High Speed Opamp Feedback
Transcript of High Speed Opamp Feedback
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SECTION 1
HIGH SP EED OP ER ATIONAL AMP LIFIER S
Wa l t Kes ter
INTRODUCTION
High speed a na log signa l processing applicat ions, su ch as video and
communications, require op amps which have wide bandwidth, fast settling time,
low distort ion a nd n oise, high out put curr ent , good DC perform an ce, an d opera te a t
low su pply voltages. Th ese devices a re widely used as gain blocks, cable dr ivers,
ADC pr e-amps, cur ren t-to-voltage converter s, etc. Achieving higher ban dwidths for
less power is extremely critical in today's porta ble and bat ter y-operat ed
communications equipment. The rapid progress made over the last few years in
high-speed linea r circuits h as hinged n ot only on th e developmen t of IC processes
but also on innovative circuit topologies.
The evolut ion of high speed pr ocesses by using am plifier ba ndwidth as a function of
supply curr ent as a figure of mer it is shown in Figur e 1.1. (In th e case of dua ls,
tr iples, an d qua ds, the cur ren t per am plifier is used). Ana log Devices BiFET pr ocess,
which produced the AD712 and OP 249 (3MHz ban dwidth, 3mA cur ren t), yields
about 1MHz per mA. The CB (Complemen ta ry Bipolar ) process (AD817, AD847,
AD811, etc.) yields about 10MHz/mA of supply cur ren t. F t's of the CB pr ocess PNP
tra nsistors are a bout 700MHz, an d the NP N's about 900MHz.
The lat est gener at ion complemen ta ry bipolar process from Ana log Devices is a
high speed dielectr ically isolated process called XFCB (eXtr a Fa st Complemen ta ry
Bipolar). This process (2-4 GHz Ft m at ching PNP a nd NP N tr an sistors), coupled
with inn ovat ive circuit topologies allow op a mps to achieve n ew levels of cost-effective perform an ce at ast onishin g low quiescent curr ent s. The appr oximat e figure
of merit for th is process is t ypically 100MHz/mA, alth ough t he AD8011 op a mp is
capable of 300MHz ban dwidth on 1mA of supply curr ent due t o its un ique two-sta ge
current-feedback architecture.
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CB:1
0MHz
PERm
A
AMPLIFIER BANDWIDTH VERSUS SUPPLY CURRENTFOR ANALOG DEVICES' PROCESSES
SUPPLY CURRENT (PER AMPLIFIER), mA
BANDWIDTH(MHz)
1000
300
100
30
10
3
1
0.3 1 3 10 30
AD8001
AD8011
AD811
AD847AD817
OP482 AD712OP249
741
1.1
XFCB
:100M
HzPERmA
BiFET
:1MH
zPER
mA
a
In order to select in telligent ly the corr ect op am p for a given a pplicat ion, a n
un derst an ding of the var ious op am p topologies as well as t he t ra deoffs between
th em is r equired. Th e two most widely used t opologies ar e voltage feedback (VFB)
an d curr ent feedback (CFB). The following discussion tr eat s each in det ail an d
discusses t he similar ities and differen ces.
VOLTAGE F EEDBACK (VF B) O P AMP S
A voltage feedback (VFB) op am p is dist inguished from a curr ent feedback (CFB) op
am p by circuit topology. The VFB op am p is certa inly the m ost popular in low
frequency applicat ions, but th e CFB op amp h as some advan ta ges at h igh
frequencies. We will discuss CFB in det ail later , but first t he m ore t ra ditiona l VFB
architecture.
Ea rly IC voltage feedback op a mps wer e ma de on "all NP N" processes. These
processes were optimized for NPN tr ansistors, and the "latera l" PNP tra nsistors h ad
relatively poor performance. Lateral PNPs were generally only used as current
sources, level shifters, or for other non-critical functions. A simplified diagram of a
typical VFB op am p ma nu factu red on such a pr ocess is shown in Figur e 1.2.
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1.2
VOLTAGE FEEDBACK (VFB) OP AMPDESIGNED ON AN "ALL NPN" IC PROCESS
a
vOUT
VBIAS
IT
-VS
IT
2
CP
RT
IT
2
Q2
Q3
Q1
+VS
"LATERAL" PNP
IT
Q4"gm"STAGE
A
i = vgm
v
+
-
IT
2
gm = Ic q
kTvOUT = = v @ HF
i
jCP
gm
jCP
The inpu t st age is a differen tial pa ir consistin g of eith er a bipolar pair (Q1, Q2) or a
FE T pair. This "gm" (tra nscondu ctan ce) stage convert s th e sma ll-signal differen tial
input voltage, v, into a curr ent , i, i.e., it's tr an sfer fun ction is mea sur ed in un its of
condu ctan ce, 1/, (or m hos). The sma ll signal emit ter resista nce, re, i sappr oximat ely equa l to the r eciprocal of th e sma ll-signal gm. The formu la for t he
sma ll-signal gm of a single bipolar tr an sistor is given by th e following equa tion:
( )gmre
q
kTIC
q
kT
I T= = =
1
2, or
gmmV
I T
1
26 2.
IT is the differential pair tail current, IC is th e collector bias curr ent (IC = IT/2), q is
the electr on char ge, k is Boltzmann 's consta nt, a nd T is absolute tem perat ur e. At
+25C, VT = kT/q= 26mV (often called th e Ther ma l Volta ge, VT).
As we will see short ly, th e am plifier un ity gain-bandwidth product, fu , is equa l to
gm/2Cp, where th e capa cita nce Cp is used t o set t he domina nt pole frequ ency. Forthis reason, the ta il cur rent , IT,is ma de proportional to absolute tem perat ure
(PTAT). This cur rent tr acks the variation in r e with temperatur e thereby making
gm independent of tempera tur e. It is relatively easy to make Cp r easonably
constant over temperature.
The outpu t of one side of th e gm stage drives the emitt er of a later al PNP tra nsistor
(Q3). It is importa nt to note th at Q3 is not u sed to am plify the signa l, only to level
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shift, i.e., the signa l cur ren t va riat ion in th e collector of Q2 app ear s a t t he collector
of Q3. The outpu t collector cur ren t of Q3 develops a voltage a cross high impeda nce
node A. Cp sets t he domina nt pole of th e frequency response. Emit ter follower Q4
provides a low impeda nce out put .
The effective load a t t he h igh impedan ce node A can be repr esent ed by a resista nce,
RT, in pa ra llel with th e domina nt pole capa cita nce, Cp. The small-signal outpu t
voltage, vout , is equa l to the sma ll-signal curr ent , i, mu ltiplied by the impeda nce ofth e par allel combina tion of RT and Cp.
Figur e 1.3 shows a simple model for th e single-sta ge amplifier a nd t he
corr espondin g Bode plot. Th e Bode plot is cons tr ucted on a log-log scale for
convenience.
1.3
MODEL AND BODE PLOT FOR A VFB OP AMP
a
6dB/OCTAVE
f = UNITY GAIN FREQUENCYu
f
f = CLOSED LOOP BANDWIDTHCL
1 +
1
R2
R1
NOISE GAIN = G
= 1 +R2
R1
i = v gm
X1
R1 R2
v
vin
+
-
gm
+
- CP RT
OAOf
vOUT
f1
=2R CO PT
fu
fCL
fu
=
=
gm
2C P
fuG
R1
R2=
1 +
The low frequ ency breakp oint , fo,is given by:
foR TCp
=1
2.
Note tha t th e high frequency response is deter mined solely by gm and Cp:
vout vg m
j Cp=
.
The unity gain-bandwidth frequency, fu , occurs where | vout | =| v| . Solving t he
above equat ion for fu ,assuming | vout | =| v| :
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fug m
Cp=
2.
We can use feedback t heory to derive th e closed-loop r elationship bet ween t he
circuit's signal inp ut voltage, vin ,and it 's out put voltage, vout :
vout
v in
R
R
j Cp
gm
R
R
=+
+ +
12
1
1 12
1
.
At th e op am p 3dB closed-loop bandwidt h frequ ency, fcl, the following is true:
21
2
11
fclCpgm
R
R+
= , and hen ce
fclgm
Cp R
R
=+
2
1
12
1
, or
fclfu
R
R
=+1
2
1
.
