Applications Of OP AMPS Computer Science Essay

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An operational amplifier, which is often calledan op-ampisa DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. An op-amp produces an output voltage that is typically millions of times larger than the voltage  difference between its input terminals.

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 at the output terminal(s) (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; patterns that can be reprinted several times on one chip as part of a more complex device.

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 with tolerance to 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).

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

Circuit Notation

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

: output

: positive power supply

: negative power supply

The power supply pins ( and ) can be labeled in different ways. 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  input and a  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  is the voltage at the non-inverting terminal,  is the voltage at the inverting terminal and Gopen-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.)

The magnitude of Gopen-loop is typically very large-seldom less than a million-and therefore even a quite small difference between  and (a few micro volts 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 Gopen-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 voltage 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,

both inputs are at the same voltage;

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 op-amp and is about one megaohm in practice.

With no negative feedback, the op-amp acts as a switch. The inverting input is held at ground (0 V) by the resistor, so if the Vin applied to the non-inverting input is positive, the output will be maximum positive, and if Vin 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 Gopen-loop of the op-amp.

Adding negative feedback via Rf reduces the gain. Equilibrium will be established when Vout is just sufficient to reach around and pull the inverting input to the same voltage as Vin. As a simple example, if Vin = 1 V and Rf = Rg, Voutwill be 2 V, the amount required to keep V- at 1 V. Because of the feedback provided by Rf, this is a closed loop circuit. Its over-all gain Vout / Vin is called the closed-loop gain Gclosed-loop. Because the feedback is negative, in this case Gclosed-loop is less than the Gopen-loop of the op-amp.

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:

Infinite open-loop gain (when doing theoretical analysis, a limit may be taken as open loop gain G goes to infinity)

Infinite voltage range available at the output (vout) (in practice the voltages available from the output are limited by the supply voltages  and )

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

Infinite input impedance (so, in the diagram, , and zero current flows from  to  )

Zero input current (i.e., there is assumed to be no leakage or bias current into the device)

Zero input offset voltage (i.e., when the input terminals are shorted so that , the output is a virtual ground orvout = 0).

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, so that 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.

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 have negligible effect on the final design while others represent actual limitations of the final performance, which must be evaluated.

Applications

Use in electronics system design

The use of op-amps as circuit blocks is much easier and clearer than specifying all their individual circuit elements (transistors, resistors, etc.), whether the amplifiers used are integrated or discrete. In the first approximation op-amps can be used as if they were ideal differential gain blocks; at a later stage limits can be placed on the acceptable range of parameters for each op-amp.

Circuit design follows the same lines for all electronic circuits. A specification is drawn up governing what the circuit is required to do, with allowable limits. For example, the gain may be required to be 100 times, with a tolerance of 5% but drift of less than 1% in a specified temperature range; the input impedance not less than one megohm; etc.

A basic circuit is designed, often with the help of circuit modeling (on a computer).

Specific commercially available op-amps and other components are then chosen that meet the design criteria within the specified tolerances at acceptable cost. If not all criteria can be met, the specification may need to be modified.

A prototype is then built and tested; changes to meet or improve the specification, alter functionality, or reduce the cost, may be made.

Practical considerations

Input offset problems

It is important to note that the equations shown below, pertaining to each type of circuit, assume that an ideal op amp is used. Those interested in construction of any of these circuits for practical use should consult a more detailed reference. See the External links and Further reading sections.

Resistors used in practical solid-state op-amp circuits are typically in the kΩ range. Resistors much greater than 1 MΩ cause excessive thermal noise and make the circuit operation susceptible to significant errors due to bias or leakage currents.

Practical operational amplifiers draw a small current from each of their inputs due to bias requirements and leakage. These currents flow through the resistances connected to the inputs and produce small voltage drops across those resistances. In AC signal applications this seldom matters. If high-precision DC operation is required, however, these voltage drops need to be considered. The design technique is to try to ensure that these voltage drops are equal for both inputs, and therefore cancel. If these voltage drops are equal and the common-mode rejection ratio of the operational amplifier is good, there will be considerable cancellation and improvement in DC accuracy.

