An **operational amplifier** or **op-amp** is a very high-gain amplifier which has two inputs, one inverting (−) and one non-inverting (+). The output voltage is the difference between the + and − inputs, multiplied by the open-loop gain:

The amplifier's output can be single-ended or, less often, differential. Circuits using op-amps almost always employ negative feedback. Because the op-amp has such high gain, the behavior of the amplifier is almost completely determined by the feedback elements.

## Contents

## History[]

The operational amplifier is so called because it was originally designed to perform mathematical operations by using voltage as an analogue of another quantity. This is the basis of the analogue computer where op-amps were used to model the basic mathematical operations (addition, subtraction, integration, differentiation, and so on). In this sense a true operational amplifier is an ideal circuit element. The real ones we use, made of transistors, tubes, or other amplifying components, are approximations to this ideal. Op-amps were originally developed in the vacuum tube era, where they were used in analog computers. Modern op-amps are normally built as an integrated circuit, though occasionally with discrete transistors, and generally have uniform parameters with standardized packaging and power supply needs. Op-amps have many uses in electronics. The operational amplifier is probably the most useful single device in analog electronic circuitry. With only a handful of external components, it can be made to perform a wide variety of analog signal processing tasks. Many basic integrated circuit op-amps cost only a few cents in moderate production volume, but high-performance amplifiers with extended specifications may cost upwards of $100 US in small quantities.

## The Ideal Op-Amp[]

The *ideal* op-amp has an infinite open-loop gain (see also gain), infinite bandwidth, infinite input impedances, zero output impedance and zero noise, as well as zero input offset (exactly 0 V out when both inputs are exactly equal) and no thermal drift.

In ideal op-amps, the input currents are zero

i_{+}=i_{-}= 0

Modern integrated circuit MOSFET op-amps approximate more and more closely to these ideals in limited-bandwidth, large-signal applications at room temperature.

- To see equations and different circuits that use the operational amp go to Operational amplifier applications

## Modern op-amps[]

Most general-purpose amplifiers sell for under a dollar each. Modern designs have been engineered with ruggedness in mind as well and several op-amps are manufactured that can sustain direct short-circuits on their outputs without damage. One key to the usefulness of these circuits is in the engineering principle of feedback, particularly negative feedback, which constitutes the foundation of almost all automatic control processes. The principles presented here in operational amplifier circuits illustrate some of the scope of electronics. It is important to note that the standard op-amp used and shown in circuits is a black box idealism (a box with just inputs and outputs). Real-world op-amps are complicated integrated circuits;. See the internal circuitry for the relatively simple 741 op-amp below, for example.

## Notation[]

A typical circuit symbol for an op-amp looks like this:

Its terminals are:

- V
_{+}: non-inverting input - V
_{−}: inverting input - V
_{out}: output - V
_{S+}: positive power supply - V
_{S−}: negative power supply

The power supply pins (V_{S+} and V_{S−}) can be labeled many different ways. See IC power supply pins. For FET based op-amps, the positive, common drain supply is labeled V_{DD} and the negative, common source supply is labeled V_{SS}. For BJT based op-amps, the V_{S+} pin becomes V_{CC} and V_{S−} becomes V_{EE}. They are also sometimes labeled V_{CC+} and V_{CC−}, or even V_{+} and V_{−}, in which case the inputs would be labeled differently. The function remains the same. Often these pins are left out of the diagram for clarity, and the power configuration is described or assumed from the circuit.

The input pin polarity is often reversed in diagrams for clarity. In this case, the power supply pins remain in the same position; the more positive power pin is always on the top, and the more negative on the bottom. The entire symbol is not flipped; just the inputs.

## Use in electronics system design[]

The ability to use the general black box op-amp during circuit design makes complicated circuits much easier to work with and understand, especially in very large circuits. Op-amps can be used as if they had the idealized properties (infinite gain, perfect heat dissipation, flat frequency response, infinite input impedance, zero output impedance, and other perfect responses).

