APLIKASI OP-AMP LINIER.doc

8/16/2019 APLIKASI OP-AMP LINIER.doc

http://slidepdf.com/reader/full/aplikasi-op-amp-linierdoc 1/74



bchob%ha

bchop%ha

bchop%ln

Objectives

Chapter Ou bcthlion p % eha

18-1 n#erting-Ampli$er Circuits

18-2 &onin#erting-Ampli$er Circuits

18-3 n#erter/&onin#erter Circuits

18-4 'ifferential Ampli$ers

18-5 nstrumentation Ampli$ers

18-6 Summing Ampli$er Circuits

18-7 Current (oosters

18-8 )oltage-Controlle! CurrentSources

18-9 Automatic *ain Control

18-10 Single-Supply Operation

After stu!ying this chapter " you shoul!

be able to+

■ 'escribe se#eral applications for in#erting ampli$ers.

■ 'escribe se#eral applications for

nonin#erting ampli$ers.

■ Calculate the #oltage gain of

in#erting an! nonin#erting

ampli$ers.

■ ,plain the operation an!

characteristics of !iff erential

ampli$ers an! instrumentation

ampli$ers.

■ Calculate the output #oltage of

binary eighte! an! /0 '/A

con#erters.

■ 'iscuss current boosters an!

#oltage-controlle! current

sources.

■ 'ra a circuit shoing ho an

op amp can be operate! from a

single poer supply.

ocabular!

automatic gain control

1A*C2a#erager

buff er

current booster

!ifferential ampli$er

!ifferential input #oltage

!ifferential #oltage gain

!igital-to-analog 1'/A2

con#erter 3oating loa!

guar! !ri#ing

input trans!ucer

instrumentation ampli$er

laser trimming

linear op-amp circuit

output trans!ucer

/0 la!!er '/A con#erter

rail-to-rail op amp

sign changer

s4uelch circuit

thermistor

#oltage reference

741



230 Chapter 18

5 067

18-1 "nvertin#-$mpli%er Circuitsn this chapter an! succee!ing chapters" e ill be !iscussing many !ifferent

types of op-amp circuits. nstea! of pro#i!ing a summary page shoing all of the

circuits" small summary boes ill be gi#en containing the important formulas

for circuit un!erstan!ing. Also" here nee!e!" the fee!back resistor R f ill be

labele!a s R" R0" or other !esignations.

The in#erting amplifier is one of the most basic circuits. Pre#ious chap-

ters ha#e !iscusse! the prototype for this amplifier. One a!#antage of thisampli- fier is that its #oltage gain e4uals the ratio of the fee!back resistance to

the input resistance. Let us look at a fe applications.

&i#h-"mpe'ance (robe

8igure 69-6 shos a high-impe!ance probe that can be use! ith a !igital mul-

timeter. (ecause of the #irtual groun! in the first stage" the probe has an input

impe!ance of 677 :) at lo fre4uencies. The first stage is an in#erting

amplifier ith a #oltage gain of 7.6. The secon! stage is an in#erting amplifier

ith a #oltage gain of either 6 or 67.

The circuit of 8ig. 69-6 gi#es you the basic i!ea of the 67;6 probe. t

has a #ery high input impe!ance an! an o#erall #oltage gain of either 7.6 or 6. n

the <67 position of the sitch" the output signal is attenuate! by a factor of 67.n the <6 position" there is no attenuation of the output signal. The basic circuit

shon here can be impro#e! by a!!ing more components to increase the

ban!i!th.

$C-Couple' $mpli%er

n some applications" you !o not nee! a response that eten!s !on to =ero fre-

4uency because only ac signals !ri#e the input. 8igure 69-0 shos an ac-couple!

amplifier an! its e4uations. The #oltage gain is shon as+

0 R f Av 5 R6

8or the #alues gi#en in 8ig. 69-0" the close!-loop #oltage gain is+

Av 50677

k )67 k )

)i#ure 18-1 >igh-impe!ance probe.

0<67

?

677 k @

PO(,

6

#in

67 :@

B

677 k @ <6 6 :@

5

B

TO '::

ATT,&ATO&

<67+ A# D 7.6



231Linear Op-Amp Circuit Applications

<6+ A# D 6



5 067

gain is+

Iith the e4uations an! #alues gi#en in 8ig. 69-H" the close!-loop #oltage

Av 50677 k )67 k )

The minimum fee!back fraction is+

67 k) i 677 ) Bmin K

677 k)

K 7.776

The maimum fee!back fraction is+

67 k) i 67.6 k ) Bma K

677 k)K 7.75

f f unity 5 6 :>=" the minimum an! maimum ban!i!ths are+

f 01CL2min 5 17.776216 :>=2 5 6 k>=

f 01CL2ma 5 17.75216 :>=2 5 57 k>=

n summary" hen R #aries from 677 ) to 67 k)" the #oltage gain remains con-

stant but the ban!i!th #aries from 6 to 57 k>=.

18-2 ,oninvertin#-$mpli%erCircuits

The nonin#erting amplifier is another basic op-amp circuit. A!#antages inclu!e

stable #oltage gain" high input impe!ance" an! lo output impe!ance. >ere are

some applications.

$C-Couple' $mpli%er

8igure 69-? shos an ac-couple! nonin#erting amplifier an! its analysis e4ua-

tions. C 6 an! C 0 are coupling capacitors. C H is a bypass capacitor. sing a

bypass capacitor has the a!#antage of minimi=ing the output offset #oltage.>eres hy+ n the mi!ban! of the amplifier" the bypass capacitor has a #ery

)i#ure 18-4 AC-couple! nonin#erting ampli$er .

C 6

6 E8

B

v R0

C 0

6 E8

R f Av D B 6 R6

f 0 D Av

f c6 Din677 k @

R6

6 k @

C H

6 E8

R f

677 k @

R L

67 k @vout f c0 D

f cH D

0 pR0C 6

6

0 pR LC 0

6

0 pR6C H



B 5 1

6 6 5

f c6 5

5 65F >=

f c0 5 6

6765 6?F k>=

lo impe!ance. Therefore" the bottom of R6 is at ac groun!. n the mi!ban!" the

fee!back fraction is+

R R1 6 R f

169-62

n this case" the circuit amplifies the input #oltage as pre#iously !escribe!.

Ihen the fre4uency is =ero" the bypass capacitor C H is open an! the

fee!back fraction B increases to unity because+

B 5M

5

6M 6

6

This e4uation is #ali! if e !efine M as an etremely large #alue" hich is

hat the impe!ance e4uals at =ero fre4uency. Iith B e4ual to 6" the close!-loop

#oltage gain is unity. This re!uces the output offset #oltage to a minimum.

Iith #alues gi#en in 8ig. 69-?" e can calculate the mi!ban! #oltage

gain as+

Av 5677 k )6 k )

f f unity is 65 :>=" the ban!i!th is+

f 01CL2 565

:>=

The input coupling capacitor pro!uces a cutoff fre4uency of+

6 NN 5 6.5F >=

0 1677 k)216 82

Similarly" the output coupling capacitor C 0 an! the loa! resistance R L pro!uce a

cutoff fre4uency f c0+

0 167 k)216 82 5 65.F >=

The bypass capacitor pro!uces a cutoff fre4uency of+

f cH 5 6

0 16 k)216 82

$u'io istribution $mpli%er

8igure 69-5 shos an ac-couple! nonin#erting amplifier !ri#ing three #oltage

folloers. This is one ay to !istribute an au!io signal to se#eral !ifferent

outputs. The close!-loop #oltage gain an! ban!i!th of the first stage are gi#en

by the familiar e4uations shon in 8ig. 69-5. 8or the #alues shon" the close!-

loop #oltage gain is ?7. f f unity is 6 :>=" the close!-loop ban!i!th is 05 k>=.nci!entally" an op amp like an L:H?9 is con#enient to use in a circuit

like 8ig. 69-5 because the L:H?9 is a 4ua! G?6Nfour G?6s in a 6?-pin pack-

age. One of the op amps can be the first stage" an! the others can be the #oltage

folloers.

.)/-+itche' olta#e

ain

Some applications re4uire a change in close!-loop #oltage gain. 8igure 69-



shos a nonin#erting amplifier hose #oltage gain is controlle! by a 8,T that

acts like a sitch. The input #oltage to the 8,T is a to-state #oltage" either

=ero or V GS 1off 2. Ihen the control #oltage is lo" it e4uals V GS 1off 2 an! the 8,T

is open.



)i#ure 18-5 'istribution ampli$er .

B

OTPT A

&PT B A# D B 6 6

0

677 k @

f

HF k @

B

OTPT (

f 0 Df unity

A#

6

6 k @

B

OTPT C

)i#ure 18-6 8,T sitch controls #oltage gain.

vin

B)CC

B

LOI *AT,+

f

6

f )

,,

A# Df

B 6 6 0

0

7 ) 6

)*S 1off2

n this case" R0 is ungroun!e! an! the #oltage gain is gi#en by the usual e4uation

for a nonin#erting amplifier 1the top e4uation in 8ig. 69-2.

Ihen the control #oltage is high" it e4uals 7 ) an! the 8,T sitchis close!. This puts R0 in parallel ith R6" an! the close!-loop #oltage gain

!ecreases to+

Av 5 R f

R1 R2

6 1 169-02

n most !esigns" R0 is ma!e much larger than r ds1on2 to pre#ent the 8,T

resistance from affecting the close!-loop #oltage gain. Sometimes" you may see

se#eral resistors an! 8,T sitches in parallel ith R6 to pro#i!e a selection of

!ifferent #oltage gains.



6 6 5

6 6 5

$pplication /ample 18-1One application for 8ig. 69- is in a suelch circuit This kin! of circuit is use!

in communication recei#ers to re!uce listener fatigue by ha#ing a lo #oltage

gain hen no signal is being recei#e!. This ay" the user !oes not ha#e to listen

to static hen there is no communication signal. Ihen a signal comes in" the

#oltage gain is sitche! to high.f R6 5 677 k)" R f 5 677 k)" an! R0 5 6 k) in 8ig. 69-" hat is the

#oltage gain hen the 8,T is onQ Ihat is the #oltage gain hen the 8,T is

offQ ,plain ho the circuit can be use! as part of a s4uelch circuit.

O"O, Iith the e4uations gi#en in 8ig. 69-" the maimum #oltage

gain is+

Av 5677 k)

6 6 5 670677 k) i 6 k )

The minimum #oltage gain is+

Av 5

677

k )677 k )

Ihen a communication signal is being recei#e!" e can use a peak !etector an!

other circuits to pro!uce a high gate #oltage for the 8,T in 8ig. 69-. This pro-

!uces maimum #oltage gain hile the signal is being recei#e!. On the other

han!" hen no signal is being recei#e!" the output of the peak !etector is lo an!

the 8,T is cut off" pro!ucing minimum #oltage gain.

olta#e 8 eerence

The :C6?7H is a special-function C calle! a volta#e reerence: a circuit that

pro!uces an etremely accurate an! stable output #oltage. 8or any positi#e

supply #oltage beteen ?.5 an! ?7 )" it pro!uces an output #oltage of 0.5 ) ith

a tolerance of O6 percent. The temperature coefficient is only 67 ppm/RC. The

abbre#i- ation ppm stan!s for parts per million 16 ppm is e4ui#alent to 7.7776

percent2. Therefore" 67 ppm/RC pro!uces a change of only 0.5 m) for a 677RC

change in temperature 167 H 7.7776 percent H 677 H 0.5 ) 2. The point is

that the output #oltage is ultra-stable an! e4ual to 0.5 ) o#er a large temperature

range.

The only problem is that 0.5 ) may be too lo a #oltage reference for

many applications. 8or instance" suppose e ant a #oltage reference of 67 ).

Then" one solution is to use an :C6?7H an! a nonin#erting amplifier as shon

in 8ig. 69-G. Iith the circuit #alues shon" the #oltage gain is+

Av 5H7

k )67 k )

an! the output #oltage is+

V out 5 ?10.5 )2 5 67

)



(ecause the close!-loop #oltage gain of the nonin#erting amplifier is only ?" the

output #oltage ill be a stable #oltage reference of 67 ).



R5 06

)i#ure 18-7 )oltage reference.

BV CC

:C6?7H0.5 )

B

L:H?9

V out

R f

R f Av D B 6

V EE

H7 k @V out D Av10.5 )2

R6

67 k @

18-3 "nverter;,oninverter Circuits

n this section" e ill !iscuss circuit applications here the input signal !ri#es both inputs of the op amp simultaneously. Ihen an input signal !ri#es both in-

puts" e get both in#erting an! nonin#erting amplification at the same time.

