Today, op amps are used widely in consumer, industrial, and scientific electronics. Many standardintegrated circuit op amps cost only a few cents; however, some integrated or hybrid operational amplifiers with special performance specifications may cost overUS$100.[2] Op amps may be packaged ascomponents or used as elements of more complexintegrated circuits.
An op amp without negative feedback (a comparator)
The amplifier's differential inputs consist of a non-inverting input (+) with voltageV+ and an inverting input (−) with voltageV−; ideally the op amp amplifies only the difference in voltage between the two, which is called thedifferential input voltage. The output voltage of the op ampVout is given by the equationwhereAOL is theopen-loop gain of the amplifier (the term "open-loop" refers to the absence of an external feedback loop from the output to the input).
The magnitude ofAOL is typically very large (100,000 or more for integrated circuit op amps, corresponding to +100 dB). Thus, even small microvolts of difference betweenV+ andV− may drive the amplifier intoclipping orsaturation. The magnitude ofAOL is not well controlled by the manufacturing process, and so it is impractical to use an open-loop amplifier as a stand-alonedifferential amplifier.
Withoutnegative feedback, and optionallypositive feedback forregeneration, anopen-loop op amp acts as acomparator, although comparator ICs are better suited.[3] If the inverting input of an ideal op amp is held at ground (0 V), and the input voltageVin applied to the non-inverting input is positive, the output will be maximum positive; ifVin is negative, the output will be maximum negative.
An op amp with negative feedback (a non-inverting amplifier)
If predictable operation is desired, negative feedback is used, by applying a portion of the output voltage to the inverting input. Theclosed-loop feedback greatly reduces the gain of the circuit. When negative feedback is used, the circuit's overall gain and response is determined primarily by the feedback network, rather than by the op-amp characteristics. If the feedback network is made of components with values small relative to the op amp's input impedance, the value of the op amp's open-loop responseAOL does not seriously affect the circuit's performance. In this context, high inputimpedance at the input terminals and low output impedance at the output terminal(s) are particularly useful features of an op amp.
The response of the op-amp circuit with its input, output, and feedback circuits to an input is characterized mathematically by atransfer function; designing an op-amp circuit to have a desired transfer function is in the realm ofelectrical engineering. The transfer functions are important in most applications of op amps, such as inanalog computers.
In the non-inverting amplifier on the right, the presence of negative feedback via thevoltage dividerRf,Rg determines theclosed-loop gainACL =Vout /Vin. Equilibrium will be established whenVout is just sufficient to pull the inverting input to the same voltage asVin. The voltage gain of the entire circuit is thus1 +Rf /Rg. As a simple example, ifVin = 1 V andRf =Rg,Vout will be 2 V, exactly the amount required to keepV− at 1 V. Because of the feedback provided by theRf,Rg network, this is aclosed-loop circuit.
Another way to analyze this circuit proceeds by making the following (usually valid) assumptions:[4]
When an op amp operates in linear (i.e., not saturated) mode, the difference in voltage between the non-inverting (+) and inverting (−) pins is negligibly small.
The input impedance of the (+) and (−) pins is much larger than other resistances in the circuit.
The input signalVin appears at both (+) and (−) pins per assumption 1, resulting in a currenti throughRg equal toVin /Rg:
Because Kirchhoff's current law states that the same current must leave a node as enter it, and because the impedance into the (−) pin is near infinity per assumption 2, we can assume practically all of the same currenti flows throughRf, creating an output voltage
By combining terms, we determine the closed-loop gainACL:
The first rule only applies in the usual case where the op amp is used in a closed-loop design (negative feedback, where there is a signal path of some sort feeding back from the output to the inverting input). These rules are commonly used as a good first approximation for analyzing or designing op-amp circuits.[8]: 177
None of these ideals can be perfectly realized. A real op amp may be modeled with non-infinite or non-zero parameters using equivalent resistors and capacitors in the op-amp model. The designer can then include these effects into the overall performance of the final circuit. Some parameters may turn out to have negligible effect on the final design while others represent actual limitations of the final performance.
Real op amps differ from the ideal model in various aspects.
Finite gain
Open-loop gain is finite in real operational amplifiers. Typical devices exhibit open-loop DC gain exceeding 100,000. So long as theloop gain (i.e., the product of open-loop and feedback gains) is very large, the closed-loop gain will be determined entirely by the amount of negative feedback (i.e., it will be independent of open-loop gain). In applications where the closed-loop gain must be very high (approaching the open-loop gain), the feedback gain will be very low and the lower loop gain in these cases causes non-ideal behavior from the circuit.
Low output impedance is important for low-impedance loads; for these loads, the voltage drop across the output impedance effectively reduces the open-loop gain. In configurations with a voltage-sensing negative feedback, the output impedance of the amplifier is effectively lowered; thus, in linear applications, op-amp circuits usually exhibit a very low output impedance.Low-impedance outputs typically require highquiescent (i.e., idle) current in the output stage and will dissipate more power, so low-power designs may purposely sacrifice low output impedance.
