Operational Amplifiers – Complete Theory

Page 12 – Schmitt Trigger

                                        

The Schmitt Trigger is a comparator circuit with positive feedback. It introduces hysteresis, which improves noise immunity.

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Why Schmitt Trigger?

• Removes noise from signals
• Prevents multiple switching
• Provides stable digital output

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Positive Feedback

In this circuit, a portion of the output is fed back to the input.

Positive feedback creates two switching thresholds.

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Upper Threshold Voltage (UTP)

UTP = (R1 / (R1 + R2)) × Vsat

This is the voltage at which the output switches from negative saturation to positive saturation.

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Lower Threshold Voltage (LTP)

LTP = − (R1 / (R1 + R2)) × Vsat

This is the voltage at which the output switches from positive saturation to negative saturation.

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Hysteresis Width

Hysteresis = UTP − LTP

This difference creates a dead band that removes noise.

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Transfer Characteristic

• When Vin > UTP → Output = +Vsat
• When Vin < LTP → Output = −Vsat
• Between UTP and LTP → Output remains unchanged

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Applications

• Wave shaping circuits
• Noise filtering
• Square wave generation
• Switching circuits

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GATE Important Points

• Uses positive feedback
• Introduces hysteresis
• Two threshold voltages (UTP & LTP)
• Improves noise immunity

 

Operational Amplifiers – Complete Theory

Page 11 – Op-Amp Comparator

                                        

A Comparator is an operational amplifier circuit that compares two voltages and produces an output indicating which one is larger.

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Basic Principle

• If Vin > Vref → Output goes to positive saturation
• If Vin < Vref → Output goes to negative saturation

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Output Levels

Vout = +Vsat when Vin > Vref

Vout = -Vsat when Vin < Vref

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Types of Comparators

• Non-inverting comparator
• Inverting comparator
• Zero-crossing detector

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Zero Crossing Comparator

When reference voltage is zero:

Vref = 0

The circuit detects when the input signal crosses zero.

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Applications

• Analog to digital converters
• Level detection circuits
• Wave shaping circuits
• Signal detection systems

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GATE Important Points

• Comparator operates in open-loop mode
• Output saturates at ±Vsat
• Very high gain of op-amp
• Used in zero-crossing detection

 

Operational Amplifiers – Complete Theory

Page 10 – Op-Amp Differentiator

The Differentiator is an operational amplifier circuit that produces an output proportional to the rate of change of the input signal.

                                              

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Circuit Components

• Input capacitor (C)
• Feedback resistor (R)
• Operational amplifier
• Input voltage Vin

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Virtual Ground Concept

Since the non-inverting terminal is grounded:

V− ≈ 0

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Capacitor Current

Current through capacitor:

I = C ( dVin / dt )

Because op-amp input current ≈ 0, this same current flows through the feedback resistor.

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Voltage Across Resistor

Using Ohm’s law:

Vout = − I R

Substituting current:

Vout = − RC ( dVin / dt )

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Key Result

Output voltage is proportional to the derivative of input voltage.

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Waveform Behavior

• Ramp input → Constant output
• Triangular input → Square output
• Sine input → Cosine output

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Applications

• Edge detection circuits
• Waveform shaping
• High-pass filter circuits
• Signal processing

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GATE Important Points

• Differentiator produces output proportional to dVin/dt
• Capacitor connected at input
• Resistor in feedback path
• Acts as a high-pass circuit

 

Operational Amplifiers – Complete Theory

Page 9 – Op-Amp Integrator

The Integrator is an operational amplifier circuit that produces an output proportional to the integral of the input signal.

                                               

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Circuit Components

• Input resistor (R)
• Feedback capacitor (C)
• Operational amplifier
• Input voltage Vin

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Virtual Ground Concept

Since the non-inverting terminal is grounded:

V− ≈ 0

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Input Current

The current through the input resistor is:

I = Vin / R

Because op-amp input current ≈ 0, this current flows through the capacitor.

