Working With Op-Amps

8/13/2019 Working With Op-Amps

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u jour a little o

FIG. 2 INVERTING AC AMPLIFIER with x i voltage gain.

LET S DESIGN CIRCUITS AROUND THESTAN - plied by the closdard LM741 op-amp, powered by a (Av). For examp

and how they wo rk, we ll move on to grounded. For offset biasingvoltage followers, biasing theory, ad- R3 should have a value equders and substractors , and phase split- parallel value of R1 and R2 .ters. We ll finis hup with active filters. As shown in Fig. 2, by wiring aIn prac tice, however, as long as the coupling capacitor in series with thesupply voltage stays the same, any input resistor R1, an AC amplifier isop-amp can be substituted for the created. Notice that offset nulling isLM 741 without modifying any of our not needed and, for optimum biasing,

R3 is given a value equal to R2 .

nverting op amp

shows the gain (Av ) to be negative LM741 s FT is typically 1 MH z.because the ou tput voltage is inverted


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IG. SNON-INVERTING x 10 AC ampli-er with 100 000-ohm input impedance.

IG. GNON-INVERTING x10 AC ampli-

ea with 50-megohm input impedance.

FIG. 7-DCVOLTAGE FOLLOWER with off-et nulling.

IG. 8-AC-VOLTAGE FOLLOWER with00 000-ohm input impedance.

ies, C 2 has negligible impedance, sohe AC -voltage gain is determined byhe R2lR1 ratio; however, becausehere's no return path for output D C to

ground, the inverting input is subjecto virtually 100% DC negative feed-ack, that is, unity g ain. B ut for unity

gain, wouldn't resistor R2 need to be direct short for 100% feedback? N ot

quite; let's see why.

Exce pt for input-offset currents, noDC current flows through feedbackesistor R2, so there's no voltage dropnd, consequently, whatever voltage

appears at the output (pin6 also ap-pears at the inverting input (pin 2). Itsounds surprising, but as far as D C isconcerned, R2 looks like a short cir-cuit from pin 6 to pin 2 . For optimuminput-current biasing, R3 should havea value equal to that of R2. Clearly,the non-inverting input impedanceequals the R 3 value.

Figure 6 shows how to des ign for a

high input impedance (typically 50megohms). The low end of R 3 is takento ground via R1, and the AC-feed-back signal appearing at the R3-R1junction is virtually identical to thatappearing on the non-inverting inpu t.Consequently, near-identical signalvoltages appear at both ends of R3,which thus passes negligible signalcurrent. The apparent impedance ofthat resistor is increased to near infini-ty by that bootstrap actio n. In prac-tice, however, the input impedance islimited to about 50 me gohm s becauseof the op-amp's socket and PC-boardimpedances. For optimum input-cur-rent biasing, the sum of R2 and R3should equal R1.

oltage follow rA voltage follower produces an out-

put signal identical to the input sig-nal. The circuit functions as a unity-gain non-inverting amplifier with100% negative feedback, where the

input impedance is very high and theoutput impedance is very low. Figure7 shows a voltage follower with offsetnulling; however, there would be anoutput error of only a few millivolts byeliminating the offset nulling entirely.Notice that, for optimum input-cur-rent biasing, feedback resistor R1should have a value equal to thesource resistance of the input sign al.

The value of feedback resistorR lcan be varied over a wide range (fromzero to 100,000 ohms) without greatlyinfluencing the output accuracy. If anop-amp has a low open-lo op BW, the

FIG. 11-INPUT BIASING of an op-amp.

R1 value can usually be reduced tozero. However, many op -amp s with ahigh open-loop BW tend towards in-stability when used in the unity-gainmode. To reduce the bandwidth andenhance op-amp stability, R1 shouldbe 1000 ohm s or greater.

Figure 8 shows an AC version ofthe voltage follower. Here, the inputAC-signal is coupled through C1, and

the non-inverting input is t ied toground via R1, which determines theinput impedance. Ideally, feedbackresistor R2 should have the sa me val-ue as R1 for correcting input-currentoffsets. However, if R2's value is veryhigh, it may reduce the bandwid th toomuch; that problem can be overcomeby shunting R2 with C2. Further sta-bility can be achieved for high open-loop BW op-amps by connecting R3in series with R2.

