An operational amplifier , which is often called an op-amp , is a DC-coupled high-gain electronic voltage amplifier with differential inputs and, usually, a single output.. Typically the op-amp's very large gain is controlled by negative feedback, which largely determines the magnitude of its output ("closed-loop") voltage gain in amplifier applications, or the transfer function required (in analog computers). Without negative feedback, and perhaps with positive feedback for regeneration, an op-amp essentially acts as a comparator. High input impedance at the input terminals (ideally infinite) and low output impedance (ideally zero) are important typical characteristics.

Op-amps are among the most widely used electronic devices today, being used in a vast array of consumer, industrial, and scientific devices. Many standard IC op-amps cost only a few cents in moderate production volume; however some integrated or hybrid operational amplifiers with special performance specifications may cost over $100 US in small quantities. Op-amps sometimes come in the form of macroscopic components, (see photo) or as integrated circuit 'cells' or patterns that can be reprinted several times on one chip that is more complex, such as for a cell phone.

Modern designs are electronically more rugged than earlier implementations and some can sustain direct short circuits on their outputs without damage.

The op-amp is one type of differential amplifier. Other types of differential amplifier include the fully differential amplifier (similar to the op-amp, but with two outputs), the instrumentation amplifier (usually built from three op-amps), the isolation amplifier (similar to the instrumentation amplifier, but which works fine with common-mode voltages that would destroy an ordinary op-amp), and negative feedback amplifier (usually built from one or more op-amps and a resistive feedback network).

Circuit notation

The circuit symbol for an op-amp is shown to the right, where:

  • V_{\!+} : non-inverting input
  • V_{\!-} : inverting input
  • V_{\!\text{out}} : output
  • V_{\text{S}\!+} : positive power supply
  • V_{\text{S}\!-} : negative power supply

The power supply pins ( V_{\text{S}\!+} and V_{\text{S}\!-} ) can be labeled in different ways ( See IC power supply pins ). Despite different labeling, the function remains the same — to provide additional power for amplification of signal. Often these pins are left out of the diagram for clarity, and the power configuration is described or assumed from the circuit.

Operation

The amplifier's differential inputs consist of a V_{\!+} input and a V_{\!-} input, and 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 V_{\!+} is the voltage at the non-inverting terminal, V_{\!-} is the voltage at the inverting terminal and G open-loop is the open-loop gain of the amplifier. (The term open-loop refers to the absence of a feedback loop from the output to the input.)

Op-amp with inverting input grounded through a resistor; input at the non-inverting input, and no feedback

With no positive feedback, the op-amp acts as a switch. The inverting input is held at ground (0 V) by the resistor, so if the V in applied to the non-inverting input is positive, the output will be maximum positive, and if V in is negative, the output will be maximum negative. Since there is no feedback from the output to either input, this is an open loop circuit. The circuit's gain is just the G open-loop of the op-amp.

Standard two-resistor non-inverting amplifier circuit

Adding negative feedback via R f puts us in a different universe. Equilibrium will be established when V out is just sufficient to reach around and pull the inverting input to the same voltage as V in . As a simple example, if V in = 1 V and R f = R g , V out will be 2 V, the amount required to keep V at 1 V. Because of the feedback provided by R f , this is a closed loop circuit. Its over-all gain V out  / V in is called the closed-loop gain G closed-loop . Because the feedback is negative, in this case G closed-loop is less than the G open-loop of the op-amp.

The magnitude of G open-loop is typically very large—seldom less than a million—and therefore even a quite small difference between V_{\!+} and V_{\!-} (a few microvolts or less) will result in amplifier saturation, where the output voltage goes to either the extreme maximum or minimum end of its range, which is set approximately by the power supply voltages. Finley's law states that "When the inverting and non-inverting inputs of an op-amp are not equal, its output is in saturation." Additionally, the precise magnitude of G open-loop is not well controlled by the manufacturing process, and so it is impractical to use an operational amplifier as a stand-alone differential amplifier. If linear operation is desired, negative-feedback must be used, usually achieved by applying a portion of the output to the inverting input. The feedback enables the output of the amplifier to keep the inputs at or near the same voltage so that saturation does not occur. Another benefit is that if much negative feedback is used, the circuit's overall gain and other parameters become determined more by the feedback network than by the op-amp itself. If the feedback network is made of components with relatively constant, predictable, values such as resistors, capacitors and inductors, the unpredictability and inconstancy of the op-amp's parameters (typical of semiconductor devices) do not seriously affect the circuit's performance.

If no negative feedback is used, the op-amp functions as a switch or comparator.

Positive feedback may be used to introduce hysteresis or oscillation.

Returning to a consideration of linear (negative feedback) operation, the high open-loop gain and low input leakage current of the op-amp imply two "golden rules" that are highly useful in analysing linear op-amp circuits.

Golden rules of op-amp negative feedback

If there is negative feedback and if the output is not saturated,

  1. both inputs are at the same voltage;
  2. no current flows in or out of either input.

These rules are true of the ideal op-amp and for practical purposes are true of real op-amps unless very high-speed or high-precision performance is being contemplated (in which case account must be taken of things such as input capacitance, input bias currents and voltages, finite speed, and other op-amp imperfections, discussed in a later section.)

As a consequence of the first rule, the input impedance of the two inputs will be nearly infinite. That is, even if the open-loop impedance between the two inputs is low, the closed-loop input impedance will be high because the inputs will be held at nearly the same voltage. This impedance is considered as infinite for an ideal opamp and is about one megohm in practice.

Real and Ideal op-amps

Shown on the right is an equivalent circuit model of an operational amplifier. The main part in the amplifier is the dependent voltage source that increases in relation to the voltage across R in , thus amplifying the voltage difference b

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