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# Operational amplifier

An operational amplifier or op-amp is an electronic circuit module (normally built as an integrated circuit, but occasionally with discrete transistors or vacuum tubes) which has a non-inverting input (+), an inverting input (-) and one output. The output voltage is the difference between the + and - inputs multiplied by the open-loop gain: Vout = (V+ − V) * Gopenloop. Since op-amps have uniform parameters and often standardized packaging as well as standard power supply needs, they help in designing an application fast.

Originally, op-amps were so named because they were used to model the basic mathematical operations (add, subtract, integrate, differentiate etc) in electronic analog computers. In this sense a true operational amplifier is an ideal circuit element. The real ones we use, made of transistors, tubes etc, are approximations to this ideal. The ideal op-amp has an infinite open-loop gain, infinite bandwidth, infinite input impedances, zero output impedance and zero noise, as well as zero input offset (0.0V out when both inputs are exactly equal) and no thermal drift. Modern integrated circuit MOSFET op-amps approximate closer and closer to these ideals in limited-bandwidth, large-signal applications at room temperature. When the approximation is reasonably close, we go ahead and call the practical device an 'op-amp', forget its limitations and use the thinking and formulae given in this article.

 Contents

## Notation

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

Its terminals are:

• V+: non-inverting input
• V: inverting input
• Vout: output
• VS+: positive power supply
• VS−: negative power supply

The power supply pins (VS+ and VS−) can be labeled many different ways. For FET based op-amps, the positive, common drain supply is labeled VDD and the negative, common source supply is labeled VSS. For BJT based op-amps, the VS+ pin becomes VCC and VS− becomes VEE. They are also sometimes labeled VCC+ and VCC−, 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.

## DC Behaviour

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. Of course theory and practice differ, since op-amps have limits that the designer must keep in mind and sometimes work around.

## AC Behaviour

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 lowpasses.

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 100s of MHz.

## Applications

The operational amplifier is so called because it performs mathematical operations by using voltage as an analogue of another quantity. This is the basis for the analogue computer.

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

Vout = 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 = R1 / (R1 + R2), then:

V+ = Vin
V = K Vout
Vout = G(Vin − K Vout)

Solving for Vout / Vin, we see that the result is a linear amplifier with gain:

Vout / Vin = G / (1 + G K)

If G is very large, Vout / Vin 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 tend to output 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):

1. No current will flow into the inputs
2. 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 , VS+ or VS−.

Most single, dual and quad op-amps available have a standardised pinout 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 ~10nA) 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 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.

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.
• Short circuit protection - this is more a feature than a limitation, although it does put limits on design. Most commercial op-amps shut off when the load resistance is below a specified level.

## Internal circuitry

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 will arise due to internal parasitic capacitances, etc.

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

1. Differential amplifier
• Input stage - provides low noise amplification, high input impedance, usually a differential output
2. Voltage amplifier
• Provides high voltage gain, a single-pole frequency rolloff, usually single-ended output
3. Output amplifier
• Output stage - provides high current driving capability, low output impedance, current limiting and short circuit protection circuitry

### 741 example

From the diagram, the blue section is a differential amplifier. The base current of the inputs is not really zero, giving the 741 an input impedance of about 2 MΩ.

The sections in red are current mirrors. The input amplifier drives a current mirror load. The top left current mirror allows large common-mode voltages on the inputs without exceeding the active range of any transistor in the circuit. The top right current mirror provides a constant current load for the output circuitry, regardless of the output voltage. The lower current mirror has a very low collector current, because of the 5 kΩ resistor. It is used as a high-impedance connection to the negative power supply, to provide a reference without loading the input circuitry.

The offset null pins are used to remove any offset voltage that would exist at the output of the op-amp when zero signal is applied to the inputs.

The high voltage gain stage is NPN.

The green section is a voltage level shifter. It provides a constant voltage drop between the top and the bottom regardless of supply voltage. If the base current to the transistor is 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), then the current flowing through the 4.5 kΩ resistor will be the same, and will produce a voltage of 0.375 V. This keeps the voltage across the transistor, and the two resistors at 0.625 + 0.375 = 1 V. This serves as a bias for the two output transistors, to prevent crossover distortion. In some amps this function is achieved with diodes.

