आपरेशनल एम्प्लिफायर के उपयोग

इस लेख में आपरेशनल एम्प्लिफायर के सामान्य उपयोगों की जानकारी दी गयी है। सरलीकृत योजनात्मक आरेख का उपयोग किया गया है।

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

• ${\displaystyle V_{\text{out}}=\left\{{\begin{matrix}V_{\text{S+}}&V_{1}>V_{2}\\V_{\text{S-}}&V_{1}<V_{2}\end{matrix}}\right.}$

(where ${\displaystyle V_{\text{s}}}$ is the supply voltage and the opamp is powered by ${\displaystyle +V_{\text{s}}}$ and ${\displaystyle -V_{\text{s}}}$.)

Uses negative feedback to invert and amplify a voltage (multiplies by a negative constant, which can be greater or less than -1).

${\displaystyle V_{\text{out}}=-{\frac {R_{\text{f}}}{R_{\text{in}}}}V_{\text{in}}\!\ }$

• ${\displaystyle Z_{\text{in}}=R_{\text{in}}}$ (because ${\displaystyle V_{-}}$ is a virtual ground)
• A third resistor, of value ${\displaystyle R_{\text{f}}\|R_{\text{in}}\triangleq R_{\text{f}}R_{\text{in}}/(R_{\text{f}}+R_{\text{in}})}$, added between the non-inverting input and ground, while not necessary, minimizes errors due to input bias currents.

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

${\displaystyle V_{\text{out}}=V_{\text{in}}\left(1+{\frac {R_{2}}{R_{1}}}\right)\,}$

• Input impedance ${\displaystyle Z_{\text{in}}\approx \infty }$
  • The input impedance is at least the impedance between non-inverting (${\displaystyle +}$) and inverting (${\displaystyle -}$) inputs, which is typically 1 MΩ to 10 TΩ, plus the impedance of the path from the inverting (${\displaystyle -}$) input to ground (i.e., ${\displaystyle R_{1}}$ in parallel with ${\displaystyle R_{2}}$).
  • 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 (${\displaystyle +}$) and inverting (${\displaystyle -}$) 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

      ${\displaystyle R_{1}\|R_{2}\triangleq \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right)^{-1}={\frac {R_{1}R_{2}}{R_{1}+R_{2}}},\,}$

    which is the equivalent resistance of ${\displaystyle R_{1}}$ in parallel with ${\displaystyle R_{2}}$, between the ${\displaystyle V_{\text{in}}}$ source and the non-inverting (${\displaystyle +}$) 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 ${\displaystyle V_{\text{in}}}$ source and the non-inverting (${\displaystyle +}$) 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.

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.

${\displaystyle V_{\text{out}}={\frac {\left(R_{\text{f}}+R_{1}\right)R_{\text{g}}}{\left(R_{\text{g}}+R_{2}\right)R_{1}}}V_{2}-{\frac {R_{\text{f}}}{R_{1}}}V_{1}}$

• Differential ${\displaystyle Z_{\text{in}}}$ (between the two input pins) = ${\displaystyle R_{1}+R_{2}}$ (Note: this is approximate)

The "instrumentation amplifier", which is also shown on this page, is another form of differential amplifier that also provides high input impedance.

Whenever ${\displaystyle R_{1}=R_{2}}$ and ${\displaystyle R_{\text{f}}=R_{\text{g}}}$,

${\displaystyle V_{\text{out}}=A(V_{\text{2}}-V_{\text{1}})\,}$   and   ${\displaystyle A\triangleq {\frac {R_{\text{f}}}{R_{1}}}}$

When ${\displaystyle R_{1}=R_{\mathrm {f} }=R_{2}=R_{\mathrm {g} }}$:

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

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). Due to the strong feedback, this circuit tends to get unstable when driving a high capacity load. This can be avoided by connecting the load through a resistor.

