
ω1
H C sb g m
Cgd RS +
Since C gd and 1/g m are small, if R S is not to o high, ω H
can b e rather high (approach ω T ).
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-12
What happ ened to the Miller effect in CD amp?
1ω H C R ” gs L R ( + C ) + C S gd sb 1+g R ” 1+g R ” m m L L
Miller analysis of C : gs
g R ” 1 m L = C (1−A ) = C (1− ) = C gs v gs gs gs 1 + g R ” 1 + g R ” m L m L
agrees with ab ove result.
Note, since A → 1, C → 0. v gs
See in circuit:
iin C
+
vin
+ +
- -Avvin vout
-
C = C (1 − A ) M v
if A 1 ⇒ C 0: bootstrapping v M
C
• ⇒
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-13
2. Frequency resp onse of common-gate amplifier
VDD
is
iOUT
VSS
iSUP
IBIAS
signal source
RS
signal� load
RL
VSS
Features:
• current gain 1
• low input resistance
• high output resistance
go o d current buffer
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-14
Small-signal equivalent circuit mo del:
G
S
D +
-
vgs
+
-
vbs
gmvgs ro
roc
Cgs
Csb
gmbvbs
Cdb
is RS
Cgd iout
RL
B
vgs=vbs
(gm+gmb)vgs
is
+
-
vgs
ro
Cgs+Csb Cgd+Cdb RS roc//RL=RL'
Frequency analysis: first, op en i : s
(gm+gmb)vgs
RS
+
-
vgs
ro
C1=Cgs+Csb C2=Cgd+Cdb
RL'
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-15
Time constant asso ciated with C : 1�
(gm+gmb)vgs
RS RL'
(gm+gmb)vgs
it'
+ vt'
ro
RL' -
Don’t need to solve:
• test prob e is in parallel with R , S
• test prob e lo oks into input of amplifier ⇒ sees R ! in
R = R //R T 1 S in
And:
ro
+
-vt
it
τ = (C + C )(R //R ) 1 gs sb S in
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-16
Time constant asso ciated with C : 2
(gm+gmb)vgs
ro
roc +
-vt
it
RLRS
(gm+gmb)vgs
ro
roc
it' +
-' RS vt
Again, don’t need to solve:
• test prob e is in parallel with R L ,
• test prob e lo oks into output of amplifier ⇒ sees R out !
RT 2 = RL //R out
And:
τ2 = (Cgd + Cdb )(RL //R out )
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6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-17
Bandwidth:
1ω � H
(C + C )(R //R ) + ( C + C )(R //R ) gs sb S in gd db L out
No capacitor in Miller p osition → no Miller-like term.
Simplify:
• In a current amplifier, R � R : S in
1 1 R = R //R � R � � T 1 S in in
g + g g m mb m
• At output:
1 R = R //R = R //r //{r [1+ R (g +g + )] T 2 L out L oc o S m mb
r o or
R � R //r //[r (1 + g R )] � R T 2 L oc o m S L
Then:
1 ω � H 1 (C + C ) + (C + C )R gs sb gd db L g m
If R is not to o high, bandwidth can b e rather high (and L
approach ω ). T
6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 24-18
Key conclusions
• Common-drain amplifier:
– Voltage gain � 1, Miller effect nearly completely eliminates impact of C (bootstrapping) gs
– if R is not to o high, CD amp has high bandwidth S
• Common-gate amplifier:
– no capacitor in Miller p osition ⇒ no Miller effect
– if R is not to o high, CG amp has high bandwidth L
• R , R affect bandwidth of amplifier S L