An operational amplifier (often op amp, op-amp, or opamp) is a DC-coupled electronic amplifier with a differential input, a (usually) single-ended output voltage, and an extremely high gain. Its name comes from its original use of performing mathematical operations in analog computers. The voltage-feedback opamp (VFOA or VFA, the focus of this article) amplifies the voltage difference between its two inputs, while the less common current-feedback op amp (CFOA) amplifies the current between its two inputs.
By using negative feedback, the characteristics of an op amp application circuit (e.g., its gain, input and output impedance, bandwidth, and functionality) can be determined by external components and have little dependence on temperature coefficients or engineering tolerance in the op amp itself. This flexibility has made the op amp a popular building block in analog circuits.
Today, op amps are used widely in consumer, industrial, and scientific electronics. Many standard integrated circuit op amps cost only a few cents; however, some integrated or hybrid operational amplifiers with special performance specifications may cost over . Op amps may be packaged as components or used as elements of more complex integrated circuits.
The op amp is one type of differential amplifier. Other differential amplifier types include the fully differential amplifier (an op amp with a differential rather than single-ended output), the instrumentation amplifier (usually built from three op amps), the isolation amplifier (with galvanic isolation between input and output), and negative-feedback amplifier (usually built from one or more op amps and a resistive feedback network).
Operation
The amplifier's differential inputs consist of a non-inverting input (+) with voltage and an inverting input (−) with voltage ; ideally the op amp amplifies only the difference in voltage between the two, which is called the differential input voltage. The output voltage of the op amp is given by the equation
where is the open-loop gain of the amplifier (the term "open-loop" refers to the absence of an external feedback loop from the output to the input).
Open-loop amplifier The magnitude of is typically very large (100,000 or more for integrated circuit op amps, corresponding to +100 dB). Thus, even small microvolts of difference between and may drive the amplifier into clipping or saturation. The magnitude of is not well controlled by the manufacturing process, and so it is impractical to use an open-loop amplifier as a stand-alone differential amplifier.
Without negative feedback, and optionally positive feedback for regeneration, an open-loop op amp acts as a comparator, although comparator ICs are better suited. If the inverting input of an ideal op amp is held at ground (0 V), and the input voltage applied to the non-inverting input is positive, the output will be maximum positive; if is negative, the output will be maximum negative.
Closed-loop amplifier
If predictable operation is desired, negative feedback is used by applying a portion of the output voltage to the inverting input. The closed-loop feedback greatly reduces the gain of the circuit. When negative feedback is used, the circuit's overall gain and response are 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 response does not seriously affect the circuit's performance. In this context, high input impedance 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 a transfer function; designing an op-amp circuit to have a desired transfer function is in the realm of electrical engineering. The transfer functions are important in most applications of op amps, such as in analog computers.
In the non-inverting amplifier on the right, the presence of negative feedback via the voltage divider , determines the closed-loop gain . Equilibrium will be established when is just sufficient to pull the inverting input to the same voltage as . The voltage gain of the entire circuit is thus . As a simple example, if and , will be 2 V, exactly the amount required to keep at 1 V. Because of the feedback provided by the , network, this is a closed-loop circuit.
Another way to analyze this circuit proceeds by making the following (usually valid) assumptions: 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 signal appears at both (+) and (−) pins per assumption 1, resulting in a current through equal to :
Because Kirchhoff's current law states that the same current must leave a node as enters it, and because the impedance into the (−) pin is near infinity per assumption 2, we can assume practically all of the same current flows through , creating an output voltage
By combining terms, we determine the closed-loop gain :
Characteristics
Ideal op amps
An ideal op amp is usually considered to have the following characteristics:
Arbitrarily high open-loop gain Infinite input impedance , and thus zero input current Zero input offset voltage Unbounded output voltage range Unrestricted bandwidth with zero phase shift and infinite slew rate Zero output impedance , and thus ability to source or sink unbounded output current Zero noise No effect of common-mode voltages, as described by common-mode rejection ratio (CMRR) No effect of supply variations on the output, i.e., perfect rejection of power supply variation.
These ideals can be summarized by the two : In a negative feedback configuration, the output does whatever is necessary to make the voltage difference between the inputs zero. The inputs draw zero current.
The first rule only applies in the usual case where the op amp is used in a negative feedback design, 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.
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 in 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 Real op amps differ from the ideal model in various aspects.
Non-linear imperfections
Power considerations
Classification Op amps may be classified by their construction: discrete, built from individual transistors or tubes/valves, hybrid, consisting of discrete and integrated components, full integrated 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 acceptable operating 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 by surface-mount devices. Classification by internal compensation: op amps may suffer from high-frequency instability in some negative feedback circuits unless a small compensation capacitor modifies the phase and frequency responses. Op amps with a built-in capacitor are termed compensated, and allow circuits above some specified closed-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 called unity 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. CMOS op amps (such as the CA3140E) provide extremely high input resistances, higher than JFET-input op amps, which are normally higher than bipolar-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.
Applications
Historical timeline
1941: A vacuum tube op amp. An op amp, defined as a general-purpose, DC-coupled, high-gain, inverting feedback amplifier, is first found in "Summing Amplifier" filed by Karl D. Swartzel Jr. of Bell Labs in 1941. This design uses three vacuum tubes to achieve a gain of and operates on voltage rails of . It has a single inverting input rather than differential inverting and non-inverting inputs, as are common in today's op amps. Throughout World War II, Swartzel's design proved its value by being liberally used in the M9 artillery director designed at Bell Labs. This artillery director worked with the SCR-584 radar system to achieve extraordinary hit rates (near 90%) that would not have been possible otherwise.
1947: An op amp with an explicit non-inverting input. In 1947, the operational amplifier was first formally defined and named in a paper by John R. Ragazzini of Columbia University. In this same paper, a footnote mentions an op-amp design by a student that would turn out to be quite significant. This op amp, designed by Loebe Julie, has two major innovations. Its input stage uses a long-tailed triode pair with loads matched to reduce drift in the output and, far more importantly, it is the first op-amp design to have two inputs (one inverting, the other non-inverting). The differential input makes 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.
1949: A chopper-stabilized op amp. In 1949, Edwin A. Goldberg designed a chopper-stabilized op amp. This set-up uses a normal op amp with an additional AC amplifier that goes alongside the op amp. The chopper gets an AC signal from DC 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-amp ICs 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 from George A. Philbrick Researches. The designation on the devices shown, GAP/R, is an acronym for the complete company name. Two nine-pin 12AX7 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.