This pro!uces some interesting results because the output is the superposition of

to amplifie! signals.

The total #oltage gain ith an input signal !ri#ing both si!es of the op

amp e4uals the #oltage gain of the in#erting channel plus the #oltage gain of the

nonin#erting channel+

Av 5 Av<inv= 6 Av<non= 169-H2

Ie ill use this e4uation to analy=e the circuits of this section.

+itchable "nverter;,oninverter

8igure 69-9 shos an op amp that can function as either an in#erter or a nonin-

#erter. Iith the sitch in the loer position" the nonin#erting input is groun!e!

an! the circuit is an in#erting amplifier. Since the fee!back an! input resistances

are e4ual" the in#erting amplifier has a close!-loop #oltage gain of+

Av 5

0 R

)i#ure 18-8 e#ersible #oltage gain.

vin

&O&&),T

&),T

B)CC

B

vout

TOP POSTO&

A# D 6

(OTTO: POSTO&

A# D 6

),,



R6 6 5

Ihen the sitch is mo#e! to the upper position" the input signal !ri#es

both the in#erting an! the nonin#erting inputs simultaneously. The #oltage gain

of the in#erting channel is still+

Av1in#2 5 06

The #oltage gain of the nonin#erting channel is+

Av1non2 5

R

The total #oltage gain is the superposition or algebraic sum of the to gains+

Av 5 Av1in#2 6 Av1non2 5 06 6 0 5 6

The circuit is a sitchable in#erter/nonin#erter. t has a #oltage gain of

either 6 or 06" !epen!ing on the position of the sitch. n other or!s" the

circuit pro!uces an output #oltage ith the same magnitu!e as the input #oltage"

but the phase can be sitche! beteen 7R an! 0697R. As an eample" if vin is

65 )" vout ill be either 65 ) or 05 ) !epen!ing on the sitch position.

.)/-Controlle' +itchable "nverter

8igure 69-F is a mo!ification of 8ig. 69-9. The 8,T acts like a #oltage-controlle! resistance r ds. The 8,T has either a #ery lo or a #ery high

resistance" !epen!ing on the gate #oltage.

Ihen the gate #oltage is lo" it e4uals V GS 1off 2 an! the 8,T is

open. Therefore" the input signal !ri#es both inputs. n this case+

Av1non2 5 0

Av1in#2 5 06

an!

Av 5 Av1in#2 6 Av1non2 5 6

The circuit acts like a nonin#erting #oltage amplifier ith a close!-loop #oltage

gain of 6.Ihen the gate #oltage is high" it e4uals 7 ) an! the 8,T has a #ery

lo resistance. Therefore" the nonin#erting input is approimately groun!e!. n

this case" the circuit acts like an in#erting #oltage amplifier ith a close!-loop

#oltage gain of 06. 8or proper operation" R shoul! be at least 677 times greater

than the r ds of the 8,T.

n summary" the circuit has a #oltage gain that can be either 6 or 06"

!epen!ing on hether the control #oltage to the 8,T is lo or high.

)i#ure 18-9 8,T-controlle! re#ersible gain.

#

in

B)CC

B

#out

LOI *AT,

A# D6

>*> *AT,

A# D 6

7 )

)*S 1off2

),,



5 0G5.9

)i#ure 18-10 n#erter ith a!Justable gain.

6 0

#in

#out

B

0

6 A# 7

6 7 to 0

"nverter +ith $'justable ain

Ihen the #ariable resistor of 8ig. 69-67 is =ero" the nonin#erting input is

groun!e! an! the circuit becomes an in#erting amplifier ith a #oltage gain of

0 R0/ R6. Ihen the #ariable resistor is increase! to R0" e4ual #oltages !ri#e the

nonin#erting an! in- #erting inputs of the op amp 1common-mo!e input2.

(ecause of the common-mo!e reJection" the output #oltage is approimately

=ero. Therefore" the circuit of 8ig. 69-67 has a #oltage gain that is continuously

#ariable from0

R0/ R6 to 7.

$pplication /ample 18-2Ihen e nee! to #ary the amplitu!e of an out-of-phase signal" e can use a

circuit like the one in 8ig. 69-67. f R6 5 6.0 k) an! R0 5 F6 k)" hat are the

#alues of the maimum an! minimum #oltage gainQ

O"O, Iith the e4uation gi#en in 8ig. 69-67" the maimum #oltage

gain is+

Av 5

0F6

k )6.0 k )

The minimum #oltage gain is =ero.

($C"C/ (O*/> 18-2 n Application ,ample 69-0" hat

#alue shoul! R0 be change! to for a maimum gain of 057Q

i#n Chan#er

The circuit of 8ig. 69-66 is calle! a si#n chan#er: a rather unusual circuit

because its #oltage gain can be #arie! from 06 to 6. >ere is the theory of operation+ Ihen the iper is all the ay to the right" the nonin#erting input is

groun!e! an! the circuit has a #oltage gain of+

Av 5 06

Ihen the iper is all the ay to the left" the input signal !ri#es the non-

in#erting input as ell as the in#erting input. n this case" the total #oltage gain is

the superposition of the in#erting an! nonin#erting #oltage gains+

Av1non2 5 0

Av1in#2 5 06



Av 5 Av1in#2 6 Av1non2 5

6



R5 0n

)i#ure 18-11 e#ersible an! a!Justable gain of O6.

#in

#out

B 6 A# 6

)A/A(L,

n summary" hen the iper is mo#e! from right to left" the #oltage

gain changes continuously from 06 to 6. At the crosso#er point 1iper at

center2" a common-mo!e signal !ri#es the op amp an! the output is i!eally =ero.

$'justable an' eversible ain

8igure 69-60 shos another unusual circuit. t allos us to a!Just the #oltagegain beteen 0n an! n. The theory of operation is similar to that of the sign

changer. Ihen the iper is all the ay to the right" the nonin#erting input is

groun!e! an! the circuit becomes an in#erting amplifier ith a close!-loop

#oltage gain of+

Av 5

0nR

Ihen the iper is all the ay to the left" it can be shon that+

Av1in#2 5 0n

Av1non2 5 0n

Av 5 Av1non2 6 Av1in#2 5

n

These results can be !eri#e! by applying The#enins theorem to the circuit an!

simplifying ith algebra.

Circuits like those in 8igs. 69-66 an! 69-60 are unusual because they

ha#e no simple !iscrete counterparts. They are goo! eamples of circuits that

oul! be !ifficult to implement ith !iscrete components but are easy to buil!

ith op amps.

)i#ure 18-12 e#ersible an! a!Justable gain of On.

n

#in

n

n 6B

#out n A# n



)A/A(L,



n 5

f c 5 6

5 065.GR

$pplication /ample 18-3f R 5 6.5 k) an! nR 5 G.5 k) in 8ig. 69-60" hat is the maimum positi#e

#oltage gainQ Ihat is the #alue of the other fie! resistanceQ

O"O, The #alue of n is+

G.5 k ) N 5

56.5 k )

The maimum positi#e #oltage gain is 5. The other fie! resistor has a #alue of+

nR — 5

n0 6

516.5 k)2

5 0 65 6.9G5 k )

Iith a circuit like this" e ha#e to use a precision resistor to get a nonstan!ar!

#alue like 6.9G5 k ).

($C"C/ (O*/> 18-3 sing 8ig. 69-60" if R 5 6 k)" hat is

the maimum positi#e #oltage gain an! #alue of the other fie! resistanceQ

(hase hiter

8igure 69-6H shos a circuit that can i!eally pro!uce a phase shift of 7R to

0697R. The nonin#erting channel has an RC lag circuit" an! the in#erting

channel has to e4ual resistors ith a #alue of RF. Therefore" the #oltage gain of

the in#erting channel is alays unity. (ut the #oltage gain of the nonin#erting

channel !epen!s on the cutoff fre4uency of the RC lag circuit.

Ihen the input fre4uency is much loer than the cutoff fre4uency 1 f "" f c2" the capacitor appears open an!+

Av1non2 5 0

Av1in#2 5 06

Av 5 Av1non2 6 Av1in#2 5

6

This means that the output signal has the same magnitu!e as the input signal" an!

the phase shift is 7R" ell belo the cutoff fre4uency of the lag netork.

Ihen the input fre4uency is much greater than the cutoff fre4uency

1 f .. f c2" the capacitor appears shorte!. n this case" the nonin#erting channel

has a #oltage gain of =ero. The o#erall gain therefore e4uals the gain of in#erting

channel" hich is 06" e4ui#alent to a phase shift of 0697R.

To calculate the phase shift beteen the to etremes" e nee! to cal-

culate the cutoff fre4uency using the e4uation gi#en in 8ig. 69-6H. 8or instance"if C 5 7.700 8 an! #ariable resistor of 8ig. 69-6H is set to 6 k)" the cutoff

fre4uency is+

0 16 k)217.700 825 G.0H k>=

Iith a source fre4uency of 6 k>=" the phase shift is+

5 00 arctan6 k>=



G.0H k>=



#in #out

f

)i#ure 18-13 Phase shifter .

#in6 k>=

#out

B

C

A# D 6 1:A*&T',2

6 f c D

0 pC

f f D 0 arctanfc

#in#

f

#out

t

f the #ariable resistor is increase! to 67 k)" the cutoff fre4uency !ecreases to

G0H >= an! the phase shift increases to+

5 00 arctan6 k>=

5 0679RG0H >=

f the #ariable resistor is increase! to 677 k)" the cutoff fre4uency !ecreases to

G0.H >= an! the phase shift increases to+

5 00 arctan6 k>=

5 06G0RG0.H >=

n summary" the phase shifter pro!uces an output #oltage ith the same

magnitu!e as the input #oltage" but ith a phase angle that can be #arie!

continuously beteen 7R an! 0697R.

18-4 ierential $mpli%ersThis section ill !iscuss ho to buil! a 'ierential ampliier using an op amp.

One of the most important characteristics of a !ifferential amplifier is its C:

because the typical input signal is a small !ifferential #oltage an! a large com-

mon-mo!e #oltage.

*asic ierential $mpli%er

8igure 69-6? shos an op amp connecte! as a !ifferential amplifier. Theresistor R6F has the same nominal #alue as R6 but !iffers slightly in #alue because

of tolerances. 8or instance" if the resistors are 6 k) O 6 percent" R6 may be as

high as6767 ) an! R6F may be as lo as FF7 )" an! #ice #ersa. Similarly" R0 an! R0F

are

nominally e4ual but may !iffer slightly because of tolerances.



n 8ig. 69-6?" the !esire! input #oltage vin is calle! the 'ierential

input volta#e to !istinguish it from the common-mo!e input #oltage vin1CM 2. A

circuit



Av 52

)i#ure 18-14 'ifferential ampli$er .

6 0#in1C:2

B#in

#out

B

A# D 0

6

#in1C:2

6 0

U U V

0 A

# 1C: 2

V?

OO O

?,O@

>igh-spee! !ata flo is accom-

plishe! ith S( H.7 1ni#ersal

Serial (us H.72 by using com-

plementary signals on pairs of

ires" calle! !ifferential pairs .

These signals fee! !ifferential

amplifiers hich reJect common-

mo!e noise interference an!

pro!uce the !esire! output.

like 8ig. 69-6? amplifies the !ifferential input #oltage vin to get an output #oltage

of vout. sing the superposition theorem" it can be shon that+

vout 5 Avvin

here

0 R R1

169-?2

This #oltage gain is calle! the 'ierential volta#e #ain to !istinguish it from thecommon-mo!e #oltage gain Av1CM 2. (y using precision resistors" e can buil! a

!ifferential amplifier ith a precise #oltage gain.

A !ifferential amplifier is often use! in applications in hich the !if-

ferential input signal vin is a small !c #oltage 1milli#olts2 an! the common-mo!e

input signal is a large !c #oltage 1#olts2. As a result" the C: of the circuit be-

comes a critical parameter. 8or instance" if the !ifferential input signal is G.5 m)

an! the common-mo!e signal is G.5 )" the !ifferential input signal is 7 !( less

than the common-mo!e input signal. nless the circuit has a #ery high C:"

the common-mo!e output signal ill be obJectionably large.

C> o the Op $mp

n 8ig. 69-6?" to factors !etermine the o#erall C: of the circuit. 8irst" there

is the C: of the op amp itself. 8or a G?6C" the minimum C: is G7 !( at

lo fre4uencies. f the !ifferential input signal is 7 !( less than the common-

mo!e input signal" the !ifferential output signal ill be only 67 !( greater than

the common-mo!e output signal. This means that the !esire! signal is only H.6

times greater than the un!esire! signal. Therefore" a G?6C oul! be useless in an

application such as this.

