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MODULE 4

OPERATIONAL AMPLIFIER

Various op-amp ICs in 8-pin dual in-line packages ("DIPs")

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.[1] Typically the output of the op-amp is controlled either by negative feedback, which largely determines the magnitude of its output voltage gain, or by positive feedback, which facilitates regenerative gain and oscillation. 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.

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 2 outputs), the instrumentation amplifier (usually built from 3 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 1 or more op-amps and a resistive feedback network).

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Circuit notation

Circuit diagram symbol for an op-amp

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

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 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 V + input and a V − input, and generally the op-amp amplifies only the difference in voltage between the two. This is called the differential input voltage. Operational amplifiers are usually used with feedback loops where the output of the amplifier would influence one of its inputs. The output voltage and the input voltage it influences settles down to a stable voltage after being connected for some time, when they satisfy the internal circuit of the op amp.

In its most common use, the op-amp's output voltage is controlled by feeding a fraction of the output signal back to the inverting input. This is known as negative feedback. If that fraction is zero (i.e., there is no negative feedback) the amplifier is said to be running open loop and its output is the differential input voltage multiplied by the total gain of the amplifier, as shown by the following equation:

where V + is the voltage at the non-inverting terminal, V − is the voltage at the inverting terminal and G is the total open-loop gain of the amplifier.

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Since the magnitude of the open-loop gain is typically very large, open-loop operation results in op-amp saturation (see below in Nonlinear imperfections) unless the differential input voltage is extremely small. 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 this gain is not well controlled by the manufacturing process, and so it is impractical to use an operational amplifier as a stand-alone differential amplifier. Instead, op-amps are usually used in negative-feedback configurations.

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.

Ideal op-amp

Equivalent circuit of an operational amplifier.

Shown on the right is an example of an ideal operational amplifier. The main part in an amplifier is the dependent voltage source that increases in relation to the voltage drop across Rin, thus amplifying the voltage difference between V + and V − . Many uses have been found for operational amplifiers and an ideal op-amp seeks to characterize the physical phenomena that make op-amps useful.

Supply voltages Vcc + and Vcc − are used internally to implement the dependent voltage sources. The positive source Vs + acts as an upper bound on the output, and the negative source Vs − acts as a lower bound on the output. The internal Vs + and Vs − connections are not shown here and will vary by implementation of the operational amplifier.

For any input voltages, an ideal op-amp has the following properties:

Infinite open-loop gain (i.e., when doing theoretical analysis, limit should be taken as open loop gain Gopenloop goes to infinity)

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Infinite bandwidth (i.e., the frequency magnitude response is flat everywhere with zero phase shift).

Infinite input impedance (i.e., , and so zero current flows from V + to V − )

Zero input current (i.e., there is no leakage or bias current into the device) Zero input offset voltage (i.e., when the input terminals are shorted so that V + = V

− , the output is a virtual ground). Infinite slew rate (i.e., the rate of change of the output voltage is unbounded) and

power bandwidth (full output voltage and current available at all frequencies). Zero output impedance (i.e., Rout = 0, and so output voltage does not vary with

output current) Zero noise Infinite Common-mode rejection ratio (CMRR) Infinite Power supply rejection ratio for both power supply rails.

Because of these properties, an op-amp can be modeled as a nullor

An operational amplifier is a high gain amplifier usually consisting of one or more differential amplifier and usually followed by a level translator and an output stage.

The op-amp is a versatile device that can be used to amplify dc as well as ac input signal and was originally designed for performing mathematical operations such as addition ,subtraction,multiplication and integration.Thus the name operational amplifier stems from its original use for these mathematical operations and is abbreviated to op-amp.The first op-amp was introduced by Fairchild semiconductor in 1963,its μA 702 which set the stage for development of other IC op-amps

Internal Block Schematic of op-amp

The input stage is the dual input balanced output differential amplifier.This stage generally provides most of the voltage gain of the amplifier and also establishes the input resistance of the op-amp.The intermediate stage is usually another differential amplifier,which is driven by the output of the first stage.On most amplifiers,the intermediate stage is dual input,unbalanced output. Because of direct coupling,the dc voltage at the output of the intermediate stage is well above ground potential.Therefore,the level translator(shifting)circuits is used after the intermediate

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stage downwards to zero volts with respect to ground.The final stage is usually a push pull complementary symmetry amplifier output stage.The output stage increases the voltage swing and raises the ground supplying capabilities of the op-amp.a well designed output stage also provides low output resistance.