This demonstr at es a funda menta l property of VFB op amps: T he closed-loop
band width m ultiplied by the closed-loop gain is a constan t, i.e., the VFB op am pexhibits a constant gain-bandwidth product over most of the usable frequency range.
Some VFB op amps (called de-compensa ted) are un stable at u nity gain and a re
designed to be opera ted a t some m inimum am ount of closed-loop gain. F or th ese op
am ps, the gain-ban dwidth pr oduct is still relat ively const an t over t he r egion of
allowable gain .
Now, cons ider t he following typical example: IT = 100A, Cp = 2pF. We find t ha t:
gmI T
VT
A
mV
= = =/ 2 50
26
1
520
fugm
CpMH z= =
=
2
1
2 520 2 10 12153
( )( ).
Now, we mu st consider th e lar ge-signal resp onse of the circuit. The s lew-ra te, SR, is
simply the total available cha rging curr ent, IT/2, divided by the dom in ant pole
capacitance, Cp. For the example under consideration,
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I Cdv
dt= ,
dv
dtSR= , SR
I
C=
SRI T
Cp
A
pFV s= = =
//
2 50
225
.
The full-power ba ndwidth (FPBW) of the op am p can n ow be calculat ed from t he
formula:
FPBWSR
A
V s
VMH z= =
=
2
25
2 14
/
, ,
wher e A is the pea k am plitude of th e out put signal. If we assu me a 2V peak-to-peak
out put sinewave (cert ainly a r easona ble assum ption for high speed applicat ions),
then we obtain a FPBW of only 4MHz, even though the small-signal unity gain-
ban dwidth product is 153MHz! For a 2V p-p outpu t sin ewave, distortion will begin
to occur much lower th an th e actua l FPBW frequency. We mu st increase th e SR by
a factor of about 40 in order for t he F PBW to equa l 153MHz. The only way to do th is
is to increase th e ta il cur rent , IT,of th e input differen tial pa ir by the sa me factor.This implies a bias curr ent of 4mA in order to achieve a FP BW of 160MHz. We ar e
assu ming th at Cp is a fixed valu e of 2pF a nd can not be lowered by design.
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VFB OP AMP BANDWIDTH AND SLEW RATE CALCULATION
nn Assume that IT = 100A, Cp = 2pF
nn gmIc
VT
A
mV== == ==
50
26
1
520
nn
fugm
Cp
MHz== ==
2
153
nn Slew Rate = SR =
ITCp
V s/
/2
25==
BUT FOR 2V PEAK-PEAK OUTPUT (A = 1V)
nnFPBW
SR
AMHz== ==
24
nn Must increase IT to 4mA to get FPBW = 160MHz!!
nn Reduce gm by adding emitter degeneration resistors
a 1.4
In pr actice, th e FP BW of th e op am p should be appr oximat ely 5 to 10 times t he
ma ximum outp ut frequency in order t o achieve acceptable distort ion per form an ce
(typically 55-80dBc @ 5 t o 20MHz, but actu al s ystem requ iremen ts var y widely).
Notice, however, that increasing the tail current causes a proportional increase in
gm an d hence fu . In order t o prevent possible insta bility due to th e large increase in
fu , gm can be reduced by inserting resistors in series with the emitters of Q1 and Q2
(this t echn ique, called emitt er degeneration , also serves t o linear ize the gm transfer
function an d lower distort ion).
A major inefficiency of conventional bipolar voltage feedback op amps is their
inability to achieve high slew rat es without pr oport iona l increa ses in quiescent
curr ent (assum ing tha t Cp is fixed, an d ha s a reasonable minimum value of 2 or
3pF). This of cour se is not m ean t t o say th at high speed op amps designed using th is
ar chitectur e a re deficient, it 's just tha t ther e ar e circuit design techniques available
which allow equivalent per form an ce at lower quiescent curr ent s. This is extrem ely
importa nt in portable batt ery operat ed equipment wh ere every milliwatt of power
dissipation is critical.
VF B O p A m p s D e s ig n e d o n C o m p l e m e n t a r y B i p o la r P r o c e s s e s
With th e advent of complemen ta ry bipolar (CB) processes having high qua lity PNP
transistors as well as NPNs, VFB op amp configurations such as the one shown in
th e simplified diagram (Figur e 1.5) becam e popula r.
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1.5
VFB OP AMP USING TWO GAIN STAGES
a
IT
CP
Q3
Q2Q1
+VS
Q4
X1
-VS
+
D1
-
OUTPUT
BUFFER
Notice th at th e input differen tial pa ir (Q1, Q2) is loaded by a curr ent mirr or (Q3 and
D1). We show D1 as a diode for simplicity, but it is actually a diode-connected PNP
tr an sistor (mat ched to Q3) with t he ba se an d collector conn ected to each oth er. This
simplification will be used in many of the circuit diagrams to follow in this section.
The common emitter transistor, Q4, provides a secondvolta ge gain st age. Since the
PNP tr ansistors ar e fabricated on a complementa ry bipolar pr ocess, they ar e highquality and m atched to th e NPN s an d suita ble for voltage gain. The dominan t pole
of the a mplifier is set by Cp, and th e combinat ion of th e gain st age,Q4, and Cp is
often referr ed to as a Miller Integra tor. The unit y-gain outpu t buffer is usu ally a
complemen ta ry em itter follower.
The model for t his two-sta ge VFB op am p is shown in F igure 1.6. Notice tha t t he
unity gain-bandwidth frequency, fu , is still determ ined by the gm of the input st age
and the dominant pole capacitance, Cp. The second gain stage increases the DC
open-loop gain, but the maximum slew rate is still limited by the input stage tail
curr ent: SR = IT/Cp .
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1.6
MODEL FOR TWO STAGE VFB OP AMP
a
X1
R1
v
vin
+
-gm
+vout
VREF
R2
CP
-
IT
i = vgm
a
+
-
fu = fCL =gm
2CP
fu
R2
R1
SR =IT
CP
1+
The t wo-stage topology is widely used t hr oughout th e IC indu str y in VFB op am ps,
both precision a nd h igh speed.
Another popular VFB op am p ar chitectur e is the folded cascode as shown in Figure
1.7. An in dust ry-stan dar d video am plifier family (th e AD847) is based on t his
ar chitectu re. This circuit t akes a dvanta ge of the fast P NPs available on a CBprocess. The differen tial signa l cur ren ts in th e collectors of Q1 and Q2 a re fed to th e
emitters of a P NP cascode tra nsistor pa ir (hence the t erm folded cascode). The
collectors of Q3 and Q4 a re loaded with th e cur ren t m irr or, D1 an d Q5, an d Q4
provides voltage gain. This single-sta ge architectur e uses t he junction capa cita nce at
th e high-impeda nce node for compen sat ion (an d some variat ions of th e design bring
this node to an extern al pin so that additiona l extern al capacita nce can be added).
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1.7
AD847-FAMILY FOLDED CASCODE SIMPLIFIED CIRCUIT
a
Q2Q1
+VS
X1
-VS
+
-
Q5
Q4Q3
2IT 2IT
2IT
IT
IT
VBIAS
CCOMP
CSTRAY
D1
AC GROUND
With no emitter degenerat ion r esistors in Q1 an d Q2, and n o additiona l extern al
compensating capacitance, this circuit is only stable for high closed-loop gains.
However, un ity-gain compen sat ed versions of th is fam ily ar e available which ha ve
the a ppropriat e amount of emitter degenerat ion.
The a vailability of J FE Ts on a CB process allows not only low input bias curr ent but
also improvement s in t he t ra deoff which must be made between gm and IT foun d in
bipolar inpu t st ages. Figur e 1.8 shows a simplified diagra m of the AD845 16MHz op
amp. J FE Ts have a much lower gm per mA of ta il curr ent t ha n a bipolar tr an sistor.
This allows the input tail current (hence the slew rate) to be increased without
ha ving to increase Cp to mainta in sta bility. The un usua l thing about t his seemingly
poor per forma nce of the J FE T is tha t it is exactly wha t is needed on the inpu t st age.
