Basic Electrical Concepts

• Electric charge, current, and voltage
• Power and energy relationships
• Ideal vs. real circuit elements
• Sign conventions and reference directions
• Ohm's Law and its applications

Circuit Elements

• Resistors (fixed, variable, nonlinear)
• Independent voltage and current sources
• Dependent (controlled) sources (VCVS, VCCS, CCVS, CCCS)
• Switches and ideal components

Basic Circuit Analysis

• Series and parallel resistor combinations
• Voltage and current division
• Equivalent resistance concepts
• Simple resistive circuits
• Power calculations in DC circuits

Fundamental Laws

• Kirchhoff's Current Law (KCL)
• Kirchhoff's Voltage Law (KVL)
• Node and mesh identification
• Writing circuit equations systematically

Circuit Analysis Techniques

• Nodal analysis (node-voltage method)
• Mesh analysis (mesh-current method)
• Supernodes and supermeshes
• Circuits with dependent sources
• Selecting the best analysis method

Network Theorems

• Linearity and superposition
• Source transformations
• Thévenin's theorem
• Norton's theorem
• Maximum power transfer theorem
• Millman's theorem
• Substitution and reciprocity theorems

Capacitors

• Capacitance and capacitor construction
• i-v relationships for capacitors
• Energy storage in capacitors
• Series and parallel combinations
• Capacitor behavior with DC and time-varying signals

Inductors

• Inductance and inductor construction
• i-v relationships for inductors
• Energy storage in inductors
• Series and parallel combinations
• Mutual inductance and coupling

First-Order Circuits

• RC circuits: natural and step responses
• RL circuits: natural and step responses
• Time constants and transient behavior
• Sequential switching in first-order circuits
• Initial conditions and final values

Second-Order Circuits

• RLC circuit configurations
• Characteristic equations
• Overdamped, critically damped, and underdamped responses
• Natural frequency and damping ratio
• Complete response (natural + forced)

Sinusoidal Signals

• Sinusoidal functions and their properties
• Phase relationships
• RMS values and average power
• Leading and lagging concepts

Phasor Analysis

• Complex numbers review
• Phasor representation of sinusoids
• Impedance and admittance concepts
• Phasor diagrams
• Converting between time and frequency domains

AC Steady-State Analysis

• Impedance combinations (series/parallel)
• Nodal and mesh analysis with phasors
• AC circuit theorems (Thévenin, Norton, superposition)
• AC power calculations

AC Power

• Instantaneous power
• Average (real) power
• Reactive power
• Complex power and power triangle
• Apparent power and power factor
• Power factor correction
• Maximum power transfer in AC circuits

Magnetically Coupled Circuits

• Mutual inductance theory
• Dot convention
• Analysis of coupled coils
• Ideal transformers
• Linear and autotransformers
• Reflected impedance

Three-Phase Circuits

• Three-phase voltage generation
• Balanced wye and delta connections
• Phase and line quantities
• Three-phase power calculations
• Unbalanced three-phase systems
• Power measurement in three-phase systems

Frequency Response

• Transfer functions
• Bode plots (magnitude and phase)
• Resonance in series and parallel RLC circuits
• Quality factor and bandwidth
• Filter concepts (lowpass, highpass, bandpass, bandstop)
• Active filters vs. passive filters

Two-Port Networks

• Two-port parameters (Z, Y, h, g, ABCD)
• Interconnections of two-port networks
• Conversions between parameter sets
• Applications in modeling and analysis

Laplace Transform Methods

• Laplace transform fundamentals
• Circuit analysis in s-domain
• Transfer functions and poles/zeros
• Initial and final value theorems
• Inverse Laplace transforms
• Convolution and circuit response

Fourier Analysis

• Fourier series for periodic signals
• Fourier transform
• Frequency spectrum analysis
• Circuit response to non-sinusoidal inputs
• Harmonic analysis

State-Space Methods

• State variables and state equations
• State-space representation of circuits
• Solution of state equations
• Transfer function from state-space models

Network Topology

• Graph theory applied to circuits
• Trees and cotrees
• Fundamental cutsets and loops
• Systematic equation formulation

Analysis Techniques

Manual Analysis Methods

• Nodal analysis algorithm
• Mesh analysis algorithm
• Modified nodal analysis (MNA)
• Tableau analysis
• Loop analysis
• Cutset analysis

Simplification Techniques

• Delta-wye (Δ-Y) transformations
• Wye-delta (Y-Δ) transformations
• Source transformation algorithm
• Thévenin equivalent calculation procedure
• Norton equivalent calculation procedure
• Series-parallel reduction

Computational Methods

• Matrix formulation of circuit equations
• Gaussian elimination for circuit matrices
• LU decomposition
• Sparse matrix techniques
• Iterative solution methods (Gauss-Seidel, Jacobi)

Simulation and CAD Tools

Circuit Simulators

SPICE (Simulation Program with Integrated Circuit Emphasis)

• PSpice (commercial variant)
• LTspice (free from Analog Devices)
• ngspice (open-source)

Other Simulators

• Multisim (National Instruments)
• Proteus Design Suite
• MATLAB/Simulink with Simscape Electrical
• Cadence OrCAD
• Altium Designer

Analysis Tools

• DC operating point analysis
• AC analysis (frequency sweep)
• Transient analysis (time-domain)
• Fourier analysis
• Monte Carlo analysis
• Worst-case analysis
• Sensitivity analysis
• Noise analysis

Design and Visualization Tools

• CircuitLab (web-based)
• Falstad Circuit Simulator (web-based, educational)
• TINA-TI (Texas Instruments)
• KiCad (open-source PCB design)
• EasyEDA
• Mathematica for symbolic circuit analysis

Mathematical Tools

Software Packages

• MATLAB (symbolic and numerical computation)
• Python with libraries:
  • NumPy for numerical analysis
  • SciPy for scientific computing
  • SymPy for symbolic mathematics
  • PySpice for circuit simulation
  • Lcapy for linear circuit analysis
• Maple (symbolic computation)
• Mathematica (symbolic computation)