After initial circuit design is completed (and sometimes modeled on a computer), specific op-amps are chosen that come as close as possible to meeting the design and cost criteria. It may be that an op-amp with *every* desired parameter cannot be found and some compromise must be made to try to find the op-amp that provides the closest match to the intended functionality for each subcircuit.

The designed circuit itself will most likely need to be modified to take into account real-life op-amp qualities (less-than-perfect performance in some areas). The same is often done for almost all electronic parts during design (where they also are assumed perfect), after which adjustments must be made to make the real parts act like the ideal ones. This process of designing with ideal parts and then adjusting to match their real-world versions is generally true in the use of *all* electronic components including capacitors, inductors, resistors, transistors, diodes, etc.

After the necessary modifications, a final circuit using real op-amps results. The design goal is that any remaining errors and discrepancies will be negligible in practice.

## DC behavior[]

Open-loop gain is defined as the amplification from input to output without any feedback applied. For most practical calculations, the open-loop gain is assumed to be infinite; in reality, however, it is limited by the amount of voltage applied to power the operational amplifier, i.e. Vs+ and Vs- in the above diagram. Typical devices exhibit open loop DC gain ranging from 100,000 to over 1 million. This allows the gain in the application to be set simply and exactly by using negative feedback. Op-amps have performance limits that the designer must keep in mind and sometimes work around.

## AC behavior[]

The op-amp gain calculated at DC does not apply at higher frequencies. This effect is due to limitations within the op-amp itself, such as its finite bandwidth, and to the AC characteristics of the circuit in which it is placed. The best known stumbling-block in designing with op-amps is the tendency for the device to resonate at high frequencies, where negative feedback changes to positive feedback due to parasitic phase shift.

Typical low cost, general purpose op-amps exhibit a gain bandwidth product of a few MHz. Specialty and high speed op-amps can achieve gain bandwidth products of hundreds of MHz. For very high-frequency circuits, a completely different form of op-amp called the current-feedback operational amplifier is often used.

## Basic op-amp circuit[]

The generic op-amp has two inputs and one output. The output voltage is a multiple of the difference between the two inputs (some are made with floating, differential outputs):

- V
_{out}= G(V_{+}− V_{−})

G is the open-loop gain of the op-amp. The inputs are assumed to have very high impedance; negligible current will flow into or out of the inputs. Op-amp outputs have very low source impedance.

If the output is connected to the inverting input, after being scaled by a voltage divider K = R_{1} / (R_{1} + R_{2}), then:

An op-amp connected in the non-inverting amplifier configuration

- V
_{+}= V_{in}

- V
_{−}= K V_{out}

- V
_{out}= G(V_{in}− K V_{out})

Solving for V_{out} / V_{in}, we see that the result is a linear amplifier with gain:

- V
_{out}/ V_{in}= G / (1 + G K)

If G is very large, V_{out} / V_{in} comes close to 1 / K, which equals 1 + (R2 / R1).

This negative feedback connection is the most typical use of an op-amp, but many different configurations are possible, making it one of the most versatile of all electronic building blocks.

When connected in a negative feedback configuration, the op-amp will try to make V_{out} whatever voltage is necessary to make the input voltages equal. This, and the high input impedance, are sometimes called the two "golden rules" of op-amp design (for circuits that use feedback):

- No current will flow into the inputs.
- The input voltages will be equal to each other.

The exception is if the voltage required is greater than the op-amp's supply, in which case the output signal stops near the power supply rails, V_{S+} or V_{S−}.

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. Historically, the first integrated op-amp to become widely available was the Fairchild UA-709, in the late 1960s, but this was rapidly superseded by the much better performing 741, which is easier to use, and probably ubiquitous in electronics - all of the main manufacturers produce a version of this classic chip. The 741 is a bipolar design, and by modern standards has fairly average performance. Better designs based on the FET arrived in the late 1970s, and MOSFET versions in the early 1980s. Many of these more modern devices can be substituted into an older 741-based circuit and work with no other changes, to give better performance.

## Op-amp limitations[]

Although the design of most op-amp circuits relies on the "golden rules" above, designers should also be aware that no real op-amp can match these characteristics exactly. Listed below are some of the limitations of real op-amps, as well as how this affects circuit design.