Figure 9 achieves an extremely

FIG. 9--AC VOLTAGE FOLLOWER with 50-

megohm input impedance without guardring or 500 megohms with the guard ring.

G U A R D

R I N G

FIG.10-GUARD RING ETCHED ON A PCBas viewed through the top of the PC board.

NOTES: I I =1

B I A S I N G O U T P U T E R R O R


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FIG. 12-UNI-DIRECTIONAL BOOSTEDoutput-current drive in a DC voltage follower.

- v

FIG. 13-BI-DIRECTIONAL BOOSTEDoutput-current in a DC voltage follower.

I N P U T V 2

INPU T V,

FIG. 1GUNITY-GAIN DC ADDER.

high input impedance, where R1 isbootstrapped from the op-amp out-

put via C2, causing Rl's impedance toincrease to nea r infinity-resulting inabout a 50-megohm input imped-ance. The input impedance is stilllimited by the leakage impedances ofthe op-amp's IC socket and PCB,which can also be bootstrapped andraised to near-infinite values by usinga printed circuit guard ring sur-rounding the op-amp's input pin. Inthat case , Fig. would havea 500-megohm inpu t impedance whenusing a L M741 op-amp, or even great-er if a FET-input op-amp is used. Fig-ure 10 shows a guard ring etched on aPCB.

Biasing accuracyIn Figs. i through 9 , great emphasis

was placed on selecting componentvalues for optimum input biasing.figure 11 shows a circuit for testingthe input-offset bias. Both inputs aretied to ground via resistors Rl and R 2;equ al input bias curre nts , I,, and I,,,are drawn through those resistors,thereby generating equal voltagedrops. Because a zero-differentialvoltage appears across the input, abiasing error of zero volts will appearat the ou tpu t. If, on the othe r hand, R1and K2 do not have equal values, orthe inpu t bias currents are slightly dif-ferent, the voltage drops across eachresistor will differ; that will producean input differential voltage that willbe amplified by A to produce an

a R l R6. pF lOOK

output-offset voltage. How significantis that output-voltage error, really?

In practice, a bipolar op-amp suchas the LM 741 has a typicalI, value ofabout 200 nA (0.2 PA), producing avoltage drop of 0. 2 mV across a 1000-ohm res is tor. FET-input op-ampshave typical I, values of about 0.0 2nA, producing a voltage drop of amere 0.0 2 PV across a 1000-ohm re-sistor. Therefore, in Fig. 11, if the R1and R2 values differ by as much as10,000 ohms, a LM741 op-amp willproduce a biasing output error of only2 mV in a unity-ga in voltage follower.or 20 mV for a X 10 amplifier. If aFET-input op- am p is used in place ofthe LM 741, the b iasing output error ofthe voltage follower will be a mere 0 .2pV, and for the x 10 amp lifier, a mere2 pV

It follows that Figs. 1 through canaccept considerable latitude in their

biasing component values. With thatin mind, let's look at more circuits.

INP UT E. 9V

Current-boosted followerMost op-amps can provide max-

imum output currents of only a fewmilliamperes. However, as shown inFig. 12, the current-driving capacityof a voltage follower can be easily

I N P U T E

Q

INPUT

C 4 174- .221~-F lOOK

LM741

IOOK v

N O T E S :

V4 0J- that the base-emitter junction is wired

INPUTinto the negative-feedback loop,4 which virtually eliminates the effectsof junction non-linearity. That tech-

FIG. 1 %4-INPUT AUDIO MIXER. nique is not used in Fig. 13, which

9 v Iv 7~5

THEN, A =R1

increased by wiring an emitter-fol-lower transistor to the output. Notice

FIG. 16-DIFFERENTIAL AMPLIFIER,.or subtracter.

IOOK _

IOOK

I N P U T

R 2lOOK

N O N - I N V E RT E DOUTPUT

=_10

INVERTEDOUTPUT

P

FIG. 17-BALANCED PHASE-SPLITTER.


