Operational Amplifiers – Complete Theory

Page 15 – Active Low Pass Filter

An Active Low Pass Filter allows low-frequency signals to pass while attenuating high-frequency signals.

                                              

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Basic Components

• Operational amplifier
• Resistor (R)
• Capacitor (C)

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Working Principle

• At low frequencies → capacitor behaves like open circuit
• Signal passes through amplifier
• At high frequencies → capacitor offers low impedance
• Signal gets attenuated

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Cutoff Frequency

fc = 1 / (2πRC)

Where:

• R → Resistance
• C → Capacitance

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Frequency Response

• Passband → constant gain
• Cutoff frequency → gain reduces to 0.707
• Roll-off → −20 dB/decade

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Advantages of Active Filters

• No inductors required
• High input impedance
• Easy gain control

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Applications

• Audio signal processing
• Noise filtering
• Communication systems
• Signal conditioning circuits

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GATE Important Points

• Cutoff frequency formula: fc = 1 / (2πRC)
• Roll-off slope = −20 dB/decade
• Uses op-amp + RC network
• Important for frequency response questions

 

Operational Amplifiers – Complete Theory

Page 14 – Instrumentation Amplifier

An Instrumentation Amplifier is a precision amplifier designed to amplify small differential signals while rejecting common-mode noise.

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Main Characteristics

• Very high input impedance
• High Common Mode Rejection Ratio (CMRR)
• Accurate gain control
• Low noise amplification

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Basic Structure

The instrumentation amplifier uses three operational amplifiers.

• Two op-amps act as input buffers
• One op-amp acts as differential amplifier

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Gain Equation

Vout = (1 + 2R / Rg) × (V2 − V1)

Where:

• Rg → Gain controlling resistor
• V1, V2 → Input voltages

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Why Instrumentation Amplifier?

• Amplifies very small signals
• Rejects common-mode noise
• Provides stable and accurate gain

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Applications

• Biomedical instruments (ECG, EEG)
• Sensor signal amplification
• Data acquisition systems
• Industrial measurement systems

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GATE Important Points

• Uses three op-amps
• Very high input impedance
• High CMRR
• Gain controlled by resistor Rg

 

Operational Amplifiers – Complete Theory

Page 13 – Precision Rectifier (Super Diode)

                                                

A Precision Rectifier is an op-amp circuit that rectifies signals without the voltage drop normally caused by diodes.

It is also called a Super Diode.

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Problem with Normal Diodes

Ordinary diode rectifiers require a minimum voltage:

Vd ≈ 0.7 V (Silicon diode)

This causes errors when rectifying small signals.

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How Precision Rectifier Works

• Uses an operational amplifier with a diode
• Op-amp compensates the diode voltage drop
• Allows rectification of very small signals

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Operation

Positive Input Cycle

• Op-amp output drives the diode forward biased
• Output follows input signal

Negative Input Cycle

• Diode becomes reverse biased
• Output becomes zero

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Key Advantage

Rectifies signals even smaller than 0.7 V.

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Applications

• AC voltmeters
• Signal detectors
• Peak detection circuits
• Audio signal processing

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GATE Important Points

• Also called Super Diode
• Eliminates diode threshold voltage error
• Used for small signal rectification
• Improves measurement accuracy

 

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