DC imperfections:

- Finite gain - the effect is most pronounced when the overall design attempts to achieve gain close to the inherent gain of the op-amp.
- Finite input resistance - this puts an upper bound on the resistances in the feedback circuit.
- Nonzero output resistance - important for low resistance loads. Except for very small voltage output, power considerations usually come into play first.
- Input bias current - a small amount of current (typically ~10 nA) into the input pins is required for proper operation. This effect is aggravated by the fact that this current is mismatched slightly between the input pins (i.e., input offset current). This effect is usually important only for very low power circuits.
- Input offset voltage - the op amp will produce an output even when the input pins are at exactly the same voltage. For circuits which require precise DC operation, this effect must be compensated for. Most commercial op-amps provide an offset pin for this purpose.

AC imperfections:

- Finite bandwidth - all amplifiers have a finite bandwidth. However, this is more pronounced in op amps, which use internal frequency compensation to avoid unintentionally producing positive feedback.
- Input capacitance - most important for high frequency operation.

Nonlinear imperfections:

- Saturation - output voltage is limited to a peak value slightly less than the power supply voltage.
- Slew rate - the rate of change of the output voltage is limited (usually by the internal compensation used)

Power considerations:

- Limited output power - if high power output is desired, an op-amp specifically designed for that purpose must be used. Most op-amps are designed for lower power operation and are typically only able to drive output resistances down to 2 kΩ.
- Short circuit protection - this is more a feature than a limitation, although it does put limits on design. Most commercial op-amps outputs current-limit when the output current exceeds a specified level (around 25 mA for a 741 type.).

## Internal circuitry of 741 type op-amp[]

Although it is useful and easy to treat the op-amp as a black box with a perfect input/output characteristic, it is important to understand the inner workings, so that one can deal with problems that may arise due to internal design limitations.

Though designs vary between products and manufacturers, all op-amps have basically the same internal structure, which consists of three stages:

- Differential amplifier
- Input stage - provides low noise amplification, high input impedance, usually a differential output

- Voltage amplifier
- Provides high voltage gain, a single-pole frequency roll-off, usually single-ended output

- Output amplifier
- Output stage - provides high current driving capability, low output impedance, current limiting and short circuit protection circuitry

### Current mirrors[]

The sections outlined in red are current mirrors. The primary current, from which other standing (bias) currents are generated, is determined by the chip's power supply and the 39 kΩ resistor acting (with the two transistor diode junctions) as a current source. The current generated is approximately (V_{S+} − V_{S−} − 2V_{be}) / 39 kΩ.
The input stage DC conditions are controlled by the two current mirrors on the left. The current mirror formed by Q8/Q9 allows for large common-mode voltages on the inputs without exceeding the active range of any transistor in the circuit. The current mirror Q10/Q11 is used, indirectly, to set the input stage current. This current is set by the 5 kΩ resistor. The input stage bias control acts in the following manner.
The outputs of current mirrors, Q8/Q9 and Q10/Q11 together form a high impedance current differencing circuit. If the input stage current tends to deviate (as detected by Q8) from that set by Q10, this is mirrored in Q9 and any change in this current is corrected by altering the voltage at the bases of Q3 and Q4. Thus the input stage dc conditions are stabilised by a high gain negative feedback system.

The top-right current mirror Q12/Q13 provides a constant current load for the class A gain stage, via the collector of Q13, that is largely independent of the output voltage.

### Differential input stage[]

The blue outlined section is a differential amplifier. Q1 and Q2 are input emitter followers and together with the common base pair Q3 and Q4 form the differential input stage. In addition, Q3 and Q4 also act as level shifters and provide voltage gain to drive the class A amplifier. They also help to increase the reverse Vbe rating on the input transistors.

