PDHonline Course E272 (5 PDH)

Operational Amplifier Fundamentals and Design

2012

Instructor: George Rutkowski, PE

PDH Online | PDH Center5272 Meadow Estates Drive

Fairfax, VA 22030-6658Phone & Fax: 703-988-0088

www.PDHonline.orgwww.PDHcenter.com

An Approved Continuing Education Provider

http://www.PDHonline.orghttp://www.PDHcenter.com

2CHARACTERISTICSOF OP AMPSAND THEIR POWERSUPPLY REQUIREMENTS

The term operational amplifier refers to a high-gain dc amplifier that has adifferential input (two input leads) and a single-ended output (one outputlead). The signal output voltage Vo is larger than the differential input signalacross the two inputs by the gain factor of the amplifier (see Fig. 2-1). OpAmps have characteristics such as high input resistance, low output resis-tance, high gain, etc., that make them highly suitable for many applications, anumber of which are shown and discussed in later chapters. By examiningsome applications and comparing the characteristics of typical Op Amps, wewill see that some types are apparently better than others. The overall mostdesirable characteristics that Op Amp manufacturers strive to obtain in theirproducts are ideal characteristics. While some of these ideal characteristicsare impossible to obtain, we often assume that they exist to develop circuitsand equations that work perfectly on paper. These circuits and equationsthen work very well with practical Op Amps. Actual Op Amp characteristicsare more or less ideal, relative to conditions external to the Op Amp: signalsource resistance, load resistance, amount of feedback used, etc. Some of themore important characteristics, ideal and practical values, are given anddefined in the following sections.

2.1 OPEN-LOOP VOLTAGE GAIN* AVOL

The open-loop voltage gain A VOLof an Op Amp is its differential gain underconditions where no negative feedback is used, as shown in Figs. 2-1 and 2-2.

*In industry, the open-loop voltage gain is referred to with a variety of symbols: AVOL> Ad'AEOL>AVD' etc. .

22

Vid

-v

2.1 OPEN-LOOPVOLTAGE GAIN A VOL 23

Figure 2-1 Typical Op Amp symbol. + Vis the positive dc power supply voltage; - Vis the negative dc power supply voltage;AVOL = Va/V;d.

Ideally, its value is infinite-that is, the ideal Op Amp has an open-loopvoltage gain

or

Va = -00AVOL = V;d

(2-1a)

Va

VI - V2(2-1b)

The negative sign means that the output Va and the input V;d are out ofphase. Of course, the concept of an infinite gain is theoretical. The importantpoint to understand is that the Op Amp's output signal voltage Va should bevery much larger than its differential input signal V;d.To put it another way,the input V;d should be infinitesimal compared to any practical value ofoutput Vo. Typical open-loop gains AVOL range from about 5000 (about74 dB) to 1,000,000 (about 120 dB)-that is,

VI

5000 ::;;A VOL ::;; 1,000,000 (2-2a)

Figure 2-2 Op Amp with input volt-ages VI and V2 whose difference is V;d.Power supply voltages + V and - V areassumed if not shown.

24 OP AMPS AND THEIR POWER SUPPLY REQUIREMENTS

or

174 dB::::; A VOL ::::;120 dB I(2-2b)

with popular types of Op Amps. The fact that the output signal Vo is 5000 to106 times larger than the differential input signal V;d does not mean that Vocan actually be very large. In fact, its positive and negative peaks are limitedto values a little less than the positive and negative supply voltages beingused to power the Op Amp. Since the dc supply voltages of monolithic IC OpAmps are usually less than 20 V, the peaks of their output voltages Vo areless than 20 V. This fact, coupled with the large AVOL of the typical OpAmp, makes the voltage V;d across its inputs 1 and 2 very small. Of course,the larger the open-loop gain AVOL>the smaller V;d is in comparison to anypractical value of output signal Vo. Thus, since

Vo

AVOL = V;d(2-3a)

or

(2-3b)

then

Vo

V;d = AVOL

and therefore.

as a limit, as AVOLapproaches infmity.Vidapproaches zero

Thus, if the gain AVOL in the expression Vo/AVOL is very large, the value ofthis expression, which is V;d' must be very small. In fact, V;d is usually sosmall that we can assume there is practically no potential difference betweenthe inverting ( - ) and noninverting ( + ) inputs.