For a typical J FE T, the value of gm is appr oximat ely Is/1V (Is is the source current),
ra ther than Ic/26mV for a bipolar t r ansis tor , i.e ., abou t 40 t im es lower . Th is a llows
much higher t ail cur rent s (and higher slew rat es) for a given gm when J FETs are
used as the input sta ge.
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a
AD845 BiFET 16MHz OP AMP SIMPLIFIED CIRCUIT
1.8
-VS
CP
X1
Q2
Q3
Q1
+VS
Q4
Q6
Q5
D1
VBIAS
+
-
A New VFB Op Am p Arch i t ec t u r e fo r "Cur re n t -on -Dem a nd " P e r form an ce ,
L o w e r P o w e r , a n d I m p r o v e d Sle w R a t e
Unt il now, op am p designers ha d to mak e th e above tr adeoffs between th e input gmstage quiescent cur rent an d th e slew-ra te a nd distortion per forma nce. Ana log
Devices' has pat ent ed a n ew circuit core wh ich su pplies current-on-demand to charge
an d discha rge th e domina nt pole capa citor, Cp, while allowing the quiescent curr entto be sma ll. The ad ditiona l cur ren t is proport iona l to th e fast slewing input signal
an d a dds to th e quiescent curr ent . A simplified diagra m of th e basic core cell is
shown in Figure 1.9.
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1.9
"QUAD-CORE" VFB gm STAGE FOR CURRENT-ON-DEMAND
a
Q2Q1
+VS
-VS
+-
Q5
Q4Q3
CP1
Q6
Q7
Q8
X1
CP2
Th e quad-core (gm sta ge) consist s of tr an sistors Q1, Q2, Q3, and Q4 with th eir
emitt ers conn ected t ogeth er a s shown. Consider a positive step volta ge on t he
invertin g input. This volta ge produces a pr oportiona l cur ren t in Q1 which is
mirr ored int o Cp1 by Q5. The curr ent th rough Q1 also flows th rough Q4 an d Cp2.
At t he dyna mic ran ge limit, Q2 and Q3 ar e correspondingly tur ned off. Notice th at
the char ging an d discha rging curr ent for Cp1 a nd Cp2 is not limited by the qua dcore bias current. In practice, however, small current-limiting resistors are required
form ing an "H" resist or n etwork a s shown. Q7 and Q8 form th e second gain sta ge
(driven differen tially from t he collectors of Q5 and Q6), an d t he out put is buffered by
a u nity-gain complement ar y emitter follower.
The qua d core configura tion is paten ted (Roy Gosser, U.S. Pa ten t 5,150,074 an d
others pending), as well as the circuits which establish the quiescent bias currents
(not shown in the diagram). A number of new VFB op amps using this proprietary
configura tion have been released an d h ave un surpa ssed high frequency low
distort ion performa nce, bandwidth, a nd slew ra te a t the indicated quiescent curr ent
levels (see F igure 1.10). The AD9631, AD8036, and AD8047 ar e optimized for a gain
of +1, while th e AD9632, AD8037, an d AD8048 for a gain of +2. The sa me qua d-corear chitectur e is used as th e second stage of the AD8041 rail-to-rail output, zero-volt
input single-supply op am p. The input st age is a differentia l PNP pair wh ich a llows
th e input comm on-mode signa l to go about 200mV below th e negat ive supply rail.
The AD8042 an d AD8044 are du al a nd qu ad ver sions of th e AD8041.
"QUAD-CORE" TWO STAGE XFCB VFB OP AMPSAC CHARACTERISTICS VERSUS SUPPLY CURRENT
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PART # ISY / AMP BANDWIDTH SLEW RATE DISTORTION
AD9631/32 17mA 320MHz 1300V/s 72dBc@20MHz
AD8036/37 Clamped 20mA 240MHz 1200V/s 72dBc@20MHz
AD8047/48 5.8mA 250MHz 750V/s 66dBc@5MHz
AD8041 (1) 5.2mA 160MHz 160V/s 69dBc@10MHz
AD8042 (2) 5.2mA 160MHz 200V/s 64dBc@10MHz
AD8044 (4) 2.75mA 150MHz 170V/s 75dBc@5MHz
AD8031 (1) 0.75mA 80MHz 30V/s 62dBc@1MHz
AD8032 (2) 0.75mA 80MHz 30V/s 62dBc@1MHz
Number in ( ) indicates single, dual, or quad
a 1.10
CUR R E NT F EEDBACK (CFB ) OP AMP S
We will now exam ine th e curr ent feedback (CFB) op am p t opology which h as
recently become popular in h igh speed op am ps. The circuit concepts wer e
intr oduced ma ny year s ago, however m odern high speed complemen ta ry bipolar
processes are required to ta ke full advan tage of the ar chitectur e.
It h as long been kn own t hat in bipolar tra nsistor circuits, current s can be switched
faster than voltages, other things being equal. This forms the basis of non-
sat ur at ing emitter -coupled logic (ECL) an d devices such a s curr ent -out put DACs.
Maintaining low impedances at the current switching nodes helps to minimize the
effects of str ay capacitan ce, one of th e largest detr iment s to high speed operat ion.
The curr ent mirr or is a good example of how cur ren ts can be switched with a
minimum amount of delay.
The curr ent feedback op amp t opology is simply an a pplicat ion of th ese fun dam ent al
principles of curr ent steer ing. A simplified CFB op amp is shown in F igure 1.11. The
non-invert ing inpu t is high impedan ce an d is buffered directly to th e inverting input
thr ough t he complementa ry emitter follower buffers Q1 a nd Q2. Note tha t the
invertin g input impedan ce is very low (typically 10 to 100), becau se of the low
emitter resistan ce. In t he ideal case, it would be zero. This is a funda ment aldifference between a CFB a nd a VFB op amp, an d also a feat ur e which gives the
CFB op am p some un ique advanta ges.
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1.11
SIMPLIFIED CURRENT FEEDBACK (CFB) OP AMP
a
+VS
-VS
+ -
Q3
Q1
Q2
R1 R2
Q4
RTCP
i
i
i
X1
The collectors of Q1 an d Q2 drive cur ren t m irrors wh ich m irror t he invert ing input
curr ent to the h igh impedan ce node, modeled by RT an d Cp. The high impedan ce
node is buffered by a complementa ry un ity gain emitt er follower. Feedba ck from th e
outpu t to the inverting input acts to force the inverting input currentto zero, hence
the term Current Feedback. (In t he ideal case, for zer o invertin g input impedan ce, no
sma ll signal voltage can exist at th is node, only sma ll signal cur ren t).
Consider a p ositive step voltage a pplied to the n on-invertin g input of th e CFB op
amp. Q1 immediately sources a proportional current into the external feedback
resistors creat ing an errorcurr ent which is mirr ored to th e high impedan ce node by
Q3. The voltage developed at th e high impeda nce node is equal to this curr ent
multiplied by the equivalent impedance. This is where th e term transim pedan ce op
am p origina ted, since the tr an sfer function is an impedance, rat her t han a u nitless
voltage ra tio as in a tra ditiona l VFB op amp.
Note th at the er ror current is not limited by the inpu t sta ge bias curr ent, i.e., there
is no slew-rate lim itation in an ideal CFB op am p. The curr ent m irrors supply
current-on-demand from th e power su pplies. The nega tive feedback loop t hen forcesthe outpu t voltage to a value which r educes th e inverting input error curr ent t o zero.
The model for a CF B op am p is shown in Figur e 1.12 along with t he corr esponding
Bode plot. Th e Bode plot is p lott ed on a log-log scale, an d t he open -loop gain is
expressed as a transimpedance, T(s), with units of ohms.
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( )
a 1.12
R2R1
CFB OP AMP MODEL AND BODE PLOT
CPRTi
|T(s)|
()
fO
fCL
1
1
2R2CPRO RO
R2 R1
X1
X1
RO
VOUT
VIN
RT
R2
RO
6dB/OCTAVE
12dB/OCTAVE
fCL =
2R2CP
FORRO
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16
Examina tion of this equa tion quickly reveals tha t the closed-loop band wid th of a
CFB op am p is determ ined by th e internal d om inan t pole capacitor, Cp, and th e
external feedback resistor R2, an d is in dependent of the gain-settin g resistor, R1. This
ability to maint ain consta nt bandwidth independent of gain m akes CFB op amps
ideally suited for wideban d program ma ble gain a mplifiers.