Thedifferential input impedance of the operational amplifier is defined as the impedancebetween its two inputs; thecommon-mode input impedance is the impedance from each input to ground.MOSFET-input operational amplifiers often have protection circuits that effectively short circuit any input differences greater than a small threshold, so the input impedance can appear to be very low in some tests. However, as long as these operational amplifiers are used in a typical high-gain negative feedback application, these protection circuits will be inactive. The input bias and leakage currents described below are a more important design parameter for typical operational amplifier applications.
Additional input impedance due toparasitic capacitance can be a critical issue for high-frequency operation where it reduces input impedance and may cause phase shifts.
Input current
Due tobiasing requirements orleakage, a small amount of current[nb 2] flows into the inputs. When high resistances or sources with high output impedances are used in the circuit, these small currents can produce significant voltage drops. If the input currents are matched,and the impedance lookingout ofboth inputs are matched, then those voltages at each input will be equal. Because the operational amplifier operates on thedifference between its inputs, these matched voltages will have no effect. It is more common for the input currents to be slightly mismatched. The difference is called input offset current, and even with matched resistances a smalloffset voltage (distinct from theinput offset voltage below) can be produced. This offset voltage can create offsets or drifting in the operational amplifier.
Input offset voltage
Input offset voltage is a voltage required across the op amp's input terminals to drive the output voltage to zero.[9][nb 3] In the perfect amplifier, there would be no input offset voltage. However, it exists because of imperfections in the differential amplifier input stage of op amps. Input offset voltage creates two problems: First, due to the amplifier's high voltage gain, it virtually assures that the amplifier output will go into saturation if it is operated without negative feedback, even when the input terminals are wired together. Second, in a closed loop, negative feedback configuration, the input offset voltage is amplified along with the signal and this may pose a problem if high precision DC amplification is required or if the input signal is very small.[nb 4]
Common-mode gain
A perfect operational amplifier amplifies only the voltage difference between its two inputs, completely rejecting all voltages that are common to both. However, the differential input stage of an operational amplifier is never perfect, leading to the amplification of these common voltages to some degree. The standard measure of this defect is called thecommon-mode rejection ratio (CMRR). Minimization of common-mode gain is important innon-inverting amplifiers that operate at high gain.
Power-supply rejection
The output of a perfect operational amplifier will be independent of power supply voltage fluctuations. Every real operational amplifier has a finitepower supply rejection ratio (PSRR) that reflects how well the op amp can reject noise in its power supply from propagating to the output. With increasing frequency the power-supply rejection usually gets worse.
Temperature effects
Performance and properties of the amplifier typically changes, to some extent, with changes in temperature. Temperature drift of the input offset voltage is especially important.
Drift
Real op-amp parameters are subject to slow change over time and with changes in temperature, input conditions, etc.
Associated with the bandwidth limitation is a phase difference between the input signal and the amplifier output that can lead tooscillation in some feedback circuits. For example, a sinusoidal output signal meant to interfere destructively with an input signal of the same frequency will interfere constructively if delayed by 180 degrees formingpositive feedback. In these cases, the feedback circuit can bestabilized by means offrequency compensation, which increases thegain or phase margin of the open-loop circuit. The circuit designer can implement this compensation externally with a separate circuit component. Alternatively, the compensation can be implemented within the operational amplifier with the addition of adominant pole that sufficiently attenuates the high-frequency gain of the operational amplifier. The location of this pole may be fixed internally by the manufacturer or configured by the circuit designer using methods specific to the op amp. In general, dominant-pole frequency compensation reduces the bandwidth of the op amp even further. When the desired closed-loop gain is high, op-amp frequency compensation is often not needed because the requisite open-loop gain is sufficiently low; consequently, applications with high closed-loop gain can make use of op amps with higher bandwidths.
Distortion, and other effects
Limited bandwidth also results in lower amounts of feedback at higher frequencies, producing higher distortion, and output impedance as the frequency increases.
Amplifiers intrinsically output noise, even when there is no signal applied. This can be due to internal thermal noise and flicker noise of the device. For applications with high gain or high bandwidth, noise becomes an important consideration and alow-noise amplifier, which is specifically designed for minimum intrinsic noise, may be required to meet performance requirements.