${\displaystyle V_{\text{out}}=V_{\text{in}}\!\ }$

• ${\displaystyle Z_{\text{in}}=\infty }$ (realistically, the differential input impedance of the op-amp itself, 1 MΩ to 1 TΩ)

A summing amplifer sums several (weighted) voltages:

${\displaystyle V_{\text{out}}=-R_{\text{f}}\left({\frac {V_{1}}{R_{1}}}+{\frac {V_{2}}{R_{2}}}+\cdots +{\frac {V_{n}}{R_{n}}}\right)}$

• When ${\displaystyle R_{1}=R_{2}=\cdots =R_{n}}$, and ${\displaystyle R_{\text{f}}}$ independent

${\displaystyle V_{\text{out}}=-{\frac {R_{\text{f}}}{R_{1}}}(V_{1}+V_{2}+\cdots +V_{n})\!\ }$

• When ${\displaystyle R_{1}=R_{2}=\cdots =R_{n}=R_{\text{f}}}$

${\displaystyle V_{\text{out}}=-(V_{1}+V_{2}+\cdots +V_{n})\!\ }$

• Output is inverted
• Input impedance of the nth input is ${\displaystyle Z_{n}=R_{n}}$ (${\displaystyle V_{-}}$ is a virtual ground)

Integrates the (inverted) signal over time

${\displaystyle V_{\text{out}}=-\int _{0}^{t}{\frac {V_{\text{in}}}{RC}}\,\operatorname {d} t+V_{\text{initial}}\,}$

(where ${\displaystyle V_{\text{in}}}$ and ${\displaystyle V_{\text{out}}}$ are functions of time, ${\displaystyle V_{\text{initial}}}$ 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 ${\displaystyle \omega =0}$) and gain.
• There are several potential problems with this circuit.
  • It is usually assumed that the input ${\displaystyle V_{\text{in}}}$ 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 ${\displaystyle V_{\text{in}}}$ has no offset, the leakage or bias currents into the operational amplifier inputs can add an unexpected offset voltage to ${\displaystyle V_{\text{in}}}$ that causes the output to drift. Balancing input currents and replacing the non-inverting (${\displaystyle +}$) short-circuit to ground with a resistor with resistance ${\displaystyle R}$ 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 ${\displaystyle \omega =0}$), the offset of the output may not agree with expectations (i.e., ${\displaystyle V_{\text{initial}}}$ 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 ${\displaystyle R_{F}}$ 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 ${\displaystyle R_{F}/R}$.

Differentiates the (inverted) signal over time.

The name "differentiator" should not be confused with the "differential amplifier," which is also shown on this page. The former takes a derivative and the latter takes a difference (i.e., does subtraction).

${\displaystyle V_{\text{out}}=-RC\,{\frac {\operatorname {d} V_{\text{in}}}{\operatorname {d} t}}\,\qquad {\text{where }}V_{\text{in}}{\text{ and }}V_{\text{out}}{\text{ are functions of time.}}}$

• 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 ${\displaystyle \omega =0}$) and gain.

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.

A bistable multivibrator implemented as a comparator with hysteresis.

In this configuration, the hysteresis curve is non-inverting (i.e., very negative inputs correspond to a negative output and very positive inputs correspond to a positive output), and the switching thresholds are ${\displaystyle \pm {\frac {R_{1}}{R_{2}}}V_{\text{sat}}}$ where ${\displaystyle V_{\text{sat}}}$ is the greatest output magnitude of the operational amplifier.

Alternatively, the input and the ground may be swapped. In this configuration, the hysteresis curve is inverting (i.e., very negative inputs correspond to a positive output and vice versa), and the switching thresholds are ${\displaystyle \pm {\frac {R_{1}}{R_{1}+R_{2}}}V_{\text{sat}}}$. Such a configuration is used in the relaxation oscillator shown below.

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).

Simulates an inductor.