The solution is to use a precision op amp like an OP-7GA. t has a min-

imum C: of 667 !(. This ill significantly impro#e the operation. f the

!ifferential input signal is 7 !( less than the common-mo!e input signal" the

!ifferential output signal ill be 57 !( greater than the common-mo!e outputsignal. This oul! be fine if the C: of the op amp ere the only source of

error.

C> o /ternal 8 esistors

There is a secon! source of common-mo!e error+ the tolerance of the resistors in

8ig. 69-6?. Ihen the resistors are perfectly matche!+

R6 5 R6F

R0 5 R0F



R169-2

R1

6 1

2 1 R2F

n this case" the common-mo!e input #oltage of 8ig. 69-6? pro!uces =ero #oltage

across the op-amp input terminals.

On the other han!" hen the resistors ha#e a tolerance of O6 percent"

the common-mo!e input #oltage of 8ig. 69-6? ill pro!uce a common-mo!e

output #oltage because the mismatch in the resistances pro!uces a !ifferential

input #oltage to the op amp.

As !iscusse! in Sec. 69-H" the o#erall #oltage gain hen the same

signal !ri#es both si!es of an op amp is gi#en by+

Av<CM = 5 Av<inv= 6 Av<non= 169-52

n 8ig. 69-6?" the in#erting #oltage gain is+

Av<inv= 5

0 R2

1

an! the nonin#erting #oltage gain is+

Av<non= 5 1 R2

R F 6 R F 2 169-

G21 2

here the secon! factor is the !ecrease in the nonin#erting input signal cause!

by the #oltage !i#i!er on the nonin#erting si!e.

Iith ,4s. 169-52 through 169-G2" e can !eri#e these useful formulas+

Av<CM = 5 O2' R 1 2

Ror R 5 R 169-92

Av<CM = 5 O4' R 1 2 R

or R R

or

' R

169-F2

O2 WW Av<CM = O4' R

169-672 R R

n these e4uations" ' R/ R is the tolerance of the resistors con#erte! to the !ecimal

e4ui#alent.

8or instance" if the resistors ha#e a tolerance of O6 percent" ,4. 169-92

gi#es+

Av1CM 2 5 O016X2 5 O017.762 5 O7.70

,4uation 169-F2 gi#es+

Av1CM 2 5 O?16X2 5 O?17.762 5 O7.7?

ne4uality 169-672 gi#es+

O7.70" Av1CM 2 "

O7.7?

This says that the common-mo!e #oltage gain is beteen O7.70 an! O7.7?.Ihen necessary" e can calculate the eact #alue of Av1CM 2 ith ,4s. 169-52

through 169-G2.

Calculatin# C>

>ere is an eample of ho to calculate the C:+ n a circuit like the one in

8ig. 69-6?" resistors ith a tolerance of O7.6 percent are commonly use!.

Ihen R6 5 R0" ,4. 169-?2 gi#es a !ifferential #oltage gain of+

Av 5 06



an! ,4. 169-92 gi#es a common-mo!e #oltage gain of+

Av1CM 2 5 O017.6X2 5 O017.7762 5 O7.770



The C: has a magnitu!e of+

C: 5Y Av Y

56

5 577Y Av1CM 2 Y 7.770

hich is e4ui#alent to 5? !(. 1 Note: The #ertical bars aroun! Av an! Av1CM 2 in!i-

cate absolute #alues.2

*uere' "nputs

The source resistances !ri#ing the !ifferential amplifier of 8ig. 69-6? effecti#ely

become part of R6 an! R6F" hich changes the #oltage gain an! may !egra!e the

C:. This is a #ery serious !isa!#antage. The solution is to increase the input

impe!ance of the circuit.

8igure 69-65 shos one ay to !o it. The first stage 1the preamp2

consists of to #oltage folloers that buer 1isolate2 the inputs. This can

increase the input impe!ance to ell o#er 677 :). The #oltage gain of the first

stage is unity for both the !ifferential an! the common-mo!e input signal.

Therefore" the secon! stage 1the !ifferential amplifier2 still has to pro#i!e all the

C: for the circuit.

@heatstone *ri'#e

As pre#iously mentione!" the !ifferential input signal is often a small !c #oltage.

The reason it is small is because it is usually the output of a Iheatstone bri!ge

like that in 8ig. 69-6a. A Iheatstone bri!ge is balance! hen the ratio of

resistances on the left si!e e4uals the ratio of resistances on the right si!e+

R1 R3

R2

5 R4

169-662

)i#ure 18-15 'ifferential input ith buffere! inputs.

#in1C:2 B 6 0

B#in

#out

B

#in1C:2 6 0

'88 A:P

P,A:P

A# D 6

A# D 0

6

A# 1C:2 D 6B % 0

U

U A# 1C: 2

B % ?



v0 56

v? 56767

)i#ure 18-16 1a2 Iheatstone bri!ge; 1b2 slightly unbalance! bri!ge.

B)CC B65 )

6 H 6 k @ 6 k @

B#out BG.5 )

BHG m) BG.5HG )

0 ? 6 k @ 6767 @

1a2 1 b2

Ihen this con!ition is satisfie!" the #oltage across R0 e4uals the #oltage across

R?

an! the output #oltage of the bri!ge is =ero.

The Iheatstone bri!ge can !etect small changes in one of the resistors.

8or instance" suppose e ha#e a bri!ge ith three resistors of 6 k) an! a fourth

resistor of 6767 )" as shon in 8ig. 69-6b. The #oltage across R0 is+

0 k)165 )2 5 G.5 )

an! the #oltage across R? is approimately+

0767 )165 )2 5 G.5HG )

The output #oltage of the bri!ge is approimately+

vout 5 v? 0 v0 5 G.5HG ) 0 G.5 ) 5 HG m)

0rans'ucers

esistance R? may be an input trans'ucer: a !e#ice that con#erts a nonelectri-

cal 4uantity into an electrical 4uantity. 8or instance" a photoresistor con#erts a

change in light intensity into a change in resistance" an! a thermistor con#erts a

change in temperature into a change in resistance. Other input trans!ucers that

are common in in!ustrial systems applications inclu!e thermocop!es an!

res"stance temperatre detectors 1T's2.There is also the output trans'ucer: a !e#ice that con#erts an electrical

4uantity into a nonelectrical 4uantity. 8or instance" an L,' con#erts current into

light" an! a lou!speaker con#erts ac #oltage into soun! a#es.

A i!e #ariety of trans!ucers are commercially a#ailable for 4uantities

such as temperature" soun!" light" humi!ity" #elocity" acceleration" force"

ra!ioac- ti#ity" strain" an! pressure" to mention a fe. These trans!ucers can be

use! ith a Iheatstone bri!ge to measure nonelectrical 4uantities. (ecause the

output of a Iheatstone bri!ge is a small !c #oltage ith a large common-mo!e

#oltage" e nee! to use !c amplifiers that ha#e #ery high C:s.



vin' R

vin 5 ' R

)i#ure 18-17 (ri!ge ith trans!ucer !ri#es instrumentation ampli$er .

V CC

B65 )vin1CM 2

B6 k @

7.6X

677 k @

7.6X

R

6 k @ R6 k @

R

6 k @

TA&S'C,

R B U R

6767 @

vin vout

B

vin1CM 2 6 k @

7.6X

677 k @

7.6X

Av D R0

R6

vin DU R

V CC ? R

$ !pical $pplication

8igure 69-6G shos a typical application. Three of the bri!ge resistors ha#e a

#alue of+

R 5 6 k )

The trans!ucer has a resistance of+

R 6 ' R 5 6767

)

The common-mo!e signal is+

vin1CM 2 5 7.5V CC 5 7.5165 V 2 5 G.5

)

This is the #oltage across each of the loer bri!ge resistors hen ' R 5 7.

Ihen a bri!ge trans!ucer is acte! on by an outsi!e 4uantity such as

light" temperature" or pressure" its resistance ill change. 8igure 69-6G shos a

trans!ucer resistance of 6767 )" hich implies that ' R5

67 ). t is possible to!eri#e this e4uation for the input #oltage in 8ig. 69-6G+

4 R 6 2' RV CC 169-602

n a typical application" 0' R"" ? R an! the e4uation simplifies to+

4 RV CC 169-6H2

8or the #alues shon in 8ig. 69-6G+



vin K67

? k)165 )2 5 HG.5 m)



5 05777

Since the !ifferential amplifier has a #oltage gain of 0677" the !ifferential

output #oltage is+

vout 5 06771HG.5 m)2 5 0H.G5 )

As far as the common-mo!e signal is concerne!" ,4. 169-F2 gi#es+

Av1CM 2 5 O?17.6X2 5 O?17.7762 5 O7.77?

for the tolerance of O7.6 percent shon in 8ig. 69-6G. Therefore" the common-

mo!e output #oltage is+vout1CM 2 5 O7.77?1G.5 )2 5 O7.7H

) The magnitu!e of C: is+

C: 5 677

7.77?

hich is e4ui#alent to 99 !(.

That gi#es you the basic i!ea of ho a !ifferential amplifier is use!

ith a Iheatstone bri!ge. A circuit like 8ig. 69-6G is a!e4uate for some

applications" but can be impro#e!" as ill be !iscusse! in the folloing section.

18-5 "nstrumentation $mpli%ersThis section !iscusses the instrumentation ampliier: a !ifferential amplifier

optimi=e! for its !c performance. An instrumentation amplifier has a large #olt-

age gain" a high C:" lo input offsets" lo temperature !rift" an! high input

impe!ance.

*asic "nstrumentation $mpli%er

8igure 69-69 shos the classic !esign use! for most instrumentation amplifiers.

The output op amp is a !ifferential amplifier ith the #oltage gain of unity. The

resistors use! in this output stage are usually matche! to ithin O7.6 percent or

better. This means that the C: of the output stage is at least 5? !(.Precision resistors are commercially a#ailable from less than 6 ) to

more than 67 :)" ith tolerances of O7.76 to O6 percent. f e use matche!

resistors that are ithin O7.76 percent of each other" the C: of the output

stage can be as high as G? !(. Also" temperature !rift of precision resistors can

be as lo as 6 ppm /RC.

The first stage consists of to input op amps that act like a

preamplifier. The !esign of the first stage is etremely cle#er. Ihat makes it

so ingenious is the action of point A" the Junction beteen the to R6 resistors.

Point A acts like a #irtual groun! for a !ifferential input signal an! like a floating

point for the common-mo!e signal. (ecause of this action" the !ifferential

signal is amplifie! but the common-mo!e signal is not.

(oint $The key to un!erstan!ing ho the first stage orks is to un!erstan! hat point

A !oes. Iith the superposition theorem" e can calculate the effect of each input

ith the other =eroe!. 8or instance" assume that the !ifferential input signal is

=ero. Then only the common-mo!e signal is acti#e. Since the common-mo!e sig-

nal applies the same positi#e #oltage to each nonin#erting input" e4ual #oltages

appear at the op-amp outputs. (ecause of this" the same #oltage appears e#ery-

here along the branch that contains R6 an! R0. Therefore" point A is floating

an!



)i#ure 18-18 Stan!ar! three op-amp instrumentation ampli$er .

#in1C: 2 B

0

B#in

A #out

B 6

0

#in1C: 2

P,A:P '88 A:P

0A# D B 6

A# D 6

6 U A# 1C:2 D B % 0

A# 1C: 2 D 6

each input op amp acts like a #oltage folloer. As a result" the first stage has a

common-mo!e gain of+

Av1CM 2 5 6

nlike the secon! stage" here the R resistors ha#e to be closely

matche! to minimi=e the common-mo!e gain" in the first stage" the tolerance of

the resistors has no effect on the common-mo!e gain. This is because the entire

branch containing these resistors is floating at a #oltage of vin1CM 2 abo#e groun!.

So" the resistor #alues !o not matter. This is another a!#antage of the three op-

amp !esign of 8ig. 69-69.

The secon! step in applying the superposition theorem is to re!uce the

common-mo!e input to =ero an! to calculate the effect of the !ifferential input

signal. Since the !ifferential input signal !ri#es the nonin#erting inputs ith e4ual

an! opposite input #oltages" one op-amp output ill be positi#e an! the other ill

be negati#e. Iith e4ual an! opposite #oltages across the branch containing the

R6 an! R0 resistors" point A ill ha#e a #oltage of =ero ith respect to groun!.

n other or!s" point A is a #irtual groun! for the !ifferential signal. 8or

this reason" each input op amp is a nonin#erting amplifier an! the first stage has

a !ifferential #oltage gain of+

Av 5 R2

6 1 169-

6?2 R1

Since the secon! stage has a gain of unity" the !ifferential #oltage gain of the in-

strumentation amplifier is gi#en by ,4. 169-6?2.

