OPERATIONAL AMPLIFIER APPLICATIONS

This article illustrates some typical applications of solid-state integrated circuit operational amplifiers. A simplified schematic notation is used, and the reader is reminded that many details such as device selection and power supply connections are not shown.
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 make the circuit operation susceptible to significant errors due to bias currents.
''Note: It is important to realize that the equations shown below, pertaining to each type of circuit, assume that it is an ideal op amp. Those interested in construction of any of these circuits for practical use should consult a more detailed reference. See the External links and References sections.''

Contents

Linear circuit applications

Differential amplifier

Amplified difference

Difference amplifier

Inverting amplifier

Non-inverting amplifier

Voltage follower

Summing amplifier

Integrator

Differentiator

Comparator

Instrumentation amplifier

Schmitt trigger

Inductance gyrator

Zero level detector

Negative impedance converter (NIC)

Non-linear configurations

Precision rectifier

Peak detector

Logarithmic output

Exponential output

Other applications

See also

References

External links

Linear circuit applications

Differential amplifier

Main articles: Differential amplifier

The circuit shown is used for finding the difference 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.''
:$V\_mathrm\{out\}\; =\; V\_2\; left(\; \{\; left(\; R\_mathrm\{f\}\; +\; R\_1$
ight) R_mathrm{g} over left( R_mathrm{g} + R_2
ight) R_1}
ight) - V_1 left( {R_mathrm{f} over R_1}
ight)

★ Differential $Z\_mathrm\{in\}$ (between the two input pins) = $R\_1\; +\; R\_2$

Amplified difference

Whenever $R\_1\; =\; R\_2$ and $R\_mathrm\{f\}\; =\; R\_mathrm\{g\}$,
:$V\_mathrm\{out\}\; =\; \{R\_mathrm\{f\}\; over\; R\_1\}\; left(\; V\_2\; -\; V\_1$
ight)

Difference amplifier

When $R\_1\; =\; R\_mathrm\{f\}$ and $R\_2\; =\; R\_mathrm\{g\}$ (including previous conditions, so that $R\_1\; =\; R\_2\; =\; R\_mathrm\{f\}\; =\; R\_mathrm\{g\}$):
:$V\_mathrm\{out\}\; =\; V\_2\; -\; V\_1\; ,!$

Inverting amplifier

Inverts and amplifies a voltage (multiplies by a negative constant)
:$V\_mathrm\{out\}\; =\; -V\_mathrm\{in\}\; (\; R\_mathrm\{f\}\; /\; R\_mathrm\{in\}\; )\; !$

★ $Z\_mathrm\{in\}\; =\; R\_mathrm\{in\}$ (because $V\_-$ is a virtual ground)

★ A third resistor, of value $R\_mathrm\{f\}\; |\; R\_mathrm\{in\}\; =\; R\_mathrm\{f\}\; R\_mathrm\{in\}\; /\; (R\_mathrm\{f\}\; +\; R\_mathrm\{in\})$, added between the non-inverting input and ground, while not necessary, minimizes errors due to input bias currents.

Non-inverting amplifier

Amplifies a voltage (multiplies by a constant greater than 1)
:$V\_mathrm\{out\}\; =\; V\_mathrm\{in\}\; left(\; 1\; +\; \{R\_2\; over\; R\_1\}$
ight)

★ $Z\_mathrm\{in\}\; =\; infin$ (realistically, the input impedance of the opamp itself, 1 MΩ to 10 TΩ)

★ A third resistor, of value $R\_mathrm\{f\}\; |\; R\_mathrm\{in\}$, added between the $V\_mathrm\{in\}$ source and the non-inverting input, while not necessary, minimizes errors due to input bias currents.

Voltage follower

Used as a buffer amplifier, to eliminate loading effects or to interface impedances (connecting a device with a high source impedance to a device with a low input impedance)
:$V\_mathrm\{out\}\; =\; V\_mathrm\{in\}\; !$

★ $Z\_mathrm\{in\}\; =\; infin$ (realistically, the differential input impedance of the op-amp itself, 1 MΩ to 1 TΩ)

Summing amplifier

Sums several (weighted) voltages
:$V\_mathrm\{out\}\; =\; -\; R\_mathrm\{f\}\; left(\; \{\; V\_1\; over\; R\_1\; \}\; +\; \{\; V\_2\; over\; R\_2\; \}\; +\; cdots\; +\; \{V\_n\; over\; R\_n\}$
ight)

★ When $R\_1\; =\; R\_2\; =\; cdots\; =\; R\_n$, and $R\_mathrm\{f\}$ independent
:$V\_mathrm\{out\}\; =\; -\; left(\; \{R\_mathrm\{f\}\; over\; R\_1\}$
ight) (V_1 + V_2 + cdots + V_n ) !

