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EE105 Fall 2007 Lecture 21, Slide 1 Prof. Liu, UC Berkeley
REMINDERS• Review session: Fri. 11/9, 3-5PM in 306 Soda (HP Auditorium)• Midterm #2 (Thursday 11/15, 3:30-5PM in Sibley Auditorium)
EE105 Fall 2007 Lecture 21, Slide 2 Prof. Liu, UC Berkeley
• The impedance of CL decreases at high frequencies, so that it shunts some of the output current to ground.
• In general, if node j in the signal path has a small-signal resistance of Rj to ground and a capacitance Cj to ground, then it contributes a pole at frequency (RjCj)-1
Av Roll-Off due to CL
LDp CR
10
LDmv CjRgA
1
||
EE105 Fall 2007 Lecture 21, Slide 3 Prof. Liu, UC Berkeley
Pole Identification Example 1
inGp CR
11
LDp CR
12
0
EE105 Fall 2007 Lecture 21, Slide 4 Prof. Liu, UC Berkeley
Pole Identification Example 2
inm
G
p
Cg
R
1||
11
LDp CR
12
0
EE105 Fall 2007 Lecture 21, Slide 5 Prof. Liu, UC Berkeley
Dealing with a Floating Capacitance• Recall that a pole is computed by finding the resistance
and capacitance between a node and (AC) GROUND. • It is not straightforward to compute the pole due to CF in
the circuit below, because neither of its terminals is grounded.
EE105 Fall 2007 Lecture 21, Slide 6 Prof. Liu, UC Berkeley
Miller’s Theorem • If Av is the voltage gain from node 1 to 2, then a
floating impedance ZF can be converted to two grounded impedances Z1 and Z2:
vFF
F AZ
VV
VZZ
Z
V
Z
VV
1
1
21
11
1
121
v
FFF A
ZVV
VZZ
Z
V
Z
VV11
1
21
22
2
221
EE105 Fall 2007 Lecture 21, Slide 7 Prof. Liu, UC Berkeley
Miller Multiplication• Applying Miller’s theorem, we can convert a floating
capacitance between the input and output nodes of an amplifier into two grounded capacitances.
• The capacitance at the input node is larger than the original floating capacitance.
Fvv
F
v
F
CAjA
Cj
A
ZZ
1
1
1
1
11
Fv
v
F
v
F
CAjA
Cj
A
ZZ
11
111
1
112
EE105 Fall 2007 Lecture 21, Slide 8 Prof. Liu, UC Berkeley
Application of Miller’s Theorem
FDmGin CRgR
1
1F
DmD
out
CRg
R
1
1
1
0
EE105 Fall 2007 Lecture 21, Slide 9 Prof. Liu, UC Berkeley
MOSFET Intrinsic CapacitancesThe MOSFET has intrinsic capacitances which affect its performance at high frequencies:1. gate oxide capacitance between the gate and channel,2. overlap and fringing capacitances between the gate and the
EE105 Fall 2007 Lecture 21, Slide 10 Prof. Liu, UC Berkeley
High-Frequency MOSFET Model• The gate oxide capacitance can be decomposed into a
capacitance between the gate and the source (C1) and a capacitance between the gate and the drain (C2). – In saturation, C1 (2/3)×Cgate, and C2 0.
– C1 in parallel with the source overlap/fringing capacitance CGS
– C2 in parallel with the drain overlap/fringing capacitance CGD
EE105 Fall 2007 Lecture 21, Slide 11 Prof. Liu, UC Berkeley
Example
CS stage…with MOSFET capacitances
explicitly shownSimplified circuit for
high-frequency analysis
EE105 Fall 2007 Lecture 21, Slide 12 Prof. Liu, UC Berkeley
Transit Frequency
GS
mT C
gf 2
• The “transit” or “cut-off” frequency, fT, is a measure of the intrinsic speed of a transistor, and is defined as the frequency where the current gain falls to 1.