Becau se t he closed-loop ba ndwidth is inversely proport iona l to th e extern al feedback
resistor, R2, a CFB op a mp is u sua lly optimized for a specific R2. Increasing R2 fromit's optimu m value lowers t he ban dwidth, an d decrea sing it may lead t o oscillat ion
an d inst ability becau se of high frequen cy par asitic poles.
The frequen cy response of the AD8011 CFB op am p is shown in Figur e 1.13 for
var ious closed-loop valu es of gain (+1, +2, and +10). Note th at even a t a gain of +10,
th e closed loop ban dwidth is st ill great er t ha n 100MHz. The peak ing which occurs a t
a gain of +1 is typical of wideband CF B op am ps when used in t he n on-invert ing
mode and is due primar ily to stra y capacitance at t he inverting input . The peaking
can be redu ced by sacrificing band width a nd u sing a slightly larger feedback
resistor. The AD8011 CFB op amp represents state-of-the-art performance, and key
specifications ar e shown in F igure 1.14.
a
+4
1.13
+3
AD8011 FREQUENCY RESPONSEG = +1, +2, +10
+2
+1
0
2
3
4
1 10 100 500
FREQUENCY - MHz
1
+5
5
G = +1
RF = 1k
G = +10
RF = 500
G = +2
RF = 1k
VS= +5V OR 5V
VOUT= 200mV p-p
NORMALIZEDGAIN-dB
AD8011 CFB OP AMP KEY SPECIFICATIONS
nn 1mA Power Supply Current (+5V or 5V)
nn 300MHz Bandwidth (G = +1)
nn 2000 V/s Slew Rate
nn 29ns Settling Time to 0.1%
nn Video Specifications (G = +2)
Differential Gain Error 0.02%
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Differential Phase Error 0.06
25MHz 0.1dB Bandwidth
nn Distortion
70dBc @ 5MHz
62dBc @ 20MHz
nn Fully Specified for 5V or +5V Operation
a 1.14
Traditional current feedback op amps have been limited to a single gain stage, using
curr ent -mirrors a s previously described. The AD8011 (an d also oth ers in t his family:
AD8001, AD8002, AD8004, AD8005, AD8009, AD8013, AD8072, AD8073), un like
tra ditiona l CFB op amps uses a two-stage gain configurat ion as shown in Figure
1.15. Un til now, fully complement ar y two-gain st age CFB op am ps ha ve been
impra ctical because of their high power dissipat ion. Th e AD8011 employs a second
gain st age consist ing of a pair of complement ar y amplifiers (Q3 and Q4). Note t ha t
they ar e not connected as curr ent mirrors but as grounded-emitters. The deta iled
design of curr ent sources (I1 a nd I2), an d t heir respective bias circuits (Roy Gosser,pat ent -applied-for) ar e the key to the success of th e two-sta ge CFB circuit; th ey
keep t he a mplifier's quiescent power low, yet ar e capable of supplying current-on-
demandfor wide curr ent excur sions r equired du ring fast slewing.
a
SIMPLIFIED TWO-STAGE CFB OP AMP
1.15
-VS
CP
X1
Q2
Q3
Q1
+VS
Q4
I1
+ -
I2
CC/2
CC/2
A furt her adva nt age of th e two-sta ge amplifier is the h igher overa ll ban dwidth (for
th e sam e power), which mean s lower signal distortion an d th e ability to drive
heavier externa l loads.
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18
Thus far, we ha ve learn ed severa l key featu res of CFB op amps. The most import an t
is tha t for a given complemen ta ry bipolar I C process, CFB generally always yields
higher FPBW (hence lower distortion) than VFB for the same amount of quiescent
supply current. This is becau se th ere is pra ctically no slew-ra te limiting in CFB.
Because of this, the full power ban dwidth an d th e small signa l bandwidth a re
approxima tely the same.
The second importa nt featur e is tha t th e inverting input im pedance of a CFB op am p
is very low . This can be advant ageous when using the op amp in t he inverting mode
as a n I/V convert er, becau se th ere is much less sensitivity to invert ing input
capa citance tha n with VFB.
The third featu re is tha t the closed-loop bandwidth of a CFB op amp is determined
by the valu e of the int ernal Cp capacitor and the external feedback resistor R2 and is
relatively independent of the gain-settin g resistor R1 . We will now examine some
typical a pplications issues an d ma ke furt her compar isons between CFBs a nd VFBs.
CURRENT FEEDBACK OP AMP FAMILY
PART ISY/AMP BANDWIDTH SLEW RATE DISTORTION
AD8001 (1) 5.5mA 880MHz 1200V/s 65dBc@5MHz
AD8002 (2) 5.0mA 600MHz 1200 V/s 65dBc@5MHz
AD8004 (4) 3.5mA 250MHz 3000 V/s 78dBc@5MHz
AD8005 (1) 0.4mA 180MHz 500 V/s 53dBc@5MHz
AD8009 (1) 11mA 1000MHz 7000 V/s 80dBc@5MHz
AD8011 (1) 1mA 300MHz 2000 V/s 70dBc@5MHz
AD8012 (2) 1mA 300MHz 1200 V/s 66dBc@5MHz
AD8013 (3) 4mA 140MHz 1000 V/s G=0.02%, =0.06
AD8072 (2) 5mA 100MHz 500 V/s G=0.05%, =0.1
AD8073 (3) 5mA 100MHz 500 V/s G=0.05%, =0.1
Number in ( ) Indicates Single, Dual, Triple, or Quad
a 1.16
SUMMARY: CURRENT FEEDBACK OP AMPS
nn CFB yields higher FPBW and lower distortion than
VFB for the same process and power dissipation
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nn Inverting input impedance of a CFB op amp is low,
non-inverting input impedance is high
nn Closed-loop bandwidth of a CFB op amp is determined
by the internal dominant-pole capacitance and the
external feedback resistor, independent of the gain-
setting resistor
a 1.17
E FF E C T S OF F EEDBACK CAP ACITANCE IN OP AMP S
At t his point, the t erm noise gain needs some clarification. Noise gain is th e am oun t
by which a sma ll am plitude noise voltage source in ser ies with an input ter mina l of
an op am p is amplified when measu red a t t he output . The input voltage noise of an
op am p is modeled in th is way. It sh ould be noted th at th e DC noise gain can a lso be
used t o reflect t he inpu t offset voltage (and oth er op am p input err or sour ces) to the
output.
N oise ga in must be distinguished from signal gain . Figure 1.18 shows an op amp in
the inverting and non-inverting mode. In the non-inverting mode, notice that noise
gain is equa l to signal gain. H owever, in th e invertin g mode, th e noise gain d oesn't
chan ge, but th e signa l gain is now R2/R1. Resistors a re sh own a s feedback
elements, however, the networks may also be reactive.
FOR VFB OP AMP:
CLOSED-LOOP BW =
fCL =
a 1.18
+
-
R1R1
NOISE GAIN AND SIGNAL GAIN COMPARISON
VOUT
VIN
fu
G
+
-
VIN
VOUT
R2R2
VN VN
NON-INVERTING INVERTING
SIGNAL GAIN = 1 +
NOISE GAIN = = 1 +
SIGNAL GAIN =
NOISE GAIN = 1 +
UNITY GAIN BANDWIDTH FREQUENCYNOISE GAIN
R2
R1
R2R1
- R2
R1
R2R1
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Two oth er configur at ions a re sh own in F igure 1.19 wher e th e noise gain ha s been
increased indepen dent of signal gain by th e addit ion of R3 across the inpu t
ter mina ls of the op amp. This t echnique can be u sed to sta bilize de-compen sat ed op
am ps which ar e un sta ble for low values of noise gain. H owever, the sen sitivity to
input noise and offset voltage is correspondingly increa sed.