Test ParameterTyp. Unit

Typical Description

Input Bias CurrentµA

Each input of an operational amplifier has a certain amount of current that flows in or out of it. This is basically the leakage current of the input transistor, i.e., the base leakage current if the input transistor is bipolar, or the gate leakage current if it is a FET. This current is known as the input bias current, and is ideally zero.  

Example of an Actual Spec:

AD829: 3.3 µA typ.; 7 µA max.

Input Offset CurrentnA

This is simply the mismatch or difference between the input bias currents flowing through the inputs. This is ideally zero.

Example of an Actual Spec: AD829: 50 nA typ.; 500 nA max.

Input Offset VoltagemV

An ideal operational amplifier will give an output of 0V if both of its inputs are shorted together.  A real-world op amp will have a non-zero voltage output even if its inputs are shorted together.  This is the effect of its input offset voltage, which is the slight voltage present across its inputs brought about by its non-zero input offset current.  In essence, the input voltage offset is also the voltage that needs to be applied across the inputs of an op amp to make its output zero.

Example of an Actual Spec:

AD712C:  0.1 mV typ.; 0.3 mV max.

Open-Loop GainV/mV

This is the ratio of the op amp's output voltage to its

differential input voltage without any external feedback. Example of an Actual Spec:

AD712: 150 V/mV min.; 400 V/mV typ.

Gain-Bandwidth ProductMHz

This is the product of the op amp's open-loop voltage gain

and the frequency at which it was measured. Example of an Actual Spec:

AD829: 750 MHz for Vs=+/-15V

Slew RateV/µsec

This is the rate of change of the op amp's voltage output over

time when its gain is set to unity (Gain =1). Example of an Actual Spec:

AD712:  16 V/µsec min.; 20 V/µsec typ.

Settling Time nsec

This is the length of time for the output voltage of an operational amplifier to approach, and remain within, a certain tolerance of its final value. This is usually specified for

a fast full-scale input step. Example of an Actual Spec:

Settling time to 0.1% for a 10V step with Vs=+/-15V:  90 nsec

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Common Mode Rejection (CMR)

dB

This is the ability of an operational amplifier to cancel out or reject any signals that are common to both inputs, and amplify any signals that are differential between them. Common mode rejection is the logarithmic expression of CMRR, i.e., CMR=20logCMRR. CMRR is simply the ratio of

the differential gain to the common-mode gain. Example of an Actual Spec:

AD829:  100 dB min.; 120 dB typ.

Power Supply Rejection (PSR)

dB

PSR is a measure of an op amp’s ability to prevent its output from being affected by noise or ripples at the power supply. It is computed as the ratio of the change in the power supply voltage to the change in the op amp's output voltage (caused by the power supply change). It is often expressed in dB.

Example of an Actual Spec:

AD829:  98 dB min.; 120 dB typ. for Vs=+/-4.5V to +/-18V

Phase Margindegrees

An op amp will tend to oscillate at a frequency wherein the loop phase shift exceeds -180°, if this frequency is below the closed-loop bandwidth. The closed-loop bandwidth of a voltage-feedback op amp circuit is equal to the op amp's  bandwidth at unity gain, divided by the circuit's closed loop

gain.   The phase margin of an op amp circuit is the amount of additional phase shift at the closed loop bandwidth required to make the circuit unstable (i.e., phase shift + phase margin = -180°). As phase margin approaches zero, the loop phase shift approaches -180° and the op amp circuit approaches instability. Typically, values of phase margin much less than 45° can cause problems such as "peaking" in frequency response, and overshoot or "ringing" in step response. In order to maintain conservative phase margin, the pole generated by capacitive loading should be at least a decade above the circuit's closed loop bandwidth. Reference: www.analog.comExample of an Actual Spec: AD847:  50 degrees AD829:  60 degrees

