Electrical Circuit Analysis Course

Lesson 1 • Power and Energy in Circuits

Derives power from voltage and current and tracks energy flow. Links passive sign convention to power absorption and delivery.

Lesson 2 • Charge, Current, and Voltage

Defines fundamental electrical quantities and their physical meaning. Establishes the variable notation used throughout the course.

Lesson 3 • Ideal Circuit Elements

Introduces resistors, capacitors, inductors, and ideal sources as mathematical models. Connects element behaviour to real-world components.

Lesson 4 • Dependent Sources and Practical Models

Extends ideal sources to voltage- and current-controlled dependent sources. Prepares learners for transistor and amplifier circuit models.

Lesson 1 • Series and Parallel Resistor Combinations

Derives equivalent resistance for series and parallel networks. Enables circuit simplification before applying systematic analysis.

Lesson 2 • Node-Voltage Method

Formulates node-voltage equations using KCL at each essential node. Produces a compact matrix system solvable by linear algebra.

Lesson 3 • Mesh-Current Method

Formulates mesh-current equations using KVL around each mesh. Complements node-voltage method for planar circuit analysis.

Lesson 4 • Thévenin and Norton Equivalents

Reduces any linear two-terminal network to a single source and resistance. Enables load analysis without re-solving the full circuit.

Lesson 5 • Source Transformations and Linearity

Converts between Thévenin and Norton equivalent sources to simplify circuits. Introduces superposition as a consequence of circuit linearity.

Lesson 1 • Ideal Op-Amp Model

Defines infinite gain, infinite input impedance, and zero output impedance. Establishes the virtual short and virtual ground analysis rules.

Lesson 2 • Integrator and Differentiator Circuits

Replaces feedback resistor with capacitor to perform time-domain integration. Analyses differentiator topology and its noise sensitivity.

Lesson 3 • Practical Op-Amp Limitations

Introduces finite gain-bandwidth product, offset voltage, and slew rate. Bridges ideal analysis to real component selection and compensation.

Lesson 4 • Inverting and Non-Inverting Amplifiers

Derives closed-loop gain for both fundamental configurations using KCL. Connects gain expressions to resistor ratio selection.

Lesson 1 • Unbounded Response and Stability Concepts

Identifies conditions under which first-order circuits produce growing responses. Introduces BIBO stability as a design criterion.

Lesson 2 • Natural Response of RC and RL Circuits

Derives exponential decay from initial stored energy with no source. Defines time constant as the single parameter governing decay rate.

Lesson 3 • Capacitor and Inductor Review

Revisits energy storage element equations with emphasis on initial conditions. Connects stored energy to initial voltage and current values.

Lesson 4 • Sequential Switching and Initial Conditions

Handles circuits with multiple switching events and non-zero initial states. Applies continuity conditions to set correct initial values at each switch.

Lesson 1 • Second-Order Circuit Equations

Derives the second-order ODE for series and parallel RLC circuits. Identifies characteristic equation roots as the key to response classification.

Lesson 2 • Overdamped and Critically Damped Responses

Solves for real and repeated characteristic roots and their time-domain forms. Compares decay rates and settling behaviour across damping cases.

Lesson 3 • Step Response of Second-Order Circuits

Adds DC forcing to produce complete step response for all damping cases. Evaluates overshoot, rise time, and settling time from response parameters.

Lesson 4 • Underdamped Response and Oscillation

Solves for complex conjugate roots yielding damped sinusoidal oscillation. Defines damped natural frequency and envelope decay constant.

Lesson 1 • Power Factor Correction

Adds reactive compensation to bring power factor towards unity. Calculates required capacitor or inductor value for a target power factor.

Lesson 2 • Phasor Circuit Analysis Methods

Applies node-voltage and mesh-current methods to phasor-domain circuits. Solves for phasor voltages and currents, then converts back to time domain.

Lesson 3 • Impedance and Admittance

Derives complex impedance for R, L, and C elements in the phasor domain. Extends series and parallel combination rules to complex impedances.

Lesson 4 • Maximum Power Transfer in AC Circuits

Extends maximum power transfer theorem to complex source and load impedances. Derives conjugate matching condition for maximum average power.

Lesson 5 • Sinusoidal Sources and Phasor Representation

Defines amplitude, frequency, and phase of sinusoidal signals. Converts time-domain sinusoids to complex phasor notation.

Lesson 1 • Transfer Functions and Frequency Response

Defines the transfer function H(j) as the ratio of output to input phasors. Separates magnitude and phase responses for independent plotting.

Lesson 2 • Second-Order Passive Filters

Extends RLC resonance to band-pass and band-reject (notch) filter topologies. Relates Q factor to filter selectivity and bandwidth.

Lesson 3 • Bode Plot Construction

Builds asymptotic Bode plots from poles, zeros, and gain factors. Applies correction terms at corner frequencies for accurate sketches.

Lesson 4 • First-Order Passive Filters

Derives transfer functions for RC and RL low-pass and high-pass filters. Identifies cutoff frequency and roll-off rate from circuit parameters.

Lesson 1 • Partial Fraction Expansion and Inverse Transform

Decomposes rational s-domain expressions into partial fractions for inversion. Handles distinct, repeated, and complex conjugate pole cases.

Lesson 2 • Circuit Element Models in the s-Domain

Converts R, L, and C elements to s-domain impedances with initial condition sources. Enables direct application of KVL and KCL in the s-domain.

Lesson 3 • Laplace Transform Fundamentals

Defines the one-sided Laplace transform and its region of convergence. Builds a table of common transform pairs used in circuit analysis.

Lesson 4 • Convolution and System Response

Derives output as the convolution of input with impulse response in the time domain. Connects convolution to multiplication in the s-domain.

Lesson 5 • Transfer Functions, Poles, and Zeros

Defines the s-domain transfer function and locates poles and zeros in the complex plane. Connects pole locations to stability and transient response shape.