Operational Amplifier (OP-AMP): Working, Circuits, Formulas & Applications

Introduction

An Operational Amplifier, commonly called an OP-AMP, is one of the most important building blocks in analog electronics.

An OP-AMP is a high-gain electronic voltage amplifier designed to amplify the difference between two input voltages.

OP-AMPs are widely used in:

Voltage amplifiers
Audio amplifiers
Filters
Comparators
Integrators
Differentiators
Oscillators
Sensor interfaces
Signal conditioning
Instrumentation systems
Control systems
Analog computers
ADC and DAC circuits

A typical OP-AMP has two input terminals and one output terminal:

Inverting input (−)
Non-inverting input (+)
Output

The basic OP-AMP equation is:

VOUT = AOL × (V+ − V−)

Where:

VOUT = Output voltage
AOL = Open-loop voltage gain
V+ = Voltage at non-inverting input
V− = Voltage at inverting input

Because an OP-AMP has very high open-loop gain, practical circuits normally use negative feedback to obtain a controlled and predictable gain.

1. What Is an Operational Amplifier?

An Operational Amplifier (OP-AMP) is a high-gain differential voltage amplifier.

It amplifies the difference between its two input voltages.

The fundamental equation is:

VOUT = AOL × (V+ − V−)

The two input terminals are:

Non-inverting input (+)
An increase in this input tends to increase the output.

Inverting input (−)
An increase in this input tends to decrease the output.

The OP-AMP can be used to perform mathematical and signal-processing operations such as:

Addition
Subtraction
Integration
Differentiation
Amplification
Comparison
Filtering

2. OP-AMP Symbol

A basic OP-AMP can be represented as:

                 +VCC
                   |
                   |
        V− ───────|−\
                  |  \
                  |   \────── VOUT
        V+ ───────|+ /
                  |  /
                  | /
                   |
                 −VEE

OP-AMP terminals

Terminal	Symbol	Function
Inverting input	−	Output changes in the opposite direction
Non-inverting input	+	Output changes in the same direction
Output	VOUT	Amplified output
Positive supply	+VCC	Positive power supply
Negative supply	−VEE	Negative supply or ground/reference

The exact number of pins depends on the OP-AMP IC.

3. How Does an OP-AMP Work?

The OP-AMP compares the voltage at its two inputs.

The difference between the inputs is called the differential input voltage.

VD = V+ − V−

The OP-AMP then amplifies this voltage difference.

Therefore:

VOUT = AOL × VD

or:

VOUT = AOL × (V+ − V−)

Example

Suppose:

V+ = 2.01 V

and:

V− = 2.00 V

Therefore:

VD = 2.01 − 2.00

VD = 0.01 V

If the open-loop gain is:

AOL = 100,000

then the theoretical output would be:

VOUT = 100,000 × 0.01

VOUT = 1,000 V

However, an actual OP-AMP cannot produce 1,000 V if its supply voltage is only ±15 V.

The output will therefore move toward its available output limit and enter saturation.

This is one reason why OP-AMPs are normally operated with negative feedback when linear amplification is required.

4. Differential Inputs

An OP-AMP is a differential amplifier.

It responds to the difference between its two input voltages.

When V+ > V−

The output tends to move in the positive direction.

When V+ < V−

The output tends to move in the negative direction.

When V+ = V−

Ideally, the differential input voltage is zero.

VD = V+ − V−

Therefore:

VD = 0 V

and ideally:

VOUT = 0 V

when the OP-AMP is operating without offset and other non-ideal effects.

5. Ideal OP-AMP Characteristics

For circuit analysis, an OP-AMP is often treated as an ideal device.

The ideal OP-AMP has the following characteristics:

Parameter	Ideal Value
Open-loop voltage gain	Infinite
Input resistance	Infinite
Output resistance	Zero
Bandwidth	Infinite
Input current	Zero
Input offset voltage	Zero
CMRR	Infinite
Slew rate	Infinite
Noise	Zero

Real OP-AMPs do not have these characteristics exactly.

The ideal model is used to simplify circuit calculations.

6. The Two Golden Rules of OP-AMPs

When an OP-AMP is operating in its linear region with suitable negative feedback, two important rules can be used.

Rule 1 – Input Current Is Approximately Zero

Because the input impedance of an ideal OP-AMP is infinite:

I+ ≈ 0

and:

I− ≈ 0

Therefore, practically no current flows into the input terminals.

