Frequency Response of Transistor and MOS
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Transcript of Frequency Response of Transistor and MOS
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Frequency response I• As the frequency of the processed signals increases,
the effects of parasitic capacitance in (BJT/M!"transistors start to #anifest• The gain of the a#plifier circuits is frequency
dependent, usually decrease $ith the frequencyincrease of the input signals
• %o#puting &y hand the e'act frequency response ofan a#plifier circuits is a difficult and ti#econsu#ingtas), therefore appro'i#ate techniques for o&tainingthe *alues of critical frequencies is desira&le
• The e'act frequency response can &e o&tained fro#
co#puter si#ulations (e+g !I%-"+ .o$e*er, toopti#ie your circuit for #a'i#u# &and$idth and to)eep it sta&le one needs analytical e'pressions ofthe circuit para#eters or at least )no$ $hichpara#eter affects the required specification and ho$
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• The transfer function gi*es us the infor#ation a&out the
&eha*ior of a linearti#ein*ariant (TI" circuit/syste# fora sinusoidal e'citation $ith angular frequency
• This transfer function is nothing &ut the ratio &et$een theFourier transfor#s of the output and input signals and itis also called the frequency response of the TI circuit+
• represents the gain #agnitude of the frequencyresponse of the circuit, $hereas is the phase offrequency response+ ften, it is #ore con*enient to
e'press gain #agnitude in deci&els+• To a#plify a signal $ithout distortion, the a#plifier gain
#agnitude #ust &e the sa#e for all of the frequencyco#ponents
Frequency response II
ω ))(exp(|)(|))(exp(|)(|)( ω θ ω ω ω ω jT T jT T =∠=
|)(| ω T )(ω θ
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Frequency response of a#plifers• A bode plot sho$s the the gain #agnitude and phase in deci&les *ersus
frequency on logarith#ic scale
• A fe$ prerequisites for &ode plot3 aplace transfor# and net$or) transfer function oles and eros of transfer function Brea) frequencies
• !o#e useful rules for dra$ing highorder &ode plots3 4eco#pose transfer function into first order ter#s+
Mar) the &rea) frequencies and represent the# on the frequency a'is thecritical *alues for changes Ma)e &ode plot for each of the first order ter# For each first order ter#, )eep the 4% to the &rea) frequency constant
equal to the gain at 4% After the &rea) frequency, the gain #agnitude starts to increase or
decrease $ith a slope of 05d&/decade if the ter# is in the nu#erator or
deno#inator For phase plot, each first order ter# induces a 67 degrees of increase or
decrease at the &rea) frequency if the ter# is in the nu#erator ordeno#inator
%onsider frequencies li)e onetenth and ten ti#es the &rea) frequency andappro'i#ate the phase &y 5 and 85 degrees if the frequency is $ith thenu#erator (or 5 and 85 degrees if in the deno#inator"
Add all the first order ter#s for #agnitude and phase response
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Frequency response of 9% circuits
-+g+ 1
-+g+ 2
)/arctan()/arctan()(
)/(1log20)/(1log20|)(|
)(2
1,2
1,)(21
21)(
21
2
2
2
1
21
2
2
1
21
2
bb
bbdbv
bbv
f f f f f
f f f f f A
C R R f C R f C R R f j
C fR j f A
−=
+−+=
+==
++
+
=
θ
π π π
π
)/arctan()(
2)/(1log20)|(|
2
1,
21
1)(
b f f f
b f f
db f v A
RC b f
RCf j f v A
−=
+−=
=+
=
θ
π π
-+g+ 0
)/arctan(90)(
)/(1log20)/log(2012|)(|
)(2
1,
)/(1
)/(
)(21
2)(
2
2121
2
21
2
b
bbdbv
b
b
bv
f f f
f f f f f A
C R R f f f j
f f j
R R
R
C R R f j
C fR j f A
−=
+−+−=
+
=
+
×
+
=
++
=
θ
π π
π
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The M! Transistor
Polysilicon Aluminum
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The ;ate %apacitance
t ox
n< n<
Cross section view
L
;ate o'ide
x d x d
L d
olysilicon gate
Top view
;ate&ul)o*erlap
!ource
n<
4rain
n<W
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=
;ate %apacitance
S D
G
C GC
S D
G
C GC
S D
G
C GC
Cut-of Resistive Saturation
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Frequency response of co##on source M! a#plifer
.ighfrequency M! !#allsignal
equi*alent circuit
M!F-T co##on !ource a#plifier
!#allsignal equi*alent circuit for the M! co##on source a#plifier Frequency response analysis shows that there are three break frequencies, and mainly
the lowest one determines the upper half-power frequency, thus the -3db bandwidth
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• -'act frequency analysis of a#plifier
circuits is possi&le follo$ing the steps34ra$ s#allsignal equi*alent circuit (replace
each co#ponent in the a#plifier $ith its s#allsignal circuit"
?rite equations using *oltage and current la$s
Find the *oltage gain as a ratio of polyno#ial oflaplace *aria&le s
Factor nu#erator and deno#inator of thepolyno#ial to deter#ine &rea) frequencies