R2
R1||R3
a 1.19
+
-
R1R1
INCREASING THE NOISE GAINWITHOUT AFFECTING SIGNAL GAIN
VOUT
VIN
+
-
VIN
VOUT
R2R2
VN VN
NON-INVERTING INVERTING
SIGNAL GAIN = 1 +
NOISE GAIN = = 1 +
SIGNAL GAIN =
NOISE GAIN = 1 +
R2
R1
- R2
R1
R2
R1||R3
R3R3
Noise gain is often plott ed as a fun ction of frequ ency on a Bode plot t o determin e th e
op am p sta bility. If th e feedback is pur ely resist ive, the n oise gain is consta nt with
frequency. However, rea ctive element s in th e feedback loop will cau se it t o cha nge
with frequency. Using a log-log scale for the Bode plot allows the noise gain to be
easily drawn by simply calculatin g the brea kpoints deter mined by the frequen cies of
th e var ious poles an d zeros. The point of int ersection of the n oise gain with th e open-
loop gain n ot only determ ines th e op am p closed-loop band wid th , but a lso can be
used to analyze stability.
An excellent explana tion of how to m ak e simplifying appr oximat ions using Bodeplots t o an alyze gain a nd ph ase per form an ce of a feedback net work s is given in
Reference 4.
J ust as signal gain an d noise gain can be different, so can the signal band width and
the closed-loop band wid th . The op amp closed-loop bandwidth, fcl, is always
deter mined by t he int ersection of the n oise gain with th e open-loop frequ ency
response. The signa l bandwidt h is equ al to th e closed-loop ban dwidth only if th e
feedback net work is pur ely resistive.
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It is qu ite comm on t o use a capacitor in th e feedback loop of a VFB op am p to sha pe
th e frequency response a s in a simple single-pole lowpass filter (see F igure 1.20a).
The resu lting noise gain is plott ed on a Bode plot t o an alyze stability and ph ase
ma rgin. Sta bility of th e system is deter mined by th e net slope of th e noise gain an d
th e open loop gain wh ere t hey inter sect. For un conditional st ability, th e noise gain
plot m ust inter sect th e open loop response with a n et slope of less th an 12dB/octave.
In t his case, the net slope wher e they int ersect is 6dB/octa ve, indicat ing a sta ble
condition. Notice for t he case dr awn in F igure 1.20a, th e second pole in th efrequency response occurs a t a considerably higher frequen cy th an fu .
a 1.20
R2R1
NOISE GAIN STABILITY ANALYSIS FOR VFB AND CFB
OP AMPS WITH FEEDBACK CAPACITOR
fp=
1
2R2C2
RO
1 +
+
-
R2
A B
VFB OP AMP CFB OP AMP
fp=
1
2R2C2
fCL
f1 f
fu
UNSTABLE
|A(s)| |T(s)|
()
R1
R2
C2
In the case of the CFB op amp (Figure 1.20b), the same analysis is used, except that
th e open-loop tr an simpeda nce gain, T(s), is used to const ru ct the Bode plot. The
definition ofnoise gain (for th e pur poses of stability ana lysis) for a CF B op amp,
however, mu st be r edefined in t erm s of a currentnoise source at tached to th e
invertin g inpu t (see Figure 1.21). This cur ren t is reflected t o th e out put by an
impedan ce which we define t o be th e "curr ent noise gain" of a CFB op a mp:
" "CURRENT NOISE GAIN
Ro ZRo
Z + +
2 11
.
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22
a 1.21
RO
CURRENT "NOISE GAIN" DEFINITION
FOR CFB OP AMP FOR USE IN STABILITY ANALYSIS
i
Z1
X1
X1
i
RO
VOUT
VOUT
Z1
Z2
Z2
T(s)
CURRENT"NOISE GAIN" =
= RO+Z2(1+ )
VOUTi
ROZ1
Now, retu rn to Figure 1.20b, and observe the CFB current n oise gain plot. At low
frequencies, the CF B current noise gain is simply R2 (making the assum ption tha t
Ro is mu ch less t ha n Z1 or Z2. The first pole is deter mined by R2 and C2. As th e
frequency continu es to increa se, C2 becomes a short circuit, and a ll th e invertn g
input curr ent flows th rough Ro (refer ba ck to Figur e 1.21).
The CF B op am p is n orm ally optimized for best per form an ce for a fixed feedback
resistor, R2. Additional poles in th e tr an simpedan ce gain, T(s), occur at frequenciesabove the closed loop ba ndwidth , fcl, (set by R2). Note th at th e inter section of th e
CFB cur ren t n oise gain with th e open-loop T(s) occur s wher e th e slope of th e T(s)
function is 12dB/octave. This indicates instability and possible oscillation.
It is for t his reason th at CFB op amps are not suitable in configurations which
require capacitance in the feedback loop , such as sim ple active integra tors or lowpass
filters. They can, h owever, be used in certa in active filters su ch as t he Sa llen-Key
configur at ion sh own in F igure 1.22 which do not requ ire capacitan ce in th e feedback
network.
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a
EITHER CFB OR VFB OP AMPS CAN BE USED IN
THE SALLEN-KEY FILTER CONFIGURATION
1.22
R2R1
+
-
R2 FIXED FOR CFB OP AMP
VFB op am ps, on t he oth er h an d, ma ke very flexible active filters. A multiple
feedback 20MHz lowpass filter using t he AD8048 is shown in Figur e 1.23.
a 1.23
MULTIPLE FEEDBACK 20MHz LOWPASS FILTERUSING THE AD8048 VFB OP AMP
1VIN
R4154
C150pF
C2100pF
R1154
AD8048
R378.7
+5V
0.1F
3
2
1006 VOUT
10F
5 0.1F
5V
10F
4
7
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24
In genera l, the a mplifier should ha ve a bandwidth which is at least t en times th e
ban dwidth of th e filter if problems due to pha se shift of the am plifier ar e to be
avoided. (The AD8048 ha s a ban dwidth of over 200MHz in th is configur at ion). The
filter is designed as follows:
Choose:
Fo = Cut off Frequ ency = 20MHz = Dam ping Ra tio = 1/Q = 2H = Absolute Value of Circuit Gain
= | R4/R1| = 1
k = 2FoC1
CC H
pF24 1 1
2100=
+=
( )
, for C1 = 50pF
RHk
12
159 2= =
. , use 154
Rk H
32 1
79 6
= + =
( ).
, use 78.7
R4 = H R1 = 159.2, use 154
H IGH SP E E D CUR R E NT -TO-VOLTAGE CONVERTERS , AN D
TH E E FF E C T S OF INVERTING IN P U T CAPACITANCE
Fast op amps are useful as current-to-voltage converters in such applications as high
speed ph otodiode pr eam plifiers a nd curr ent -out put DAC buffers. A typical
application using a VFB op am p as a n I/V convert er is shown in Figur e 1.24.
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a
COMPENSATING FOR INPUT CAPACITANCE IN ACURRENT-TO-VOLTAGE CONVERTER USING VFB OP AMP
1.24
+
-
C2
R2
C1 VFBi
|A(s)|
1
fp
fx
fu
f
COMPENSATED
UNCOMPENSATED
fp=
fx =
fx = fp fu
C2 =
FOR 45 PHASE MARGIN
1
1
2R2C1
2R2C2
C1
2R2 fu
NOISEGAIN
The net input capacitan ce, C1, form s a pole at a frequen cy fp in th e noise gain
tr an sfer fun ction a s shown in t he Bode plot, an d is given by:
fpR C
=1
2 2 1.
If left uncompen sat ed, the ph ase sh ift a t t he frequen cy of inter section, fx
, will cause
insta bility an d oscillat ion. In tr oducing a zero at fx by adding feedback capacitor C2
sta bilizes the circuit a nd yields a ph ase m ar gin of about 45 degrees. The location of
th e zero is given by:
fxR C
=1
2 2 2.
Although th e a ddition of C2 actu ally decrea ses t he pole frequen cy slightly, this effect
is negligible if C2
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26
This value of C2 will yield a ph ase m ar gin of about 45 degrees. Increasin g the
capacitor by a factor of 2 increa ses th e pha se ma rgin to about 65 degrees (see
Referen ces 4 a nd 5).