Rule 2 – Input Voltages Are Approximately Equal

With negative feedback:

V+ ≈ V−

This condition is commonly called a virtual short.

Important:

The two input terminals are not physically connected.

They simply have approximately the same voltage under the appropriate feedback conditions.

7. Negative Feedback

Negative feedback is one of the most important concepts in OP-AMP circuits.

A portion of the output signal is fed back to the inverting input.

                  Feedback
                     │
                     ▼
Vin ───────► OP-AMP Circuit ───────► VOUT
                  ▲
                  │
                  └───────────────┐
                                  │
                                  └── Feedback

Negative feedback provides:

Stable gain
Predictable gain
Improved linearity
Reduced distortion
Increased bandwidth
Better circuit stability

The feedback network usually contains resistors, capacitors, or other components.

8. Inverting Amplifier

The inverting amplifier is one of the most common OP-AMP circuits.

Basic circuit

                     Rf
              ┌────/\/\/\────┐
              │              │
              │              │
Vin ── Rin ───●──────────────┤−
       /\/\                   │\
                              │ \
                              │  \──── VOUT
                              │  /
                       GND ───┤+/
                              │/

The voltage gain is:

AV = −Rf / Rin

Where:

AV = Voltage gain
Rf = Feedback resistor
Rin = Input resistor

Example

Suppose:

Rin = 10 kΩ

Rf = 100 kΩ

Then:

AV = −100 kΩ / 10 kΩ

AV = −10

If:

VIN = 0.2 V

then:

VOUT = AV × VIN

VOUT = −10 × 0.2

VOUT = −2 V

The negative sign means that the output is inverted relative to the input.

The input and output are approximately 180° out of phase for a linear sinusoidal signal within the circuit’s operating bandwidth.

9. Non-Inverting Amplifier

In a non-inverting amplifier, the input signal is applied to the non-inverting (+) input.

Voltage gain

AV = 1 + (Rf / R1)

Where:

Rf = Feedback resistor
R1 = Resistor connected from the inverting input toward the reference/ground

Example

Suppose:

Rf = 90 kΩ

R1 = 10 kΩ

Then:

AV = 1 + (90 kΩ / 10 kΩ)

AV = 1 + 9

AV = 10

If:

VIN = 0.5 V

then:

VOUT = 10 × 0.5

VOUT = 5 V

The output has the same polarity/phase as the input.

10. Voltage Follower

A voltage follower is also called a:

Unity-gain buffer
Buffer amplifier

The output is directly connected to the inverting input.

             ┌──────────────┐
VIN ────────►│ +            │
             │    OP-AMP    │────── VOUT
             │ −            │
             └──────┬───────┘
                    │
                    └────────── VOUT

The voltage gain is:

AV = 1

Therefore:

VOUT = VIN

Although the voltage gain is one, the voltage follower is extremely useful.

Applications

Buffering
Impedance matching
Sensor interfaces
Isolation between circuit stages
ADC input buffering

11. Summing Amplifier

A summing amplifier combines multiple input voltages.

V1 ── R1 ──┐
           │
V2 ── R2 ──┤
           ├────●──── OP-AMP ──── VOUT
V3 ── R3 ──┤    │
           │    │
           │    Rf
           │   /\/\
           │    │
           └────┘

For an inverting summing amplifier:

VOUT = −Rf × [(V1/R1) + (V2/R2) + (V3/R3)]

For equal input resistors:

R1 = R2 = R3 = R

the equation becomes:

VOUT = −(Rf/R) × (V1 + V2 + V3)

Applications

Audio mixers
Analog computers
DAC circuits
Signal processing
Mathematical addition

12. Differential Amplifier

A differential amplifier amplifies the difference between two input signals.

The ideal relationship can be written as:

VOUT = AD × (V2 − V1)

Where:

AD = Differential gain
V2 = One input voltage
V1 = Other input voltage

Differential amplifiers are widely used in:

Sensor interfaces
Instrumentation
Data acquisition
Measurement systems
Noise rejection

13. Comparator Using an OP-AMP

An OP-AMP can be operated without negative feedback as a comparator.

                 ┌──────────────┐
VIN ────────────►│ +            │
                 │    OP-AMP    │────── VOUT
VREF ───────────►│ −            │
                 └──────────────┘

If:

VIN > VREF

the output moves toward the positive output level.

If:

VIN < VREF

the output moves toward the negative output level.

Important

A general-purpose OP-AMP can sometimes be used for simple comparison tasks, but a dedicated comparator IC is normally better for high-speed switching applications.

14. OP-AMP Integrator

An OP-AMP can be used to perform mathematical integration.

A capacitor is used in the feedback path.

The ideal integrator equation is:

VOUT = −(1 / Rin × C) × ∫VIN dt

A clearer text representation is:

VOUT = −1/(Rin × C) × ∫VIN dt

Where:

Rin = Input resistance
C = Feedback capacitance

Applications

Analog computers
Signal processing
Active filters
Waveform generation
Ramp generation

15. OP-AMP Differentiator

An OP-AMP differentiator produces an output proportional to the rate of change of the input signal.

The ideal equation is:

VOUT = −Rf × C × (dVIN/dt)

Where:

Rf = Feedback resistor
C = Input capacitor

Applications

Edge detection
Pulse generation
Waveform processing
Signal processing

Important

An ideal differentiator can strongly amplify high-frequency noise.

Practical differentiator circuits therefore use additional resistors and capacitors to limit the frequency response.

16. OP-AMP as an Active Filter

An OP-AMP can be combined with resistors and capacitors to create active filters.

Common types are:

Low-Pass Filter

Allows lower-frequency signals to pass while attenuating higher-frequency signals.

High-Pass Filter

Allows higher-frequency signals to pass while attenuating lower-frequency signals.

Band-Pass Filter

Allows a selected range of frequencies to pass.

Band-Stop Filter

Attenuates a selected range of frequencies.

Active filters can provide:

Frequency selection
Voltage gain
Buffering
Signal conditioning

17. Important OP-AMP Parameters

17.1 Open-Loop Gain

Open-loop gain is the gain of an OP-AMP without feedback.

AOL = VOUT / (V+ − V−)

Real OP-AMPs have a finite but usually very high open-loop gain.

17.2 Input Impedance

Input impedance determines how much current the OP-AMP input draws from the signal source.

High input impedance is generally desirable because it reduces loading of the previous circuit.

17.3 Output Impedance

Output impedance determines how strongly the OP-AMP can drive a load.

A lower output impedance is generally desirable.

17.4 Input Offset Voltage

Input offset voltage is the small differential voltage that appears at the input because of imperfections in the internal circuitry.

It is usually represented as:

VOS

A lower offset voltage is important in precision applications.

17.5 Input Bias Current

Real OP-AMP inputs have small currents.

These are called input bias currents.

They become especially important when high-value resistors are used.

18. Slew Rate

Slew rate is the maximum rate at which the output voltage can change.

The basic relationship is:

SR = dVOUT/dt

Slew rate is commonly specified in:

V/µs

For example, suppose an OP-AMP has a slew rate of:

SR = 1 V/µs

This means the output can change at a maximum rate of approximately 1 volt per microsecond under the specified test conditions.

A low slew rate can cause distortion when amplifying large, high-frequency signals.

19. Gain-Bandwidth Product

The Gain-Bandwidth Product, commonly abbreviated as GBW, describes the relationship between closed-loop gain and bandwidth for many OP-AMPs.

A simplified relationship is:

GBW ≈ Gain × Bandwidth

Therefore:

Bandwidth ≈ GBW / Gain

Example

Suppose:

GBW = 1 MHz

and:

Closed-loop gain = 10

Then approximately:

Bandwidth = 1 MHz / 10

Bandwidth ≈ 100 kHz

The actual frequency response depends on the specific OP-AMP and circuit configuration.

20. CMRR – Common-Mode Rejection Ratio

CMRR stands for:

Common-Mode Rejection Ratio

It describes how effectively an OP-AMP rejects signals that appear simultaneously on both inputs.

The basic relationship is:

CMRR = AD / ACM

Where:

AD = Differential gain
ACM = Common-mode gain

In decibels:

CMRR(dB) = 20 × log₁₀(AD / ACM)

A high CMRR is desirable in precision measurement systems.

21. PSRR – Power Supply Rejection Ratio

PSRR stands for:

Power Supply Rejection Ratio

It describes how effectively an OP-AMP rejects changes or disturbances on its power supply.

A high PSRR is useful in:

Precision instrumentation
Audio equipment
Sensor systems
Battery-powered circuits
Measurement systems

22. OP-AMP Saturation

An OP-AMP cannot normally produce unlimited output voltage.