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Capacitor Current Equation

Current through capacitor:

I = C ( dVout / dt )

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Derivation

Equating currents:

Vin / R = C ( dVout / dt )

Rearranging:

dVout / dt = Vin / RC

Integrating:

Vout = − (1 / RC) ∫ Vin dt

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Key Result

Output voltage is proportional to the integral of input voltage.

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Waveform Behavior

• Square input → Triangular output
• Constant input → Ramp output
• Sine input → Cosine output

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Applications

• Analog computers
• Signal processing
• Waveform generation
• Control systems

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GATE Important Points

• Integrator produces output proportional to ∫Vin dt
• Uses capacitor in feedback path
• Important for waveform conversion
• Common question: square → triangular waveform

 

Operational Amplifiers – Complete Theory

Page 8 – Differential Amplifier (Subtractor)

                                     

The Differential Amplifier is an operational amplifier circuit that amplifies the difference between two input signals.

It is also called a Subtractor Circuit.

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Purpose of Differential Amplifier

• Amplifies the difference between two voltages
• Rejects common noise signals
• Used in instrumentation and sensor circuits

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Circuit Components

• Four resistors (R1, R2, R3, R4)
• Two input voltages (V1 and V2)
• One operational amplifier

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Voltage at Non-Inverting Terminal

Using voltage divider:

V+ = (R4 / (R3 + R4)) × V2

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Voltage at Inverting Terminal

Using op-amp property:

V− ≈ V+

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Output Voltage Derivation

The general output equation is:

Vout = (R2 / R1) (V2 − V1)

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Special Case (Balanced Differential Amplifier)

If

R1 = R3 R2 = R4

Then

Vout = (R2/R1) (V2 − V1)

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Applications

• Instrumentation amplifiers
• Noise rejection circuits
• Sensor signal conditioning
• Data acquisition systems

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GATE Important Points

• Amplifies difference between two inputs
• Rejects common-mode signals
• Used in instrumentation amplifiers
• Important concept: Common Mode Rejection Ratio (CMRR)

 

Operational Amplifiers – Complete Theory

Page 7 – Summing Amplifier (Adder)

                               

                  

The Summing Amplifier is an op-amp circuit used to add multiple input voltages.

It is also called an Adder Circuit.

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Circuit Configuration

• Multiple input signals connected through resistors
• All inputs applied to the inverting terminal
• Non-inverting terminal grounded
• Feedback resistor connected from output to input

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Virtual Ground Concept

Since the non-inverting terminal is grounded:

V− ≈ 0

This node behaves like a virtual ground.

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Input Currents

Each input produces a current:

I1 = V1 / R1

I2 = V2 / R2

I3 = V3 / R3

Total current entering the node:

I = I1 + I2 + I3

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Output Voltage

The output voltage is:

Vout = −Rf ( V1/R1 + V2/R2 + V3/R3 )

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Special Case (Equal Resistors)

If

R1 = R2 = R3 = Rf

Then

Vout = − (V1 + V2 + V3)

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Applications

• Audio mixers
• Signal processing
• Digital to analog converters
• Analog computation

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GATE Important Points

• Summing amplifier adds multiple inputs
• Uses virtual ground concept
• Output is inverted
• Weighted sum possible

 

Operational Amplifiers – Complete Theory

Page 6 – Voltage Follower (Buffer Amplifier)

The Voltage Follower is a special case of the non-inverting amplifier.

In this circuit the output is directly connected to the inverting terminal.

                                        

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Circuit Configuration

• Input applied to non-inverting terminal (+)
• Output connected directly to inverting terminal (−)
• No external feedback resistor

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Virtual Short Concept

For an ideal op-amp:

V+ ≈ V−

Since

V+ = Vin

and output is connected to the inverting terminal:

V− = Vout

Therefore

Vout = Vin

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Voltage Gain

Av = Vout / Vin = 1

This is why it is called a Unity Gain Amplifier.

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Important Characteristics

• Very high input impedance
• Very low output impedance
• Gain = 1
• No phase inversion

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Applications

• Impedance matching
• Signal buffering
• Isolation between circuits
• Sensor interface circuits

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GATE Important Points

• Voltage follower = unity gain amplifier
• Gain = 1
• Used for impedance matching
• Output follows input voltage