Conceptual set-up to measure fT
in
mT
inTminm
in
out
C
g
CjgZg
I
I
1
1
in
inin Z
VI
inmout VgI
EE105 Fall 2007 Lecture 21, Slide 13 Prof. Liu, UC Berkeley
Small-Signal Model for CS Stage0
EE105 Fall 2007 Lecture 21, Slide 14 Prof. Liu, UC Berkeley
… Applying Miller’s Theorem
GDDminThevinp CRgCR
1
1,
GDDm
outD
outp
CRg
CR1
1
1,
Note that p,out > p,in
EE105 Fall 2007 Lecture 21, Slide 15 Prof. Liu, UC Berkeley
Direct Analysis of CS Stage• Direct analysis yields slightly different pole locations
and an extra zero:
outinXYoutXYinDThev
outXYDinThevThevXYDmp
outXYDinThevThevXYDmp
XY
mz
CCCCCCRR
CCRCRRCRg
CCRCRRCRg
C
g
1
1
1
2
1
EE105 Fall 2007 Lecture 21, Slide 16 Prof. Liu, UC Berkeley
I/O Impedances of CS Stage
GDDmGSin CRgCjZ
1
1
DDBGD
out RCCj
Z ||1
0
EE105 Fall 2007 Lecture 21, Slide 17 Prof. Liu, UC Berkeley
CG Stage: Pole Frequencies
Xm
S
Xp
Cg
R
1||
1,
SBGSX CCC
YDYp CR
1,
DBGDY CCC
CG stage with MOSFET capacitances shown
0
EE105 Fall 2007 Lecture 21, Slide 18 Prof. Liu, UC Berkeley
AC Analysis of Source Follower• The transfer function of a
source follower can be obtained by direct AC analysis, similarly as for the emitter follower (ref. Lecture 14, Slide 6)
1
1
2
jbja
gC
j
v
v m
GS
in
out
m
SBGDGDS
SBGSSBGDGSGDm
S
g
CCCRb
CCCCCCg
Ra
0
EE105 Fall 2007 Lecture 21, Slide 19 Prof. Liu, UC Berkeley
Example
1
22111
22111111
))((
m
DBGDSBGDGDS
DBGDSBGSGDGSGDm
S
g
CCCCCRb
CCCCCCCg
Ra
1
1
2
jbja
gC
j
v
v m
GS
in
out
EE105 Fall 2007 Lecture 21, Slide 20 Prof. Liu, UC Berkeley
Source Follower: Input Capacitance
Sm
GSGDin Rg
CCC
1
• Recall that the voltage gain of a source follower isS
m
Sv
Rg
RA
1
Follower stage with MOSFET capacitances shown
0
Sm
GSGSvX Rg
CCAC
11
• CXY can be decomposed into CX and CY at the input and output nodes, respectively:
EE105 Fall 2007 Lecture 21, Slide 21 Prof. Liu, UC Berkeley
Example
1211
1 ||1
1GS
OOmGDin C
rrgCC
0
EE105 Fall 2007 Lecture 21, Slide 22 Prof. Liu, UC Berkeley
Source Follower: Output Impedance
mGS
GSG
X
X
gCj
CRj
i
v
1
• The output impedance of a source follower can be obtained by direct AC analysis, similarly as for the emitter follower (ref. Lecture 14, Slide 9)
0
EE105 Fall 2007 Lecture 21, Slide 23 Prof. Liu, UC Berkeley
Source Follower as Active Inductor
CASE 1: RG < 1/gm CASE 2: RG > 1/gm
• A follower is typically used to lower the driving impedance, i.e. RG is large compared to 1/gm, so that the “active inductor” characteristic on the right is usually observed.
mGS
GSGout gCj
CRjZ
1
EE105 Fall 2007 Lecture 21, Slide 24 Prof. Liu, UC Berkeley
Example
33
321 1||
mGS
GSOOout gCj
CrrjZ
03
EE105 Fall 2007 Lecture 21, Slide 25 Prof. Liu, UC Berkeley
MOS Cascode Stage• For a cascode stage, Miller multiplication is smaller
than in the CS stage.
11
21,
mm
Y
XXYv g
gv
vA
XYX CC 2
EE105 Fall 2007 Lecture 21, Slide 26 Prof. Liu, UC Berkeley
Cascode Stage: Pole Frequencies
12
11
,
1
1
GDm
mGSG
Xp
Cg
gCR
211
221
2
,
11
1
SBGDm
mGSDB
m
Yp
CCgg
CCg
22,
1
GDDBDoutp CCR
Cascode stage with MOSFET capacitances shown
(Miller approximation applied)0
EE105 Fall 2007 Lecture 21, Slide 27 Prof. Liu, UC Berkeley