(ecause the first stage has a common-mo!e gain of unity" the o#erall

common-mo!e gain e4uals the common-mo!e gain of the secon! stage+

Av<CM = 5 O2' R — 169-652



R



Av 52

6 6 5

To ha#e high C: an! lo offsets" precision op amps must be use!

hen buil!ing the instrumentation amplifier of 8ig. 69-69. A typical op amp

use! in the three op-amp approach of 8ig. 69-69 is the OP-7GA. t has the

folloing orst-case parameters+ nput offset #oltage is 7.705 m)" input bias

current is 0 nA" input offset current is 6 nA" AV#L is 667 !(" C: is 667 !("

an! temperature !rift is 7. )/RC.

A final point about 8ig. 69-69+ Since point A is a #irtual groun! ratherthan a mechanical groun!" the R6 resistors in the first stage !o not ha#e to be sep-

arate resistors. Ie can use a single resistor RG

that e4uals 0 R6

ithout changing

the operation of the first stage. The only !ifference is that the !ifferential #oltage

gain is ritten as+

2 R RG

6 1 169-62

The factor of 0 appears because RG 5 0 R6.

$pplication /ample 18-4n 8ig. 69-69" R6 5 6 k)" R0 5 677 k)" an! R 5 67 k). Ihat is the !ifferential

#oltage gain of the instrumentation amplifierQ Ihat is the common-mo!e

#oltage gain if the resistor tolerances in the secon! stage are O7.76 percentQ

f vin 5

67 m) an! vin1CM 2 5 67 )" hat are the #alues of the !ifferential an! com-

mon-mo!e output signalsQ

O"O, Iith the e4uations gi#en in 8ig. 69-69" the #oltage gain of the

preamp is+

Av 5677

k )6 k )

Since the #oltage gain of the secon! stage is 06" the #oltage gain of the instru-

mentation amplifier is 0676.

The common-mo!e #oltage gain of the secon! stage is+

Av1CM 2 5 O017.76X2 5 O017.77762 5 O7.7770

Since the first stage has a common-mo!e #oltage gain of 6" the common-mo!e

#oltage gain of the instrumentation amplifier is O7.7770.

A !ifferential input signal of 67 m) ill pro!uce an output signal of+

vout 5 0676167 m)2 5 06.76 )

A common-mo!e signal of 67 ) ill pro!uce an output signal of+

vout1CM 2 5 O7.7770167 )2 5 O0 m)

,#en though the common-mo!e input signal is 6777 times greater than the !if-

ferential input" the C: of the instrumentation amplifier pro!uces a com-

mon-mo!e output signal that is approimately 577 times smaller than the !iffer-

ential output signal.

($C"C/ (O*/> 18-4 epeat Application ,ample 69-? ith

R0 5 57 k) an! O7.6 percent secon!-stage resistor tolerance.



v 5494

OO O ?,O@

:onolithic instrumentation

amplifiers" like the A'07" fin!

many applications in the me!ical

instrumentation fiel!. One such

application is in electrocar!iog-

raphy 1,C*2 monitor circuits.

uar' rivin#

(ecause the !ifferential signal out of a bri!ge is small" a shiel!e! cable is often

use! to isolate the signal-carrying ires from electromagnetic interference. (ut

this creates a problem. Any leakage current beteen the inner ires an! the

shiel! ill a!! to the lo input bias an! offset currents. (esi!es the leakage

current" the shiel!e! cable a!!s capacitance to the circuit" hich slos !on

the response of the circuit to a change in trans!ucer resistance. To minimi=e the

effects of leakage current an! cable capacitance" the shiel! shoul! be

bootstrappe! to the common-mo!e potential. This techni4ue is knon as #uar'

'rivin#

8igure 69-6Fa shos one ay to bootstrap the shiel! to the com-

mon-mo!e #oltage. A ne branch containing the resistors labele! RH is a!!e!

to the output of the first stage. This #oltage !i#i!er picks off the common-mo!e

#oltage an! fee!s it to a #oltage folloer. The guar! #oltage is fe! back to the

shiel!" as shon. Sometimes" separate cables are use! for each input. n this

case" the guar! #oltage is connecte! to both shiel!s" as shon in 8ig. 69-6Fb.

"nte#rate' "nstrumentation $mpli%ers

The classic !esign of 8ig. 69-69 can be integrate! on a chip ith all the compo-

nents shon in 8ig. 69-69" ecept RG. This eternal resistance is use! to control

the #oltage gain of the instrumentation amplifier. 8or instance" the A'07 is amonolithic instrumentation amplifier. The !ata sheet gi#es this e4uation for its

#oltage gain+

RG

6 1 169-6G2

The 4uantity ?F.? k) is the sum of the to R0 resistors. The C manu-

facturer uses laser trimmin# to get a precise #alue of ?F.? k). The or! tr"m

refers to a fine a!Justment rather than a coarse a!Justment. Laser trimming

means

)i#ure 18-19 *uar! !ri#ing to re!uce leakage currents an! capacitance of shiel! cable.

#in1C: 2B

S>,L','

CA(L,

0

H

6

#in

6

H

0

*A'

#in1C:2

*A' )OLTA*,



1a2 1 b2



Av 5

)i#ure 18-20 1a2 A monolithic instrumentation ampli$er; 1b2 guar! !ri#ing ith an A'07.

V CC

B65 )0

Bvin

?FF @

V7.6X

0 G

6

RG A'07

59

H

V EE

65 )

6

RG

vout 0

RG

0

9

H

1a2 1b2

burning off resistor areas on a semicon!uctor chip ith a laser to get an

etremely precise #alue of resistance.8igure 69-07a shos the A'07 ith an RG of ?FF ). This is a

precision resistor ith a tolerance of O7.6 percent. The #oltage gain is+

?F.? k ) N 6 6 5

677?FF

The p"not 1pin numbers2 of the A'07 is similar to that of a G?6C since pins 0

an! H are for the input signals" pins ? an! G are for the supply #oltages" an! pin

is the output. Pin 5 is shon groun!e!" the usual case for the A'07. (ut this

pin !oes not ha#e to be groun!e!. f necessary for interfacing ith another

circuit" e can offset the output signal by applying a !c #oltage to pin 5.

f guar! !ri#ing is use!" the circuit can be mo!ifie! as shon in

8ig. 69-07b. The common-mo!e #oltage !ri#es a #oltage folloer hose outputis connecte! to the shiel! of the cable. A similar mo!ification is use! if separate

cables are use! for the inputs.

n summary" monolithic instrumentation amplifiers typically ha#e a

#oltage gain beteen 6 an! 6777 that can be set ith one eternal resistor" a

C: greater than 677 !(" an input impe!ance greater than 677 :)" an input

offset #oltage less than 7.6 m)" a !rift of less than 7.5 )/RC" an! other

outstan!ing parameters.

18-6 ummin# $mpli%er CircuitsIe !iscusse! the basic summing amplifier in Chap. 6. &o" let us look at

some #ariations of this circuit.

he ubtracter

8igure 69-06 shos a circuit that subtracts to input #oltages to pro!uce an out-

put #oltage e4ual to the !ifference of v6 an! v0. >ere is ho it orks+ nput v6

!ri#es an in#erter ith a #oltage gain of unity. The output of the first stage is0v6. This #oltage is one of the inputs to the secon!-stage summing circuit. The

other input is v0. Since the gain of each channel is unity" the final output #oltage

e4uals v6 minus v0.



# ?

)i#ure 18-21 Subtracter .

#6

B

B

#0

#out #out D #6 #0

ummin# on *oth "nputs

Sometimes you may see a circuit like 8ig. 69-00. t is nothing more than a sum-

ming circuit that has in#erting an! nonin#erting inputs. The in#erting si!e of the

amplifier has to input channels" an! the nonin#erting si!e has to input chan-

nels. The total gain is the superposition of the channel gains.

The gain of each in#erting channel is the ratio of the fee!back resistor

R f to input channel resistance" either R6 or R0. The gain of each nonin#ertingchannel is+

R f6 6

R6 i R0

re!uce! by the #oltage-!i#i!er factor of the channel" either+

R? i R5

RH 6 R? i R5

or

RH i R5

R? 6 RH i R5

8igure 69-00 gi#es the e4uations for the gain of each channel. After getting each

channel gain" e can calculate total output #oltage.

)i#ure 18-22 Summing ampli$er using both si!es of the op amp.

#6#out D A#6#6 B A# 0#0 B A# H#H B A# ?#?

#0

0

#out

# 66

A# 0 D 0

B f ? 5

H 6 0

#H

H B ? 5

#? 6 0

?

? B H 5



5 0

5 0H

2

2

—

$pplication /ample 18-5n 8ig. 69-00" R6 5 6 k)" R0 5 0 k)" RH 5 H k)" R? 5 ? k)" R5 5 5 k)" an!

R f 5 k). Ihat is the #oltage gain of each channelQ

O"O, Iith the e4uations gi#en in 8ig. 69-00" the #oltage gains are+

Av6 50

k 6 k )

Av0 50

k )0 k )

6 k) i 0 k )

6 k) i 0 k )

? k) i 5 k )

H k) 6 ? k) i 5 k)5 ?.0

H k) i 5 k )

? k) 6 H k) i 5 k)5 H.6F

($C"C/ (O*/> 18-5 epeat Application ,ample 69-5 using

6 k) for R f .

he $vera#er

8igure 69-0H is an avera#er: a circuit hose output e4uals the a#erage of the

input #oltages. ,ach channel has a #oltage gain of+

Av5

R5

6H R H

Ihen all amplifie! outputs are a!!e!" e get an output that is the a#erage of all

input #oltages.

The circuit shon in 8ig. 69-0H has three inputs. Any number of inputs

can be use!" as long as each channel input resistance is change! to nR" here n is

the number of channels.

;$ Converter

n !igital electronics" a 'i#ital-to-analo# <;$= converter takes a binary repre-

sente! #alue an! con#erts it into a #oltage or current. This #oltage or current ill

)i#ure 18-23 A#eraging circuit.

H

#6 #

H

out

1#6 B #0 B #H2D

H

#0

H #H



#out



254 Chapter 18

)i#ure 18-24 (inary-eighte! '/A con#erter changes !igital input to analog #oltage.

7 )#H

0 #0

?

#6

9 #7 B

#out

6.9G5 )

#out D 1#H B 7.5#0 B 7.05#6 B 7.605#72

1a2 1 b2

be proportional to the input binary #alue. To metho!s of '/A con#ersion are

often use!" the binary-eighte! '/A con#erter an! the /0 la!!er '/A

con#erter.

The binary-eighte! '/A con#erter is shon in 8ig. 69-0?. This circuit pro!uces an output #oltage e4ual to the eighte! sum of the inputs. The $e"%ht

is the same as the gain of the channel. 8or instance" in 8ig. 69-0? a the channel

gains are+

AvH 5 06

Av0 5 07.5

Av6 5 07.05

Av7 5 07.605

The input #oltages are !igital or to-state" hich means that they ha#e a #alue of

either 6 or 7. Iith ? inputs" there are 6 possible input combinations of vHv0v6v7+

7777" 7776" 7767" 7766" 7677" 7676" 7667" 7666" 6777" 6776" 6767" 6766" 6677"

6676" 6667" an! 6666.Ihen all inputs are =ero 177772" the output is+

vout 5 7

Ihen vHv0v6v7 is 7776" the output is+

vout 5 017.6052 5 07.605

Ihen vHv0v6v7 is 7767" the output is+

vout 5 017.052 5 07.05

an! so on. Ihen the inputs are all 6s 166662" the output is maimum an! e4uals+

vout 5 016 6 7.5 6 7.05 6 7.6052 5 06.9G5

f the '/A con#erter of 8ig. 69-0? is !ri#en by a circuit that pro!uces

the 7777 to 6666 se4uence of numbers gi#en earlier" it ill pro!uce these output

#oltages+ 7" 07.605" 07.05" 07.HG5" 07.5" 07.05" 07.G5" 07.9G5" 06"

06.605"

06.05" 06.HG5" 06.5" 06.05" 06.G5" an! 06.9G5. Ihen #iee! on an oscillo-

scope" the output #oltage of the '/A con#erter ill look like the negati#e-going

staircase shon in 8ig. 69-0?b.

