Physics

Operational Amplifiers: Theory and Design

A rigorous study of Operational Amplifiers for engineering students, covering ideal theory, non-ideal characteristics, frequency response, linear/non-linear applications, active filters, and oscillators.

Skill focus

Derive transfer functions for complex active circuits
Analyze frequency response and stability using Gain-Bandwidth Product
Design active filters (Butterworth, Chebyshev) to specific requirements
Implement non-linear signal processing circuits (Precision Rectifiers, Log Amps)
Design sinusoidal oscillators using Barkhausen criteria

Lesson map

Progress through the sequence or jump to any lesson. Estimated total time: 530 minutes.

Progress: 0/5 (0%)

INTERACTIVECore90 min
Module 1: Ideal vs. Practical Op-Amps
Moving beyond the ideal model to understand real-world limitations essential for precision design.
Learning objectives
- Contrast ideal parameters with practical datasheets (741, TL071, OP07)
- Model input offset voltage ($V_{os}$), input bias current ($I_B$), and offset current ($I_{os}$)
- Analyze the effect of finite Open-Loop Gain ($A_{OL}$) on closed-loop error
Guided steps
1. read20 min
  Activity: Datasheet Comparison
2. read25 min
  Derivation: Finite Gain Error
Prereq: Circuit Analysistheorymodelingerror analysis
INTERACTIVECore100 min
Module 2: Frequency Response & Slew Rate
Analyzing how Op-Amps behave at high frequencies and the trade-off between Gain and Bandwidth.
Learning objectives
- Understand the dominant pole approximation and internal compensation
- Calculate Bandwidth using Gain-Bandwidth Product (GBP)
- Analyze Slew Rate ($SR$) limitations for large signal applications
Guided steps
1. quiz15 min
  Problem: Power Bandwidth
2. lab30 min
  Lab: Slew Rate Distortion
  Observe triangular distortion on a sine wave.
Prereq: Bode PlotsPrereq: Laplace Transformsac analysisstabilitybandwidth
INTERACTIVEChallenge120 min
Module 3: Linear Computational Circuits
Using Op-Amps to perform mathematical operations: Addition, Subtraction, Integration, and Differentiation.
Learning objectives
- Design Summing and Difference Amplifiers for signal mixing
- Analyze Instrumentation Amplifiers for low-noise measurement
- Design Integrators and Differentiators with stability compensation
Guided steps
1. read40 min
  Derivation: Instrumentation Amp
2. project45 min
  Design Project: Analog PID Controller
  Complete design of an analog PID controller for process control.
Prereq: eng-intro-ideal-practicalmathinstrumentationanalog computing
VIDEOChallenge100 min
Module 4: Active Filter Topologies
Design of frequency-selective circuits using Op-Amps to eliminate loading effects and provide gain.
Learning objectives
- Compare Active vs. Passive filters (Loading effect, Gain)
- Design First-Order Low-Pass and High-Pass filters
- Design Second-Order Sallen-Key filters (Butterworth, Chebyshev)
- Analyze filter response using Bode Plots
Guided steps
1. project60 min
  Design Project: 2nd Order Butterworth LPF
2. lab30 min
  Lab: Bode Plot Analysis
  Simulate frequency response.
Prereq: eng-frequency-responsePrereq: Complex NumbersfiltersSallen-KeyButterworth
VIDEOChallenge120 min
Module 5: Precision Rectifiers & Oscillators
Advanced applications involving non-linear feedback and positive feedback for signal generation.
Learning objectives
- Analyze Precision Half-Wave and Full-Wave Rectifiers
- Understand the Barkhausen Criteria for oscillation
- Analyze RC Phase Shift and Wein Bridge Oscillators
Guided steps
1. read40 min
  Derivation: Wein Bridge Beta
2. quiz15 min
  Quiz: Oscillation Theory
Prereq: eng-linear-computationalPrereq: Feedback Theoryoscillatorsnonlinearrectifiers

Overview

Level: Advanced
Guided time: 900 min
Prerequisites: Circuit Analysis (Mesh/Nodal)Laplace TransformsSemiconductor PhysicsBode Plots
Keywords: #op-amp#operational amplifier#op amp#amplifier#analog electronics#feedback control#active filters#signal conditioning#instrumentation#741#LM358#TL081#circuit design#electronics

Skill focus

Derive transfer functions for complex active circuits

Analyze frequency response and stability using Gain-Bandwidth Product

Design active filters (Butterworth, Chebyshev) to specific requirements

Implement non-linear signal processing circuits (Precision Rectifiers, Log Amps)

Design sinusoidal oscillators using Barkhausen criteria

Lesson map

Progress through the sequence or jump to any lesson. Estimated total time: 530 minutes.