In pr actice, th e optimu m valu e of C2 ma y be optimized experimen ta lly by var ying it
slight ly to optimize th e out put pulse response.
A similar a na lysis can be applied to a CFB op am p as sh own in F igure 1.25. In t hiscase, however, the low invert ing input impeda nce, Ro, great ly reduces the sen sitivity
to inpu t capa cita nce. In fact, an ideal CFB with zero input im pedan ce would be
totally insensitive to any amount of input capacitance!
a 1.25
RO
R2
COMPENSATING FOR INPUT CAPACITANCE IN A
CURRENT-TO-VOLTAGE CONVERTER USING CFB OP AMP
+ 1
fp
UNCOMPENSATED2R2C2
R2 ffx
|T(s)|
-
iC1
C2
R2
RO
fp=
fCL
COMPENSATED
FOR 45 PHASE MARGIN
2ROC1
1
1
2RO||R2C1
fx=
fx= fp
fCL
C2= C1
2R2fCL
The pole cau sed by C1 occur s a t a frequency fp:
fpRo R C RoC
= 1
2 2 1
1
2 1 ( || ).
This pole frequ ency will be genera lly be mu ch higher t ha n t he case for a VFB op
am p, and t he pole can be ignored completely if it occur s at a frequen cy great er t ha n
th e closed-loop band width of the op am p.
We next introduce a compensating zero at the frequency fx by insert ing the
capacitor C2:
fxR C
=1
2 2 2.
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27
As in the case for VFB, fx is th e geomet ric mean of fp and f cl:
fx fp fu= .
Solving the equations for C2 and rearranging it yields:
CRo
R
C
R fcl2
2
1
2 2=
.
There is a significant advant age in u sing a CF B op amp in th is configurat ion as can
be seen by compar ing th e similar equ at ion for C2 r equired for a VFB op am p. If th e
un ity-gain ba ndwidth product of th e VFB is equal t o the closed-loop ban dwidth of
th e CFB (at t he optimum R2), then th e size of th e CFB compen sat ion capa citor, C2,
is reduced by a factor of R Ro2 / .
A compa rison in an actu al a pplicat ion is sh own in F igure 1.26. The full scale outpu t
curr ent of the DAC is 4mA, the n et capacita nce at t he inverting input of the op ampis 20pF, and t he feedback resistor is 500. In th e case of the VFB op amp, th e poledue t o C1 occur s a t 16MH z. A compen sat ing capacitor of 5.6pF is r equired for 45
degrees of phase m ar gin, an d th e signa l bandwidth is 57MHz.
a 1.26
LOW INVERTING INPUT IMPEDANCE OF CFBOP AMP MAKES IT RELATIVELY INSENSITIVE TO INPUT
CAPACITANCE WHEN USED AS A
CURRENT-TO-VOLTAGE CONVERTER
+
1
fu = 200MHz
500-4mA
C1
C2
R2
VFB
fp=
2ROC1
+
-
C1
C2
R2
CFB
5004mA
20pF20pF
fCL = 200MHz
RO = 50
= 160MHz
C2 = 1.8pF
fx = 176MHz
1fp
=2R2C1
= 16MHz
C2 = 5.6pF
fx = 57MHz
For t he CF B op am p, however, becau se of th e low invertin g input impedan ce (Ro =
50 ), th e pole occurs a t 160Mhz, th e requ ired compen sat ion capa citor is a bout1.8pF, and the corresponding signal bandwidth is 176MHz. In actual practice, the
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28
pole frequency is so close to the closed-loop bandwidth of the op amp that it could
probably be left u ncompen sat ed.
It sh ould be noted th at a CFB op amp's r elative insensitivity to inverting input
capacitan ce is when it is used in th e inverting mode. In th e non-invert ing mode,
even a few picofara ds of str ay capacitan ce on the invert ing input can cause
significant gain-peaking and potential instability.
Anoth er a dvan ta ge of th e low inverting inpu t impeda nce of th e CFB op amp is when
it is used as a n I/V convert er t o buffer t he outpu t of a h igh speed cur ren t outpu t
DAC. When a step fun ction curr ent (or DAC switching glitch) is applied to th e
inverting input of a VFB op am p, it can produce a large voltage tra nsient u ntil the
signa l can propagate th rough the op am p to its out put an d negative feedback is
regain ed. Back-to-back Schottky diodes are often used t o limit t his volta ge swing as
shown in F igure 1.27. These diodes mu st be low capa cita nce, small geomet ry devices
becau se th eir capacitan ce adds to the total input capa citance.
A CFB op am p, on t he other ha nd, pr esent s a low impeda nce (Ro) to fast switching
curr ent s even before th e feedback loop is closed, th ereby limiting th e voltage
excursion without the requirement of the external diodes. This greatly improves thesett ling time of th e I/V convert er.
1.27
LOW INVERTING INPUT IMPEDANCE OF CFB OP AMPHELPS REDUCE AMPLITUDE OF FAST DAC TRANSIENTS
a
R2
* SCHOTTKYCATCHDIODES
CURRENT-OUTPUT
DAC
I
* NOT REQUIRED FOR CFB OP AMPBECAUSE OF LOW INVERTING INPUT IMPEDANCE
-
+VFB
NOISE COMP ARISONS BE TWEEN VF B AN D CFB OP AMP S
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Op am p n oise ha s t wo component s: low frequency noise whose spectra l density is
inversely proport iona l to th e squa re r oot of th e frequ ency an d white noise at
medium an d h igh frequencies. The low-frequency noise is kn own a s 1/f noise (th e
noise powerobeys a 1/f law - th e noise voltage or n oise curr ent is proport iona l to
1/f). The frequency at which th e 1/f noise spectr al den sity equa ls th e white n oise isknown a s th e "1/f Corn er F requ ency" an d is a figur e of merit for t he op am p, with
th e low values ind icat ing better perform an ce. Values of 1/f corner frequency vary
from a few Hz for th e most m odern low noise low frequency am plifiers t o severa lhu ndr eds, or even t housa nds of Hz for h igh-speed op am ps.
In m ost applicat ions of high speed op amps, it is the tota l out put rm s noise th at is
genera lly of inter est. Becau se of th e high ban dwidths, th e chief cont ribut or t o th e
out put rm s noise is th e white n oise, and th at of th e 1/f noise is negligible.
In order t o bett er u nder sta nd t he effects of noise in high speed op amps, we use th e
classical noise model shown in Figur e 1.28. This diagram identifies a ll possible white
noise sour ces, including th e extern al noise in t he source an d th e feedback resistors.
The equa tion allows you t o calculat e th e tota l out put rm s noise over t he closed-loop
ban dwidth of th e amp lifier. This formu la work s quite well when t he frequen cy
response of th e op am p is relat ively flat. If ther e is more tha n a few dB of highfrequency peaking, however, the actual noise will be greater than the predicted
becau se t he contr ibution over th e last octa ve before th e 3db cutoff frequ ency will
dominate. In most applications, the op amp feedback network is designed so that the
bandwidth is relatively flat, and the formula provides a good estimate. Note that
BW in t he equ at ion is th e equivalent n oise bandwidt h wh ich, for a single-pole
system, is obta ined by m ultiplying th e closed-loop ba ndwidth by 1.57.
1.28
OP AMP NOISE MODEL FOR A
FIRST-ORDER CIRCUIT WITH RESISTIVE FEEDBACK
R1
VON
Rp
In-
In+
VON =2
R2
fcl = CLOSED LOOP BANDWIDTH
In-2 R 2
2 + In+2 RP
2 1 +R1
R2+ Vn
2 + 4kTR 2 + 4kTR1 + 4kTR P1 +
21 +
2
Vn
VR2J
VR1J
VRPJ
BW = 1.57fcl
BWR2
R1
2 R2
R1
R2
R1
+
a
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30
Figur e 1.29 shows a ta ble which indicat es how the individual noise cont ribut ors a re
referred t o th e out put . After calculat ing the in dividua l noise spectra l densities in
this ta ble, they can be squared, added, and then the squ ar e root of the su m of the
squa res yields th e RSS value of th e out put noise spectra l density since all the
sources are u ncorr elated. This value is mu ltiplied by the squ ar e root of th e noise
ban dwidth (noise band width = closed-loop bandwidt h mu ltiplied by a corr ection
factor of 1.57) to obta in t he final valu e for t he out put rm s noise.
REFERRING ALL NOISE SOURCES TO THE OUTPUT
NOISE SOURCE EXPRESSED AS
A VOLTAGE
MULTIPLY BY THIS FACTOR TO REFER
TO THE OP AMP OUTPUT
Johnson Noise in Rp:
4kTRpNoise Gain
R
R== ++1
2
1
Non-Inverting Input Current Noise
Flowing in Rp:
In+Rp
Noise GainR
R== ++1
2
1
Input Voltage Noise:
VnNoise Gain
R
R== ++1
2
1
Johnson Noise in R1:
4 1kTR
R2/R1 (Gain from input of R1 to Output)
Johnson Noise in R2:
4 2kTR 1
Inverting Input Current Noise
Flowing in R2:
In-R2
1
a 1.29
Typical high speed op am ps with ban dwidths greater tha n 150MHz or so, and
bipolar input stages have input voltage noises ranging from about 2 to 20nV/Hz. Toput voltage n oise in perspective, let's look at th e J ohn son noise spectr al den sity of a
resistor:
vn
kTR BW= 4 ,
where k is Boltzman n's consta nt, T is th e absolute t emperat ure, R is th e resistor
value, an d BW is th e equivalent n oise ban dwidth of inter est. (The equivalent noise
ban dwidth of a single-pole system is 1.57 times th e 3dB frequency). Using th e
formula, a 100 resistor h as a noise density of 1.3nV/Hz, and a 1000 resistorabout 4n V/Hz (values are at room temperature: 27C, or 300K).
The base-emitter in a bipolar t ra nsistor ha s a n equivalent n oise voltage sour ce
which is due t o the "shot noise" of th e collector curr ent flowing in t he t ra nsistor's
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(noiseless) incremen ta l emitter r esistan ce, re. The curr ent noise is proport iona l to
th e squa re r oot of th e collector curr ent , Ic. The emitter resist an ce, on the other
ha nd, is inversely proport iona l to the collector cur ren t, so the shot-noise voltage is
inversely proportional to the square root of the collector current. (Reference 5, Section
9).
Volta ge noise in F ET-input op am ps ten ds to be lar ger th an for bipolar ones, but
current noise is extremely low (generally only a few tens of fA/Hz) becau se of th elow input bias currents. However, FET-inputs are not generally required for op ampapplicat ions r equiring bandwidths grea ter t han 100MHz.
Op amps also have input curr ent noise on each input. F or high-speed FET-input op
amps, th e gate current s ar e so low tha t input cur rent noise is almost a lways
negligible (measured in fA/Hz).
For a VFB op am p, the inverting a nd n on-inverting input cur rent noise ar e typically
equa l, an d almost a lways un corr elated. Typical values for wideban d VFB op amps
ra nge from 0.5pA/Hz t o 5pA/Hz. The input cur rent noise of a bipolar input stageis increased wh en inpu t bias-cur rent can cellation generat ors ar e added, becau se
their curr ent n oise is not corr elated, and t herefore a dds (in an RSS man ner) to the
intr insic curr ent noise of the bipolar st age.
The inpu t volta ge noise in CF B op am ps ten ds to be lower t ha n for VFB op amps
ha ving the sa me appr oximat e bandwidth. This is because t he input stage in a CFB
op am p is usually operat ed at a h igher curr ent, th ereby reducing the emitter
resista nce an d hen ce the voltage n oise. Typical values for CF B op amps r an ge from
about 1 t o 5nV/Hz.
The input cur rent noise of CFB op am ps tends t o be larger t han for VFB op amps
because of the generally higher bias current levels. The inverting and non-inverting
current noise of a CFB is usually different because of the unique input architecture,and ar e specified separat ely. In m ost cases, the inverting input curr ent noise is the
larger of th e two. Typical inpu t cur ren t n oise for CF B op am ps ra nges from 5 t o
40pA/Hz.
The gener al pr inciple of noise calculation is th at un corr elated n oise sources add in a
root-sum-squar es man ner, which m eans tha t if a noise sour ce ha s a contr ibution t o
th e out put noise of a system wh ich is less th an 20% of th e am plitude of th e noise
from other noise sour ce in th e system, th en its cont ribut ion t o th e total system n oise
will be less tha n 2% of th e total, an d th at noise sour ce can a lmost invar iably be
ignored - in ma ny cases, noise sources sma ller t ha n 33% of the lar gest can be
ignored. This can simplify th e calculations usin g the form ula, a ssum ing the corr ect
decisions a re m ade r egard ing the sour ces to be included a nd t hose to be neglected.
The sources which dominat e the outp ut noise ar e highly dependen t on th e closed-
loop gain of the op amp. Notice that for high values of closed loop gain, the op amp
voltage n oise will tend be th e chief cont ribut or t o the outpu t n oise. At low gains , the
effects of th e input curr ent noise mu st a lso be consider ed, and m ay dominat e,
especially in th e case of a CF B op amp.
Feedforwa rd/feedback resistors in h igh speed op am p circuits m ay r an ge from less
than 100 to more th an 1k, so it is difficult to genera lize a bout th eir cont ribut ion
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to th e tota l out put noise with out kn owing th e specific values an d th e closed loop
gain. The best way to make the calculations is to write a simple computer program
which perform s th e calculat ions a ut omatically an d include a ll noise sour ces. In m ost
high speed applicat ions, t he sour ce impeda nce noise can be neglected for source
impedances of 100 or less.
Figur e 1.30 shows an example calcula tion of tota l out put noise for t he AD8011
(300MHz, 1mA) CFB op amp. All six possible sources are included in the calculation.The appropriate multiplying factors which reflect the sources to the output are also
shown on t he diagra m. F or G=2, the close-loop ba ndwidt h of the AD8011 is
180MHz. The corr ection factor of 1.57 in th e final calculation convert s t his sin gle-
pole bandwidth into the circuits equivalent noise bandwidth.
a 1.30
AD8011 OUTPUT NOISE ANALYSIS
(G)
+
-
RS
50
fCL = 180MHz
1.8nV/Hz
0.5nV/Hz
4nV/Hz
4nV/Hz
5nV/Hz
4nV/Hz4nV/Hz
5pA/Hz4nV/Hz
AD8011
5pA/Hz
0.9nV/Hz
2nV/Hz
R11k
R2
1k
OUTPUT NOISE SPECTRAL DENSITY = 8.7nV/Hz
TOTAL NOISE = 8.71.57 X 180 X 106 = 146V rms
(G RS)
(G)
(1)
(R2)
(-R2/R1)
G = 1 +R2R1
In comm un icat ions applications, it is comm on to specify the noise figure (NF) of an
am plifier. Figure 1.31 shows th e definition. NF is the r at io of th e total int egrat ed
out put noise from a ll sour ces to the t otal out put noise which would resu lt if th e op
am p were "noiseless" (this noise would be th at of the sour ce resistan ce multiplied by
th e gain of th e op am p using t he closed-loop bandwidth of th e op am p to ma ke th ecalculat ion). Noise figure is expressed in dB. The value of the source resist an ce must
be specified, an d in m ost RF systems, it is 50. Noise figure is use ful incomm un icat ions r eceiver design, since it can be used t o mea sur e th e decrease in
signal-to-noise ra tio. For inst an ce, a n am plifier with a noise figure of 10dB following
a st age with a s ignal-to-noise ra tio of 50dB redu ces the signa l-to-noise rat io to 40dB.