The staircase #oltage !emonstrates that the '/A con#erter !oes not pro-

!uce a continuous range of output #alues. Therefore" strictly speaking" its output

is not truly analog. Lo-pass filter circuits can be connecte! to the output to pro-

#i!e a smoother transition beteen output steps.



2 N

A ?-input '/A con#erter has 6 possible outputs" an 9-input A/ '

con- #erter has 05 possible outputs" an! a 6-input '/A con#erter has 5"5H

possible outputs. This means that the negati#e-going staircase #oltage of 8ig.

69-0?b can ha#e 05 steps ith an 9-input con#erter an! 5"5H steps ith a 6-

input con- #erter. A negati#e-going staircase #oltage like this is use! in a !igital

multimeter along ith other circuits to measure the #oltage numerically.

The binary-eighte! '/A con#erter can be use! in applications here

the number of inputs is limite! an! here high precision is not re4uire!. Ihen

a higher number of inputs is use!" a higher number of !ifferent resistor #alues is

re4uire!. The accuracy an! stability of the '/A con#erter !epen!s on the

absolute accuracy of the resistors an! their ability to track each other ith

temperature #ariations. (ecause the input resistors all ha#e !ifferent #alues"

i!entical tracking characteristics are !ifficult to obtain. Loa!ing problems can

also eist ith this type of '/A con#erter because each input has a !ifferent

input impe!ance #alue.

The ;2 la''er ;$ converter: shon in 8ig. 69-05" o#ercomes the

limitations of the binary-eighte! '/A con#erter an! is the metho! most often

use! in integrate!-circuit '/A con#erters. (ecause only to resistor #alues are

re4uire!" this metho! len!s itself to Cs ith 9-bit or higher binary inputs an!

pro#i!es a higher !egree of accuracy. 8or simplicity" 8ig. 69-05 is shon as

a

?-bit '/A con#erter. The sitches &7 &H oul! normally be some type ofacti#e sitch. The sitches connect the four inputs to either groun! 1logic 72 or

6V ref 1logic 62. The la!!er netork con#erts the possible binary input #alues

from 7777 through 6666 to one of 6 uni4ue output #oltage le#els. n the '/A

con#erter shon in 8ig. 69-05" &7 is consi!ere! to be the least significant input

bit 1LS(2" hile &H is the most significant bit 1:S(2.

To !etermine the '/A con#erters output #oltage" you must first change

the binary input #alue to its !ecimal-e4ui#alent #alue (&. This can be !one by+

*", 5 < D0 H 20= 6 < D1 H 21= 6 < D2 H 22= 6 < D3 H 23= 169-

692

Then" the output #oltage ill be foun! by+

V out 5 0<*", H 2V re9 = 169-6F2

here N e4uals the number of inputs.

8or more !etails on this circuits operation" the '/A con#erter can be

The#eni=e!. This analysis can be foun! in Appen!i '.

)i#ure 18-25 /0 la!!er '/A con#erter .

f

07 k @

5 6

67 k @

G

67 k @

0

9

67 k @

H ?

#out

07 k @ 07 k @

'7

07 k @

'6

07 k @

'0

07 k @

'H



B

),,

V out 5 01 F

V out 5 01 F

—

R

#

B

$pplication /ample 18-6n 8ig. 69-05" &7 5 6" &6 5 7" &0 5 7" an! &H 5 6. sing a V ref #alue of 65

)" !etermine the !ecimal e4ui#alent of the binary input 1(&2 an! the output

#oltage of the con#erter.

O"O, sing ,4. 169-692" the !ecimal e4ui#alent can be foun! by+

(& 5 16 H 072 6 17 H 062 6 17 H 002 6 16 H 0H2 5 F

The output #oltage of the con#erter is foun! by using ,4. 169-6F2 as+

0? 2 H 0 15 V

2

62167 V 2 5 05.05 V

($C"C/ (O*/> 18-6 sing 8ig. 69-05" hat is the largest

an! smallest output #oltage possible ith at least one input being a logic 6Q

18-7 Current *oostersThe short-circuit output current of an op amp is typically 05 mA or less. One ay

to get more output current is to use a poer op amp like the L:G5 or L:60.

These op amps ha#e short-circuit output currents of H an! 67 A. Another ay to

get more short-circuit output current is to use a current booster: a poer

transistor or other !e#ice that has a current gain an! a higher current rating than

the op amp.

ni'irec tional *ooster

8igure 69-0 shos one ay to increase the maimum loa! current. The output

of an op amp !ri#es an emitter folloer. The close!-loop #oltage gain is+

Av 5 R2

6 1 169-0721

)i#ure 18-26 ni!irectional current booster increases short-circuit output

current.

vin

B)CCA D

0B 6

6

=out=out1CL2 D

( D 6

6 B A)OL(

0v

6 B 0

ma D b!c SC

6 L out



Av 52

n this circuit" the op amp no longer has to supply the loa! current. nstea!" it

only has to supply base current to the emitter folloer. (ecause of the current

gain of the transistor" the maimum loa! current is increase! to+

I ma 5 b'c I SC 169-062

here ' SC is the short-circuit output current of the op amp. This means that an op

amp like a G?6C can ha#e a maimum output current of 05 mA increase! by a

factor of !c. 8or instance" a (97 is an npn poer transistor ith !c 5 677.

f it is use! ith a G?6C" the short-circuit output current increases to+ ' ma 5 677105 mA2 5 0.5 A

The circuit can !ri#e lo-impe!ance loa!s because the negati#e

fee!back re!uces the output impe!ance of the emitter folloer by a factor of 6

6 AV#L B. Since the emitter folloer alrea!y has a lo output impe!ance" the

close!-loop output impe!ance ill be #ery small.

*i'irec tional

Current

The !isa!#antage of the current booster shon in 8ig. 69-0 is its n"d"rect"ona!

!oad crrent( 8igure 69-0G shos one ay to get a b"d"rect"ona! !oad crrent(

An in#erting amplifier !ri#es a Class-( push-pull emitter folloer. n thiscircuit" the close!-loop #oltage gain is+

0 R R1

169-002

Ihen the input #oltage is positi#e" the loer transistor is con!ucting an! the

loa! #oltage is negati#e. Ihen the input #oltage is negati#e" the upper transistor

is con!ucting an! the output #oltage is positi#e. n either case" the maimum

output current is increase! by the current gain of the con!ucting transistor. Since

the Class-( push-pull emitter folloer is insi!e the fee!back loop" the close!-

loop output impe!ance is #ery small.

ail-to-ail Op $mps

Current boosters are sometimes use! in the final stage of an op amp. 8or instance"

the :CHH07? is a rail-to-rail op amp that has a current-booste! output of 97

mA. Ra"!)to)ra"! refers to the supply lines of an op amp because they look like

rails on a schematic !iagram. Ra"!)to)ra"! operat"on means that the input an!

output #oltages can sing all the ay to the positi#e or negati#e supply #oltages.

)i#ure 18-27 (i!irectional current booster .

0

B)CC

6

B)CC A# D 0

6

=out

6 B A)OL(

vin

B L vout

( D 6

' D b '

),,

ma !c SC

),,



5 056

5 7.76F0

* out1CL2 5G5 )

8or instance" the G?6C !oes not ha#e a rail-to-rail output because the

output is alays 6 to 0 ) less than either supply #oltage. On the other han!" the

:CHH07? !oes ha#e a rail-to-rail output because its output #oltage can sing to

ithin 57 m) of either supply #oltage" close enough to 4ualify as rail-to-rail. ail-

to-rail op amps allo a !esigner to make full use of the a#ailable supply #oltage

range.

$pplication /ample 18-7n 8ig. 69-0G" R6 5 6 k) an! R0 5 56 k). f a G?6C is use! for the op amp"

hat is the #oltage gain of the circuitQ Ihat is the close!-loop output

impe!anceQ Ihat is the shorte!-loa! current of the circuit if each transistor has a

current gain of 605Q

O"O, Iith the e4uations gi#en in 8ig. 69-0" the #oltage gain is+

Av 5056

k )6 k )

The fee!back fraction is+

B 5 6 k )

6 k) 6 56 k )

Since the G?6C has a typical #oltage gain of 677"777 an! an open-loop output

impe!ance of G5 )" the close!-loop output impe!ance is+

6 6 1677"777217.76F025 7.7HF )

Since the G?6C has a shorte!-loa! current of 05 mA" the booste! #alue of the

shorte!-loa! current is+

' ma 5 605105 mA2 5 H.6H A

($C"C/ (O*/> 18-7 sing 8ig. 69-0G" change R0 to 0G k ).

'etermine the ne #oltage gain" * out1CL2 an! ' ma" hen each transistor has a cur-

rent gain of 677.

18-8 olta#e-Controlle'

Current ourcesThis section !iscusses circuits that allo an input #oltage to control an output

current. The loa! may be floating or groun!e!. All the circuits are #ariations of

the )CS prototype" hich means that they are #oltage-controlle! current

sources" also knon as #oltage-to-current con#erters.

)loatin# 6oa'

8igure 69-09 shos the )CS prototype. The loa! may be a resistor" a relay" or



a motor. (ecause of the #irtual short beteen the input terminals" the in#erting

input



#

i out 5in

vin0 1

)i#ure 18-28 ni!irectional )CS ith 3oating loa!.

B)CCiout D #in

vin B )L1ma2 D )CC #in

LOA'

L1ma2

)CCD

in

6

),, ' ma D ' SC

is bootstrappe! to ithin micro#olts of the nonin#erting input. Since #oltage vin

appears across R" the loa! current is+

v R

169-0H2

Since the loa! resistance !oes not appear in this e4uation" the current is

in!epen!- ent of the loa! resistance. State! another ay" the loa! appears to be

!ri#en by a #ery stiff current source. As an eample" if vin is 6 ) an! R is 6 k)"

"out is 6 mA.

f the loa! resistance is too large in 8ig. 69-09" the op amp goes into sat-

uration an! the circuit no longer acts like a stiff current source. f a rail-to-rail op

amp is use!" the output can sing all the ay to 6V CC . Therefore" the maimum

loa! #oltage is+

V L<ma= 5 V CC 0 vin 169-0?2

8or eample" if V CC is 65 ) an! vin is 6 )" V L1ma2 is 6? ). f the op amp !oes

not ha#e a rail-to-rail output" e can subtract 6 to 0 ) from V L1ma2.

Since the loa! current e4uals vin/ R" e can !eri#e this e4uation for themaimum loa! resistance that can be use! ithout saturating the op amp+

R L<ma= 5 R <V CC = 169-052

As an eample" if R is 6 k)" V CC is 65 )" an! vin is 6 )" then R L1ma2 5 6?

k ).Another limitation on a #oltage-controlle! current source is the short-

circuit output current of the op amp. 8or instance" a G?6C has a short-circuit

output current of 05 mA. As an e4uation" the short-circuit current out of the con-

trolle! current source in 8ig. 69-09 is+

I ma 5 I SC 169-02

here ' SC is the short-circuit output current of the op amp.



$pplication /ample 18-8f the current source of 8ig. 69-09 has R 5 67 k)" vin 5 6 )" an! V CC 5 65 )"

hat is the output currentQ Ihat is the maimum loa! resistance that can be use!ith this circuit if vin can be as large as 67 )Q



B)CC

LOA'

67 )

5 7.6 mA

R169-0G2

O"O, Iith the e4uations of 8ig. 69-09" the output current is+

"out 5 6 )67 k )

The maimum loa! resistance is+

R L1ma2 5 167 k)2 1 65 )0 6 2 5 5 k )

($C"C/ (O*/> 18-8 Change R to 0 k) an! repeat Application

,ample 69-9.

roun'e' 6oa'

f a loatin# loa' is all right an! the short-circuit current is a!e4uate" a circuit

like 8ig. 69-09 orks ell. (ut if the loa! nee!s to be groun!e! or more short-

circuit current is nee!e!" e can mo!ify the basic circuit as shon in 8ig. 69-0F.

Since the collector an! emitter currents of the transistor are almost e4ual" the

current through R is approimately e4ual to the loa! current. (ecause of the

#irtual short beteen the op-amp inputs" the in#erting input #oltage

approimately e4uals vin. Therefore" the #oltage across R e4uals V CC minus vin an!

the current through R is gi#en by+

i out 5V CC 0

v in

8igure 69-0F shos the e4uations for maimum loa! #oltage" maimum

loa! resistance" an! short-circuit output current. &otice that the circuit uses a

current booster on the output si!e. This increases the short-circuit output

current to+

I ma 5 b'c I SC 169-092

Output Current irec tl! (roportional

to "nput olta#e

n 8ig. 69-0F" the loa! current !ecreases hen the input #oltage increases.

