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Operational amplifier applications

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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 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

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.

Differential amplifier

[ V_\mathrm = V_2 \left( + R_1 \right) R_\mathrm \over \left( R_\mathrm + R_2 \right) R_1} \right) - V_1 \left( \over R_1} \right) ]
  • Differential [Z_\mathrm] (between the two input pins) = [R_1 + R_2]

Amplified difference

When [R_1 = R_2] and [R_\mathrm = R_\mathrm],

[ V_\mathrm = \over R_1} \left( V_2 - V_1 \right) ]

Difference amplifier

When [R_1 = R_\mathrm] and [R_2 = R_\mathrm] (including when [R_1 = R_2 = R_\mathrm = R_\mathrm]):

[ V_\mathrm = V_2 - V_1 \,\!]

Inverting amplifier

Inverts and amplifies a voltage (multiplies by a negative constant)

Inverting amplifier

[ V_\mathrm = -V_\mathrm ( R_\mathrm / R_\mathrm ) \!\ ]

Non-inverting amplifier

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

Non-inverting amplifier

[ V_\mathrm = V_\mathrm \left( 1 + \right)]

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)

Voltage follower

[ V_\mathrm = V_\mathrm \!\ ]

Summing amplifier

Sums several (weighted) voltages

Summing amplifier

[ V_\mathrm = - R_\mathrm \left( + + \cdots + \right) ]
[ V_\mathrm = - \left( \over R_1} \right) (V_1 + V_2 + \cdots + V_n ) \!\ ]
[ V_\mathrm = - ( V_1 + V_2 + \cdots + V_n ) \!\ ]

Integrator

Integrates the (inverted) signal over time

Integrating amplifier

[ V_\mathrm = \int_0^t - \over RC} \, dt + V_\mathrm ]
(where [V_\mathrm] and [V_\mathrm] are functions of time, [V_\mathrm] is the output voltage of the integrator at time t = 0.)

Differentiator

Differentiates the (inverted) signal over time.

The name "differentiator" should not be confused with the "differential amplifier", also shown on this page.

Differentiating amplifier

[ V_\mathrm = - R C \, \over dt} ]
(where [V_\mathrm] and [V_\mathrm] are functions of time)

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

Comparator

  • [ V_\mathrm = \left\ V_\mathrm & V_1 > V_2 \\ V_\mathrm & V_1 < V_2 \end\right. ]
  • See article for details

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

Instrumentation amplifier

  • Is made by adding a non-inverting buffer to each input of the differential amplifier to increase the input impedance.
  • See article for details

A comparator with hysteresis

Schmitt trigger

  • See article for details

Simulates an inductor

Gyrator.png

  • See article for details

Zero level detector

Voltage divider reference

Creates a resistor having a negative value for any signal generator

Negative impedance converter

  • In this case, the ratio between the input voltage and the input current (thus the input resistance) is given by:
[R_\mathrm = - R_3 \frac]
for more information see the main article Negative impedance converter.

Non-linear configurations

Behaves like an ideal diode for the load, which is here represented by a generic resistor [R_\mathrm].

Super diode
  • 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.

Peak detector
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

Logarithmic configuration
[v_\mathrm = -V_ \ln \left( \frac} \cdot R} \right)]
where [I_\mathrm] is the saturation current.

[\frac} = I_\mathrm = I_\mathrm]
where [I_\mathrm] is the current through the diode. As known, the relationship between the current and the voltage for a diode is:

[I_\mathrm = I_\mathrm \left( e^}}} - 1 \right)]
This, when the voltage is greater than zero, can be approximated by:

[I_\mathrm \simeq I_\mathrm e^ \over V_} ]
Putting these two formulae together and considering that the output voltage [V_\mathrm] is the inverse of the voltage across the diode [V_\mathrm], the relationship is proven.

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

Exponential output

Exponential configuration
[v_\mathrm = - R I_\mathrm e^ \over V_}]
where [I_\mathrm] is the saturation current.

[I_\mathrm = I_\mathrm \left( e^}}} - 1 \right)]
when the voltage is greater than zero, it can be approximated by:

[I_\mathrm \simeq I_\mathrm e^ \over V_} ]
The output voltage is given by:
[v_\mathrm = -R I_\mathrm\,]

Other applications

See also

External links

has more about this subject:

References

 

From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.

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