---

📢 Job Notification Source List

Category	Organization / Platform	Website Link	Purpose
Central Govt	Staff Selection Commission (SSC)	Visit Site	SSC CGL, CHSL, MTS Jobs
Banking	Institute of Banking Personnel Selection (IBPS)	Visit Site	Bank PO, Clerk, RRB Jobs
Railway	Railway Recruitment Board (RRB)	Visit Site	NTPC, Group D, Railway Jobs
Central Govt	Union Public Service Commission (UPSC)	Visit Site	Civil Services & Recruitment
State Govt	State Public Service Commission (PSC)	Search your State PSC Official Website	State Level Govt Jobs
Job Alerts	FreeJobAlert	Visit Site	Daily Job Updates (Quick List)
Job Alerts	Sarkari Result	Visit Site	Trending Jobs & Results
Private Jobs	Naukri	Visit Site	Private Company Jobs
Private Jobs	Indeed	Visit Site	Global Job Search
Professional	LinkedIn Jobs	Visit Site	Networking + Jobs

---

📚 Shaktimatha Learning

Career • Jobs • Skills • Growth

 

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.

                                              

---

Basic Components

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

---

Working Principle

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

---

Cutoff Frequency

fc = 1 / (2πRC)

Where:

• R → Resistance
• C → Capacitance

---

Frequency Response

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

---

Advantages of Active Filters

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

---

Applications

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

---

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.

            ..  .                                   

---

Main Characteristics

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

---

Basic Structure

The instrumentation amplifier uses three operational amplifiers.

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

---

Gain Equation

Vout = (1 + 2R / Rg) × (V2 − V1)

Where:

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

---

Why Instrumentation Amplifier?

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

---

Applications

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

---

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.

---

Problem with Normal Diodes

Ordinary diode rectifiers require a minimum voltage:

Vd ≈ 0.7 V (Silicon diode)

This causes errors when rectifying small signals.

---

How Precision Rectifier Works

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

---

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

---

Key Advantage

Rectifies signals even smaller than 0.7 V.

---

Applications

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

---

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.

---

Why Schmitt Trigger?

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

---

Positive Feedback

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

Positive feedback creates two switching thresholds.

---

Upper Threshold Voltage (UTP)

UTP = (R1 / (R1 + R2)) × Vsat

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

---

Lower Threshold Voltage (LTP)

LTP = − (R1 / (R1 + R2)) × Vsat

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

---

Hysteresis Width

Hysteresis = UTP − LTP

This difference creates a dead band that removes noise.

---

Transfer Characteristic

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

---

Applications

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

---

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.

---

Basic Principle

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

---

Output Levels

Vout = +Vsat when Vin > Vref

Vout = -Vsat when Vin < Vref

---

Types of Comparators

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

---

Zero Crossing Comparator

When reference voltage is zero:

Vref = 0

The circuit detects when the input signal crosses zero.

---

Applications

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

---

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.

                                              

---

Circuit Components

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

---

Virtual Ground Concept

Since the non-inverting terminal is grounded:

V− ≈ 0

---

Capacitor Current

Current through capacitor:

I = C ( dVin / dt )

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

---

Voltage Across Resistor

Using Ohm’s law:

Vout = − I R

Substituting current:

Vout = − RC ( dVin / dt )

---

Key Result

Output voltage is proportional to the derivative of input voltage.

---

Waveform Behavior

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

---

Applications

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

---

GATE Important Points

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