For example, if an OP-AMP is powered by:

+15 V and −15 V

the output cannot normally exceed the supply rails.

The actual output voltage may remain somewhat inside the supply rails depending on:

OP-AMP type
Load resistance
Output current
Temperature
Supply voltage

A rail-to-rail output OP-AMP is designed to operate closer to the supply rails.

23. Single-Supply OP-AMP

Many modern OP-AMPs operate from a single power supply.

For example:

VCC = 5 V

and:

VEE = 0 V

In a single-supply circuit, the input and output signals must remain within the OP-AMP’s specified voltage ranges.

For AC signal processing, a reference voltage can sometimes be created at approximately half the supply voltage:

VREF ≈ VCC / 2

For a 5 V supply:

VREF ≈ 2.5 V

This reference can be used to bias an AC signal so that it can be processed by the OP-AMP without requiring a negative supply.

24. Dual-Supply OP-AMP

Traditional OP-AMP circuits often use positive and negative supply voltages.

For example:

+15 V

and:

−15 V

This allows signals to swing around 0 V.

Dual supplies are commonly used in:

Laboratory equipment
Audio circuits
Precision analog circuits
Instrumentation systems

25. Ideal OP-AMP vs Real OP-AMP

Parameter	Ideal OP-AMP	Real OP-AMP
Open-loop gain	Infinite	Very high but finite
Input impedance	Infinite	Very high
Output impedance	Zero	Low
Bandwidth	Infinite	Limited
Input current	Zero	Small
Offset voltage	Zero	Small but non-zero
CMRR	Infinite	Finite
PSRR	Infinite	Finite
Slew rate	Infinite	Limited
Noise	Zero	Present
Output swing	Unlimited in ideal model	Limited
Power consumption	Zero in ideal model	Finite

26. Common OP-AMP ICs

Some commonly encountered OP-AMP families include:

IC	Configuration	Common Use
LM741	Single	General-purpose/educational
LM358	Dual	Single-supply circuits
LM324	Quad	General-purpose applications
TL081	Single	JFET-input applications
TL072	Dual	Audio and low-noise applications
NE5532	Dual	Audio applications
LM2904	Dual	Industrial/automotive applications

Always check the exact manufacturer’s datasheet before designing a circuit, because electrical specifications can vary between device versions.

27. OP-AMP Applications

OP-AMPs are used in many areas of electronics.

Audio Electronics

Audio preamplifiers
Tone control
Active filters
Mixers
Signal conditioning

Instrumentation

Sensor amplifiers
Differential amplifiers
Precision measurement
Signal conditioning

Control Systems

Feedback circuits
Error amplifiers
Control loops

Signal Processing

Filters
Integrators
Differentiators
Waveform processing

Embedded Systems

ADC signal conditioning
Sensor interfaces
Voltage scaling
Reference circuits

Industrial Electronics

Transducers
Process control
Monitoring
Measurement systems

28. OP-AMP Circuit Formula Table

Circuit	Formula
Basic OP-AMP	VOUT = AOL × (V+ − V−)
Inverting amplifier	AV = −Rf / Rin
Non-inverting amplifier	AV = 1 + (Rf / R1)
Voltage follower	AV = 1
Summing amplifier	VOUT = −Rf × [(V1/R1) + (V2/R2) + …]
Differential amplifier	VOUT = AD × (V2 − V1)
Integrator	VOUT = −1/(R × C) × ∫VIN dt
Differentiator	VOUT = −Rf × C × (dVIN/dt)
Slew rate	SR = dVOUT/dt
CMRR	CMRR = AD / ACM

29. OP-AMP Circuit Comparison

Circuit	Main Function	Gain	Phase
Inverting amplifier	Amplification	−Rf/Rin	Inverted
Non-inverting amplifier	Amplification	1 + Rf/R1	Same phase
Voltage follower	Buffer	1	Same phase
Summing amplifier	Addition	Depends on resistors	Usually inverted
Differential amplifier	Difference amplification	Depends on circuit	Depends on inputs
Integrator	Mathematical integration	Frequency dependent	Frequency dependent
Differentiator	Mathematical differentiation	Frequency dependent	Frequency dependent
Comparator	Voltage comparison	Very high/open-loop	Switching

