This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.
The operational amplifier is arguably 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. It is also quite affordable, most general-purpose amplifiers selling for under a dollar apiece. Modern designs have been engineered with durability in mind as well: several "op-amps" are manufactured that can sustain direct short-circuits on their outputs without damage.
AnÂ Operational amplifierÂ ("op-amp") is aÂ DC-coupledÂ high-gainÂ electronic voltageÂ amplifierÂ with a differential input and, usually, a single-ended output.An op-amp produces an output voltage that is typically hundreds of thousands times larger than the voltageÂ differenceÂ between its input terminals.
Operational amplifiers are important building blocks for a wide range of electronic circuits. They had their origins inÂ analog computersÂ where they were used in many linear, non-linear and frequency-dependent circuits. Their popularity in circuit design largely stems from the fact the characteristics of the final elements (such as theirÂ gain) are set by external components with little dependence on temperature changes and manufacturing variations in the op-amp itself..
The op-amp is one type ofÂ differential amplifier. Other types of differential amplifier include theÂ fully differential amplifierÂ (similar to the op-amp, but with two outputs), theÂ instrumentation amplifierÂ (usually built from three op-amps), theÂ isolation amplifierÂ (similar to the instrumentation amplifier, but with tolerance to common-mode voltages that would destroy an ordinary op-amp), andÂ negative feedback amplifierÂ (usually built from one or more op-amps and a resistive feedback network).
Circuit diagram symbol for an op-amp
The circuit symbol for an op-amp is shown to the right, where:
: non-inverting input
: inverting input
: positive power supply
: negative power supply
The power supply pins (Â andÂ ) can be labeled in different ways (SeeÂ IC power supply pins). Despite different labeling, the function remains the same - to provide additional power for amplification of the signal. Often these pins are left out of the diagram for clarity, and the power configuration is described or assumed from the circuit.
Voltage Gain, (A)
InfiniteÂ - The main function of an operational amplifier is to amplify the input signal and the more open loop gain it has the better, so for an ideal amplifier the gain will be infinite.
Input impedance, (Zin)
InfiniteÂ - Input impedance is assumed to be infinite to prevent any current flowing from the source supply into the amplifiers input circuitry.
Output impedance, (Zout)
ZeroÂ - The output impedance of the ideal operational amplifier is assumed to be zero so that it can supply as much current as necessary to the load.
InfiniteÂ - An ideal operational amplifier has an infinite Frequency Response and can amplify any frequency signal so it is assumed to have an infinite bandwidth.
Offset Voltage, (Vio)
ZeroÂ - The amplifiers output will be zero when the voltage difference between the inverting and non-inverting inputs is zero.
From these "idealized" characteristics above, we can see that the input resistance is infinite, soÂ no current flows into either input terminalÂ (the current rule) and that theÂ differential input offset voltage is zeroÂ (the voltage rule). It is important to remember these two properties as they help understand the workings of the amplifier with regards to analysis and design of operational amplifier circuits.
The op-amp is basically a differential amplifier having a large voltage gain, very high input impedance and low output impedance. The op-amp has a "inverting" or (-) input and "noninverting" or (+) input and a single output. The op-amp is usually powered by a dual polarity power supply in the range of +/- 5 volts to +/- 15 volts. A simple dual polarity power supply is shown in the figure below which can be assembled with two 9 volt batteries.
n thisÂ Inverting AmplifierÂ circuit the operational amplifier is connected with feedback to produce a closed loop operation. There are two very important rules to remember about inverting amplifiers is that, "no current flows into the input terminal" and that "V1 equals V2". This is because the junction of the input and feedback signal (X) is at the same potential as the positive (+) input which is at zero volts or ground then, the junction is aÂ "Virtual Earth". Because of this virtual earth node the input resistance of the amplifier is equal to the value of the input resistor,Â RinÂ and the closed loop gain of the inverting amplifier can be set by the ratio of the two external resistors.
We said above that there are two very important rules to remember aboutÂ Inverting AmplifiersÂ or any operational amplifier for that matter and they are.
1.Â Â No Current Flows into the Input Terminals
2.Â Â The Differential Input Voltage is Zero as V1 = V2 = 0Â (Virtual Earth)
Then by using these two rules we can find the equation for calculating the gain of an inverting amplifier, using first principles.
Current (Â iÂ ) flows through the resistor network as shown.