Input Voltage Range, Common Mode

V

This is the maximum voltage (negative or positive) that can be applied at both inputs of an operational amplifier at the

same time, with respect to the ground. Examples of Actual Specs:

AD712: +14.5V, -11.5 V typ. for Vs=+/-15 V; AD844: +/- 10V for Vs=+/-15 V

Input  Voltage Range, Differential

V

This is the maximum voltage (negative or positive) that can

be applied across the two inputs of an operational amplifier. Example of an Actual Spec:  AD712: +/-20V

Output Voltage Swing+/-V

This is the maximum output voltage that the op amp can deliver without saturation or clipping for a given load and

operating supply voltage. Example of an Actual Spec: +/-11V min.; +/-13V typ. for R=1K; Vs=+/-15V

Input Resistance or

M This is the small-signal resistance between the two inputs

(both ungrounded) of an op amp.

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Impedance, Differential

Example of an Actual Spec: OP27C:  0.7 Mmin.; 4 M typ.

Input Resistance or Impedance, Common Mode

G

Each input of an op amp has a resistance with respect to ground. The common mode input resistance of an op amp is the equivalent resistance value of the op amp's two input resistances in parallel. This is the resistance of the two inputs

shorted together with respect to ground. Example of an Actual Spec: OP27C:  2 G typ.

Output Resistance or Impedance

This is the small-signal resistance or impedance between the

output of an op amp and ground. Example of an Actual Spec: AD844:  15  typ., open loop

Power Supply RangeV

This refers to the minimum and maximum values of supply voltages that the negative and positive supplies of an

operational amplifier can accept. Example of an Actual Spec:

AD712:  +/- 4.5V min.; +/-18V max.

Quiescent CurrentmA

This is the non-signal power supply current that the op amp will consume within a specified power supply voltage operating range.

Example of an Actual Spec:

AD712:  5 mA typ.; 6.8 mA max. for Vs=+/-15V

Total Power DissipationmW

The total DC power supplied to the op amp minus the power

delivered by the op amp to its load. Example of an Actual Spec:

OP27: 90-100 mW typ.; 140-170 mW max.

Operational Amplifiers:

The operational amplifier is a direct-coupled high gain amplifier usable from 0 to over 1MH Z to which feedback is added to control its overall response characteristic i.e. gain and bandwidth. The op-amp exhibits the gain down to zero frequency.

Such direct coupled (dc) amplifiers do not use blocking (coupling and by pass) capacitors since these would reduce the amplification to zero at zero frequency. Large by pass capacitors may be used but it is not possible to fabricate large capacitors on a IC chip. The capacitors fabricated are usually less than 20 pf. Transistor, diodes and resistors are also fabricated on the same chip.

Differential Amplifiers:

Differential amplifier is a basic building block of an op-amp. The function of a differential amplifier is to amplify the difference between two input signals.

How the differential amplifier is developed? Let us consider two emitter-biased circuits as shown in fig. 1.

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Fig. 1

The two transistors Q1 and Q2 have identical characteristics. The resistances of the circuits are equal, i.e. RE1 = R E2, RC1 = R C2 and the magnitude of +VCC is equal to the magnitude of ?VEE. These voltages are measured with respect to ground.

To make a differential amplifier, the two circuits are connected as shown in fig. 1. The two +VCC and ?VEE supply terminals are made common because they are same. The two emitters are also connected and the parallel combination of RE1 and RE2 is replaced by a resistance RE. The two input signals v1 & v2 are applied at the base of Q1 and at the base of Q2. The output voltage is taken between two collectors. The collector resistances are equal and therefore denoted by RC = RC1 = RC2.

Ideally, the output voltage is zero when the two inputs are equal. When v1 is greater then v2 the output voltage with the polarity shown appears. When v1 is less than v2, the output voltage has the opposite polarity.

The differential amplifiers are of different configurations.

The four differential amplifier configurations are following:

1. Dual input, balanced output differential amplifier. 2. Dual input, unbalanced output differential amplifier. 3. Single input balanced output differential amplifier. 4. Single input unbalanced output differential amplifier.