The input (yellow) and output (green) of a saturated op amp in an inverting amplifier
Saturation
Output voltage is limited to a minimum and maximum value close to thepower supply voltages.[nb 5] The output of older op amps can reach to within one or two volts of the supply rails. The output of so-calledrail-to-rail op amps can reach to within millivolts of the supply rails when providing low output currents.[10]
Slew rate limiting
The amplifier's output voltage reaches its maximum rate of change, theslew rate, usually specified in volts per microsecond (V/μs). When slew rate limiting occurs, further increases in the input signal have no effect on the rate of change of the output. Slew rate limiting is usually caused by the input stage saturating; the result is a constant currenti driving a capacitanceC in the amplifier (especially those capacitances used to implement itsfrequency compensation); the slew rate is limited bydv/dt =i/C.Slewing is associated with thelarge-signal performance of an op amp. Consider, for example, an op amp configured for a gain of 10. Let the input be a 1V, 100 kHz sawtooth wave. That is, the amplitude is 1V and the period is 10 microseconds. Accordingly, the rate of change (i.e., the slope) of the input is 0.1 V per microsecond. After 10× amplification, the output should be a 10V, 100 kHz sawtooth, with a corresponding slew rate of 1V per microsecond. However, the classic741 op amp has a 0.5V per microsecond slew rate specification so that its output can rise to no more than 5V in the sawtooth's 10-microsecond period. Thus, if one were to measure the output, it would be a 5V, 100 kHz sawtooth, rather than a 10V, 100 kHz sawtooth.Next consider the same amplifier and 100 kHz sawtooth, but now the input amplitude is 100mV rather than 1V. After 10× amplification the output is a 1V, 100 kHz sawtooth with a corresponding slew rate of 0.1V per microsecond. In this instance, the 741 with its 0.5V per microsecond slew rate will amplify the input properly.Modern high-speed op amps can have slew rates in excess of 5,000V per microsecond. However, it is more common for op amps to have slew rates in the range 5–100V per microsecond. For example, the general purpose TL081 op amp has a slew rate of 13V per microsecond. As a general rule, low power and small bandwidth op amps have low slew rates. As an example, the LT1494 micropower op amp consumes 1.5 microamp but has a 2.7 kHz gain-bandwidth product and a 0.001V per microsecond slew rate.
The output voltage may not be accurately proportional to the difference between the input voltages producing distortion. This effect will be very small in a practical circuit where substantial negative feedback is used.
Phase reversal
In some integrated op amps, when the published common mode voltage is violated (e.g., by one of the inputs being driven to one of the supply voltages), the output may slew to the opposite polarity from what is expected in normal operation.[11][12] Under such conditions, negative feedback becomes positive, likely causing the circuit tolock up in that state.
The output current must be finite. In practice, most op amps are designed to limit the output current to prevent damage to the device, typically around 25 mA for a type 741 IC op amp. Modern designs are electronically more robust than earlier implementations and some can sustain directshort circuits on their outputs without damage.
Limited output voltage
Output voltage cannot exceed the power supply voltage supplied to the op amp. The maximum output of most op amps is further reduced by some amount due to limitations in the output circuitry.Rail-to-rail op amps are designed for maximum output levels.[10]
Output sink current
The output sink current is the maximum current allowed to sink into the output stage. Some manufacturers provide an output voltage vs. the output sink current plot which gives an idea of the output voltage when it is sinking current from another source into the output pin.
Limited dissipated power
The output current flows through the op amp's internal output impedance, generating heat that must be dissipated. If the op amp dissipates too much power, then its temperature will increase above some safe limit. The op amp must shut down or risk being damaged.Modern integratedFET orMOSFET op amps approximate more closely the ideal op amp than bipolar ICs when it comes to input impedance and input bias currents. Bipolars are generally better when it comes to inputvoltage offset, and often have lower noise. Generally, at room temperature, with a fairly large signal, and limited bandwidth, FET and MOSFET op amps now offer better performance.
Sourced by many manufacturers, and in multiple similar products, an example of a bipolar transistor operational amplifier is the 741 integrated circuit designed in 1968 by David Fullagar atFairchild Semiconductor afterBob Widlar's LM301 integrated circuit design.[13] In this discussion, we use the parameters of thehybrid-pi model to characterize the small-signal, grounded emitter characteristics of a transistor. In this model, the current gain of a transistor is denotedhfe, more commonly denotedβ.[14]
Voltage amplifier (outlinedmagenta) — provides high voltage gain, a single-pole frequencyroll-off, and in turn drives the
Output amplifier (outlinedcyan andgreen) — provides high current gain (lowoutput impedance), along with output current limiting, and output short-circuit protection.
The input stage consists of a cascadeddifferential amplifier (outlined in dark blue) followed by a current-mirroractive load. This constitutes atransconductance amplifier, turning a differential voltage signal at the bases of Q1, Q2 into a current signal into the base of Q15.
It entails two cascaded transistor pairs, satisfying conflicting requirements. The first stage consists of the matched NPNemitter follower pair Q1, Q2 that provide high input impedance. The second is the matched PNPcommon-base pair Q3, Q4 that eliminates the undesirableMiller effect; it drives anactive load Q7 plus matched pair Q5, Q6.
That active load is implemented as a modifiedWilson current mirror; its role is to convert the (differential) input current signal to a single-ended signal without the attendant 50% losses (increasing the op amp's open-loop gain by3 dB).[nb 6] Thus, a small-signal differential current in Q3 versus Q4 appears summed (doubled) at the base of Q15, the input of the voltage gain stage.