Then, theÂ Closed-Loop Voltage GainÂ of an Inverting Amplifier is given as.
and this can be transposed to give:
The negative sign in the equation indicates an inversion of the output signal with respect to the input as it is 180oÂ out of phase. This is due to the feedback being negative in value.
Non inverting Amplifier:
The noninverting amplifier is connected so that the input signal goes directly to the noninverting input (+) and the input resistor RA is grounded. In this configuration, the input impedance as seen by the signal is much greater since the input will be following the applied signal and not held constant by the feedback current. As the signal moves in either direction, the output will follow in phase to maintain the inverting input at the same voltage as the input (+). The voltage gain is always more than 1 and can be worked out from Vgain = (1+ RB/RA).
The voltage follower, also called a buffer, provides a high input impedance, a low output impedance, and unity gain. As the input voltage changes, the output and inverting input will change by an equal amount.
The amplifier's differential inputs consist of aÂ Â input and aÂ Â input, and ideally the op-amp amplifies only the difference in voltage between the two, which is called theÂ differential input voltage. The output voltage of the op-amp is given by the equation,
whereÂ Â is the voltage at the non-inverting terminal,Â Â is the voltage at the inverting terminal andÂ AOLÂ is theÂ open-loopÂ gain of the amplifier. (The term "open-loop" refers to the absence of a feedback loop from the output to the input.)
Typically the op-amp's very large gain is controlled byÂ negative feedback, which largely determines the magnitude of its output ("closed-loop") voltage gain in amplifier applications, or theÂ transfer function required (inÂ analog computers). Without negative feedback, and perhaps withÂ positive feedback forregeneration, an op-amp acts as aÂ comparator. High inputÂ impedanceÂ at the input terminals and low output impedance at the output terminal(s) are important typical characteristics.
With no negative feedback, the op-amp acts as a comparator. The inverting input is held at ground (0 V) by the resistor, so if the Vinapplied to the non-inverting input is positive, the output will be maximum positive, and if VinÂ is negative, the output will be maximum negative. Since there is no feedback from the output to either input, this is anÂ open loop circuit. The circuit's gain is just theÂ GOLÂ of the op-amp.
Adding negative feedback via the voltage divider Rf,RgÂ reduces the gain. Equilibrium will be established when VoutÂ is just sufficient to reach around and "pull" the inverting input to the same voltage as Vin. As a simple example, if VinÂ = 1â€‰V and RfÂ = Rg, VoutÂ will be 2â€‰V, the amount required to keep V-Â at 1â€‰V. Because of the feedback provided by Rf,RgÂ this is aÂ closed loopcircuit. Its over-all gain VoutÂ /Â VinÂ is called theclosed-loop gainÂ ACL. Because the feedback is negative, in this caseÂ ACLÂ is less than theÂ AOLÂ of the op-amp.
The magnitude ofÂ AOLÂ is typically very large-10,000 or more for integrated circuit op-amps-and therefore even a quite small difference betweenÂ Â andÂ Â drives the amplifier output nearly to the supply voltage. This is calledÂ saturationÂ of the amplifier. The magnitude ofÂ AOLÂ is not well controlled by the manufacturing process, and so it is impractical to use an operational amplifier as a stand-aloneÂ differential amplifier. If predictable operation is desired,Â negative feedbackÂ is used, by applying a portion of the output voltage to the inverting input. TheÂ closed loopÂ feedback greatly reduces the gain of the amplifier. If 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, stable values, the unpredictability and inconstancy of the op-amp's parameters 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 introduceÂ hysteresisÂ or oscillation.
Ideal and real op-amps
An equivalent circuit of an operational amplifier that models some resistive non-ideal parameters.
An ideal op-amp is usually considered to have the following properties, and they are considered to hold for all input voltages:
InfiniteÂ open-loop gain (when doing theoretical analysis, aÂ limitÂ may be taken as open loop gainÂ AOLÂ goes to infinity)
Infinite voltage range available at the output (vout) (in practice the voltages available from the output are limited by the supply voltagesÂ Â andÂ )
InfiniteÂ bandwidthÂ (i.e., the frequency magnitude response is considered to be flat everywhere with zeroÂ phase shift).
InfiniteÂ input impedanceÂ (so, in the diagram,Â , and zero current flows fromÂ Â toÂ Â )
Zero input current (i.e., there is assumed to be noÂ leakageÂ orÂ biasÂ current into the device)
ZeroÂ input offset voltageÂ (i.e., when the input terminals are shorted so thatÂ , the output is aÂ virtual groundÂ orÂ voutÂ = 0).