30. OP-AMP Learning Infographic

                    OPERATIONAL AMPLIFIER
                           OP-AMP
                             │
              ┌──────────────┴──────────────┐
              │                             │
          TWO INPUTS                     OUTPUT
              │                             │
       ┌──────┴──────┐                      │
       │             │                      │
       ▼             ▼                      ▼
      (+)           (−)                   VOUT
 Non-Inverting   Inverting
       │             │
       └──────┬──────┘
              │
              ▼
      DIFFERENTIAL VOLTAGE
              │
              ▼
       HIGH VOLTAGE GAIN
              │
              ▼
       NEGATIVE FEEDBACK
              │
      ┌───────┼────────┐
      │       │        │
      ▼       ▼        ▼
   Amplifier Buffer  Filter
      │
      ├── Inverting
      ├── Non-Inverting
      ├── Summing
      ├── Differential
      ├── Integrator
      └── Differentiator

31. OP-AMP Learning Roadmap

START
  │
  ▼
What is an OP-AMP?
  │
  ▼
Learn OP-AMP Symbol
  │
  ▼
Understand (+) and (−) Inputs
  │
  ▼
Learn Ideal OP-AMP
  │
  ▼
Learn Golden Rules
  │
  ▼
Understand Negative Feedback
  │
  ├──────────────┐
  ▼              ▼
Inverting     Non-Inverting
Amplifier     Amplifier
  │              │
  └──────┬───────┘
         ▼
   Voltage Follower
         │
         ▼
   Summing Amplifier
         │
         ▼
 Differential Amplifier
         │
         ▼
    Integrator
         │
         ▼
   Differentiator
         │
         ▼
    Active Filters
         │
         ▼
Practical OP-AMP Parameters
         │
         ▼
    Real-World Design

32. OP-AMP Design Checklist

Before designing an OP-AMP circuit, check the following:

Parameter	Question
Supply voltage	Is the supply voltage within the datasheet limits?
Input range	Is the input within the common-mode range?
Gain	Can the required gain be achieved?
Bandwidth	Is enough bandwidth available?
Slew rate	Is the slew rate sufficient?
Output	Can the required output voltage be produced?
Load	Can the OP-AMP drive the load?
Stability	Is the feedback circuit stable?
Offset	Is the offset voltage acceptable?
Bias current	Is the input bias current acceptable?
Noise	Is the noise level acceptable?
Decoupling	Are supply bypass capacitors provided?

33. Common OP-AMP Mistakes

Mistake 1 – Assuming the Inputs Are Physically Connected

The inputs are not physically connected.

The correct assumption under suitable negative feedback is:

V+ ≈ V−

Mistake 2 – Ignoring Supply Voltage

The OP-AMP cannot generate an output voltage beyond its specified output range.

Mistake 3 – Ignoring Input Common-Mode Range

Even if the supply voltage is correct, the input voltage may still be outside the allowed common-mode range.

Mistake 4 – Ignoring Slew Rate

A circuit may have enough theoretical gain and bandwidth but still distort a large, fast-changing signal because of limited slew rate.

Mistake 5 – Using Very Large Resistors Without Considering Their Effects

Large resistor values can increase:

Thermal noise
Offset caused by bias current
Susceptibility to interference

Mistake 6 – Forgetting Supply Decoupling

Supply bypass capacitors are often required close to the OP-AMP power pins.

The appropriate capacitor values and placement should follow the manufacturer’s recommendations and the circuit requirements.

34. Worked Example – Inverting Amplifier

Design Requirement

Design an inverting amplifier with a gain of:

AV = −20

Choose:

Rin = 10 kΩ

The gain equation is:

AV = −Rf / Rin

Therefore:

−20 = −Rf / 10 kΩ

Therefore:

Rf = 200 kΩ

Final component values

Component	Value
Rin	10 kΩ
Rf	200 kΩ
Voltage gain	−20

If:

VIN = 100 mV

then:

VOUT = −20 × 0.1 V

VOUT = −2 V

This result is valid only if the selected OP-AMP has sufficient supply voltage, output swing, bandwidth, slew rate, and load-driving capability.

35. Worked Example – Non-Inverting Amplifier

Requirement

Design a non-inverting amplifier with a gain of 11.

The equation is:

AV = 1 + Rf/R1

Choose:

R1 = 10 kΩ

Therefore:

11 = 1 + Rf/10 kΩ

Subtract 1:

10 = Rf/10 kΩ

Therefore:

Rf = 100 kΩ

Final design

Component	Value
R1	10 kΩ
Rf	100 kΩ
Voltage gain	11

If:

VIN = 0.2 V

then:

VOUT = 11 × 0.2 V

VOUT = 2.2 V

36. Frequently Asked Questions – OP-AMP

What is an OP-AMP?