The (class-A) voltage gain stage (outlined inmagenta) consists of the two NPN transistors Q15 and Q19 connected in aDarlington configuration and uses the output side of current mirror formed by Q12 and Q13 as its collector (dynamic) load to achieve its high voltage gain. The output sink transistor Q20 receives its base drive from the common collectors of Q15 and Q19; the level-shifter Q16 provides base drive for the output source transistor Q14. The transistor Q22 prevents this stage from delivering excessive current to Q20 and thus limits the output sink current.
The output stage (Q14, Q20, outlined in cyan) is aClass AB amplifier. It provides an output drive with impedance of about50 Ω, in essence, current gain. Transistor Q16 (outlined in green) provides the quiescent current for the output transistors and Q17 limits output source current.
Biasing circuits provide appropriate quiescent current for each stage of the op amp.
The39 kΩ resistor connecting thediode-connected transistors Q11 and Q12, and the given supply voltageVS =VS+ −VS−, determine the current in thecurrent mirrors, (matched pairs) Q10/Q11 and Q12/Q13. The collector current of Q11,i11 × 39 kΩ =VS − 2VBE. For the typicalVS =20 V, the standing current in Q11 and Q12 (as well as in Q13) would be about1 mA. A supply current for a typical 741 of about2 mA agrees with the notion that these two bias currents dominate the quiescent supply current.[16]
Transistors Q11 and Q10 form aWidlar current mirror, with quiescent current in Q10i10 such thatln(i11/i10) =i10 ×5 kΩ /28 mV, where5 kΩ represents the emitter resistor of Q10, and28 mV isVT, thethermal voltage at room temperature. In this casei10 ≈20 μA.
The biasing circuit of this stage is set by a feedback loop that forces the collector currents of Q10 and Q9 to (nearly) match. Any small difference in these currents provides drive for the common base of Q3 and Q4.[nb 7] The summed quiescent currents through Q1 and Q3 plus Q2 and Q4 is mirrored from Q8 into Q9, where it is summed with the collector current in Q10, the result being applied to the bases of Q3 and Q4.
The quiescent currents through Q1 and Q3 (also Q2 and Q4)i1 will thus be half ofi10, of order about10 μA. Input bias current for the base of Q1 (also Q2) will amount toi1/β; typically around50 nA,[16] implying a current gainhfe ≈ 200 for Q1 (also Q2).
This feedback circuit tends to draw the common base node of Q3/Q4 to a voltageVcom − 2VBE, whereVcom is the input common-mode voltage. At the same time, the magnitude of the quiescent current is relatively insensitive to the characteristics of the components Q1–Q4, such ashfe, that would otherwise cause temperature dependence or part-to-part variations.
Transistor Q7 drives Q5 and Q6 into conduction until their (equal) collector currents match that of Q1/Q3 and Q2/Q4. The quiescent current in Q7 isVBE /50 kΩ, about35 μA, as is the quiescent current in Q15, with its matching operating point. Thus, the quiescent currents are pairwise matched in Q1/Q2, Q3/Q4, Q5/Q6, and Q7/Q15.
Quiescent currents in Q16 and Q19 are set by the current mirror Q12/Q13, which is running at approximately1 mA. The collector current in Q19 tracks that standing current.[further explanation needed]
In the circuit involving Q16 (variously namedrubber diode orVBE multiplier), the4.5 kΩ resistor must be conducting about100 μA, with Q16VBE ≈700 mV. ThenVCB must be about0.45 V, andVCE ≈1.0 V. Because the Q16 collector is driven by a current source and the Q16 emitter drives into the Q19 collector current sink, the Q16 transistor establishes a voltage difference between the Q14 base and the Q20 base of about1 V, regardless of the common-mode voltage of Q14/Q20 bases. The standing current in Q14/Q20 will be a factorexp(100 mV·mm/VT) ≈ 36 smaller than the1 mA quiescent current in the class A portion of the op amp. This (small) standing current in the output transistors establishes the output stage in class AB operation and reduces thecrossover distortion of this stage.
The input stage with Q1 and Q3 is similar to an emitter-coupled pair (long-tailed pair), with Q2 and Q4 adding some degenerating impedance. The input impedance is relatively high because of the small current through Q1–Q4. A typical 741 op amp has a differential input impedance of about2 MΩ.[16] The common mode input impedance is even higher, as the input stage works at an essentially constant current.
A differential voltageVin at the op amp inputs (pins 3 and 2, respectively) gives rise to a small differential current in the bases of Q1 and Q2iin ≈Vin / (2hiehfe). This differential base current causes a change in the differential collector current in each leg byiinhfe. Introducing the transconductance of Q1,gmhfe /hie, the (small-signal) current at the base of Q15 (the input of the voltage gain stage) isVingm / 2.