Voltage divider reference

• Zener sets reference voltage

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:

${\displaystyle R_{\text{in}}=-R_{3}{\frac {R_{1}}{R_{2}}}}$

In general, the components ${\displaystyle R_{1}}$, ${\displaystyle R_{2}}$, and ${\displaystyle R_{3}}$ need not be resistors; they can be any component that can be described with an impedance.

Produces a pure sine wave.

Although there are some limitations, this super diode circuit behaves like an ideal diode for the load ${\displaystyle R_{\text{L}}}$.

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

${\displaystyle v_{\text{out}}=-V_{\gamma }\ln \left({\frac {v_{\text{in}}}{I_{\text{S}}\,R}}\right)}$

where ${\displaystyle I_{\text{S}}}$ 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:

${\displaystyle {\frac {v_{\text{in}}}{R}}=I_{\text{R}}=I_{\text{D}}}$

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

${\displaystyle I_{\text{D}}=I_{\text{S}}\left(e^{\frac {V_{\text{D}}}{V_{\gamma }}}-1\right).}$

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

${\displaystyle I_{\text{D}}\simeq I_{\text{S}}e^{\frac {V_{\text{D}}}{V_{\gamma }}}.}$

Putting these two formulae together and considering that the output voltage is the negative of the voltage across the diode (${\displaystyle V_{\text{out}}=-V_{\text{D}}}$), the relationship is proven.

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

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

${\displaystyle v_{\text{out}}=-RI_{\text{S}}e^{\frac {v_{\text{in}}}{V_{\gamma }}}}$

where ${\displaystyle I_{\text{S}}}$ 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:

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

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

${\displaystyle I_{\text{D}}\simeq I_{\text{S}}e^{\frac {V_{\text{D}}}{V_{\gamma }}}.}$

The output voltage is given by:

${\displaystyle v_{\text{out}}=-RI_{\text{D}}.\,}$

• आपरेशनल एम्प्लिफायर
• परिशुद्ध दिष्टकारी
• करेंट-फीडबैक आपरेशन एम्प्लिफायर
• आपरेशनल ट्रांसकंडक्टेंस एम्प्लिफायर (Operational transconductance amplifier)
• आवृत्ति समायोजन (Frequency compensation)

• Paul Horowitz and Winfield Hill, The Art of Electronics. 2^nd ed. Cambridge University Press, Cambridge, 1989 ISBN 0-521-37095-7
• Sergio Franco, Design with Operational Amplifiers and Analog Integrated Circuits, 3^rd ed., McGraw-Hill, New York, 2002 ISBN 0-07-232084-2

• Introduction to op-amp circuit stages, second order filters, single op-amp bandpass filters, and a simple intercom
• Op Amps for Everyoneपीडीऍफ (1.96 MiB)
• Hyperphysics – descriptions of common applications
• Single supply op-amp circuit collectionपीडीऍफ (163 KiB)
• Op-amp circuit collectionपीडीऍफ (962 KiB)
• A Collection of Amp Applicationsपीडीऍफ (1.06 MiB) – Analog Devices Application note
• Basic OpAmp Applicationsपीडीऍफ (173 KiB)
• Handbook of operational amplifier applicationsपीडीऍफ (2.00 MiB) – Texas Instruments Application note
• Low Side Current Sensing Using Operational Amplifiers
• Logarithmic amplifier
• Precision half-wave rectifier
• Precision full-wave rectifier
• Log/anti-log generators, cube generator, multiply/divide ampपीडीऍफ (165 KiB)
• Logarithmically variable gain from a linear variable component
• ECE 209: Operational amplifier basics – Brief document explaining zero error by naive high-gain negative feedback. Gives single OpAmp example that generalizes typical configurations.
• ECE 327: Practical Integrators and Operational Amplifier Offset – Discusses sources of and ways of fixing offset and drift problems.
• ECE 327: Voltage Regulators Procedures and Explanations – In the "Improving dynamic performance" section, discusses methods of using bypass capacitors to improve PSRR of components in designs.
• Impedance and admittance transformations using operational amplifiers by D. H. Sheingold