If the input currents into the operational amplifier are equal, to reduce offset voltage the designer must ensure that the DC resistance looking out of each input is also matched. In general input currents differ, the difference being called the input offset current, Ios. Matched external input resistances Rin will still produce an input voltage error of  Rin·Ios Most manufacturers provide a method for tuning the operational amplifier to balance the input currents (e.g., "offset null" or "balance" pins that can interact with an external voltage source attached to a potentiometer). Otherwise, a tunable external voltage can be added to one of the inputs in order to balance out the offset effect. In cases where a design calls for one input to be short-circuited to ground, that short circuit can be replaced with a variable resistance that can be tuned to mitigate the offset problem.  .

Note that many operational amplifiers that have MOSFET-based input stages have input leakage currents that will truly be negligible to most designs.

Power supply effects

Although the power supplies are not shown in the operational amplifier designs below, they can be critical in operational amplifier design.

Power supply imperfections (e.g., power signal ripple, non-zero source impedance) may lead to noticeable deviations from ideal operational amplifier behavior. For example, operational amplifiers have a specified power supply rejection ratio that indicates how well the output can reject signals that appear on the power supply inputs. Power supply inputs are often noisy in large designs because the power supply is used by nearly every component in the design, and inductance effects prevent current from being instantaneously delivered to every component at once. As a consequence, when a component requires large injections of current (e.g., a digital component that is frequently switching from one state to another), nearby components can experience sagging at their connection to the power supply. This problem can be mitigated with copious use of bypass capacitors placed connected across each power supply pin and ground. When bursts of current are required by a component, the component can bypass the power supply by receiving the current directly from the nearby capacitor (which is then slowly charged by the power supply).

Additionally, current drawn into the operational amplifier from the power supply can be used as inputs to external circuitry that augment the capabilities of the operational amplifier. For example, an operational amplifier may not be fit for a particular high-gain application because its output would be required to generate signals outside of the safe range generated by the amplifier. In this case, an external push-pull amplifier can be controlled by the current into and out of the operational amplifier. Thus, the operational amplifier may itself operate within its factory specified bounds while still allowing the negative feedback path to include a large output signal well outside of those bounds.

Circuit applications

Comparator

Comparator

Compares two voltages and switches its output to indicate which voltage is larger.

(where Vs is the supply voltage and the opamp is powered by + Vs and − Vs.)

Inverting amplifier

Inverting amplifier

An inverting amplifier uses negative feedback to invert and amplify a voltage. The Rf resistor allows some of the output signal to be returned to the input. Since the output is 180° 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.

Zin = Rin (because V − is a virtual ground)

A third resistor, of value , 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 Rf to Rin. That is:

The presence of the negative sign is a convention indicating that the output is inverted. For example, if Rf is 10,000 Ω and Rin is 1,000 Ω, then the gain would be -10000Ω/1000Ω, which is -10.

Non-inverting amplifier

Non-inverting amplifier

Amplifies a voltage (multiplies by a constant greater than 1)

Input impedance 

The input impedance is at least the impedance between non-inverting ( + ) and inverting ( − ) inputs, which is typically 1 MΩ to 10 TΩ, plus the impedance of the path from the inverting ( − ) input to ground (i.e., R1 in parallel with R2).

Because negative feedback ensures that the non-inverting and inverting inputs match, the input impedance is actually much higher.

Although this circuit has a large input impedance, it suffers from error of input bias current.

The non-inverting ( + ) and inverting ( − ) 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 are matched, their effect can be mitigated by ensuring the DC impedance looking out 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 the difference between the two inputs.

A resistor of value

which is the equivalent resistance of R1 in parallel with R2, between the Vin source and the non-inverting ( + ) input will ensure the impedances looking out 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 the CMRR is good.

Very often, the input currents are not matched.

Most operational amplifiers provide some method of balancing the two input currents (e.g., by way of an external potentiometer).

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 the Vin source and the non-inverting ( + ) input. The resistance can be tuned until the offset voltages at each input are matched.

Operational amplifiers with MOSFET-based input stages have input currents that are so small that they often can be neglected.

