# 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।

## रेखीय परिपथों में प्योग (Linear circuit applications)

### तुलना करने के लिये (Comparator)

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

• $V_{\text{out}}=\left\{{\begin{matrix}V_{\text{S+}}&V_{1}>V_{2}\\V_{\text{S-}}&V_{1} (where $V_{\text{s}}$ is the supply voltage and the opamp is powered by $+V_{\text{s}}$ and $-V_{\text{s}}$ .)

### इन्वर्टिंग एम्प्लिफायर (Inverting amplifier)

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

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

### व्युत्क्रम न करने वाला एम्प्लिफायर (Non-inverting amplifier)

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

$V_{\text{out}}=V_{\text{in}}\left(1+{\frac {R_{2}}{R_{1}}}\right)\,$ • Input impedance $Z_{\text{in}}\approx \infty$ • 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., $R_{1}$ in parallel with $R_{2}$ ).
• 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 ($+$ ) 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
$R_{1}\|R_{2}\triangleq \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right)^{-1}={\frac {R_{1}R_{2}}{R_{1}+R_{2}}},\,$ which is the equivalent resistance of $R_{1}$ in parallel with $R_{2}$ , between the $V_{\text{in}}$ 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 $V_{\text{in}}$ 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.

### डिफरेंशियल एम्प्लिफायर (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.

$V_{\text{out}}={\frac {\left(R_{\text{f}}+R_{1}\right)R_{\text{g}}}{\left(R_{\text{g}}+R_{2}\right)R_{1}}}V_{2}-{\frac {R_{\text{f}}}{R_{1}}}V_{1}$ • Differential $Z_{\text{in}}$ (between the two input pins) = $R_{1}+R_{2}$ (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.

#### Amplified difference

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

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

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

$V_{\mathrm {out} }=V_{2}-V_{1}\,\!$ ### वोल्टेज अनुगामी (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). 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.

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

### योजी प्रवर्धक (Summing amplifier)

A summing amplifer sums several (weighted) voltages:

$V_{\text{out}}=-R_{\text{f}}\left({\frac {V_{1}}{R_{1}}}+{\frac {V_{2}}{R_{2}}}+\cdots +{\frac {V_{n}}{R_{n}}}\right)$ • When $R_{1}=R_{2}=\cdots =R_{n}$ , and $R_{\text{f}}$ independent
$V_{\text{out}}=-{\frac {R_{\text{f}}}{R_{1}}}(V_{1}+V_{2}+\cdots +V_{n})\!\$ • When $R_{1}=R_{2}=\cdots =R_{n}=R_{\text{f}}$ $V_{\text{out}}=-(V_{1}+V_{2}+\cdots +V_{n})\!\$ • Output is inverted
• Input impedance of the nth input is $Z_{n}=R_{n}$ ($V_{-}$ is a virtual ground)

### समाकलनी (Integrator)

Integrates the (inverted) signal over time

$V_{\text{out}}=-\int _{0}^{t}{\frac {V_{\text{in}}}{RC}}\,\operatorname {d} t+V_{\text{initial}}\,$ (where $V_{\text{in}}$ and $V_{\text{out}}$ are functions of time, $V_{\text{initial}}$ 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 $\omega =0$ ) and gain.
• There are several potential problems with this circuit.
• It is usually assumed that the input $V_{\text{in}}$ 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 $V_{\text{in}}$ has no offset, the leakage or bias currents into the operational amplifier inputs can add an unexpected offset voltage to $V_{\text{in}}$ 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 $\omega =0$ ), the offset of the output may not agree with expectations (i.e., $V_{\text{initial}}$ 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 $R_{F}$ 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 $R_{F}/R$ .

### अवकलित्र (Differentiator)

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).
$V_{\text{out}}=-RC\,{\frac {\operatorname {d} V_{\text{in}}}{\operatorname {d} t}}\,\qquad {\text{where }}V_{\text{in}}{\text{ and }}V_{\text{out}}{\text{ are functions of time.}}$ • 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 $\omega =0$ ) and gain.

### इंस्ट्रुमेंटेशन एम्प्लिफायर (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

### स्क्मिट ट्रिगर (Schmitt trigger)

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 $\pm {\frac {R_{1}}{R_{2}}}V_{\text{sat}}$ where $V_{\text{sat}}$ 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 $\pm {\frac {R_{1}}{R_{1}+R_{2}}}V_{\text{sat}}$ . Such a configuration is used in the relaxation oscillator shown below.

### रिलैक्शेशन एम्प्लिफायर (Relaxation oscillator)

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).

### इंदडक्टैंस गाइरेटर (Inductance gyrator)

Simulates an inductor.

### शून्य स्तर अनुसूचक (Zero level detector)

Voltage divider reference

• Zener sets reference voltage

### ऋणात्मक प्रतिबाधा परिवर्तक (Negative impedance converter (NIC))

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

### वीन-ब्रिज दोलक (Wien bridge oscillator)

Produces a pure sine wave.

## अरेखीय संरचनाएं (Non-linear configurations)

### Precision rectifier

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

### Logarithmic output

• The relationship between the input voltage $v_{\text{in}}$ and the output voltage $v_{\text{out}}$ is given by:
$v_{\text{out}}=-V_{\gamma }\ln \left({\frac {v_{\text{in}}}{I_{\text{S}}\,R}}\right)$ where $I_{\text{S}}$ 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:
${\frac {v_{\text{in}}}{R}}=I_{\text{R}}=I_{\text{D}}$ where $I_{\text{D}}$ is the current through the diode. As known, the relationship between the current and the voltage for a diode is:
$I_{\text{D}}=I_{\text{S}}\left(e^{\frac {V_{\text{D}}}{V_{\gamma }}}-1\right).$ This, when the voltage is greater than zero, can be approximated by:
$I_{\text{D}}\simeq I_{\text{S}}e^{\frac {V_{\text{D}}}{V_{\gamma }}}.$ Putting these two formulae together and considering that the output voltage is the negative of the voltage across the diode ($V_{\text{out}}=-V_{\text{D}}$ ), 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 $v_{\text{in}}$ and the output voltage $v_{\text{out}}$ is given by:
$v_{\text{out}}=-RI_{\text{S}}e^{\frac {v_{\text{in}}}{V_{\gamma }}}$ where $I_{\text{S}}$ 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:
$I_{\text{D}}=I_{\text{S}}\left(e^{\frac {V_{\text{D}}}{V_{\gamma }}}-1\right)$ when the voltage is greater than zero, it can be approximated by:

$I_{\text{D}}\simeq I_{\text{S}}e^{\frac {V_{\text{D}}}{V_{\gamma }}}.$ The output voltage is given by:

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