This portion of the op amp cleverly changes a differential signal at the op amp inputs to a single-ended signal at the base of Q15, and in a way that avoids wastefully discarding the signal in either leg. To see how, notice that a small negative change in voltage at the inverting input (Q2 base) drives it out of conduction, and this incremental decrease in current passes directly from Q4 collector to its emitter, resulting in a decrease in base drive for Q15. On the other hand, a small positive change in voltage at the non-inverting input (Q1 base) drives this transistor into conduction, reflected in an increase in current at the collector of Q3. This current drives Q7 further into conduction, which turns on current mirror Q5/Q6. Thus, the increase in Q3 emitter current is mirrored in an increase in Q6 collector current; the increased collector currents shunts more from the collector node and results in a decrease in base drive current for Q15. Besides avoiding wasting3 dB of gain here, this technique decreases common-mode gain and feedthrough of power supply noise.
A current signali at Q15's base gives rise to a current in Q19 of orderiβ2 (the product of thehfe of each of Q15 and Q19, which are connected in aDarlington pair). This current signal develops a voltage at the bases of output transistors Q14 and Q20 proportional to thehie of the respective transistor.
Output transistors Q14 and Q20 are each configured as an emitter follower, so no voltage gain occurs there; instead, this stage provides current gain, equal to thehfe of Q14 and Q20.
The current gain lowers the output impedance and although the output impedance is not zero, as it would be in an ideal op amp, with negative feedback it approaches zero at low frequencies.
The net open-loop small-signal voltage gain of the op amp is determined by the product of the current gainhfe of some 4 transistors. In practice, the voltage gain for a typical 741-style op amp is of order 200,000,[16] and the current gain, the ratio of input impedance (about2–6 MΩ) to output impedance (around50 Ω) provides yet more (power) gain.
In the present circuit, if the input voltages change in the same direction, the negative feedback makes Q3/Q4 base voltage follow (with2VBE below) the input voltage variations. Now the output part (Q10) of Q10–Q11 current mirror keeps up the common current through Q9/Q8 constant in spite of varying voltage. Q3/Q4 collector currents, and accordingly the output current at the base of Q15, remain unchanged.
In the typical 741 op amp, the common-mode rejection ratio is90 dB,[16] implying an open-loop common-mode voltage gain of about 6.
The innovation of the Fairchild μA741 was the introduction offrequency compensation via an on-chip (monolithic) capacitor, simplifying application of the op amp by eliminating the need for external components for this function. The30 pF capacitor stabilizes the amplifier viaMiller compensation and functions in a manner similar to an op-ampintegrator circuit. Also known asdominantpole compensation because it introduces a pole that masks (dominates) the effects of other poles into the open loop frequency response; in a 741 op amp this pole can be as low as10 Hz (where it causes a−3 dB loss of open loop voltage gain).
This internal compensation is provided to achieveunconditional stability of the amplifier in negative feedback configurations where the feedback network is non-reactive and theloop gain isunity or higher. In contrast, amplifiers requiring external compensation, such as the μA748, may require external compensation or closed-loop gains significantly higher than unity.
Theoffset null pins may be used to place external resistors (typically in the form of the two ends of a potentiometer, with the slider connected toVS–) in parallel with the emitter resistors of Q5 and Q6, to adjust the balance of the Q5/Q6 current mirror. The potentiometer is adjusted such that the output is null (midrange) when the inputs are shorted together.
The transistors Q3, Q4 help to increase the reverseVBE rating; The base-emitter junctions of the NPN transistors Q1 and Q2 break down at around7 V, but the PNP transistors Q3 and Q4 haveVBE breakdown voltages around50 V.[17]
Variations in the quiescent current with temperature, or due to manufacturing variations, are common, socrossover distortion may be subject to significant variation.
The output range of the amplifier is about one volt less than the supply voltage, owing in part toVBE of the output transistors Q14 and Q20.
The25 Ω resistor at the Q14 emitter, along with Q17, limits Q14 current to about25 mA; otherwise, Q17 conducts no current. Current limiting for Q20 is performed in the voltage gain stage: Q22 senses the voltage across Q19's emitter resistor (50 Ω); as it turns on, it diminishes the drive current to Q15 base. Later versions of this amplifier schematic may show a somewhat different method of output current limiting.
While the 741 was historically used in audio and other sensitive equipment, such use is now rare because of the improvednoise performance of more modern op amps. Apart from generating noticeable hiss, 741s and other older op amps may have poorcommon-mode rejection ratios and so will often introduce cable-borne mains hum and other common-mode interference, such as switch "clicks", into sensitive equipment.
The '741' has come to often mean a generic op-amp IC (such as μA741, LM301, 558, LM324, TBA221 — or a more modern replacement such as the TL071). The description of the 741 output stage is qualitatively similar for many other designs (that may have quite different input stages), except:
Some devices (μA748, LM301, LM308) are not internally compensated. Hence, they provide a pin for wiring an external capacitor from output to some point within the operational amplifier, if used in low closed-loop gain applications.[18]
Some modern devices haverail-to-rail output capability, meaning that the output can range from within a few millivolts of the positive supply voltage to within a few millivolts of the negative supply voltage.[10]
hybrid, consisting of discrete andintegrated components,
fullintegrated circuits — most common, having displaced the former two due to low cost.