Differential amplifier

Differential amplifier

The circuit shown is used for finding the difference of two voltages each multiplied by some constant (determined by the resistors).

Differential Zin (between the two input pins) = R1 + R2 (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 high input impedance.

Whenever  and , the differential gain is

   and   

When  and  the differential gain is A = 1 and the circuit acts as a differential follower:

Voltage follower

Voltage follower

Used as a buffer amplifier to eliminate loading effects (e.g., connecting a device with a high source impedance to a device with a low input impedance).

 (realistically, the differential input impedance of the op-amp itself, 1 MΩ to 1 TΩ)

Due to the strong (i.e., unity gain) feedback and certain non-ideal characteristics of real operational amplifiers, this feedback system is prone to have poor stability margins. Consequently, the system may be unstable when connected to sufficiently capacitive loads. In these cases, a lag compensation network (e.g., connecting the load to the voltage follower through a resistor) can be used to restore stability. The manufacturer data sheet for the operational amplifier may provide guidance for the selection of components in external compensation networks. Alternatively, another operational amplifier can be chosen that has more appropriate internal compensation.

Summing amplifier

Summing amplifier

A summing amplifer sums several (weighted) voltages:

When , and Rf independent

When 

Output is inverted

Input impedance of the nth input is Zn = Rn (V − is a virtual ground)

Integrator

Integrating amplifier

Integrates the (inverted) signal over time

(where Vin and Vout are functions of time, Vinitial is the output voltage of the integrator at time t = 0.)

Note that this can also be viewed as a low-pass electronic filter. It is a filter with a single pole at DC (i.e., where ω = 0) and gain.

There are several potential problems with this circuit.

It is usually assumed that the input Vin has zero DC component (i.e., has a zero average value). Otherwise, unless the capacitor is periodically discharged, the output will drift outside of the operational amplifier's operating range.

Even when Vin has no offset, the leakage or bias currents into the operational amplifier inputs can add an unexpected offset voltage to Vin that causes the output to drift. Balancing input currents and replacing the non-inverting ( + ) short-circuit to ground with a resistor with resistance R can reduce the severity of this problem.

Because this circuit provides no DC feedback (i.e., the capacitor appears like an open circuit to signals with ω = 0), the offset of the output may not agree with expectations (i.e.,Vinitial may be out of the designer's control with the present circuit).

Many of these problems can be made less severe by adding a large resistor RF in parallel with the feedback capacitor. At significantly high frequencies, this resistor will have negligible effect. However, at low frequencies where there are drift and offset problems, the resistor provides the necessary feedback to hold the output steady at the correct value. In effect, this resistor reduces the DC gain of the "integrator" - it goes from infinite to some finite value RF / R.

Differentiator

Differentiating amplifier

Differentiates the (inverted) signal over time.

Note that this can also be viewed as a high-pass electronic filter. It is a filter with a single zero at DC (i.e., where ω = 0) and gain. The high pass characteristics of a differentiating amplifier can lead to unstable behavior when the circuit is used in an analog servo loop. For this reason the system function would be re-formulated to use integrators.

Instrumentation amplifier

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

Is made by adding a non-inverting buffer to each input of the differential amplifier to increase the input impedance.

Schmitt trigger

A bistable multivibrator implemented as a comparator with hysteresis.

Non-inverting Schmitt trigger

In this configuration, the input voltage is applied through the resistor R1 (which may be the source internal resistance) to the non-inverting input and the inverting input is grounded or referenced. The hysteresis curve is non-inverting and the switching thresholds are  where Vsat is the greatest output magnitude of the operational amplifier.

Inverting Schmitt trigger

Alternatively, the input source and the ground may be swapped. Now the input voltage is applied directly to the inverting input and the non-inverting input is grounded or referenced. The hysteresis curve is inverting and the switching thresholds are . Such a configuration is used in the relaxation oscillator shown below.

Relaxation oscillator

Relaxation oscillator implemented with inverting Schmitt trigger and RC network

By using an RC network to add slow negative feedback to the inverting Schmitt trigger, a relaxation oscillator is formed. The feedback through the RC network causes the Schmitt trigger output to oscillate in an endless symmetric square wave (i.e., the Schmitt trigger in this configuration is an astable multivibrator).