InfiniteÂ slow rateÂ (i.e., the rate of change of the output voltage is unbounded) and power bandwidth (full output voltage and current available at all frequencies).
InfiniteÂ Common-mode rejection ratioÂ (CMRR)
InfiniteÂ Power supply rejection ratioÂ for both power supply rails.
In practice, none of these ideals can be realized, and various shortcomings and compromises have to be accepted. Depending on the parameters of interest, a real op-amp may be modeled to take account of some of the non-infinite or non-zero parameters using equivalent resistors and capacitors in the op-amp model. The designer can then include the effects of these undesirable, but real, effects into the overall performance of the final circuit. Some parameters may turn out to haveÂ negligibleÂ effect on the final design while others represent actual limitations of the final performance, that must be evaluated.
OP AMP AS A COMPARATOR
AnÂ operational amplifierÂ (op-amp) has a well balanced difference input and a very highÂ gain. The parallels in the characteristics allows the op-amps to serve as comparators in some functions.
A standard op-amp operating in open loop configuration (without negative feedback) can be used as a comparator. When the non-inverting input (V+) is at a higher voltage than the inverting input (V-), the high gain of the op-amp causes it to output the most positive voltage it can. When the non-inverting input (V+) drops below the inverting input (V-), the op-amp outputs the most negative voltage it can. Since the output voltage is limited by the supply voltage, for an op-amp that uses a balanced, split supply, (powered by Â± VS) this action can be written:
VoutÂ =Â Ao(V1Â âˆ’Â V2)
In practice, using anÂ operational amplifierÂ as a comparator presents several disadvantages as compared to using a dedicated comparator:
Op-amps are designed to operate in the linear mode with negative feedback. Hence, an op-amp typically has a lengthy recovery time from saturation. Almost all op-amps have an internal compensation capacitor which imposesÂ slew rateÂ limitations for high frequency signals. Consequently an op-amp makes a sloppy comparator withÂ propagation delaysÂ that can be as slow as tens of microseconds.
Since op-amps do not have any internal hysteresis an external hysteresis network is always necessary for slow moving input signals.
The quiescent current specification of an op-amp is valid only when the feedback is active. Some op-amps show an increased quiescent current when the inputs are not equal.
A comparator is designed to produce well limited output voltages that easily interface with digital logic. Compatibility with digital logic must be verified while using an op-amp as a comparator.
Main article:Â Comparator
Compares two voltages and switches its output to indicate which voltage is larger.
(whereÂ VsÂ is the supply voltage and the opamp is powered byÂ +Â VsÂ andÂ âˆ’Â Vs.)
An inverting amplifier uses negative feedback to invert andÂ amplifyÂ a voltage. The Rin,RfÂ resistor network allows some of the output signal to be returned to the input. Since the output is 180Â° out of phase, this amount is effectively subtracted from the input, thereby reducing the input into the operational amplifier. This reduces the overall gain of the amplifier and is dubbed negative feedback.
ZinÂ =Â RinÂ (becauseÂ VÂ âˆ’Â is aÂ virtual ground)
A third resistor, of valueÂ , added between the non-inverting input and ground, while not necessary, minimizes errors due to input bias currents.
The gain of the amplifier is determined by the ratio of RfÂ to Rin. That is:
The presence of the negative sign is a convention indicating that the output is inverted. For example, if RfÂ is 10 000 Î© and RinÂ is 1 000 Î©, then the gain would be -10 000Î©/1 000Î©, which is -10.Â
Theory of operation: An Ideal Operational Amplifier has 2 characteristics that imply the operation of the inverting amplifier: Infinite input impedance, and infinite differential gain. Infinite input impedance implies there is no current in either of the input pins because current cannot flow through an infinite impedance. Infinite differential gain implies that both the (+) and (-) input pins are at the same voltage because the output is equal to infinity times (V+ - V-). As the output approaches any arbitrary finite voltage, then the term (V+ - V-) approaches 0, thus the two input pins are at the same voltage for any finite output.
