Operational amplifier applications: Difference between revisions

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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. Those interested in construction of any of these circuits for practical use should consult a more detailed textbook such as ref. 1 below.

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.

Linear circuit applications

Inverting amplifier configuration

Inverts and amplifies a voltage (multiplies by a negative constant)
V_out = −V_in (R_f / R_in)
Z_in = R_in (because V₋ is a virtual ground)

Non-inverting amplifier configuration

Amplifies a voltage (multiplies by a constant greater than 1)
V_out = V_in (1 + R₂ / R₁)
Z_in = ∞ (realistically, the input impedance of the op-amp itself, 1 MΩ to 10¹² Ω)

Voltage follower

Used as a buffer, 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_out = V_in
Z_in = ∞ (realistically, the differential input impedance of the op-amp itself, 1 MΩ to 10¹² Ω)

Difference amplifier

For independent R₁, R₂, R₃, R₄ (differential amplifier):

V_{\mathrm {out} }=V_{2}\left({\left(R_{3}+R_{1}\right)R_{4} \over \left(R_{4}+R_{2}\right)R_{1}}\right)-V_{1}\left({R_{3} \over R_{1}}\right)

For R₁ = R₂ and R₃ = R₄ (amplified difference),

V_{\mathrm {out} }={R_{3} \over R_{1}}\left(V_{2}-V_{1}\right)

For R₁ = R₃ and R₂ = R₄ (also for R₁ = R₂ = R₃ = R₄) (difference amplifier):

V_{\mathrm {out} }=V_{2}-V_{1}\,\!

Differential Z_in (between the two input pins) = R₁ + R₂

An instrumentation amplifier is made by adding a voltage follower to each input to increase the input impedance.

Summing amplifier

Sums several (weighted) voltages
Output is inverted
For independent R₁, R₂, ... R_n

V = − R_f (V₁ / R₁ + V₂ / R₂ + ... + V_n / R_n)

For R₁ = R₂ = ... = R_n, and R_F independent

V = − (R_f / R₁) (V₁ + V₂ + ... + V_n)

For R₁ = R₂ = ... = R_n = R_f

V = − (V₁ + V₂ + ... + V_n)

Input impedance Z_n = R_n, for each input (V₋ is a virtual ground)

Integrator

Integrates the (inverted) signal over time (where V_in and V_out are functions of time)
$V_{\mathrm {out} }=\int _{0}^{t}-{V_{\mathrm {in} } \over RC}\,dt+V_{\mathrm {initial} }$
(V_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 (where V_in and V_out are functions of time)
$V_{\mathrm {out} }=-RC\,{dV_{\mathrm {in} } \over dt}$
Note that this can also be viewed as a type of electronic filter.

Comparator

Compares two voltages and outputs one of two states depending on which is greater
$V_{\mathrm {out} }=\left\{{\begin{matrix}V_{S+}&V_{1}>V_{2}\\V_{S-}&V_{1}<V_{2}\end{matrix}}\right.$
See article for details

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
See article for details

Schmitt trigger

A comparator with hysteresis
See article for details

Inductance gyrator

Simulates an inductor
See article for details

Zero level detector Voltage divider reference Zener sets reference voltage

Negative impedance converter (NIC)

This configuration 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:

R_{\mathrm {in} }=-R_{3}{\frac {R_{1}}{R_{2}}}

for more information see the main article Negative impedance converter.

Non-linear configurations

Super diode

The super diode is a configuration which behaves like an ideal diode for the load, which is now 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 super diode.

Exponential configuration

The relationship between the input voltage $v_{\mathrm {in} }$ and the output voltage $v_{\mathrm {out} }$ is given by:

v_{\mathrm {out} }=-V_{\gamma }\ln \left({\frac {v_{\mathrm {in} }}{I_{\mathrm {S} }\cdot R}}\right)

where $I_{\mathrm {S} }$ is the saturation current.

If the operational amplifier is considered ideal, the positive pin is virtually grounded, so the current through the resistor, thus through the diode, is:

{\frac {v_{\mathrm {in} }}{R}}=I_{\mathrm {D} }

where $I_{\mathrm {D} }$ is the current through the diode. As known, the relationship between the current and the voltage for a diode is:

I_{\mathrm {D} }=I_{\mathrm {S} }\left(e^{\frac {V_{\mathrm {D} }}{V_{\gamma }}}-1\right)

that, when the voltage is greater then 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 inverse of that across the diode, the relationship is proven.

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

Logarithm configuration

The relationship between the input voltage $v_{\mathrm {in} }$ and the output voltage $v_{\mathrm {out} }$ is given by:

v_{\mathrm {out} }=-RI_{\mathrm {S} }e^{v_{\mathrm {in} } \over V_{\gamma }}