8igure 69-H7 shos a circuit in hich the loa! current is !irectly proportional

to the input #oltage. (ecause of the #irtual short on the input terminals of the

)i#ure 18-29 ni!irectional )CS ith single-en!e! loa!.

B)CC

iout D)CC #in

vin B

)L1ma2 D #in

L1ma2 D

)CC

' ma D b!c ' SC

#in 6

),,



B

),,

LOA'

i out 5in

i out 5in

)i#ure 18-30 Another uni!irectional )CS ith single-en!e! loa!.

B)CC

iout D

#in

B)CC

()L1ma2 D )CC #in

)CC L1ma2 D 6

#in

B)CC

' D b '

vin

Z6B

A

),,

Z0ma !c SC

first op amp" the emitter current in +6 is vin/ R. Since the +6 collector current is

approimately the same as the emitter current" the #oltage across the collector R

is vin an! the #oltage at no!e A is+

V A 5 V CC 0 vin

This is the nonin#erting input to the secon! op amp.

(ecause of the #irtual short beteen the input terminals of the secon!

op amp" the #oltage at no!e B is+

V B 5 V A

The #oltage across the final R is+V R 5 V CC 0 V B 5 V CC 0 1V CC 0 vin2 5 vin

Therefore" the output current is approimately+

v R

169-0F2

8igure 69-H7 shos the e4uations for analy=ing this circuit. Again" a

current booster increases the short-circuit output current by a factor !c.

&o+lan' Current ource

The current source of 8ig. 69-H7 pro!uces a uni!irectional loa! current. Ihen

a bi!irectional current is nee!e!" the >olan! current source of 8ig. 69-H6 may

be use!. 8or a preliminary un!erstan!ing of ho it orks" consi!er the special

case of R L 5 7. Ihen the loa! is shorte!" the nonin#erting input is groun!e!"

the in#erting input is at #irtual groun!" an! the output #oltage is+

vout 5 0vin

On the loer si!e of the circuit" the output #oltage ill appear across R in series

ith the shorte! loa!. The current through R is+

0v R

169-H72



1 2

5 07.0 mA

)i#ure 18-31 >olan! current source is a bi!irectional )CS.

vin

B)CC

#in

)CC #in

0

B L1ma2 D0

)CC 6

#

),,

LOA'

Ihen the loa! is shorte!" all this current flos through the loa!. The minus sign

means that the loa! #oltage is in#erte!.

Ihen the loa! resistance is greater than =ero" the analysis is much more

complicate! because the nonin#erting input is no longer groun!e! an! the in#ert-

ing input is no longer a #irtual groun!. nstea!" the nonin#erting input #oltage

e4uals the #oltage across the loa! resistor. After riting an! sol#ing se#eral

e4ua- tions" e can sho that ,4. 169-H72 is still #ali! for any loa! resistance"

pro#i!e! the op amp !oes not go into saturation. Since R L !oes not appear in the

e4uation" the circuit acts like a stiff current source.

8igure 69-H6 shos the analysis e4uations. 8or instance" if V CC 5 65"

vin 5 H )" an! R 5 6 k)" the maimum loa! resistance that can be use!

ithout saturating the op amp is+

65 )

0 N

R L1ma2 56 k )

H)0 6 5 0 k )

$pplication /ample 18-9The >olan! current source of 8ig. 69-H6 has R 5 65 k)" vin 5 H )" an! V CC 5

65 ). Ihat is the output currentQ Ihat is the largest loa! resistance that can be

use! ith this circuit if the maimum input #oltage is F )Q

O"O, Iith the e4uations of 8ig. 69-H6+

"out 50H

)65 k )

The maimum loa! resistance is+

0 1 60 ) 0 6 2 5 6.99 k ) R L1ma2 565 k ) 65 )

($C"C/ (O*/> 18-9 epeat Application ,ample 69-F ith



R 5 67 k ).



18-9 $utomatic ain Control AGC stan!s for automatic #ain control n many electronic communications sys-

tems" like ra!io an! tele#ision" e ant the #oltage gain to change automatically

hen the input signal changes. Specifically" hen the input signal increases" e

ant the #oltage gain to !ecrease. n this ay" the output #oltage of an amplifier

ill be approimately constant. One reason for anting A*C in a ra!io or

tele#ision is to keep the #olume from changing abruptly hen e tune in !ifferent

stations.

$u'io $C

8igure 69-H0 shos an au!io A*C circuit. +6 is a 8,T use! as a #oltage-

controlle! resistance. 8or small-signal operation ith !rain #oltages near =ero"

the 8,T operates in the ohmic region an! has a resistance of r ds to ac signals.

The r ds of a 8,T can be controlle! by the gate #oltage. The more negati#e the

gate #oltage is" the larger r ds becomes. Iith a 8,T like the 0&?96" r ds can #ary

from

677 ) to more than 67 :).

RH an! +6 act like a #oltage !i#i!er hose output #aries beteen 7.776vi

an! vin. Therefore" the nonin#erting input #oltage is beteen 7.776vin an! vin" a

7-!( range. The output #oltage of the nonin#erting amplifier is 1 R0 / R6 6

62

times this input #oltage.

n 8ig. 69-H0" the output #oltage is couple! to the base of +0. 8or a peak-

to- peak output less than 6.? )" +0 is cut off because there is no bias on it. Iith

+0 off" capacitor C 0 is uncharge! an! the gate of +6 is at 0V EE " enough negati#e

#oltage to cut off the 8,T. This means that maimum input #oltage reaches the

nonin#erting input. n other or!s" an output #oltage of less than 6.? ) p-p implies

that the circuit acts like a nonin#erting #oltage amplifier ith a maimum input

signal.

Ihen the output peak-to-peak #oltage is greater than 6.? )" +0

con!ucts an! charges capacitor C 0. This increases the gate #oltage an! !ecreases

r ds. Iith a smaller r ds" the output of the RH an! +6 #oltage !i#i!er !ecreases an!

there is less input #oltage to the nonin#erting input. n other or!s" the o#erall

#oltage gain of the circuit !ecreases hen the peak-to-peak output #oltage is

greater than 6.? ).

)i#ure 18-32 8,T use! as a #oltage-controlle! resistance in A*C circuit.

6 k @

6

?G k @

0

B)CC 0A# D

6

B 6 r

r !s

B

677 k@

H voutvin B

!s H

C6

),,

Z0

Z6 ?

5 C0



),,



v A 5 ds

)i#ure 18-33 A*C circuit use! ith small input signals.

0

0 B r !s

v in

B)A*C

5 vA 6

H

B)CC

B

),,

vout

A# D 6 5 B B r !s

?

),,

The larger the output #oltage" the smaller the #oltage gain. This ay"

the output #oltage increases only slightly for large increases in the input signal.

One reason for using A*C is to re!uce su!!en increases in signal le#el an!

pre#ent o#er!ri#ing a lou!speaker. f you are listening to a ra!io" you !o not

ant an une- pecte! increase in the signal le#el to bombar! your ears. nsummary" e#en though the input #oltage of 8ig. 69-H0 #aries o#er a 7-!( range"

the peak-to-peak output is only slightly more than 6.? ).

6o+-evel i'eo $C

The signal out of a tele#ision camera has fre4uencies from 7 to ell o#er ? :>=.

8re4uencies in this range are calle! v"deo fre,enc"es( 8igure 69-HH shos a

stan!ar! techni4ue for #i!eo A*C that has been use! for fre4uencies up to 67

:>=. n this circuit" the 8,T acts like a #oltage-controlle! resistance. Ihen the

A*C #oltage is =ero" the 8,T is cut off by the negati#e bias an! its r ds is mai-

mum. As the A*C #oltage increases" the r ds of the 8,T !ecreases.

The input #oltage to the in#erting amplifier comes from the #oltage

!i#i!er forme! by R5" R" an! r ds. This #oltage is gi#en by+

R 6

R R5 6 R 6 r ds

vin

The #oltage gain of the in#erting amplifier is+

Av 50 R0

R6

n this circuit" the 8,T is a #oltage-controlle! resistance. The more positi#e

the A*C #oltage" the smaller the #alue of r ds an! the loer the input #oltage to

the in#erting amplifier. This means that the A*C #oltage controls the o#erall#oltage gain of the circuit.

Iith a i!eban! op amp" the circuit orks ell for input signals up to

approimately 677 m). (eyon! this le#el" the 8,T resistance becomes a func-

tion of the signal le#el in a!!ition to the A*C #oltage. This is un!esirable

because only the A*C #oltage shoul! control the o#erall #oltage gain.

&i#h-evel i'eo $C

8or high-le#el #i!eo signals" e can replace the 8,T ith an L,'-photoresistor

combination like 8ig. 69-H?. The resistance RG of the photoresistor !ecreases as



the amount of light increases. Therefore" the larger the A*C #oltage" the loer

the



v A 5 G

)i#ure 18-34 A*C circuit use! ith large input signals.

0

0 B G

v in

B)A*C

5 vA 6

H

G

B)CC

B

),,

vout

A# D 6 5 B B G

#alue of RG. As before" the input #oltage !i#i!er controls the amount of #oltage

!ri#ing the in#erting #oltage amplifier. This #oltage is gi#en by+

R 6

R R5 6 R 6 RG

vin

The circuit can han!le high-le#el input #oltages up to 67 ) because the photocellresistance is unaffecte! by larger #oltages an! is a function only of V A*C. Also"

there is almost total isolation beteen the A*C #oltage an! the input #oltage vin.

$pplication /ample 18-10f r ds #aries from 57 ) to 607 k) in 8ig. 69-H0" hat is the maimum #oltage

gainQ Ihat is the minimum #oltage gainQ

O"O, sing the #alues an! e4uations of 8ig. 69-H0" the maimum#oltage gain is+

Av 5 1 ?G k ) 607 k)6 k)

6 6 2 607 k) 6 677 k)

5 0.0

The minimum #oltage gain is+

Av 5 1 ?G k ) 57 )6 k)

6 6 2 57 ) 6 677 k)5 7.70?

($C"C/ (O*/> 18-10 n Application ,ample 69-67" hat

#alue shoul! r ds !rop to for a #oltage gain of 6Q

18-10 in#le-uppl! Operationsing !ual supplies is the typical ay to poer op amps. (ut this is not

necessary or e#en !esirable in some applications. This section !iscusses the

in#erting an! nonin#erting amplifiers running off a single positi#e supply.



)i#ure 18-35 Single-supply in#erting ampli$er .

0

B)CC

C66 C

A# D 0

6

vin 0

vout

B ?

f 6 D6

0 p 6C6

B)CC

CH

L f 0 D6

0 p LC0

f H D6

0 p 1 /02CH

"nvertin# $mpli%er

8igure 69-H5 shos a single-supply in#erting #oltage amplifier that can be use!

ith ac signals. The V EE supply 1pin ?2 is groun!e!" an! a #oltage !i#i!er applies

half the V CC supply to the nonin#erting input. (ecause the to inputs are #irtuallyshorte!" the in#erting input has a 4uiescent #oltage of approimately 67.5V CC .

n the !c-e4ui#alent circuit" all capacitors are open an! the circuit is a

#oltage folloer that pro!uces a !c output #oltage of 67.5V CC . nput offsets are

minimi=e! because the #oltage gain is unity.

n the ac-e4ui#alent circuit" all capacitors are shorte! an! the circuit is

an in#erting amplifier ith a #oltage gain of 0 R0 / R6. 8igure 69-H5 shos the

analysis e4uations. Iith these" e calculate the three loer cutoff fre4uencies.

A bypass capacitor is use! on the nonin#erting input" as shon in

8ig. 69-H5. This re!uces the poer-supply ripple an! noise appearing at the

nonin#erting input. To be effecti#e" the cutoff fre4uency of this bypass circuit

shoul! be much loer than the ripple fre4uency out of the poer supply.

[ou can calculate the cutoff fre4uency of this bypass circuit ith the e4uation

gi#en in 8ig. 69-H5.