An OP-AMP, or operational amplifier, is a high-gain differential voltage amplifier used for amplification, buffering, filtering, mathematical operations, comparison and signal conditioning.

Why is it called an operational amplifier?

It was originally developed for analog computing systems, where OP-AMP circuits were used to perform mathematical operations such as addition, subtraction, integration and differentiation.

What are the main terminals of an OP-AMP?

The main terminals are:

Non-inverting input (+)
Inverting input (−)
Output
Positive power supply
Negative power supply or ground/reference

Some devices have additional pins for functions such as offset adjustment, shutdown or compensation.

What is the basic OP-AMP equation?

The basic open-loop relationship is:

VOUT = AOL × (V+ − V−)

where AOL is the open-loop voltage gain.

What is the difference between an inverting and non-inverting amplifier?

An inverting amplifier has a negative voltage gain:

AV = −Rf/Rin

The output is inverted relative to the input.

A non-inverting amplifier has a positive voltage gain:

AV = 1 + Rf/R1

The output has the same polarity/phase as the input.

What is a virtual short?

A virtual short means that the two OP-AMP inputs have approximately equal voltage when the OP-AMP is operating linearly with appropriate negative feedback.

V+ ≈ V−

They are not physically connected.

What is virtual ground?

A virtual ground is a circuit node that is maintained at approximately 0 V through circuit operation and feedback, even though it is not physically connected to ground.

A common example is the inverting input of an inverting amplifier when the non-inverting input is connected to ground.

Why is negative feedback used in OP-AMP circuits?

Negative feedback controls the overall circuit gain and generally improves linearity, stability and bandwidth.

It also makes the circuit behavior depend more on external components than on the OP-AMP’s extremely high open-loop gain.

What happens when an OP-AMP is used without feedback?

Without negative feedback, the extremely high open-loop gain can cause the output to move rapidly toward one of the output limits even for a small input difference.

This mode is useful for comparison applications but is generally unsuitable for linear amplification.

What is OP-AMP saturation?

Saturation occurs when the output reaches the maximum or minimum voltage that the OP-AMP can produce under the given supply and load conditions.

What is slew rate?

Slew rate is the maximum rate of change of the OP-AMP output voltage.

SR = dVOUT/dt

It is commonly specified in V/µs.

What is CMRR?

CMRR means Common-Mode Rejection Ratio.

It indicates how effectively the OP-AMP rejects voltage signals that are common to both inputs.

A high CMRR is desirable in precision differential measurement systems.

What is PSRR?

PSRR means Power Supply Rejection Ratio.

It indicates how effectively the OP-AMP rejects disturbances or variations on its power supply.

What is input offset voltage?

Input offset voltage is a small differential voltage caused by imperfections inside a real OP-AMP.

It can produce an unwanted output error, particularly in high-gain DC circuits.

What is input bias current?

Input bias current is the small current associated with the OP-AMP input terminals.

It can cause voltage errors when the input circuit contains large resistance values.

Can an OP-AMP operate from a single power supply?

Yes.

Many modern OP-AMPs are designed for single-supply operation.

However, the input common-mode range and output voltage range must be checked.

What is a rail-to-rail OP-AMP?

A rail-to-rail OP-AMP is designed so that its input and/or output voltage can operate close to the supply rails.

The exact performance varies between devices.

What is a voltage follower?

A voltage follower is a unity-gain OP-AMP circuit.

VOUT = VIN

It is mainly used as a buffer.

Why use a voltage follower if its gain is only one?

The voltage follower provides:

Very high input impedance
Low output impedance
Isolation between circuit stages
Improved ability to drive the following circuit

Therefore, it can transfer a voltage without significantly loading the source.

What is an OP-AMP integrator?

An OP-AMP integrator produces an output proportional to the integral of the input signal.

VOUT = −1/(R × C) × ∫VIN dt

It is used in signal processing, waveform generation and active filters.

What is an OP-AMP differentiator?

A differentiator produces an output proportional to the rate of change of the input signal.

VOUT = −Rf × C × (dVIN/dt)

Practical differentiators normally include frequency-limiting components.

What is an active filter?

An active filter uses active components such as OP-AMPs together with resistors and capacitors.