IC op amps may be classified in many ways, including:
Device grade, including acceptableoperating temperature ranges and other environmental or quality factors. For example: LM101, LM201, and LM301 refer to the military, industrial, and commercial versions of the same component. Military and industrial-grade components offer better performance in harsh conditions than their commercial counterparts but are sold at higher prices.
Classification by package type may also affect environmental hardiness, as well as manufacturing options;DIP, and other through-hole packages are tending to be replaced bysurface-mount devices.
Classification by internal compensation: op amps may suffer from high frequencyinstability in somenegative feedback circuits unless a small compensation capacitor modifies the phase and frequency responses. Op amps with a built-in capacitor are termedcompensated, and allow circuits above some specifiedclosed-loop gain to be stable with no external capacitor. In particular, op amps that are stable even with a closed loop gain of 1 are calledunity gain compensated.
Single, dual and quad versions of many commercial op-amp IC are available, meaning 1, 2 or 4 operational amplifiers are included in the same package.
Rail-to-rail input (and/or output) op amps can work with input (and/or output) signals very close to the power supply rails.[10]
CMOS op amps (such as the CA3140E) provide extremely high input resistances, higher thanJFET-input op amps, which are normally higher thanbipolar-input op amps.
Programmable op amps allow the quiescent current, bandwidth and so on to be adjusted by an external resistor.
Manufacturers often market their op amps according to purpose, such as low-noise pre-amplifiers, wide bandwidth amplifiers, and so on.
The use of op amps as circuit blocks is much easier and clearer than specifying all their individual circuit elements (transistors, resistors, etc.), whether the amplifiers used are integrated or discrete circuits. In the first approximation op amps can be used as if they were ideal differential gain blocks; at a later stage, limits can be placed on the acceptable range of parameters for each op amp.
Circuit design follows the same lines for allelectronic circuits. A specification is drawn up governing what the circuit is required to do, with allowable limits. For example, the gain may be required to be 100 times, with a tolerance of 5% but drift of less than 1% in a specified temperature range; the input impedance not less than onemegohm; etc.
A basic circuit is designed, often with the help ofelectronic circuit simulation. Specific commercially available op amps and other components are then chosen that meet the design criteria within the specified tolerances at acceptable cost. If not all criteria can be met, the specification may need to be modified.
A prototype is then built and tested; additional changes to meet or improve the specification, alter functionality, or reduce the cost, may be made.
Without feedback, the op amp may be used as avoltage comparator. Note that a device designed primarily as a comparator may be better if, for instance, speed is important or a wide range of input voltages may be found since such devices can quickly recover from full-on or full-offsaturated states.
Avoltage level detector can be obtained if a reference voltageVref is applied to one of the op amp's inputs. This means that the op amp is set up as a comparator to detect a positive voltage. If the voltage to be sensed,Ei, is applied to op amp's (+) input, the result is a noninverting positive-level detector: whenEi is aboveVref,VO equals+Vsat; whenEi is belowVref,VO equals−Vsat. IfEi is applied to the inverting input, the circuit is an inverting positive-level detector: whenEi is aboveVref,VO equals−Vsat.
Azero voltage level detector (Ei = 0) can convert, for example, the output of a sine-wave from a function generator into a variable-frequency square wave. IfEi is a sine wave, triangular wave, or wave of any other shape that is symmetrical around zero, the zero-crossing detector's output will be square. Zero-crossing detection may also be useful in triggeringTRIACs at the best time to reduce mains interference and current spikes.
Schmitt trigger implemented by a non-inverting comparator
Another typical configuration of op amps is with positive feedback, which takes a fraction of the output signal back to the non-inverting input. An important application of positive feedback is the comparator with hysteresis, theSchmitt trigger.
An op amp connected in the non-inverting amplifier configuration
In a non-inverting amplifier, the output voltage changes in the same direction as the input voltage.
The gain equation for the op amp is
However, in this circuitV− is a function ofVout because of the negative feedback through theR1,R2 network.R1 andR2 form avoltage divider, and asV− is a high-impedance input, it does not load it appreciably. Consequently
where
Substituting this into the gain equation, we obtain
Solving for:
If is very large, this simplifies to
The non-inverting input of the operational amplifier needs a path for DC to ground; if the signal source does not supply a DC path, or if that source requires a given load impedance, then the circuit will require another resistor from the non-inverting input to ground. When the operational amplifier's input bias currents are significant, then the DC source resistances driving the inputs should be balanced.[19] The ideal value for the feedback resistors (to give minimal offset voltage) will be such that the two resistances in parallel roughly equal the resistance to ground at the non-inverting input pin. That ideal value assumes the bias currents are well matched, which may not be true for all op amps.[20]
An op amp connected in the inverting amplifier configuration
In an inverting amplifier, the output voltage changes in an opposite direction to the input voltage.