The differential amplifier formed by Q1 - Q4 drives a current mirror active load formed by transistors Q5 - Q7. Q7 increases the accuracy of the current mirror by decreasing the amount of signal current required from Q3 to drive the bases of Q5 and Q6. This current mirror provides differential to single ended conversion as follows:

The signal current of Q3 is the input to the current mirror while the output of the mirror (the collector of Q6) is connected to the collector of Q4. Here, the signal currents of Q3 and Q4 are summed. For differential input signals, the signal currents of Q3 and Q4 are equal and opposite. Thus, the sum is twice the individual signal currents. This completes the differential to single ended conversion.

The open circuit signal voltage appearing at this point is given by the product of the summed signal currents and the paralleled collector resistances of Q4 and Q6. Since the collectors of Q4 and Q6 appear as high resistances to the signal current, the open circuit voltage gain of this stage is very high.

It should be noted that the base current at the inputs is not zero and the effective (differential) input impedance of a 741 is about 2 MΩ The offset null pins can be used in conjunction with a potentiometer to remove any offset voltage that would exist at the output of the op-amp when zero signal is applied between the inputs.

### Class A gain stage[]

The section outlined in magenta is the class A gain stage. It consists of two NPN transistors in a Darlington configuration and uses the output side of a current mirror as its collector load to achieve high gain. The 30 pF capacitor provides frequency selective negative feedback around the class A gain stage to stabilise the amplifier in feedback configurations. This technique is called Miller compensation and functions in a similar manner to an op-amp integrator circuit. It is also known as 'dominant pole compensation' because it introduces a dominant pole (one which masks the effects of other poles) into the open loop frequency response. This pole can be as low as 10 Hz in a 741 amplifier and it introduces a −3 dB loss into the open loop response at this frequency. This is done to achieve unconditional stability of the amplifier down to unity closed loop gain and makes this type of internally compensated amplifier easier to use.

### Output bias circuitry[]

The green outlined section (based around Q16) is a voltage level shifter or V_{BE} multiplier; a type of voltage source. In the circuit as shown, Q16 provides a constant voltage drop between its collector and emitter regardless of the current passing through the circuit. If the base current to the transistor is assumed to be zero, and the voltage between base and emitter (and across the 7.5 kΩ resistor) is 0.625 V (a typical value for a BJT in the active region), then the current flowing through the 4.5 kΩ resistor will be the same as that through the 7.5 kΩ, and will produce a voltage of 0.375 V across it. This keeps the voltage across the transistor, and the two resistors at 0.625 + 0.375 = 1 V. This serves to bias the two output transistors slightly into conduction preventing crossover distortion. In some discrete component amplifiers this function is achieved with (usually 2)silicon diodes.

### Output Stage[]

The output stage (outlined in cyan) is a Class AB push-pull emitter follower (Q14, Q20) amplifier with the bias set by the V_{BE} multiplier voltage source Q16 and its base resistors. This stage is effectively driven by the collectors of Q13 and Q19. The output range of the amplifier is about 1 volt less than the supply voltage, owing in part to Vce(sat) of the output transistors.

The 25 ohm resistor in the output stage acts as a current sense to provide the output current limiting function which limits the current flow in the emitter follower Q14 to about 25 mA for the 741. Current limiting for the negative output is done by sensing the voltage across Q19's emitter resistor and using this to reduce the drive into Q15's base. Later versions of this amplifier schematic may show a slightly different method of output current limiting. The output resistance is not zero as it would be in an ideal op-amp but with negative feedback it approaches zero.

## Common applications[]

*Main article: Operational amplifier applications*

## Other applications[]

- audio and video pre-amplifiers and buffers
- voltage comparators
- differential amplifiers
- differentiators and integrators
- filters
- precision rectifiers
- voltage and current regulators
- analogue calculators
- analogue-to-digital converters
- digital-to-analogue converters
- voltage clamps
- oscillators and waveform generators

## See also[]

- Operational amplifier applications
- Active filter
- Analog computer

- Current-feedback operational amplifier
- Operational tranconductance amplifier

## External links[]

Template:Wikibookspar

- Introduction to op-amp circuit stages, second order filters, single op-amp bandpass filters, and a simple intercom
- A table of standard applications
- Hyperphysics - descriptions of common applications
- Single supply op-amp circuit collection
- Op-amp circuit collection

Additional applications: