Frequency Response of Transistor and MOS

8/16/2019 Frequency Response of Transistor and MOS

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1

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


8/20


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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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1:

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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1>

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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18

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

Frequency Response of Transistor and MOS

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