To begin analysis, first it is noted that with the (+) pin grounded, the (-) must also be at 0 volts potential due to implication 2. with the (-) at 0 volts, the current through Rin (from left to right) is given by I = Vin/Rin by Ohm's law. Second, since no current is flowing into the op amp through the (-) pin due to implication 1, all the current through Rin must also be flowing through Rf (see Kirchoff's Current Law). Therefore, with V- = 0 volts and I(Rf) = Vin/Rin the output voltage given by Ohm's law is -Vin*Rf/Rin.
Real op amps have both finite input impedance and differential gain, however both are high enough as to induce error that is considered negligible in most applications.
Amplifies a voltage (multiplies by a constant greater than 1)
The input impedance isÂ at leastÂ the impedance between non-inverting (Â +Â ) and inverting (Â âˆ’Â ) inputs, which is typically 1 MÎ© to 10 TÎ©, plus the impedance of the path from the inverting (Â âˆ’Â ) input to ground (i.e.,Â R1Â in parallel withÂ R2).
Because negative feedback ensures that the non-inverting and inverting inputs match, the input impedance is actuallyÂ much higher.
Although this circuit has a large input impedance, it suffers from error of input bias current.
The non-inverting (Â +Â ) and inverting (Â âˆ’Â ) inputs draw small leakage currents into the operational amplifier.
These input currents generate voltages that act like unmodeled input offsets. These unmodeled effects can lead to noise on the output (e.g., offsets or drift).
Assuming that the two leaking currents areÂ matched,Â their effect can be mitigated by ensuring the DC impedance lookingÂ outÂ of each input is the same.
The voltage produced by each bias current is equal to the product of the bias current with the equivalent DC impedance looking out of each input. Making those impedances equal makes the offset voltage at each input equal, and so the non-zero bias currents will have no impact on theÂ differenceÂ between the two inputs.
A resistor of value
which is the equivalent resistance ofÂ R1Â in parallel withÂ R2, between theÂ VinÂ source and the non-inverting (Â +Â ) input will ensure the impedances lookingÂ outÂ of each input will be matched.
The matched bias currents will then generate matched offset voltages, and their effect will be hidden to the operational amplifier (which acts on the difference between its inputs) so long as theÂ CMRRÂ is good.
Very often, the input currents areÂ notÂ matched.
Most operational amplifiers provide some method of balancing the two input currents (e.g., by way of an externalpotentiometer).
Alternatively, an external offset can be added to the operational amplifier input to nullify the effect.
Another solution is to insert a variable resistor between theÂ VinÂ source and the non-inverting (Â +Â ) input. The resistance can be tuned until the offset voltages at each input are matched.
Operational amplifiers withÂ MOSFET-based input stages have input currents that are so small that they often can be neglected.
The circuit shown is used for finding theÂ differenceÂ of two voltages each multiplied by some constant (determined by the resistors).
The name "differential amplifier" should not be confused with the "differentiator", also shown on this page.
DifferentialÂ ZinÂ (between the two input pins) =Â R1Â +Â R2Â (Note: this is approximate)
For common-mode rejection, anything done to one input must be done to the other. The addition of a compensation capacitor in parallel with Rf, for instance, must be balanced by an equivalent capacitor in parallel with Rg.
The "instrumentation amplifier", which is also shown on this page, is another form of differential amplifier that also provides highÂ input impedance.
WheneverÂ Â andÂ , the differential gain is
Â Â and Â Â
WhenÂ Â andÂ Â the differential gain is A = 1 and the circuit acts as a differential follower:
MAXIM Application Note 1108: Understanding Single-Ended, Pseudo-Differential and Fully-Differential ADC Input - Retrieved November 10, 2007
http://www.analog.com/static/imported-files/tutorials/MT-044.pdf Analog devices MT-044 TUTORIAL]
Jung, Walter G. (2004). "Chapter 8: Op Amp History". Op Amp Applications Handbook. Newnes. p.Â 777. ISBNÂ 9780750678445. http://books.google.com/books?id=dunqt1rt4sAC. Retrieved 2008-11-15.Â
Jung, Walter G. (2004). "Chapter 8: Op Amp History". Op Amp Applications Handbook. Newnes. p.Â 779. ISBNÂ 9780750678445. http://books.google.com/books?id=dunqt1rt4sAC. Retrieved 2008-11-15.Â
A.P. Malvino, Electronic Principles (2nd Ed. 1979. ISBN 0-07-039867-4) p.Â 476.
D.F. Stout Handbook of Operational Amplifier Circuit Design (McGraw-Hill, 1976, ISBN 007061797X ) pp.Â 1-11.