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Fig. 2

These configurations are shown in fig. 2, and are defined by number of input signals used and the way an output voltage is measured. If use two input signals, the configuration is said to be dual input, otherwise it is a single input configuration. On the other hand, if the output voltage is measured between two collectors, it is referred to as a balanced output because both the collectors are at the same dc potential w.r.t. ground. If the output is measured at one of the collectors w.r.t. ground, the configuration is called an unbalanced output.

A multistage amplifier with a desired gain can be obtained using direct connection between successive stages of differential amplifiers. The advantage of direct coupling is that it removes the lower cut off frequency imposed by the coupling capacitors, and they are therefore, capable of amplifying dc as well as ac input signals.

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Real vs Ideal Op-ampReadily available, inexpensive IC op-amps have characteristics which are reasonable approximations of an ideal op-amp (data from Simpson):

These characteristics lead to the golden rules for op-amps. They all

Vo=A(V1-V2)

This is the basic op-amp equation in which the output offset voltage is assumed to be zero.The graphic representation of this equation is shown;where the output voltage ,Vo is plotted against input difference voltage Vid,keeping gain A constant.The output voltage cannot exceed the positive and negative saturation voltage.These saturation voltages are specified by an output voltage swing ratings of an op-amp for given values of supply voltages.The output voltage is directly proportional to the input difference voltage until it reaches the saturation voltages and thereafter the output voltage remains constant.

This curve is called ideal voltage transfer curve

Open loop OPAMP Configuration:

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In the case of amplifiers the term open loop indicates that no connection, exists between input and output terminals of any type. That is, the output signal is not fedback in any form as part of the input signal.

In open loop configuration, The OPAMP functions as a high gain amplifier. There are three open loop OPAMP configurations.

The Differential Amplifier:

Fig. 1, shows the open loop differential amplifier in which input signals vin1 and vin2 are applied to the positive and negative input terminals.

Fig. 1

Since the OPAMP amplifies the difference the between the two input signals, this configuration is called the differential amplifier. The OPAMP amplifies both ac and dc input signals. The source resistance R in1 and Rin2 are normally negligible compared to the input resistance Ri. Therefore voltage drop across these resistances can be assumed to be zero.

Therefore

v1 = vin1 and v2 = vin2.

vo = Ad (vin1 ? vin2 )

where, Ad is the open loop gain.

The Inverting Amplifier:

If the input is applied to only inverting terminal and non-inverting terminal is grounded then it is called inverting amplifier.This configuration is shown in fig. 2.

v1= 0, v2 = vin.

vo = -Ad vin

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Fig. 2

The negative sign indicates that the output voltage is out of phase with respect to input 180 ° or is of opposite polarity. Thus the input signal is amplified and inverted also.

The non-inverting amplifier:  

In this configuration, the input voltage is applied to non-inverting terminals and inverting terminal is ground as shown in fig. 3.

v1 = +vin                  v2 = 0

vo = +Ad vin

This means that the input voltage is amplified by Ad and there is no phase reversal at the output.

Fig. 3

In all there configurations any input signal slightly greater than zero drive the output to saturation level. This is because of very high gain. Thus when operated in open-loop, the output of the OPAMP is either negative or positive saturation or switches between positive and negative saturation levels. Therefore open loop op-amp is not used in linear applications.

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Slew Rate of Op Amp CircuitsE.L. Dove, 2/13/2004The slew rate (SR) is defined as the maximum rate of change of the output of an op amp circuit. The SR in general describes the degradation effect on the high frequency response of the active amplifier (one with an op amp) near or at the rated maximum output voltage swing. This effect is generally due to the compensating capacitor and not to the transistor circuits internal to the op amp. In short, the SR effect is due to the maximum supplied current available for charging up the compensating capacitor.We know that the current required to charge a capacitor is

I = c dv/dtThe Slew Rate is found from

SR=I dv/d tmax

Consider the following example. Suppose that the input signal to a 741-based unity gain amplifier configuration is a 20kHz sine wave. What is the largest possible amplitude of the input signal to avoid distortion due to slewing?The Slew Rate is found as the maximum of this derivative, ordv0/dt = M 2pi f cos 2pift

SR= M 2pifM

.