4ra$ &ode plot to appro'i#ate the frequencyresponse
-'act frequency response of a#plifiers
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The Miller -ffect• %onsider the situation that an i#pedance is connected
&et$een input and output of an a#plifier
The sa#e current flo$s fro# (out" the top input ter#inal if ani#pedance is connected across the input ter#inals
The sa#e current flo$s to (in" the top output ter#inal if ani#pedance is connected across the output ter#inal
This is )no$ as Miller -ffect T$o i#portant notes to apply Miller -ffect3
There should &e a co##on ter#inal for input and output The gain in the Miller -ffect is the gain after connecting feed&ac)
i#pedance
Miller in Z ,
Miller out Z ,
f
Z
Graphs from Prentice Hall
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• If the feed&ac) i#pedance is a capacitor ,then
the Miller capacitance reflected across the inputter#inal is +
• Therefore, connecting a capacitance fro# the
input to output is equi*alent to connecting a
capacitance
• 4ue to Miller effect, a s#all feed&ac)
capacitance appears across the input ter#inals
as a #uch larger equi*alent capacitance $ith alarge gain (e+g+ "+ At high frequencies,
this large capacitance has a lo$ i#pedance that
tends to short out the input signal
f C
Application of Miller -ffect
)1(
1,
v f
Miller in AC j
Z −
=
ω
f C
)1( v f AC −
80|| >v A
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BJT s#allsignal #odels (for BJT a#plifiers"
The #odel for high-frequency analysisπ − Hybrid
The #odel for low-frequency analysisβ π −r
The &asespreading resistance for the &ase region (*ery s#all"
The dyna#ic resistance of the &ase e#itter region
The feed&ac) resistance fro# collector to &ase (*ery large"
Account for the up$ard slope of the output characteristic
The depletion capacitance of the collectorto&ase region
The diffusion capacitance of the &asetoe#itter @unction π
µ
µ
π β
C
C I V r
r
I V r r
CQ Ao
CQT
x
/
/
=
=
ote3 in the follo$ing analysis of the %-, -F and %B a#plifier in the ne't three slides, $e $ill
assu#e for si#plicity (though they still appear in the s#all signal #odels"+∞== µ r r x ,0
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Miller -ffect3 co##on e#itter a#plifier I
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Miller -ffect3 co##on e#itter a#plifier II
Assu#e the current flo$ing through is *ery s#all co#pared to , then
the gain $ill &e considering the input ter#inal of the a#plifier at
b’ to ground.
Applying the #iller effect for the a#plifier, the follo$ing si#plified circuit can &e
o&tained3
Thus, the total capacitance fro# ter#inal b’ to ground is gi*en as follo$s
(neglect the #iller capacitance fro# output ter#inal c to ground"3
The &rea) frequency, thus the 2d& frequency is set &y the 9% lo$pass filter
(other *oltage controlled current source, resistance does not contri&ute to the
&rea) frequency"+ is a main limiting factor for -3db bandwidth+
π v g m µ C
'
' Lmvb R g A −=
)1( ' LmT R g C C C ++= µ π
T s
bC R
f '2
1
π =
µ C π v g m
µ C
π r R R R R s s |||||| 21'=
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1=
-#itterfollo$er a#plifier
• sing Miller -ffect, $eo&tain the a&o*eequi*alent circuit+ If
neglecting , Itsho$s that the &rea)frequency is
µ r r x ,
L o L
! s s
Lm sT
Lm
T
T T
b
R Rr R
R R R
R g r R R
R g C C C
C R f
||||
||
)]1([||
1
2
1
'
'
''
'
=
=
+=
+
+=
=
π
π µ
π
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For appro'i#ate analysis, $e can neglect the si#plified
equi*alent circuit can &e sho$n in (c"+ 4eri*e the transfer function for this circuit, it sho$s t$o
&rea) frequencies ($ith typical *alues, is appro'i#ately 2d& &and$idth"
)(,),( "ir"uit o#enr r "ir"uit s$ort r o x µ
L" Lm s s L
b s
b R R R g r R R R RC f RC f ||),/1(||||||, 2
1
, 2
1 '''2'1
====π
µ π π π
1b f
%o##on &ase a#plifier
• ?hat a&out a#plifier thatdo not ha*e capacitanceconnected directly fro#
output to the inputC
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Fullydifferential a#plifier
To esti#ate the 2dB &and$idth of this one, note that the circuit if fully sy##etric,
so only the half circuit needs to &e analyed+ The node *oltage at D is 5 in
s#allsignal analysis+ Therefore $e only need to analye the righthand side
circuit, $hich is actually a co##one#itter a#plifier analyed &efore+ !o the
2dB &and$idth of a co##one#itter a#plifier applies here+
D
D
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%ascode a#plifier and differential a#plifier
• The cascode a#plifier can &e*ie$ed as a common-emitter a#plifier $ith a common-base
a#plifier+• 4ue to lo$ input i#pedance of
E0, the *oltage gain of E1 iss#all+ !o, Miller effect on E1 iss#all+
• The -#ittercoupled differentiala#plifier can &e *ie$ed as aemitter-follower a#plifiercascaded $ith a common-base a#plifier (&oth ha*e $ider&and$idth than co##one#itter
a#plifier"+Graphs from Prentice Hall