,oninvertin# $mpli%er

n 8ig. 69-H" only a positi#e supply is being use!. To get maimum output

sing" you nee! to bias the nonin#erting input at half the supply #oltage" hich

is con- #eniently !one ith an e4ual-resistor #oltage !i#i!er. This pro!uces a !c

input of

67.5V CC at the nonin#erting input. (ecause of the negati#e fee!back" the in#ert-

ing input is bootstrappe! to the same #alue.

n the !c-e4ui#alent circuit" all capacitors are open an! the circuit has a

#oltage gain of unity" hich minimi=es the output offset #oltage. The !c output

#oltage of the op amp is 67.5V CC

" but this is blocke! from the final loa! by the

output coupling capacitor.

n the ac-e4ui#alent circuit" all capacitors are shorte!. Ihen an ac

signal !ri#es the circuit" an amplifie! output signal appears across R L. f a rail-to-

rail op amp is use!" the maimum peak-to-peak unclippe! output is V CC . 8igure

69-H gi#es the e4uations for calculating the cutoff fre4uencies.

in#le-uppl! Op $mps

Although e can use or!inary op amps ith a single supply" as shon in

8igs. 69-H5 an! 69-H" there are some op amps that are optimi=e! for single-



supply



L

)i#ure 18-36 Single-supply nonin#erting ampli$er .

vin

C6

B

B)CC

C0

vout

0A# D B 6 6

6f 6

D

f 0 D

06

f H D

CH

0 p 1 /02C6

6

0 p LC0

6

0 p 6CH

operation. 8or instance" the L:H0? is a 4ua! op amp that eliminates the nee!

for !ual supplies. t contains four internally compensate! op amps in a single package" each ith an open-loop #oltage gain of 677 !(" input biasing current

of

?5 nA" input offset current of 5 nA" an! input offset #oltage of 0 m). t runs

off a single positi#e supply #oltage that can ha#e any #alue beteen H an! H0 ).

(e- cause of this" the L:H0? is con#enient to use as an interface ith !igital

circuits that run off a single positi#e supply of 65 ).

ummar!

/C 18-1 ",/",-

$>(")"/ C"C"1

n#erting-ampli$er circuits !iscusse!

in this section inclu!e! a high-

impe!ance probe 1<67 an! <62" an

ac-couple! ampli$er" an! an

a!Justable-ban!i!th circuit.

/C 18-2 ,O,",/ ",-

$>(")"/ C"C"1

&onin#erting-ampli$er circuits !is-

cusse! in this section inclu!e! an

ac-couple! ampli$er" an au!io !istri-

bution ampli$er" a 8,T-sitche!

ampli$er" an! a #oltage reference.

/C 18-3 ",// ;

,O,",//

C"C"1

The circuits !iscusse! in this section

are the sitchable in#erter/nonin-

#erter " the 8,T-controlle! sitchable

in#erter" the sign changer " the

a!Just- able an! re#ersible gain

circuit" an! the phase shifter .

/C 18-4 "))//,"$

$>(")"/

To factors !etermine the o#erall

C: of a !ifferential ampli$er+

the C: of each op amp an! the

C: of the matche! resistors.

The input signal is usually a small

!ifferential #oltage an! a large

common-mo!e #oltage comingfrom a Iheatstone bri!ge.

/C 18-5

",>/,$"O

, $>(")"/

An instrumentation ampli$er is a !if-

ferential ampli$er optimi=e! for large

#oltage gain" high C:" lo input

offsets" lo-temperature !rift" an!

high input impe!ance. nstrumenta-

tion ampli$ers can be built ith the



classic three op-amp circuit" using

precision op amps" or ith an inte-

grate! instrumentation ampli$er .

/C 18-6 >>",

$>(")"/ C"C"1

The topics !iscusse! in this section

ere the subtracter " summing on

both inputs" the a#erager " an! the'/A con#erter . The '/A con#erter is

use! in !igital multimeters to

measure #oltages" currents" an!

resistances.

/C 18-7 C/, *OO/

Ihen the short-circuit output current

of an op amp is too lo" one

solution is to use a current booster

on the output si!e of the circuit.

Typically" the current booster is a

transistor hose base current is

supplie! by

the op amp. (ecause of the transistor

current gain" the short-circuit output

current is increase! by the factor .



? R

R6 6

R6

6 6 RF 6 R F

R

out 1 N & re

/C 18-8 O6$/-

CO,O/

C/, O7C/

Ie can buil! current sources that

are controlle! by an input #olt-

age. The loa!s may be 3oating or

groun!e!. The loa! currents may be

uni!irectional or bi!irectional. The

>olan! current source is a bi!i-

rectional #oltage-controlle! current

source.

erivations

/C 18-9 $O>$"C

$", CO,O

n many applications e ant the

#oltage gain of a system to change

automatically as nee!e! to maintain

an almost constant output #oltage.

n ra!io an! tele#ision recei#ers"

A*C pre#ents su!!en an! large

changes in the #olume of the soun!

out of the speakers.

/C 18-10 ",/-7((6B

O(/$"O,

Although op amps normally use !ual

supplies" there are applications for

hich only a single supply is

preferre!. Ihen ac-couple!

ampli$ers are nee!e!" single-supply

ampli$ers are easily implemente! by

biasing the nonsignal si!e of the op

amp to half the positi#e supply

#oltage. Some op amps are

optimi=e! for single-supply operation.

169-H2 *ain for in#erter/nonin#erter circuits+

Av 5 Av1in#2 6

Av1non2

See 8igs. 69-9 through 69-6H. The total #oltage gain is the

superposition of the in#erting an! nonin#erting #oltage

gains. Ie use it hen the input signal is being applie!

to both inputs.

169-52 Common-mo!e #oltage gain+

Av1CM 2 5 Av1in#2 6 Av1non2

See 8igs. 69-6?" 69-65" an! 69-69. This is similar to ,4. 169-H2

because it is the superposition of gains.

169-G2 O#erall nonin#erter gain+

169-6H2 nbalance! Iheatstone bri!ge+

vin K' R

V CC

See 8ig. 69-6G. This e4uation is #ali! for small changes

in the resistance of the trans!ucer .

169-62 nstrumentation ampli$er+

Av 50 R0

G

See 8igs. 69-69 an! 69-07. This is the #oltage gain of the

$rst stage of the classic three op-amp instrumentation

ampli$er .

169-692 (inary-to-!ecimal e4ui#alent+

(& 5 1 &o H 072 6 1 &6 H 0

62 6 1 &0 H 0

02 6 1 &H

H 0H2

Av1non2 5 1 R0 2 1 R0F

6 0169-6F2 /0 la!!er output #oltage+

See 8ig. 69-6?. This is the #oltage gain of the nonin#erting

si!e re!uce! by the #oltage-!i#i!er factor.

169-92 Common-mo!e gain for R6 5 R0+

Av1CM 2 5 O0 ' R

See 8igs. 69-65 an! 69-69. This is the common-mo!e

gain cause! by the resistor tolerances hen the

resistors of the !ifferential ampli$er are e4ual an!

matche!.

169-662 Iheatstone bri!ge+

R6 RH

V 5 0(&

H 0V 0

169-062 Current booster+

' ma 5 !c ' SC

See 8igs. 69-0 through 69-H7. The short-circuit current

of an op amp is increase! by the current gain of a

transistor beteen the op amp an! the loa!.

169-0H2 )oltage-controlle! current sources+

"out 5vin

R05

R?

See 8ig. 69-6a. This is the e4uation for balance in a

Iheatstone bri!ge.

R

See 8igs. 69-09 through 69-H6. n #oltage-controlle! current

sources" the input #oltage is con#erte! to a stiff output

current.

el-est

1 "n a linear op-amp circuit: the

a. Signals are alays sine

a#es b. Op amp !oes not go

intosaturation

c. nput impe!ance isi!eally in$nite

!. *ain-ban!i!th pro!uctis constant

2 "n an ac ampli%er usin# an opamp +ith couplin# an' b!- passcapacitors: the output osetvolta#e is

a. \ero

b. :inimum c.



:aimum

!. nchange!

3 o use an op amp: !ou nee'at least

a. One supply

#oltage b. To

supply #oltages

c. One coupling

capacitor !. One

bypass capacitor



!. (e ac-couple!



C

(roblems

/C 18-1 ",/",-$>(")"/ C"C"1

18-1 n the probe of 8ig. 69-6" R6 5 67 :)" R0 5 07 :)" RH 5 65 k)" R? 5 65 k)" an! R5 5 G5 k). Ihat istheattenuation of the probe in each sitch positionQ

18-2 n the ac-couple! in#erting ampli$er of 8ig. 69-0"

R6 5 6.5 k)" R f 5 G5 k)" R L 5 65 k)" C 6 5 6 8"C 0 5 ?.G 8" an! f unity 5 6 :>=. Ihat is the#oltage

gain in the mi!ban! of the ampli$erQ Ihat are theupper an! loer cutoff fre4uenciesQ

18-3 n the a!Justable-ban!i!th circuit of 8ig. 69-H" R6 5 67 k) an! R f 5 697 k). f the 677-)resistor is change! to 6H7 ) an! the #ariableresistor to05 k)" hat is the #oltage gainQ Ihat are themini- mum an! maimum ban!i!th if f unity 5 6:>=Q

18-4 Ihat is the output #oltage in 8ig. 69-HGQ Ihat

are the minimum an! maimum ban!i!thQ1se f unity 5 6 :>=.2

)i#ure 18-37

R f

677 k @

B65 )

R6

/C 18-2 ,O,",/",-$>(")"/ C"C"1

18-5 n 8ig. 69-?" R6 5 0 k)" R f 5 90 k)" R L 5 05 k)" C 6 5

0.0 8" C 0 5 ?.G 8" an! f unity 5 H :>=. Ihat is

the #oltage gain in the mi!ban! of the ampli$erQIhat are the upper an! loer cutoff fre4uenciesQ

18-6 Ihat is the #oltage gain in the mi!ban! of 8ig. 69-H9Q Ihat are the upper an! loercutoff fre4uenciesQ

18-7 n the !istribution ampli$er of

8ig. 69-5" R6 5 0 k)" R f 5 677 k)" an! vin 5 67m).Ihat is the output #oltage for A" B" an! C Q

18-8 The 8,T-sitche! ampli$er of 8ig. 69- has these#alues+ R6 5 F6 k)" R f 5 60 k)" an! R0 5 6 k ).f vin 5 0 m)" hat is the output #oltage henthe gate is loQ Ihen it is highQ

18-9 f V GS 1off 2 5 05 )" hat are the minimum an!maimum output #oltages in 8ig. 69-HFQ

18-10 The #oltage reference of 8ig. 69-G is mo!i$e! toget R6 5 67 k) an! R f 5 67 k). Ihat is thene output reference #oltageQ

/C 18-3 ",// ;,O,",// C"C"1

R0 5 67 k). Ihat is the maimum positi#egainQ The maimum negati#e gainQ

? m)6.5 k @

5 k @

R

677 @

0

G

G?6C

HB

?

V EE

65 )

18-12 Ihat is the #oltage gain in 8ig. 69-66 hen the iper vout is at the groun! en!Q Ihen it is 67 percent aay

from groun!Q

18-13 Precision resistors are use! in 8ig. 69-60. f R 5 5k )" nR 5 G5 k)" an! nR/1n 0 62 R 5 5.H k)" hat

are the maimum positi#e an! negati#e gainsQ

18-14 n the phase shifter of 8ig. 69-6H" RF 5 67 k)" R 500 k)" an! C 5 7.70 8. Ihat is the phase shifthen the input fre4uency is 677 >=Q 6 k>=Q 67k>=Q

)i#ure 18-38

V CC

B65 )6

vin

0 m)

R0

677 k @

B

G?6C

V EE

65 )

67 m 8

R L

67 k @

vout

R6

H.H k @

R f

657 k @



C H?.G m 8



V

L

)i#ure 18-39

vin

6 m)

RG

77 @

B

G?6C

R f Rvout9 k @ 67 k @

R0

6 k @ R6

07 k @

7 )

5 )

/C 18-4 "))//,"$ $>(")"/

18-15 The !ifferential ampli$er of 8ig. 69-6? has R6 5

6.5 k) an! R0 5 H7 k). Ihat is the !iff erential#oltage gainQ The common-mo!e gainQ 1/ esistor tolerance 5 O7.6 percent.2

18-16 n 8ig. 69-65" R6 5 6 k) an! R0 5 07 k). Ihat isthe !ifferential #oltage gainQ The common-mo!e gainQ 1/ esistor tolerance 5 O6 percent.2

18-17 n the Iheatstone bri!ge of 8ig. 69-6" R6 5 67k )" R0 5 07 k)" RH 5 07 k)" an! R? 5 67 k). sthe bri!ge balance!Q

18-18 n the typical application of 8ig. 69-6G" trans!ucer resistance changes to F95 ). Ihat is the $nal

output #oltageQ

/C 18-5 ",>/,$"O, $>(")"/

18-19 n the instrumentation ampli$er of 8ig. 69-69" R6 5 6 k) an! R0 5 FF k). Ihat is the output#oltage if vin 5 0 m)Q f three OP-7GA opamps are use! an! R 5 67 k) O 7.5 percent"hat is the C: of the instrumentation

ampli$erQ

18-20 n 8ig. 69-6F" vin1CM 2 5 5 ). f RH 5 67 k)" hat

!oes the guar! #oltage e4ualQ

18-21 The #alue of RG is change! to 6779 ) in 8ig. 69-07.Ihat is the !ifferential output #oltage if the !iff er-ential input #oltage is 07 m)Q

18-25 The '/A con#erter of 8ig. 69-0? has an input of v7 5 5 )" v6 5 7" v0 5 5 )" an! vH 5 7. Ihat isthe output #oltageQ

18-26 n 8ig. 69-05" if the number of binary inputs is e- pan!e! to eight an! &G to &7 e4uals 67677676" !e-termine the !ecimal-e4ui#alent input #alue (&.

