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EECE488 Set 6 - Frequency Respose of Amplifiers 1SM
EECE488: Analog CMOS Integrated Circuit Design
Set 6
Frequency Response of Amplifiers
Shahriar MirabbasiDepartment of Electrical and Computer Engineering
University of British [email protected]
EECE488 Set 6 - Frequency Respose of Amplifiers 2SM
Simple Pole
sCRsCvv io /1
/1/+
=
11/
+=
sRCvv io
fRCjf
vv
i
o
π211)(
+=
RCf
ffj
fvv
p
p
i
o
π21 ,
)(1
1)( =+
=
iv ovR
C
EECE488 Set 6 - Frequency Respose of Amplifiers 5SM
Miller Capacitive Multiplication
C1 = CF(1− Av)
C2 = CF(1− A−1v ) ≈ CF
EECE488 Set 6 - Frequency Respose of Amplifiers 6SM
Applicability of Miller’s Theorem
If the only signal path between X and Y is through impedance Z then Miller’s theorem is typically not applicable.
EECE488 Set 6 - Frequency Respose of Amplifiers 7SM
Applicability of Miller’s Theorem
Miller’s Theorem is typically useful in the cases where there is impedance in parallel with the main signal path.
EECE488 Set 6 - Frequency Respose of Amplifiers 8SM
Poles and Nodes
Interacting Poles
Non-Interacting Poles: One pole associated with each node
EECE488 Set 6 - Frequency Respose of Amplifiers 9SM
Common Source
f p,in =1
2πRS CGS + (1+ gmRD )CGD[ ]
f p,out =1
2π CGD + CDB( )RD[ ]
Neglecting input/output interaction,
EECE488 Set 6 - Frequency Respose of Amplifiers 10SM
Common Source
f p,in =1
2π RS CGS + (1+ gmRD)CGD[ ]+ RD(CGD + CDB )( )
Assume D =s
ω p1
+1⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
sω p2
+1⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ =
s2
ω p1ω p 2
+s
ω p1
+1 , ω p2 >> ω p1
[ ] 1()1()()(
)2 ++++++++
−=
DBGDDGSSGDDmSDBGDDBGSGDGSDS
DmGD
i
o
CCRCRCRgRsCCCCCCRRsRgsC
vv
EECE488 Set 6 - Frequency Respose of Amplifiers 11SM
Common Source
f p,out =RS (1+ gmRD )CGD + RSCGS + RD (CGD + CDB )
2πRS RD(CGSCGD + CGSCDB + CGDCDB )
GSDBGDD
outp CCCR
f large for , )(2
1, +
≈π
f p,out ≈ gmRS RDCGD
2πRS RD(CGSCGD + CGSCDB + CGDCDB )
≈ gm2π (CGS + CDB )
, for large CGD
EECE488 Set 6 - Frequency Respose of Amplifiers 12SM
Common Source
Right half plane zero, from the numerator of vo/vi
sCGD − gm
. . . → fz =
+gm
2πCGD
vovi
=(sCGD−gm)RD
s2RSRD(CGSCGD +CGSCSB +CGDCDB)+s RS(1+ gmRD)CGD +RSCGS +RD(CGD +CDB)[ ]+1
EECE488 Set 6 - Frequency Respose of Amplifiers 13SM
Common Gate
f pX =1
2π CGS + CSB( ) RS || 1gm + gmb
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
f pY =1
2π CGD + CDB( )RD[ ]
EECE488 Set 6 - Frequency Respose of Amplifiers 14SM
Source Follower (Common Drain)
( ) mGSLGDSmLGDGDGSLGSS
GSm
gCCCRgsCCCCCCRssCg
vivo
+++++++
=)(2
f p1 ≈gm
2π gmRSCGD + CL + CGS( ) , assuming f p2 >> f p1
= 1
2π RSCGD +CL + CGS
gm
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
EECE488 Set 6 - Frequency Respose of Amplifiers 15SM
Source Follower Input Impedance
At low frequencies, gmb >>| sCL |
Zin ≈1
sCGS
1+ gm / gmb( )+1/ gmb
∴ Cin = CGSgmb /(gm + gmb ) + CGD (same as Miller)
LmbGS
m
GSin sCgsC
gsC
Z+⎟⎟
⎠
⎞⎜⎜⎝
⎛++=
111
, GDC Neglecting
EECE488 Set 6 - Frequency Respose of Amplifiers 16SM
Source Follower
LC
|| << s,frequencie high At
GS
m
LGSin
Lmb
Csg
sCsCZ
sCg
2
11++≈
At high frequencies, overall input impedance includes CGD in parallel with series combination of CGS and CLand a negative resistance equal to -gm/(CGSCLω2).
EECE488 Set 6 - Frequency Respose of Amplifiers 17SM
Source Follower Output Impedance
ZOUT =VX / IX
=sRSCGS +1gm + sCGS
≈1/gm , at low frequencies ≈ RS , at high frequencies
EECE488 Set 6 - Frequency Respose of Amplifiers 18SM
Source Follower Output Impedance
R2 =1/ gm
R1 = RS −1/gm
L = CGS
gm
RS −1/gm( )
Output impedance inductance dependent on source impedance, RS!
EECE488 Set 6 - Frequency Respose of Amplifiers 19SM
Source Follower Ringing
Output ringing due to tuned circuit formed with CL and inductive component of output impedance.
EECE488 Set 6 - Frequency Respose of Amplifiers 21SM
Cascode Stage
f pA =1
2πRS CGS1 + CGD1 1+ gm1
gm 2 + gmb 2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
( )2211
22
22 GSSBDBGD
mbmpX CCCC
ggf+++
+=
π
f pY =1
2πRD CDB 2 + CL + CGD2( )