★ When $R\_1\; =\; R\_2\; =\; cdots\; =\; R\_n\; =\; R\_mathrm\{f\}$
:$V\_mathrm\{out\}\; =\; -\; (\; V\_1\; +\; V\_2\; +\; cdots\; +\; V\_n\; )\; !$

★ Output is inverted

★ Input impedance $Z\_n\; =\; R\_n$, for each input ($V\_-$ is a virtual ground)

Integrator

Integrates the (inverted) signal over time
:$V\_mathrm\{out\}\; =\; int\_0^t\; -\; \{V\_mathrm\{in\}\; over\; RC\}\; ,\; dt\; +\; V\_mathrm\{initial\}$
(where $V\_mathrm\{in\}$ and $V\_mathrm\{out\}$ are functions of time, $V\_mathrm\{initial\}$ 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.
''The name "differentiator" should not be confused with the "differential amplifier", also shown on this page.''
$V\_mathrm\{out\}\; =\; -\; RC\; left(\; \{dV\_mathrm\{in\}\; over\; dt\}$
ight)
(where $V\_mathrm\{in\}$ and $V\_mathrm\{out\}$ are functions of time)

★ Note that this can also be viewed as a type of electronic filter.

Comparator

Main articles: Comparator

Compares two voltages and outputs one of two states depending on which is greater

★
ight.

Instrumentation amplifier

Main articles: 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 inverting buffer to each input of the differential amplifier to increase the input impedance.

Schmitt trigger

Main articles: Schmitt trigger

A comparator with hysteresis
Hysteresis from to .

Inductance gyrator

Main articles: Gyrator

Simulates an inductor.

Zero level detector

Voltage divider reference

★ Zener sets reference voltage

Negative impedance converter (NIC)

Main articles: 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:
:
for more information see the main article Negative impedance converter.

Non-linear configurations

Precision rectifier

Main articles: Precision rectifier

Behaves like an ideal diode for the load, which is here represented by a generic resistor $R\_mathrm\{L\}$.

★ This basic configuration has some limitations. For more information and to know the configuration that is actually used, see the main article.

Peak detector

When the switch is closed, the output goes to zero volts. When the switch is opened for a certain time interval, the capacitor will charge to the maximum input voltage attained during that time interval.
The charging time of the capacitor must be much shorter than the period of the highest appreciable frequency component of the input voltage.

Logarithmic output

★ The relationship between the input voltage $v\_mathrm\{in\}$ and the output voltage $v\_mathrm\{out\}$ is given by:
:
ight)
where $I\_mathrm\{S\}$ is the ''saturation current''.

★ 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 $I\_mathrm\{D\}$ is the current through the diode. As known, the relationship between the current and the voltage for a diode is:
:
ight)
This, when the voltage is greater than zero, can be approximated by:
:$I\_mathrm\{D\}\; simeq\; I\_mathrm\{S\}\; e^\{V\_mathrm\{D\}\; over\; V\_\{gamma\}\}$
Putting these two formulae together and considering that the output voltage $V\_mathrm\{out\}$ is the inverse of the voltage across the diode $V\_mathrm\{D\}$, the relationship is proven.
Note that this implementation does not consider temperature stability and other non-ideal effects.

Exponential output

★ The relationship between the input voltage $v\_mathrm\{in\}$ and the output voltage $v\_mathrm\{out\}$ is given by:
:$v\_mathrm\{out\}\; =\; -\; R\; I\_mathrm\{S\}\; e^\{v\_mathrm\{in\}\; over\; V\_\{gamma\}\}$
where $I\_mathrm\{S\}$ is the ''saturation current''.

★ Considering the operational amplifier ideal, then the negative pin is virtually grounded, so the current through the diode is given by:
:
ight)
when the voltage is greater than zero, it can be approximated by:
:$I\_mathrm\{D\}\; simeq\; I\_mathrm\{S\}\; e^\{V\_mathrm\{D\}\; over\; V\_\{gamma\}\}$
The output voltage is given by:
:$v\_mathrm\{out\}\; =\; -R\; I\_mathrm\{D\},$

Other applications

★ audio and video pre-amplifiers and buffers

★ voltage comparators

★ differential amplifiers

★ differentiators and integrators

★ filters

★ precision rectifiers

★ voltage regulator and current regulator

★ analog-to-digital converter

★ digital-to-analog converter

★ voltage clamps

★ oscillators and waveform generators

★ Schmitt trigger

★ Gyrator

★ Comparator

★ Active filter

★ Analog computer

See also

★ Current-feedback operational amplifier

★ Operational transconductance amplifier

★ Frequency compensation

References

★ Paul Horowitz and Winfield Hill, "The Art of Electronics 2nd Ed. " Cambridge University Press, Cambridge, 1989 ISBN 0-521-37095-7

★ Sergio Franco, "Design with Operational Amplifiers and Analog Integrated Circuits," 3rd Ed., McGraw-Hill, New York, 2002 ISBN 0-07-232084-2

External links

★ Introduction to op-amp circuit stages, second order filters, single op-amp bandpass filters, and a simple intercom

★

★ Hyperphysics — descriptions of common applications

★

★

★ — Analog Devices Application note

★

★ — Texas Instruments Application note

★ Low Side Current Sensing Using Operational Amplifiers

★ Logarithmic amplifier

★ Precision half-wave rectifier

★ Precision full-wave rectifier

★

★ Logarithmically variable gain from a linear variable component