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a 1.31
NOISE FIGURE OF AN OP AMP
+
-RS
50
NOISE FIGURE = 20log = 13.7dB
AD80110.9nV/Hz
R2
1k
R1
1k
8.7
1.8
TOTAL = 8.7nV/Hz
NOISE FIGURE = 20logTOTAL OUTPUT NOISE
OUTPUT NOISE DUE TO RS
1.8nV/HzG
The ra tio is comm only expressed in dB an d is useful in signal chain a na lysis. In th e
previous exam ple, the tota l out put voltage noise was 8.7nV/Hz. Integrat ed over theclosed loop ba ndwidth of th e op am p (180MHz), this yielded an out put noise of
146V rm s. The noise of th e 50 source resista nce is 0.9nV/Hz. If the op am p werenoiseless (with noiseless feedback r esistors), th is noise would appear at th e outpu t
mu ltiplied by th e noise gain (G=2) of th e op am p, or 1.8nV/Hz. The total outputrms noise just due t o the sour ce resistor int egrated over t he sa me ban dwidth is
30.3V rm s. The n oise figure is calculat ed as:
NF dB=
=20 10146
30 313 7log
.. .
The same result can be obtained by working with spectral densities, since the
bandwidths used for th e integration ar e the sam e and cancel each other in the
equation.
NF dB=
=20 108 7
1 813 7log
.
.. .
HIGH SPEED OP AMP NOISE SUMMARY
nn Voltage Feedback Op Amps:
uu Voltage Noise: 2 to 20nV/Hzuu Current Noise: 0.5 to 5pA/Hz
nn Current Feedback Op Amps:
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uu Voltage Noise: 1 to 5nV/Hzuu Current Noise: 5 to 40pA/Hz
nn Noise Contribution from Source Negligible if < 100
nn Voltage Noise Usually Dominates at High Gains
nn Reflect Noise Sources to Output and Combine (RSS)
nn Errors Will Result if there is Significant
High Frequency Peaking
a 1.32
DC CHARACTERISTICS OF H IGH SP E E D OP AMP S
High speed op amps a re optimized for ba ndwidth an d sett ling time, not for pr ecisionDC characteristics as found in lower frequency op amps such as the industry
standard OP27. In spite of this, however, high speed op amps do have reasonably
good DC per form an ce. The m odel shown in Figur e 1.33 shows how to reflect th e
input offset voltage and the offset currents to the output.
a 1.33
VO = VOS 1 + + Ib+R3 1 + - I b-R2
IF Ib+ = Ib- AND R3 = R1||R2
V O = VOS 1 +
MODEL FOR CALCULATING TOTAL
OP AMP OUTPUT VOLTAGE OFFSET
Ib-
VOS
+
-
R3
R2R1
R2
R1
Ib+
R2
R1
R2
R1
VO
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Inpu t offset voltages of high speed bipolar in put op am ps ar e ra rely tr immed, since
offset voltage ma tching of th e inpu t st age is excellent, typically ra nging from 1 to
3mV, with offset temperature coefficients of 5 to 15V/C.
Input bias curr ents on VFB op am ps (with n o input bias curr ent compensat ion
circuits) ar e appr oximat ely equa l for (+) an d () input s, an d can r an ge from 1 to 5A.
The output offset voltage due to the input bias curr ents can be nulled by mak ing the
effective source resista nce, R3, equa l to th e pa ra llel combina tion of R1 an d R2.
This scheme will not work, however, with bias-curr ent compen sat ed VFB op am ps
which h ave additional curren t genera tors on t heir inputs. In t his case, the net input
bias curr ent s ar e not necessar ily equa l or of th e sam e polar ity. Op am ps designed for
rail-to-rail input operation (parallel PNP and NPN differential stages as described
later in th is section) ha ve bias cur ren ts wh ich a re a lso a function of the comm on-
mode inpu t voltage. Exter na l bias cur ren t cancellation schemes a re ineffective with
th ese op am ps also. It sh ould be noted, however, th at it is often desira ble to ma tch
th e source impedan ce seen by the (+) an d () input s of VFB op am ps to minimize
distortion.
CFB op amps generally ha ve unequal an d un corr elated input bias curren ts becau seth e (+) an d () input s ha ve completely differen t a rchitectur es. For this r eason,
extern al bias curr ent can cellation schemes ar e also ineffective. CFB input bias
curr ents ra nge from 5 to 15A, being generally higher at the invert ing input
OUTPUT OFFSET VOLTAGE SUMMARY
nn High Speed Bipolar Op Amp Input Offset Voltage:
uu Ranges from 1 to 3mV for VFB and CFB
uu Offset TC Ranges from 5 to 15V/C
nn High Speed Bipolar Op Amp Input Bias Current:uu For VFB Ranges from 1 to 5A
uu For CFB Ranges from 5 to 15A
nn Bias Current Cancellation Doesn't Work for:
uu Bias Current Compensated Op Amps
uu Current Feedback Op Amps
a 1.34
P S R R C HARACTERISTICS OF H IGH SP E E D OP AMP S
As with most op am ps, th e power supp ly rejection ra tio (PSRR) of high speed op
am ps falls off ra pidly at higher frequencies. Figur e 1.35 shows the P SRR for t he
AD8011 CFB 300MHz CFB op amp. N otice th at at DC, the P SRR is near ly 60dB,
however, a t 10MH z, it falls to only 20dB, indicatin g th e need for excellent ext ern al
LF a nd H F decoupling. These nu mber s ar e fairly typical of most h igh speed VFB or
CFB op amps, alth ough t he DC PSRR m ay ra nge from 55 to 80dB depending on t he
op am p.
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a 1.35
AD8011 POWER SUPPLY REJECTION RATIO
+10
0
-10
-20
-30
-50
-60
-70
100k 1M 10M 100M 500M
FREQUENCY - Hz
-40
-80
-90
+PSRR
-PSRR
PSRR-dB
VS = +5V OR 5V
G = +2
RF = 1k
The power pins of op am ps mu st be decoupled directly to a la rge-area ground pla ne
with capa citors wh ich h ave minimal lead length. It is genera lly recommended tha t a
low-indu ctan ce cera mic surface mount capacitor (0.01F to 0.1F) be used for t he
high frequency noise. The lower frequency noise can be decoupled with low-
inducta nce ta nt alum electr olytic capacitors (1 to 10F).
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R E F E R E N C E S
1. Thoma s M. Freder iksen , In t u i t i ve Oper a t i ona l Am p l if ie r s ,
McGraw-Hill, 1988.
2. Sergio Franco, Current Feedback Amplifiers, E DN , Ja n.5, 1989.
3. Roy Gosser , U .S Pa t en t 5,150,074.
4. J a m es L. Melsa a nd Don ald G. Sch ult z, L in e a r C o n t r o l S ys t e m s ,
McGraw-Hill, 1969, pp. 196-220.
5. Am p l ifi e r App l ica t i on s Gu i de , Analog Devices, Inc., 1992,
Section 3.
6. Walter G. J ung, I C O p a m p C o o k b o o k , T h i r d E d i t i o n ,
Howar d S am s & Co., 1986, ISBN: 0-672-22453-4.
7. Pa ul R. Gray an d Robert G. Meyer, Ana l ys i s an d Des i gn o f Ana l ogI n t e g r a t e d C i r c u i t s , T h i r d E d i t i o n , J ohn Wiley, 1993.
8. J . K. Roberge, O p e r a t i o n a l Am p li fi e r s -T h e o r y a n d P r a c t i ce ,
J ohn Wiley, 1975.
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S e c o n d E d i t i on , J ohn Wiley, Inc., 1988.
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Ana l og Di a logue 25t h Ann i ve r s a r y I s s ue , pp. 19-31, 1991.
11. D. St ou t, M. Ka ufm an , H a n d b o o k o f O p e r a t i o n a l Am p l ifi e r C i r c u i t
Des ign , New York , McGra w-Hill, 1976.
12. J oe Buxton , Careful Design Tam es High-Sp eed Op Am ps, E l e c t r o n i c
Des ign , April 11, 1991.
13. J . Dosta l, Oper a t i on a l Am p l if ie r s , Elsevier Scientific Publishing,
New York, 1981.
14. Bar rie Gilbert , Cont emporary Feedback Am plifier Design ,
15. Sergio Franco, Des i gn w i t h Oper a t i on a l Am p l ifi e r s an d Ana l og ICs ,McGraw-Hill Book Company, 1988.
16. J era ld Graeme, P ho t od i ode Am p l ifi e r s -Op Am p So l u t i on s ,
Gain Technology Corporation, 2700 W. Broadway Blvd., Tucson,
AZ 85745, 1996.