As with the non-inverting amplifier, we start with the gain equation of the op amp:
This time,V− is a function of bothVout andVin due to the voltage divider formed byRf andRin. Again, the op-amp input does not apply an appreciable load, so
Substituting this into the gain equation and solving forVout:
IfAOL is very large, this simplifies to
A resistor is often inserted between the non-inverting input and ground (so both inputs see similar resistances), reducing theinput offset voltage due to different voltage drops due tobias current, and may reduce distortion in some op amps.
ADC-blockingcapacitor may be inserted in series with the input resistor when afrequency response down to DC is not needed and any DC voltage on the input is unwanted. That is, the capacitive component of the input impedance inserts a DCzero and a low-frequencypole that gives the circuit abandpass orhigh-pass characteristic.
The potentials at the operational amplifier inputs remain virtually constant (near ground) in the inverting configuration. The constant operating potential typically results in distortion levels that are lower than those attainable with the non-inverting topology.[citation needed]
Most single, dual and quad op amps available have a standardized pin-out which permits one type to be substituted for another without wiring changes. A specific op amp may be chosen for its open loop gain, bandwidth, noise performance, input impedance, power consumption, or a compromise between any of these factors.
1941: A vacuum tube op amp. An op amp, defined as a general-purpose, DC-coupled, high-gain, inverting feedback amplifier, is first found inU.S. patent 2,401,779 "Summing Amplifier" filed byKarl D. Swartzel Jr. of Bell Labs in 1941. This design used threevacuum tubes to achieve a gain of90 dB and operated on voltage rails of±350 V. It had a single inverting input rather than differential inverting and non-inverting inputs, as are common in today's op amps. ThroughoutWorld War II, Swartzel's design proved its value by being liberally used in the M9artillery director designed at Bell Labs. This artillery director worked with theSCR-584 radar system to achieve extraordinary hit rates (near 90%) that would not have been possible otherwise.[21]
GAP/R K2-W: a vacuum-tube op amp (1953)
1947: An op amp with an explicit non-inverting input. In 1947, the operational amplifier was first formally defined and named in a paper byJohn R. Ragazzini of Columbia University.[22] In this same paper a footnote mentioned an op-amp design by a student that would turn out to be quite significant. This op amp, designed byLoebe Julie, had two major innovations. Its input stage used a long-tailedtriode pair with loads matched to reduce drift in the output and, far more importantly, it was the first op-amp design to have two inputs (one inverting, the other non-inverting). The differential input made a whole range of new functionality possible, but it would not be used for a long time due to the rise of the chopper-stabilized amplifier.[21]
1949: A chopper-stabilized op amp. In 1949, Edwin A. Goldberg designed achopper-stabilized op amp.[23] This set-up uses a normal op amp with an additionalAC amplifier that goes alongside the op amp. The chopper gets an AC signal fromDC by switching between the DC voltage and ground at a fast rate (60 or 400 Hz). This signal is then amplified, rectified, filtered and fed into the op amp's non-inverting input. This vastly improved the gain of the op amp while significantly reducing the output drift and DC offset. Unfortunately, any design that used a chopper couldn't use the non-inverting input for any other purpose. Nevertheless, the much-improved characteristics of the chopper-stabilized op amp made it the dominant way to use op amps. Techniques that used the non-inverting input were not widely practiced until the 1960s when op-ampICs became available.
1953: A commercially available op amp. In 1953, vacuum tube op amps became commercially available with the release of the model K2-W fromGeorge A. Philbrick Researches, Incorporated. The designation on the devices shown, GAP/R, is an acronym for the complete company name. Two nine-pin12AX7 vacuum tubes were mounted in an octal package and had a model K2-P chopper add-on available. This op amp was based on a descendant of Loebe Julie's 1947 design and, along with its successors, would start the widespread use of op amps in industry.[24]
GAP/R model P45: a solid-state, discrete op amp (1961).
1961: A discrete IC op amp. With the birth of thetransistor in 1947, and the silicon transistor in 1954, the concept of ICs became a reality. The introduction of theplanar process in 1959 made transistors and ICs stable enough to be commercially useful. By 1961, solid-state, discrete op amps were being produced. These op amps were effectively small circuit boards with packages such asedge connectors. They usually had hand-selected resistors in order to improve things such as voltage offset and drift. The P45 (1961) had a gain of 94 dB and ran on ±15 V rails. It was intended to deal with signals in the range of±10 V.
1961: A varactor bridge op amp. There have been many different directions taken in op-amp design.Varactor bridge op amps started to be produced in the early 1960s.[25][26] They were designed to have extremely small input current and are still amongst the best op amps available in terms of common-mode rejection with the ability to correctly deal with hundreds of volts at their inputs.
GAP/R model PP65: a solid-state op amp in a potted module (1962)
1962: An op amp in a potted module. By 1962, several companies were producing modular potted packages that could be plugged intoprinted circuit boards.[citation needed] These packages were crucially important as they made the operational amplifier into a singleblack box which could be easily treated as a component in a larger circuit.