*As the value of open-loop gain AVOL approaches infinity, the value of differential input voltageV;d approaches zero if Vo *- O.

2.3 INPUT RESISTANCE R; 25

2.2 OUTPUT OFFSET VOLTAGE Voo

The output offset voltage Voo of an Op Amp is its output voltage to groundor common under conditions when its differential input voltage V;d= 0 Y.Ideally Voo= 0 Y. In practice, due to imbalances and inequalities in thedifferential amplifiers within the Op Amp itself (see Fig. 1-12), some outputoffset voltage Voo will usually occur even though the input V;d = 0 Y. In fact,if the open-loop gain A VOL of the Op Amp is high and if no feedback isused, the output offset is large enough to saturate the output. In such cases,the output voltage is either a little less than the positive source voltage + Vor the negative source - V. This is not as serious as it first appears becausecorrective measures are fairly simple to apply and because the Op Amp isseldom used without some feedback. When corrective action is taken to bringthe output to 0 Y, when the applied input signal is 0 Y, the Op Amp is saidto be balanced or nulled.

If both inputs are at the same finite potential, causing VI - V2 = V;d =o Y, and if the output Vo = 0 Y as a result, the Op Amp is said to have anideal common-mode rejection (CMR). Though most practical Op Amps havea good CMR capability, they do pass some common-mode (CM) voltage tothe load Ru Typically though, the load's common-mode output voltage v"mois hundreds or thousands of times smaller than the input common-modevoltage v"m' A thorough discussion of the practical Op Amp's CMR capabil-ity and its applications is given in a later chapter.

2.3 INPUT RESISTANCE Ri

The Op Amp's input resistance Rj is the resistance seen looking into itsinputs 1 and 2 as shown in Fig. 2-3. Ideally, Rj = 00 O. Practical Op Amps'input resistances are not infinite but instead range from less than 5 kO toover 20 MO, depending on type. Though resistances in the low end of thisrange seem a bit small compared to the desired ideal (000), they can be quitelarge compared to the low internal resistances of some signal sources thatcommonly drive the inputs of Op Amps. Generally, if a high-resistance signalsource is to drive an Op Amp, the Op Amp's input resistance should berelatively large. As we will see later, the effective input resistance Rj(etf) ismade considerably larger than the manufacturer's specified Rj by use of

Figure 2-3 Input resistance Rj is theresistance seen looking into the inputs1 and 2.

26 OP AMPS AND THEIR POWER SUPPLY REQUIREMENTS

2

Figure 2-4 Output resistance Ro tends to reduce output voltage Vo'

negative feedback. Manufacturers usually specify their Op amps' input resis-tances as measured under open-loop conditions (no feedback). In most linearapplications, Op Amps are wired with feedback and this improves (increases)the effective resistance seen by the signal source driving the Op Amp.

2.4 OUTPUT RESISTANCE Ro

With a differential input signal V;dapplied, the Op Amp behaves like a signalgenerator as the load connected to the output sees it. As shown in Fig. 2-4,the Op Amp is equivalent to a signal source generating an open-circuitvoltage of AVOLV;d and having an internal resistance of Ro' This Ro is theOp Amp's output resistance and ideally should be 0 n. Obviously, if Ro =o .0 in the circuit of Fig. 2-4, all of the generated output signal AVOLV;dappears at the output and across the load RL. Depending on the type of OpAmp, specified output resistance Ro values range from a few ohms to a fewhundred ohms and are usually measured under open-loop (no feedback)conditions. Fortunately, the effective output resistance Ro(eff)is considerablysmaller when the Op Amp is used with feedback. In fact, in most applicationsusing feedback, the effective output resistance of the Op Amp is very nearlyideal (0 .0). The effect feedback has on output resistance is discussed in morespecific terms later.