18-27 n 8ig. 69-05" if the binary inputs ere epan!e!so &G to &7 e4uale! 76677667" hat oul! bethe output #oltageQ

18-28 n 8ig. 69-05" using an input reference #oltage of 0.5 )" !etermine the smallest incremental output#oltage step.

/C 18-7 C/, *OO/

18-29 The nonin#erting ampli$er of 8ig. 69-?7 has a cur-

rent-booste! output. Ihat is the #oltage gain ofthe circuitQ f the transistor has a current gain of 677" hat is the short-circuit output currentQ

18-30 Ihat is the #oltage gain in 8ig. 69-?6Q f the tran-sistors ha#e a current gain of 605" hat is theshort-circuit output currentQ

)i#ure 18-40

V CC

B65 )

/C 18-6 7>>", $>(")"/ C"C"1

18-22 Ihat !oes the output #oltage e4ual in 8ig. 69-06

if R 5 67 k)" v6 5 057 m)" an! v0 5 0H7 m)Q

18-23 n the summing circuit of 8ig. 69-00" R6 5 67 k )" R0 5 07 k)" RH 5 65 k)" R? 5 65k)" R5 5 H7 k )" an! R f 5 G5 k). Ihat is theoutput #oltage if v6 5 6 m)" v0 5 0 m)" vH 5 Hm)" an!v? 5 ? m)Q

vin

R6

B

G?6C

EE

R0

?G k @

R L

B

vout

18-24 The a#eraging circuit of 8ig. 69-0H has R 5 67k ).

Iha

t is

the output if v6 5 6.5 )"

v0 5 0.5 )" an!



vH 5 ?.7 )Q 0 k @ 677 @



)i#ure 18-41

R0

67 k @

V CC

B65 )

R6

V CC

B65 )

G?6C

B ?

V EE

65 )

/C 18-8 O$/-CO,O/

C/, O7C/

18-31 Ihat is the loa! current in 8ig. 69-?0aQ The ma-

imum loa! resistance that can be use! ithoutsaturating the op ampQ

18-32 Calculate the output current in 8ig. 69-?0b. Also"ork out the maimum #alue of loa! resistance.

18-33 f R 5 67 k) an! V cc 5 65 ) in the #oltage-con-trolle! current source of 8ig. 69-H7" hat is theoutput current hen the input #oltage is H )QThe maimum loa! resistanceQ

18-34 The >olan! current source of 8ig. 69-H6 has R 50 k) an! R L 5 577 ). Ihat is the output currenthen the input #oltage is )Q Ihat is the

R

677 @

V EE

65 )

maimum loa! resistance that can be use! iththis circuit if the input #oltage is ne#er greaterthan G.5 )Q 1se supply #oltages of O65 ).2

/C 18-9 $O>$"C $", CO,O

18-35 n the A*C circuit of 8ig. 69-H0" R6 5 67 k)" R0 5677 k)" RH 5 677 k)" an! R? 5 67 k). f r ds can#ary from 077 ) to 6 :)" hat is the minimum#oltage gain of the circuitQ The maimumQ

18-36 n the lo-le#el A*C circuit of 8ig. 69-HH" R6 55.6 k)" R0 5 56 k)" R5 5 9 k)" an! R 5 6 k ).f r ds can #ary from 607 ) to 5 :)" hat is

the minimum #oltage gain of the circuitQ ThemaimumQ

)i#ure 18-42

V CC

B65 )

R

H.H k @

vin

V CC

B65 ) V CC

B65 )

G?6C

V EE

vin

R LB5 )

G?6C

B

657 @ 65 ) V EE

65 )

R

0 k @

1a2 1b2



B

B

G

18-37 n the high-le#el A*C circuit of 8ig. 69-H?" R6 567 k)" R0 5 67 k)" R5 5 G5 k)" an! R 5 6.0 k).f

RG can #ary from 697 ) to 67 :)" hat is the mini-

mum #oltage gain of the circuitQ The maimumQ

18-38 Ihat is the #oltage gain in the single-supply in-

#erting ampli$er of 8ig. 69-?HQ The three loer

cutoff fre4uenciesQ

18-39 n the single-supply nonin#erting ampli$er of 8ig. 69-H" R 5 9 k)" R6 5 6.5 k)" R0 5 65 k)" R L

5 65 k)" )" C 6 5 6 8" C 0 5 0.0 8" an! C H 5 H.H

8. Ihat is the #oltage gainQ The three loer cut-off fre4uenciesQ

)i#ure 18-43

R0

90 k @

C 6

v H.H k @

V CC

B65 )

C 0in 0

67 m 8

V CC

B65 )

R

F6 k @

G?6C

?

R C H

R L

67 k @

vout

F6 k @ ?.G m 8

Critical hinAin#

18-40 Ihen sitching beteen the positions of 8ig. 69-9"

there is a brief perio! of time hen the sitch istemporarily open. Ihat is the output #oltage at

this timeQ Can you suggest ho to pre#ent thisfrom happeningQ

18-41 An in#erting ampli$er has R6 5 6 k) an! R f 5 677

k ).f these resistances ha#e tolerances of O6 percent"hat is the maimum possible #oltage gainQ TheminimumQ

18-42 Ihat is the #oltage gain in the mi!ban! of thecircuit shon in 8ig. 69-??Q

18-43 The transistors of 8ig. 69-?6ha#e

!c

5

57. f the input #oltage is 7.5 )" hat is the basecurrent in the con!ucting transistorQ

)i#ure 18-44

vin

00 k @ .9 k @

RS

6 k @

B

HB

G 67 m 8

B

V CC

B65 )

G?6C

0vout

0&HF7? ?

?G k @

R0

67 k @

R E

5. k @ 67 m 8 B

RH R f

6 k @

67 m 8



V A V B

V C V &

V E V -

V G

O] 0 5 7 7 ?57 ?57 ?57

. 6 0 5 7 7 ?57 7 7

. 0 0 5 7 7 077 077 077

. H 0 5 0 0 ^6H.5 ) ^6H.5 ) ^6H.5 )

. ? 0 7 7 7 077 077 077

. 5 0 5 H 7 7 7 7

. 7 5 7 7 057 057 057

. G 0 5 H H ^6H.5 ) ^6H.5 ) ^6H.5 )

. 9 0 5 7 7 057 057 057

. F 0 5 7 7 7 7 7

. 67 0 5 5 5 ^6H.5 ) ^6H.5 ) ^6H.5 )

roubleshootin#

se 8ig. 69-?5 for the remaining problems.

Any resistor may be open or shorte!. Also" connecting

ires C'" ,8" A" or ]( may be open. )oltage #alues

are in milli#olts unless otherise in!icate!.

18-44 8in! Troubles . 6 to . H.

18-45 8in! Troubles . ? to . .

18-46 8in! Troubles . G to . 67.

)i#ure 18-45

/ AB0 m)

V CC

6

6 k@ &

C

0 B

677 k @

V CC

E -H

0

BG

GG?6C

vout

B5 m)

R0

0 k @

B65 )

0

G

?

V EE

65 )

HB

?

V EE

65 )

1a2

Trouble

Troubleshooting

1b2

>ultisim roubleshootin# (roblems

The :ultisim troubleshooting $les are foun! on the

nstructor / esources section of Connect for E!ectron"c

1r"nc"p!es" in a fol!er name! :ultisim Troubleshooting

Circuits 1:TC2. See page <) for more !etails. 8or this

chapter " the $les are labele! :TC69-?G through :TC69-

56 an! are base! on the circuit of 8ig. 69-?5.

Open up an! troubleshoot each of the respecti#e$les. Take measurements to !etermine if there is a fault an!"if so" !etermine the circuit fault.

18-47 Open up an! troubleshoot $le :TC69-?G.

18-48 Open up an! troubleshoot $le :TC69-?9.

18-49 Open up an! troubleshoot $le :TC69-?F.

18-50 Open up an! troubleshoot $le :TC69-57.

18-51 Open up an! troubleshoot $le :TC69-56.



i#ital;$nalo# rainer !stem

The folloing 4uestions" 69-50 through 69-5" are

!irecte! toar! the schematic !iagram of the 'igital/

Analog Trainer System foun! on the nstructor

/ esources section of Connect for E!ectron"c 1r"nc"p!e. A

full nstruction :anual for the :o!el <]-G77 trainer can

be foun! at .elenc o.com.

18-52 Ihat type of op amp circuit is the L:H69 1C672 use! inQ

.ob "ntervie+ uestions

18-53 Ihat is the purpose of ) Q

18-54 f the input signal to the op amp is 7.5 ) p-p" hat is theop ampLs output signal le#elQ

18-55 f F opene!" hat oul! happen to the L:H69 outputsignalQ

18-56 Ihat shoul! the approimate ban!i!th be for thisampli$erQ

6. 'ra the schematic !iagram of

an ac-couple! in#erting ampli$er

ith a #oltage gain of 677. 'is-

cuss the theory of operation.

0. 'ra the schematic !iagram of a

!ifferential ampli$er built ith an

op amp. Ihat are the factors that

!etermine the C:Q

H. 'ra the schematic !iagramof the classic three op-amp in-

strumentation ampli$er. Tell

me hat the $rst stage !oes to

the !ifferential an! common-

mo!e signals.

?. Ihy !oes the instrumentation am-

pli$er ha#e more than one stageQ

5. [ou ha#e !esigne! a simple

op- amp circuit for a particular

application. 'uring your initial

testing"

you $n! that the op amp is #ery

hot to the touch. Assuming that

the circuit has been correctly

brea!boar!e!" hat is the most

likely problem an! hat can

you !o to correct itQ

. ,plain ho an in#erting ampli-

$er is use! in a high-impe!ance

probe 1<67 an! <62.G. n 8ig. 69-6" hy !oes the

probe see a high impe!anceQ

,plain ho the #oltage gain is

calculate! in each sitch

position.

9. Ihat can be sai! about the

analog output of a '/A con#erter

hen it is compare! ith the !ig-

ital inputQ

F. [ou ant to construct a

portable op-amp circuit that runs

off a

single F-) battery using a G?6C.

Ihat is one ay you can !o thisQ

>o oul! you ha#e to mo!ify

this circuit if a !c response is

re4uire!Q

67. >o coul! you increase the out-

put current of an op ampQ

66. Ihy is no resistor or !io!e

biasing re4uire! in the circuit of 8ig. 69-0GQ

60. Ihen orking ith op amps" one

often hears the term ra"!2 as in a

ra"!)to)ra"! amp!"3er( To hat !oes

that term referQ

6H. Can a G?6 be operate! ith a

single supply #oltageQ f so"

!iscuss hat oul! be re4uire!

for an in#erting ampli$er .

el-est $ns+ers

1 b 9 ! 175 !

2 b 10 a 18 !

3 a 115 b 19 b

4 c 12 c 20 a

5 c 13 ! 21 !

6 b 14 c 22 b

7 b 15 b 23 c

8 ! 16 c 24 a

(ractice (roblem $ns+ers

18-2 R0 5 7 k )

18-3 & 5 G.5; n 5 6.65?k )

18-4 Av 5 56; Av1C:2 5

7.770;

vout 5 0567 m);vout1C:2 5 O07 m)

18-5 Av6 5 06; Av 0 5 07.5; Av H 5 6.7; Av? 5 7.GF9

18-6 largest V out 5 0F.HG5 );smallest V out 5 07.05 )

18-7 Av 5 00G; * out1CL2 5 7.706 ); ' ma 5 0.5 A

http://www.elenco.com/








18-8 "out 5 7.5 mA; R L1ma2 5

6 k )

18-9 "out 5 07.H mA; R L1ma2 5

6.05 k )

18-10 r ds 5 0.6H k )

APLIKASI OP-AMP LINIER.doc

Documents

Transcript of APLIKASI OP-AMP LINIER.doc