1963: A monolithic IC op amp. In 1963, the first monolithic IC op amp, the μA702 designed byBob Widlar at Fairchild Semiconductor, was released. Monolithic ICs consist of a single chip as opposed to a chip and discrete parts (a discrete IC) or multiple chips bonded and connected on a circuit board (a hybrid IC). Almost all modern op amps are monolithic ICs; however, this first IC did not meet with much success. Issues such as an uneven supply voltage, low gain and a small dynamic range held off the dominance of monolithic op amps until 1965 when the μA709[27] (also designed by Bob Widlar) was released.
1968: Release of the μA741. The popularity of monolithic op amps was further improved with the release of the LM101 in 1967, which solved a variety of issues, and the subsequent release of the μA741 in 1968. The μA741 was extremely similar to the LM101 except that Fairchild's manufacturing processes allowed them to include a 30 pF compensation capacitor inside the chip instead of requiring external compensation. This simple difference has made the 741the canonical op amp and many modern amps base their pinout on the 741s. The μA741 is still in production, and has become ubiquitous in electronics—many manufacturers produce a version of this classic chip, recognizable by part numbers containing741.
1970: First high-speed, low-input current FET design.In the 1970s high speed, low-input current designs started to be made by usingFETs. These would be largely replaced by op amps made withMOSFETs in the 1980s.
LH0033CG: a high speed hybrid IC op amp
1972: Single sided supply op amps being produced. A single sided supply op amp is one where the input and output voltages can be as low as the negative power supply voltage instead of needing to be at least two volts above it. The result is that it can operate in many applications with the negative supply pin on the op amp being connected to the signal ground, thus eliminating the need for a separate negative power supply.
The LM324 (released in 1972) was one such op amp that came in a quad package (four separate op amps in one package) and became an industry standard. In addition to packaging multiple op amps in a single package, the 1970s also saw the birth of op amps in hybrid packages. These op amps were generally improved versions of existing monolithic op amps. As the properties of monolithic op amps improved, the more complex hybrid ICs were quickly relegated to systems that are required to have extremely long service lives or other specialty systems.
An op amp in a mini DIP package
Recent trends. Recently[when?] supply voltages in analog circuits have decreased (as they have in digital logic) and low-voltage op amps have been introduced reflecting this. Supplies of 5 V and increasingly 3.3 V (sometimes as low as 1.8 V) are common. To maximize the signal range modern op amps commonly have rail-to-rail output (the output signal can range from the lowest supply voltage to the highest) and sometimes rail-to-rail inputs.[10]
^abThe power supply pins (VS+ andVS−) can be labeled in different ways (SeeIC power supply pins). Often these pins are left out of the diagram for clarity, and the power configuration is described or assumed from the circuit.
^Typically ~10 nanoamperes, nA, forbipolar op amps, tens of picoamperes, pA, forJFET input stages, and only a fewpA forMOSFET input stages.
^This definition hews to the convention of measuring op-amp parameters with respect to the zero voltage point in the circuit, which is usually half the total voltage between the amplifier's positive and negative power rails.
^Many older designs of operational amplifiers have offset null inputs to allow the offset to be manually adjusted away. Modern precision op amps can have internal circuits that automatically cancel this offset usingchoppers or other circuits that measure the offset voltage periodically and subtract it from the input voltage.
^That the output cannot reach the power supply voltages is usually the result of limitations of the amplifier'soutput stage transistors.
^Lee, Thomas H. (November 18, 2002)."IC Op-Amps Through the Ages"(PDF). EE214 Fall 2002 Course Notes. Stanford University. Handout #18. Archived fromthe original(PDF) on October 24, 2012. RetrievedJuly 5, 2011.
^Lu, Liang-Hung."Electronics 2, Chapter 10"(PDF). National Taiwan University, Graduate Institute of Electronics Engineering. Archived fromthe original(PDF) on 2014-06-30. Retrieved2014-02-22.
^An input bias current of1 μA through a DC source resistance of10 kΩ produces a10 mV offset voltage. If the other input bias current is the same and sees the same source resistance, then the two input offset voltages will cancel out. Balancing the DC source resistances may not be necessary if the input bias current and source resistance product is small.
Operational Amplifiers and Linear Integrated Circuits; 6th Ed; Robert Coughlin, Frederick Driscoll; Prentice Hall; 529 pages; 2001;ISBN978-0-13-014991-6.
Operational Amplifiers - Design and Applications; 1st Ed; Jerald Graeme, Gene Tobey, Lawrence Huelsman;Burr-Brown & McGraw Hill; 473 pages; 1971;ISBN978-0-07-064917-0.
Books with opamp chapters
Learning the Art of Electronics - A Hands-On Lab Course; 1st Ed; Thomas Hayes,Paul Horowitz; Cambridge; 1150 pages; 2016;ISBN978-0-521-17723-8. (Part 3 is 268 pages)