2.5 BANDWIDTH BW

The bandwidth BW of an amplifier is defined as the range of frequencies atwhich the output voltage does not drop more than 0.707 of its maximumvalue while the input voltage amplitude is constant. Ideally, an Op Amp'sbandwidth BW = 00. An infinite bandwidth is one that starts with dc andextends to infinite cycles/second (Hz). It is indeed idealistic to expect such a

2.6 RESPONSE TIME 27

bandwidth from any kind of amplifier. Practical Op Amps fall far short of thisideal. In fact, limited high-frequency response is a shortcoming of monolithicIC Op Amps. While some types of Op amps can be used to amplify signals upto a few megahertz, they require carefully chosen feedback and externallywired compensating components. Most general-purpose IC Op Amps arelimited to less than I-MHz bandwidth and more often are used with signalswell under a few kilohertz, especially if any significant gain is expected ofthem. The limited high-frequency response of Op Amps is not a seriousmatter with most types of instrumentation in which Op Amps are usedextensively. Chapter 6 discusses high frequency characteristics of Op Amps.

2.6 RESPONSETIME

The response time of an amplifier is the time it takes the output of anamplifier to change after the input voltage changes. Ideally, response time = 0seconds; that is, the output voltage should respond instantly to any change onthe input. Figure 2-5 shows an Op Amp's typical output-voltage response to astep input voltage when wired for unity gain. Manufacturers also specify aslew rate that gives the circuit designer a good idea of how fast a given OpAmp responds to changes of input voltage. Note that the time scale in Fig.2-5 is in microseconds (J-Ls)and that the output voltage, when changing,overshoots the level it eventually settles at. Overshoot is the ratio of theamount of overshoot to the steady-state deviation expressed as a percentage.For example, if we observe the responding output voltage of Fig. 2-5 on anoscilloscope whose vertical deflection sensitivity is at 10 V/ cm, and theamount of overshoot measures 0.2 cm, the percentage of overshoot is

0.2cm

Steady-state deflection X 100 = 2 cm X 100 = 10%.

Amount of overshoot

Figure 2-5 Typical Op Amp response to a step input voltage when wired as a voltagefollower {unity gain}.

Step input Overshootvoltage t

10 V! . :--I

OV! 1\ , , I Time (ps)-- 20.

- 10 VI- L.-\,r Respondingoutput

Slew --\voltage

rate

28 OP AMPS AND THEIR POWER SUPPLY REQUIREMENTS

From time to time we will refer to the various ideal characteristics, andhere is a summary:

(1) Open-loop voltage gain A VOL= 00.(2) Output offset voltage Voo = 0 V.(3) Input resistance Rj = 00 n.(4) Output resistance Ro = 0 n.(5) Bandwidth BW = 00Hz.(6) Response time = 0 s.

2.7 POWER SUPPLY REQUIREMENTS

In many applications, the Op Amp's output voltage Vo must be capable ofswinging in both positive and negative directions. In such applications, theOp Amp requires two source voltages: one positive (+ V) and the othernegative (- V) with respect to ground or a common point. These dc sourcevoltages must be well filtered and regulated; otherwise the Op amp's outputvoltage will vary with the power supply variations. The output voltage of anOp Amp varies more or less with power supply variations, depending on itscIosed-loop* voltage gain and sensitivity factor S which is usually specifiedon the manufacturer's data sheets. An ideal Op Amp has a sensitivity factorS = 0, which means that power supply voltage variations have no effect on itsoutput. Practical Op Amps, however, are affected by changes in the supplyvoltages, and therefore regulated supplies are used to keep Op Amp outputsresponsive to differential input voltages only.