Positive feedback configurations

Another typical configuration of op-amps is the positive feedback, which takes a fraction of the output signal back to the non-inverting input. An important application of it is the comparator with hysteresis (i.e., the Schmitt trigger).

Basic single stage amplifiers

Non-inverting amplifier

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

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The general 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):

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:

then:

, where G > 0

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

If G is very large, comes close to .

Inverting amplifier

Because it does not require a differential input, this negative feedback connection was the most typical use of an op-amp in the days of analog computers.[citation needed] It remains very popular,[citation needed] but many different configurations are possible, making it one of the most versatile of all electronic building blocks.

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An op-amp connected in the inverting amplifier configuration

By applying KCL at the inverting input,

However, because the input current into any operational amplifier is assumed to be zero,

and so

By applying KVL at the output,

However, because the operational amplifier is in a negative-feedback configuration, the inverting input v − can be assumed to match the non-inverting input v + . In particular,

and so v − is a virtual ground. Therefore,

Hence, closed loop gain [6]

Some Variations: o A resistor is often inserted between the non-inverting input and ground (so

both inputs "see" similar resistances), reducing the input offset voltage due

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to different voltage drops due to bias current, and may reduce distortion in some op-amps.

o A DC-blocking capacitor may be inserted in series with the input resistor when a frequency 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 DC zero and a low-frequency pole that gives the circuit a bandpass or high-pass characteristic.

Other applications audio- and video-frequency pre-amplifiers and buffers voltage comparators differential amplifiers differentiators and integrators filters precision rectifiers precision peak detectors voltage and current regulators analog calculators analog-to-digital converters digital-to-analog converter voltage clamps oscillators and waveform generators

Limitations of real op-amps

Real op-amps can only approach this ideal: in addition to the practical limitations on slew rate, bandwidth, offset and so forth mentioned above, real op-amp parameters are subject to drift over time and with changes in temperature, input conditions, etc. Modern integrated FET or MOSFET op-amps approximate more closely the ideal op-amp than bipolar ICs where large signals must be handled at room temperature over a limited bandwidth; input impedance, in particular, is much higher, although the bipolar op-amps usually exhibit superior (i.e., lower) input offset drift and noise characteristics.

Where the limitations of real devices can be ignored, an op-amp can be viewed as a black box with gain; circuit function and parameters are determined by feedback, usually negative. IC op-amps as implemented in practice are moderately complex integrated circuits; see the internal circuitry for the relatively simple 741 op-amp below, for example.

DC imperfections

Real operational amplifiers suffer from several non-ideal effects:

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Finite gain Open-loop gain is defined as the amplification from input to output without any feedback applied. For mathematical calculations, the ideal open-loop gain is infinite; however, it is finite in real operational amplifiers. Typical devices exhibit open-loop DC gain ranging from 100,000 to over 1 million. So long as the loop gain (i.e., the product of open-loop and feedback gains) is very large, the circuit gain will be determined entirely by the amount of negative feedback (i.e., it will be independent of open-loop gain). In cases where closed-loop gain must be very high, the feedback gain will be very low, and the low feedback gain causes low loop gain; in these cases, the operational amplifier will cease to behave ideally.

Finite input impedance 

The input impedance of the operational amplifier is defined as the impedance between its two inputs. It is not the impedance from each input to ground. In the typical high-gain negative-feedback applications, the feedback ensures that the two inputs sit at the same voltage, and so the impedance between them is made artificially very high. Hence, this parameter is rarely an important design parameter. Because MOSFET-input operational amplifiers often have protection circuits that effectively short circuit any input differences greater than a small threshold, 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 and the negative feedback will render the input impedance to be practically infinite. The input bias and leakage currents described below are a more important design parameter for typical operational amplifier applications.

Non-zero output impedance 

Low output impedance is important for low resistance loads; for these loads, the voltage drop across the output impedance of the amplifier will be significant. Hence, the output impedance of the amplifier reflects the maximum power that can be provided. Similarly, low-impedance outputs typically require high quiescent (i.e., idle) current in the output stage and will dissipate more power. So low-power designs may purposely sacrifice low-impedance outputs.