Inductance gyrator

Inductance gyrator

Simulates an inductor (i.e., provides inductance without the use of a possibly costly inductor). The circuit exploits the fact that the current flowing through a capacitor behaves through time as the voltage across an inductor. The capacitor used in this circuit is smaller than the inductor it simulates and its capacitance is less subject to changes in value due to environmental changes.

Zero level detector

Voltage divider reference

Zener sets reference voltage

Negative impedance converter (NIC)

Negative impedance converter

Creates a resistor having a negative value for any signal generator

In this case, the ratio between the input voltage and the input current (thus the input resistance) is given by:

In general, the components R1, R2, and R3 need not be resistors; they can be any component that can be described with animpedance.

Wien bridge oscillator

Wien bridge oscillator

Produces a pure sine wave.

Precision rectifier

Precision rectifier

The voltage drop VF across the forward biased diode in the circuit of a passive rectifier is undesired. In this active version, the problem is solved by connecting the diode in the negative feedback loop. The op-amp compares the output voltage across the load with the input voltage and increases its own output voltage with the value of VF. As a result, the voltage drop VF is compensated and the circuit behaves as an ideal (super) diode with VF = 0 V.

The circuit has speed limitations at high frequency because of the slow negative feedback.

Logarithmic output

Logarithmic configuration

The relationship between the input voltage vin and the output voltage vout is given by:

where IS is the saturation current and VT is the thermal voltage.

If the operational amplifier is considered ideal, the negative pin is virtually grounded, so the current flowing into the resistor from the source (and thus through the diode to the output, since the op-amp inputs draw no current) is:

where ID is the current through the diode. As known, the relationship between the current and the voltage for a diode is:

This, when the voltage is greater than zero, can be approximated by:

Putting these two formulae together and considering that the output voltage is the negative of the voltage across the diode (Vout = − VD), the relationship is proven.

Note that this implementation does not consider temperature stability and other non-ideal effects.

Exponential output

Exponential configuration

The relationship between the input voltage vin and the output voltage vout is given by:

where IS is the saturation current and VT is the thermal voltage.

Considering the operational amplifier ideal, then the negative pin is virtually grounded, so the current through the diode is given by:

when the voltage is greater than zero, it can be approximated by:

The output voltage is given by:

Future Scope

1. An operational amplifier, comprising: a dynamic biasing stage operable to convert a differential input voltage to a dynamic drive current; an input stage responsively coupled to the differential input voltage and the dynamic drive current, said input stage configured as a folded cascode circuit including a differential pair of transistors; an output gain stage responsively coupled to the differential pair of transistors and having a pair of bipolar output transistors, the output transistors having emitters each having a load resistor and being coupled to an output; and a compensation capacitor coupled to the output of the output gain stage and directly coupled to a supply voltage. 

2. The amplifier as specified in claim 1 wherein the output gain stage transistors each have a base emitter voltage and a collector current, wherein the collector currents increase exponentially as the respective base emitter voltage increases. 

3. The amplifier as specified in claim 1 wherein the output transistors are about half the size as the differential pair of transistors. 

4. The amplifier as specified in claim 1 further comprising an output buffer coupled to an amplifier output. 

5. An operational amplifier, comprising: a dynamic biasing stage operable to convert a differential input voltage to a dynamic drive current; an input stage responsively coupled to the differential input voltage and the dynamic drive current, said input stage configured as a folded cascode circuit including a differential pair of transistors; an output gain stage responsively coupled to the input stage and having a pair of transistors each having a base emitter voltage and a collector current, wherein the collector currents increase exponentially as the respective base emitter voltage increases; and a compensation capacitor coupled to an output of the output gain stage and directly coupled to the supply voltage. 

6. The amplifier as specified in claim 5 wherein the output gain stage transistors each have a load resistor. 

7. The amplifier as specified in claim 5 wherein the output gain stage transistors are about half the size as the differential pair of transistors. 

8. The amplifier as specified in claim 5 further comprising an output buffer coupled to an amplifier output. 

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