Progress: 0/5 (0%)

INTERACTIVECore90 min
Module 1: Ideal vs. Practical Op-Amps
Moving beyond the ideal model to understand real-world limitations essential for precision design.
Learning objectives
- Contrast ideal parameters with practical datasheets (741, TL071, OP07)
- Model input offset voltage ($V_{os}$), input bias current ($I_B$), and offset current ($I_{os}$)
- Analyze the effect of finite Open-Loop Gain ($A_{OL}$) on closed-loop error
Guided steps
1. read20 min
  Activity: Datasheet Comparison
2. read25 min
  Derivation: Finite Gain Error
Prereq: Circuit Analysistheorymodelingerror analysis
INTERACTIVECore100 min
Module 2: Frequency Response & Slew Rate
Analyzing how Op-Amps behave at high frequencies and the trade-off between Gain and Bandwidth.
Learning objectives
- Understand the dominant pole approximation and internal compensation
- Calculate Bandwidth using Gain-Bandwidth Product (GBP)
- Analyze Slew Rate ($SR$) limitations for large signal applications
Guided steps
1. quiz15 min
  Problem: Power Bandwidth
2. lab30 min
  Lab: Slew Rate Distortion
  Observe triangular distortion on a sine wave.
Prereq: Bode PlotsPrereq: Laplace Transformsac analysisstabilitybandwidth
INTERACTIVEChallenge120 min
Module 3: Linear Computational Circuits
Using Op-Amps to perform mathematical operations: Addition, Subtraction, Integration, and Differentiation.
Learning objectives
- Design Summing and Difference Amplifiers for signal mixing
- Analyze Instrumentation Amplifiers for low-noise measurement
- Design Integrators and Differentiators with stability compensation
Guided steps
1. read40 min
  Derivation: Instrumentation Amp
2. project45 min
  Design Project: Analog PID Controller
  Complete design of an analog PID controller for process control.
Prereq: eng-intro-ideal-practicalmathinstrumentationanalog computing
VIDEOChallenge100 min
Module 4: Active Filter Topologies
Design of frequency-selective circuits using Op-Amps to eliminate loading effects and provide gain.
Learning objectives
- Compare Active vs. Passive filters (Loading effect, Gain)
- Design First-Order Low-Pass and High-Pass filters
- Design Second-Order Sallen-Key filters (Butterworth, Chebyshev)
- Analyze filter response using Bode Plots
Guided steps
1. project60 min
  Design Project: 2nd Order Butterworth LPF
2. lab30 min
  Lab: Bode Plot Analysis
  Simulate frequency response.
Prereq: eng-frequency-responsePrereq: Complex NumbersfiltersSallen-KeyButterworth
VIDEOChallenge120 min
Module 5: Precision Rectifiers & Oscillators
Advanced applications involving non-linear feedback and positive feedback for signal generation.
Learning objectives
- Analyze Precision Half-Wave and Full-Wave Rectifiers
- Understand the Barkhausen Criteria for oscillation
- Analyze RC Phase Shift and Wein Bridge Oscillators
Guided steps
1. read40 min
  Derivation: Wein Bridge Beta
2. quiz15 min
  Quiz: Oscillation Theory
Prereq: eng-linear-computationalPrereq: Feedback Theoryoscillatorsnonlinearrectifiers

Energy and Work

Explore conservation of energy through simulations and real-world applications.

Advanced400 mins guided

#work
#energy
#power
#conservation

View lesson map ->

Physics

Motion and Forces

Experiment with Newton's laws using real-time data visualization tools.

Intermediate450 mins guided

#forces
#acceleration
#vectors
#kinematics

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Overview

Level

Advanced

Guided time

900 min

Prerequisites

Circuit Analysis (Mesh/Nodal)Laplace TransformsSemiconductor PhysicsBode Plots

Keywords

#op-amp#operational amplifier#op amp#amplifier#analog electronics#feedback control#active filters#signal conditioning#instrumentation#741#LM358#TL081#circuit design#electronics

Operational Amplifiers: Theory and Design

Skill focus

Lesson map

Module 1: Ideal vs. Practical Op-Amps

Module 2: Frequency Response & Slew Rate

Module 3: Linear Computational Circuits

Module 4: Active Filter Topologies

Module 5: Precision Rectifiers & Oscillators

Related topics

Energy and Work

Motion and Forces

Overview

Operational Amplifiers: Theory and Design

Skill focus

Lesson map

Module 1: Ideal vs. Practical Op-Amps

Module 2: Frequency Response & Slew Rate

Module 3: Linear Computational Circuits

Module 4: Active Filter Topologies

Module 5: Precision Rectifiers & Oscillators

Related topics

Energy and Work

Motion and Forces

Overview