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Circuits 1

Title: Circuits 1 Audience: College students majoring in electrical engineering or computer science Credits: 4 (3 lecture hours, 3 laboratory hours per week)

Course Description

This course provides a comprehensive introduction to analog electrical systems with particular emphasis on audio circuits and signals. Students explore the fundamental principles governing electrical circuit behavior through both theoretical analysis and hands-on laboratory experimentation.

The course bridges mathematical foundations with practical applications, using audio systems as a unifying theme. Students learn to analyze circuits in both time and frequency domains, developing intuition for how components like resistors, capacitors, and inductors shape electrical signals. The operational amplifier (op-amp) serves as a gateway to active circuit design, enabling students to build functional audio processing circuits.

Laboratory work reinforces theoretical concepts through construction and measurement of real circuits. Students gain proficiency with oscilloscopes, function generators, and spectrum analyzers while building audio amplifiers, filters, and signal processing circuits.

Prerequisites

Students should have completed:

  • Introduction to calculus (derivatives and integrals)
  • Basic algebra including complex number operations
  • Fundamental physics covering electricity and magnetism (recommended)

Topics Covered

Foundational Concepts

  • Voltage, current, and power in electrical circuits
  • Resistance and Ohm's Law
  • Series and parallel circuit configurations
  • Voltage and current dividers
  • Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL)
  • Node voltage and mesh current analysis methods
  • Thevenin and Norton equivalent circuits
  • Maximum power transfer theorem

Reactive Components

  • Capacitance: physical principles, energy storage, and transient behavior
  • Inductance: magnetic field storage, mutual inductance basics
  • RC and RL circuit transient analysis
  • Time constants and exponential responses

AC Circuit Analysis

  • Sinusoidal steady-state analysis
  • Complex numbers and their application to circuit analysis
  • Phasors and phasor diagrams
  • Impedance and admittance
  • AC power: instantaneous, average, and reactive power
  • Power factor and its significance in audio systems

Frequency Domain Analysis

  • Introduction to Fourier Series for periodic signals
  • Harmonic content of audio signals
  • Transfer functions and frequency response
  • Bode plots: magnitude and phase representations
  • Resonance in RLC circuits
  • Quality factor (Q) and bandwidth

Filter Networks

  • Low-pass filter design and applications
  • High-pass filter design and applications
  • Band-pass and band-reject filters
  • Bass and treble tone control circuits
  • Filter order and roll-off characteristics

Operational Amplifiers

  • Ideal op-amp model and assumptions
  • Inverting and non-inverting amplifier configurations
  • Voltage followers and buffer circuits
  • Summing amplifiers for audio mixing
  • Differential amplifiers
  • Integrator and differentiator circuits
  • Op-amp frequency limitations and slew rate

Audio Applications

  • Audio signal characteristics and specifications
  • Preamplifier design for low-level signals
  • Power amplifier basics
  • Distortion: harmonic and intermodulation
  • Signal-to-noise ratio considerations

Topics Not Covered

The following topics are beyond the scope of this introductory course and are typically covered in subsequent courses:

  • Digital circuits and logic design - covered in Digital Systems courses
  • Semiconductor physics - covered in Electronics I
  • Transistor-level amplifier design (BJT, FET circuits) - covered in Electronics I
  • Advanced filter design (Butterworth, Chebyshev, elliptic) - covered in Signal Processing
  • Complete Fourier Transform theory - covered in Signals and Systems
  • Laplace Transform methods - covered in Circuits II or Signals and Systems
  • Transmission lines and RF circuits - covered in Electromagnetics
  • Power electronics and switching converters - covered in Power Electronics
  • Control systems and feedback stability - covered in Control Systems
  • Microcontroller interfacing - covered in Embedded Systems
  • PCB design and layout - covered in Electronics Lab II
  • Three-phase power systems - covered in Power Systems

Learning Objectives

Upon successful completion of this course, students will be able to:

Remember (Recall facts and basic concepts)

  1. Define voltage, current, resistance, capacitance, and inductance with correct units
  2. State Kirchhoff's Voltage Law and Kirchhoff's Current Law
  3. List the characteristics of an ideal operational amplifier
  4. Identify the symbols for common circuit components (resistors, capacitors, inductors, op-amps)
  5. Recall the relationships between frequency, period, and angular frequency
  6. State the formulas for series and parallel combinations of resistors, capacitors, and inductors

Understand (Explain ideas or concepts)

  1. Explain the physical meaning of impedance in AC circuits
  2. Describe how capacitors and inductors store energy differently
  3. Interpret Bode plots to determine filter characteristics
  4. Explain the concept of resonance in RLC circuits and its significance
  5. Describe the relationship between time domain and frequency domain representations
  6. Explain why power factor matters in AC power systems
  7. Describe how harmonic distortion affects audio signal quality
  8. Explain the role of negative feedback in op-amp circuits

Apply (Use information in new situations)

  1. Apply Kirchhoff's laws to solve for unknown voltages and currents in DC circuits
  2. Calculate the time constant and transient response of RC and RL circuits
  3. Use phasor analysis to solve AC circuit problems
  4. Apply complex impedance methods to analyze circuits with multiple reactive components
  5. Design inverting and non-inverting amplifiers to achieve specified gain
  6. Calculate the cutoff frequency of first-order RC filters
  7. Use Thevenin's theorem to simplify complex circuits
  8. Apply superposition to analyze circuits with multiple sources

Analyze (Draw connections among ideas)

  1. Analyze the frequency response of filter circuits to predict behavior across the audio spectrum
  2. Determine the harmonic content of periodic waveforms using Fourier Series
  3. Analyze op-amp circuits to identify gain, input impedance, and output characteristics
  4. Compare the performance of different filter topologies for a given application
  5. Analyze measurement data to characterize circuit behavior and identify deviations from ideal models
  6. Distinguish between different types of distortion in audio amplifier circuits
  7. Analyze the trade-offs between bandwidth, gain, and stability in amplifier design

Evaluate (Justify a decision or course of action)

  1. Evaluate component selections based on tolerance, power rating, and cost constraints
  2. Assess whether a circuit design meets specified performance requirements
  3. Critique measurement techniques and identify sources of experimental error
  4. Evaluate the suitability of different op-amp configurations for specific audio applications
  5. Judge the adequacy of a filter design for removing unwanted frequency components
  6. Assess the impact of non-ideal component behavior on circuit performance

Create (Produce new or original work)

  1. Design a complete bass/treble tone control circuit meeting specified frequency response requirements
  2. Construct and test a functional audio preamplifier from component-level specifications
  3. Develop a measurement procedure to characterize amplifier distortion
  4. Create circuit simulations to verify theoretical predictions before laboratory construction
  5. Design a multi-stage audio signal processing chain incorporating amplification and filtering
  6. Build and document a working audio project integrating multiple concepts from the course

Assessment Methods

  • Weekly problem sets (25%)
  • Two midterm examinations (25%)
  • Final examination (15%)
  • Final project (10%)

Required Materials

  • Computer with Chrome or FireFox web browser
  • Access to a generative AI tool as Claude Code