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f

~ O U T

VIN SLOPE

FREQUENCY w

LOW-PASS FILTERS b

FREQUENCY

HIGH-PASS FILTERS d

signal voltages; if the com pon ent val-ues are chosen such that R2= R4 andR1 = R3 , then the voltage gain,A ,equals R2/RI.

Balanced phase-splitterA phase-splitter has two outputs

that are identical in both amplitudeand form, but one output is phase-shifted by 180 degrees relative to the

other. Figure 17 shows a unity-gainDC phase splitter. Here , IC1 acts as aunity-gain non-inverting amplifier,while IC2 acts as a unity-gain invert-ing amplifier that provides the 180degrees phase-shifted output.

Active filtersFilter circuits are used to reject un-

wanted frequencies while passing fre-quencies that the designer wants. Thelow-pass RC filter in F ig. 18-a. passeslow-frequency s ignals , but re jectshigh-frequency signals. On ce the out-~ u talls to 3 dB at a break or

cross-over frequency, as Fig. 18-bFIG. 18-1st-ORDER RC FILTERS FREQUENCY RESPONSE CURVES: a) s a passive low- shows, the out,,ut continues to rolloffpass filter and b) s its frequency response; c) s a passive high-pas: '

* , . .rilrer ana 01 IS 11srequency response. at a rate of 6 'd ~ io ct av e (20 dB/de-

cade) as the frequency increases. Forexa mp le, a 1-kHz low-pass filter gives

Adders and subtractors 3-dB rejection at 1 kHz, 9-dB rejec-IMP~K NCE Figure 14 shows a unity-gain DC- tion at 2 1


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the feedback network of an op-ampmaking what are known as "active"filters. Let's look at practical d esig ns.

Figure 19 shows a Butterworth 2nd-order low-pass filter with a break fre-

T quency at 10 kHz. That design givesunity gain within its passband. Tochange the break frequency, simplychange either theR or the C value. Amajor disadvantage of Fig. 19 is that

1f

c 2nRCthe value of C2 must be preciselytwice the value of C1 for correct oper-

F IG . 23-2N D-O R[4ER ~ ~ O - H ZIGH-PASS ation and, in practice, that can resultequal-value-com ponent active filter. in some rather odd component values.

FIG. 24--4TH-ORDER 100-HZ HIGH-PASS FILTER.

FIG . 25-300-HZ TO3.4- HZ SPEECH FILTERwith 2nd-order response.

to a 10-kHz signal). Notice that theoctave of 1 kHz is 2 kH z, and theoctave of 2 kHz is 4 kHz; each octavecauses an added attenuation of6 dB.

The high-pass RC filter in Fig.18-c, passes high-frequency signals

but rejects low-frequency signals.After the output is 3-dB down at abreak frequency, as Fig. 18 d shows,the output continues to roll-off at arate of 6 dBIoctave.

Each of the two filter circu its uses asingle RC stage, and is known as the"1st order" filter. If we cascade "nufilter stag es, it would be know n as an"nth order" filter, and would have anoutput slope beyond the break fre-quency of (n x 6 dB)/octave.

Unfortunately, simple RC filterscannot be simply cascaded, becauseeach filter section would interact witheach other, resulting in poor perfor-mance. All of that can be overcomeby incorporating the same filter into

Figure 20 shows an alternative2nd-order 10-kHz low-pass filter, whichovercomes that design snag by usingequal capacitor values. Notice herethat the op-amp is designed to give avoltage gain 4 dB) via R2 and R1.

Figure 21 shows how equal-value-componen t filters can be cascaded tomake a 4th-ord er low-pass filter with aslope of 24 dB/octave.

Figures 22 and 23 shows a unity-gain and equal-value component ver-sions, respectively, of 2nd-order 100-Hz high-pass filters. Figure24 showsa 4th-order 100-Hz high-pass filter.T h e o p e r a t i n g f r e q u e n c y c a n b echanged by increasing either the re-sistor or capacitor values to reduce thebreak frequ ency . Fina ly, Fi g. 25

shows how a high-pass anti low-passfilter can be wired in seriesto make a300-Hz to 3.4-kHz speech filter thatgives 1%-dB/octavee.ie:;ion to al l sig-nals outside of thai range. R-E

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Working With Op-Amps