Active filters can provide both filtering and voltage gain.

What is the difference between an OP-AMP and a comparator?

An OP-AMP is primarily designed for linear amplification with feedback.

A comparator is designed specifically to compare two voltages and produce a switching output.

A dedicated comparator is generally preferred for fast switching applications.

Can an OP-AMP amplify DC?

Yes.

An OP-AMP can amplify DC signals, provided the input voltage, output voltage, offset, bias current and other specifications are suitable.

Can an OP-AMP amplify AC?

Yes.

OP-AMPs are widely used for AC amplification.

However, the signal frequency must be within the practical bandwidth of the circuit.

Why does an OP-AMP have high input impedance?

High input impedance reduces the amount of current drawn from the signal source.

This minimizes loading of the previous circuit.

Why is low output impedance useful?

Low output impedance allows the OP-AMP to drive the next circuit stage more effectively.

What is gain-bandwidth product?

Gain-bandwidth product, or GBW, describes the approximate relationship between closed-loop gain and bandwidth.

A simplified relationship is:

GBW ≈ Gain × Bandwidth

Therefore:

Bandwidth ≈ GBW / Gain

Why does OP-AMP bandwidth decrease when gain increases?

For many internally compensated OP-AMPs, the gain-bandwidth product is approximately constant over the useful frequency range.

Therefore, increasing closed-loop gain generally reduces the available bandwidth.

Why does an OP-AMP need a power supply?

The OP-AMP uses energy from its power supply to operate its internal transistor circuitry and drive the output.

The input signal controls the output; the power supply provides the energy required for amplification.

Can an OP-AMP output voltage exceed its supply voltage?

Normally, no.

The output is limited by the OP-AMP’s supply rails and its output-stage characteristics.

What is a rail-to-rail output?

A rail-to-rail output stage is designed to produce an output voltage very close to the positive and/or negative supply rails.

The exact output range depends on the device and load.

Why are decoupling capacitors used with OP-AMPs?

Decoupling capacitors help provide a low-impedance local supply path for transient currents and reduce the effect of high-frequency supply disturbances.

They should generally be placed close to the OP-AMP supply pins according to the manufacturer’s recommendations.

37. OP-AMP Quick Revision

                OP-AMP QUICK REVISION

             OPERATIONAL AMPLIFIER
                      │
        ┌─────────────┴─────────────┐
        │                           │
        ▼                           ▼
   NON-INVERTING                INVERTING
     INPUT (+)                  INPUT (−)
        │                           │
        └───────────┬───────────────┘
                    │
                    ▼
             DIFFERENTIAL INPUT
                    │
                    ▼
               HIGH GAIN
                    │
                    ▼
            NEGATIVE FEEDBACK
                    │
       ┌────────────┼────────────┐
       ▼            ▼            ▼
   AMPLIFIER      BUFFER       FILTER
       │
       ├── Inverting
       ├── Non-Inverting
       ├── Summing
       ├── Differential
       ├── Integrator
       └── Differentiator

Important formulas

Basic OP-AMP:

VOUT = AOL × (V+ − V−)

Inverting amplifier:

AV = −Rf/Rin

Non-inverting amplifier:

AV = 1 + Rf/R1

Voltage follower:

AV = 1

Integrator:

VOUT = −1/(R × C) × ∫VIN dt

Differentiator:

VOUT = −Rf × C × (dVIN/dt)

Slew rate:

SR = dVOUT/dt

CMRR:

CMRR = AD/ACM

38. Summary

An Operational Amplifier (OP-AMP) is a fundamental building block of analog electronics.

The most important concepts to understand are:

OP-AMP has differential inputs.
The non-inverting input is marked +.
The inverting input is marked −.
The basic relationship is VOUT = AOL × (V+ − V−).
Ideal OP-AMP input current is assumed to be zero.
With suitable negative feedback, V+ ≈ V−.
Negative feedback controls the circuit gain.
Inverting amplifier gain is −Rf/Rin.
Non-inverting amplifier gain is 1 + Rf/R1.
A voltage follower has a gain of one.
OP-AMPs can perform addition, subtraction, integration and differentiation.
OP-AMPs can be used to build active filters.
Real OP-AMPs have limitations such as finite bandwidth, offset voltage, bias current and slew rate.
Supply voltage, common-mode range and output swing must always be considered.
The manufacturer’s datasheet should be checked before using a specific OP-AMP in a real circuit.