Input current 

Due to biasing requirements or leakage, a small amount of current (typically ~10 nanoamperes for bipolar op-amps, tens of picoamperes for JFET input stages, and only a few pA for MOSFET input stages) flows into the inputs. When large resistors or sources with high output impedances are used in the circuit, these small currents can produce large unmodeled voltage drops. If the input currents are matched and the impedance looking out of both inputs are matched, then the voltages produced at each input will be equal. Because the operational amplifier operates on the difference between its inputs, these matched voltages will have no

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effect (unless the operational amplifier has poor CMRR, which is described below). It is more common for the input currents (or the impedances looking out of each input) to be slightly mismatched, and so a small offset voltage can be produced. This offset voltage can create offsets or drifting in the operational amplifier. It can often be nulled externally; however, many operational amplifiers include offset null or balance pins and some procedure for using them to remove this offset. Some operational amplifiers attempt to nullify this offset automatically.

Input offset voltage 

This voltage, which is what is required across the op-amp's input terminals to drive the output voltage to zero,[7][nb 1] is related to the mismatches in input bias current. In the perfect amplifier, there would be no input offset voltage. However, it exists in actual op-amps because of imperfections in the differential amplifier that constitutes the input stage of the vast majority of these devices. 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 2]

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 identical voltages to some degree. The standard measure of this defect is called the common-mode rejection ratio (denoted CMRR). Minimization of common mode gain is usually important in non-inverting amplifiers (described below) that operate at high amplification.

Temperature effects 

All parameters change with temperature. Temperature drift of the input offset voltage is especially important.

Power-supply rejection 

The output of a perfect operational amplifier will be completely independent from ripples that arrive on its power supply inputs. Every real operational amplifier has a specified power supply rejection ratio (PSRR) that reflects how well the op-amp can reject changes in its supply voltage. Copious use of bypass capacitors can improve the PSRR of many devices, including the operational amplifier.

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AC imperfections

The op-amp gain calculated at DC does not apply at higher frequencies. To a first approximation, the gain of a typical op-amp is inversely proportional to frequency. This means that an op-amp is characterized by its gain-bandwidth product. For example, an op-amp with a gain bandwidth product of 1 MHz would have a gain of 5 at 200 kHz, and a gain of 1 at 1 MHz. This low-pass characteristic is introduced deliberately, because it tends to stabilize the circuit by introducing a dominant pole. This is known as frequency compensation.

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

Other imperfections include:

Finite bandwidth — all amplifiers have a finite bandwidth. This creates several problems for op amps. First, associated with the bandwidth limitation is a phase difference between the input signal and the amplifier output that can lead to oscillation in some feedback circuits. The internal frequency compensation used in some op amps to increase the gain or phase margin intentionally reduces the bandwidth even further to maintain output stability when using a wide variety of feedback networks. Second, reduced bandwidth results in lower amounts of feedback at higher frequencies, producing higher distortion, noise, and output impedance and also reduced output phase linearity as the frequency increases.

Input capacitance — most important for high frequency operation because it further reduces the open loop bandwidth of the amplifier.

Common mode gain — See DC imperfections, above.

Nonlinear imperfections Saturation — output voltage is limited to a minimum and maximum value close to

the power supply voltages.[nb 3] Saturation occurs when the output of the amplifier reaches this value and is usually due to:

o In the case of an op-amp using a bipolar power supply, a voltage gain that produces an output that is more positive or more negative than that maximum or minimum; or

o In the case of an op-amp using a single supply voltage, either a voltage gain that produces an output that is more positive than that maximum, or a signal so close to ground that the amplifier's gain is not sufficient to raise it above the lower threshold.[nb 4]

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Slewing — the amplifier's output voltage reaches its maximum rate of change. Measured as the slew rate, it is usually specified in volts per microsecond. When slewing occurs, further increases in the input signal have no effect on the rate of change of the output. Slewing is usually caused by internal capacitances in the amplifier, especially those used to implement its frequency compensation.

Non-linear transfer function — The output voltage may not be accurately proportional to the difference between the input voltages. It is commonly called distortion when the input signal is a waveform. This effect will be very small in a practical circuit if substantial negative feedback is used.

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