आपरेशनल एम्प्लिफायर के उपयोग

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

अनुक्रम

रेखीय परिपथों में प्योग (Linear circuit applications)[संपादित करें]

तुलना करने के लिये (Comparator)[संपादित करें]

कम्परेटर (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 < V_2 \end{matrix}\right.

(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)[संपादित करें]

इन्वर्ट करने वाला एम्प्लिफायर

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)[संपादित करें]

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 \infin
    • 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)[संपादित करें]

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[संपादित करें]

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[संपादित करें]

When R_1 = R_\mathrm{f} = R_2 = R_\mathrm{g}:

 V_\mathrm{out} =  V_2 - V_1 \,\!

वोल्टेज अनुगामी (Voltage follower)[संपादित करें]

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}} = \infin (realistically, the differential input impedance of the op-amp itself, 1 MΩ to 1 TΩ)

योजी प्रवर्धक (Summing amplifier)[संपादित करें]

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)[संपादित करें]

Integrating amplifier

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 )[संपादित करें]

Differentiating amplifier

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.}

इंस्ट्रुमेंटेशन एम्प्लिफायर (Instrumentation amplifier)[संपादित करें]

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)[संपादित करें]

A bistable multivibrator implemented as a comparator with hysteresis.

Schmitt trigger with non-inverting hysteretic switching characteristic

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.

Schmitt trigger with inverting hysteretic switching characteristic

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)[संपादित करें]

Relaxation oscillator implemented with inverting Schmitt trigger and RC network

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)[संपादित करें]

Inductance gyrator

Simulates an inductor.

शून्य स्तर अनुसूचक (Zero level detector)[संपादित करें]

Voltage divider reference

  • Zener sets reference voltage

ऋणात्मक प्रतिबाधा परिवर्तक (Negative impedance converter (NIC))[संपादित करें]

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:
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 )[संपादित करें]

Wien bridge oscillator

Produces a pure sine wave.

अरेखीय संरचनाएं (Non-linear configurations)[संपादित करें]

Precision rectifier[संपादित करें]

Precision rectifier

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

Logarithmic output[संपादित करें]

Logarithmic configuration
  • 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[संपादित करें]

Exponential configuration
  • The relationship between the input voltage v_{\text{in}} and the output voltage v_{\text{out}} is given by:
v_{\text{out}} = -R I_{\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}} = -R I_{\text{D}}.\,

अन्य उपयोग[संपादित करें]

इन्हें भी देखें[संपादित करें]

सन्दर्भ[संपादित करें]

अन्य पठनीय सामग्री[संपादित करें]

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