The capacitor is used as part of a low pass filter (on the base of an emitter follower) to reduce the frequency response of the amp to prevent oscillations. This technique is called Miller Compensation and functions as an internal capacitive feedback.

The output in cyan is a push-pull emitter follower amplifier. It is driven by a PNP emitter-follower. The output range of the amplifier is about 1 volt less than the supply voltage, since the collector-emitter voltage of the output transistors can never go completely to zero. The resistors in the output mean that the current provided by the output is limited (about 25 mA for the 741), and the output resistance is not zero without feedback. With negative feedback it approaches zero. The output stage has current limiting circuitry.

## Common Configurations

The resistors used in these configurations are typically in the kΩ range. <1 kΩ range resistors cause excessive current flow and possible damage to the device. >1 MΩ range resistors cause excessive thermal noise and bias currents.

Zout for all of the amplifiers is ideally 0 Ω. Realistically, it is 1 Ω to 1 kΩ, depending on the device.

### Inverting amplifier

• Inverts and amplifies a voltage (multiplies by a negative constant)
• Vout = −Vin (Rf / Rin)
• Zin = Rin (because V is a virtual ground)

### Non-inverting amplifier

• Amplifies a voltage (multiplies by a constant greater than 1)
• Vout = Vin (1 + R2 / R1)
• Zin = ∞ (realistically, the input impedance of the op-amp itself, 1 MΩ to 1012 Ω)

### Voltage follower

• Used as a buffer, to eliminate loading effects or to interface impedances (connecting a device with a high source impedance to a device with a low input impedance)
• Vout = Vin
• Zin = ∞ (realistically, the input impedance of the op-amp itself, 1 MΩ to 1012 Ω)

### Difference amplifier

• For independent R1,R2,R3,R4 (differential amplifier):
• $V_{out} = V_2 \left( { \left( R_3 + R_1 \right) R_4 \over \left( R_4 + R_2 \right) R_1} \right) - V_1 \left( {R_3 \over R_1} \right)$
• For R1 = R2 and R3 = R4 (amplified difference),
• $V_{out} = {R_3 \over R_1} \left( V_2 - V_1 \right)$
• For R1 = R3 and R2 = R4 (also for R1 = R2 = R3 = R4) (difference amplifier):
• $V_{out} = V_2 - V_1 \,\!$
• Differential Zin (between the two input pins) = R1 + R2
• An instrumentation amplifier is made by adding a voltage follower to each input to increase the input impedance.

### Summing amplifier

• Sums several (weighted) voltages
• Output is inverted
• For independent R1, R2, ... Rn
• V = − Rf (V1 / R1 + V2 / R2 + ... + Vn / Rn)
• For R1 = R2 = ... = Rn, and RF independent
• V = − (Rf / R1) (V1 + V2 + ... + Vn)
• For R1 = R2 = ... = Rn = Rf
• V = − (V1 + V2 + ... + Vn)
• Input impedance Zn = Rn, for each input (V is a virtual ground)

### Integrator

• Integrates the (inverted) signal over time (where Vin and Vout are functions of time)
• $V_{out} = \int_0^t - {V_{in} \over RC} \, dt + V_{initial}$
(Vinitial is the output voltage of the integrator at time t = 0.)
• Note that this can also be viewed as a type of electronic filter.

### Differentiator

• Differentiates the (inverted) signal over time (where Vin and Vout are functions of time)
• $V_{out} = - R C \, {d V_{in} \over dt}$
• Note that this can also be viewed as a type of electronic filter.

### Comparator

• Compares two voltages and outputs one of two states depending on which is greater
• $V_{out} = \left\{\begin{matrix} V_{S+} & V_1 > V_2 \\ V_{S-} & V_1 < V_2 \end{matrix}\right.$
• See article for details

### Instrumentation amplifier

• Combines very high input impedance, high common-mode rejection, low DC offset , and other properties used in making very accurate, low-noise measurements
• See article for details

### Schmitt trigger

• A comparator with hysteresis
• See article for details

### Inductance gyrator

• Simulates an inductor
• See article for details