Circuit Analysis Tutorials
Free, in-depth guides covering the fundamentals of circuit analysis. Written at the undergraduate ECE level with worked examples and equations you can verify in the CircuitMath editor.
Fundamentals
Kirchhoff's Voltage Law (KVL): Complete Guide
Learn KVL from first principles: sign conventions, step-by-step mesh examples, common mistakes, and how CircuitMath automates loop equations.
FundamentalsKirchhoff's Current Law (KCL): Complete Guide
Master KCL: conservation of charge, node equations, supernodes, and a step-by-step 4-node worked example.
FundamentalsOhm's Law and Circuit Elements in the s-Domain
Review Ohm's law, understand impedance of R, L, and C in the Laplace domain, and see why s-domain analysis simplifies circuit solving.
FundamentalsVoltage Divider Equation: Derivation and Applications
Derive the voltage divider from KVL and Ohm's law, understand loading effects, and explore biasing and sensing applications.
FundamentalsCurrent Divider Equation: Derivation and Examples
Understand the current divider rule from KCL, derive multi-branch formulas, and learn when current division is most useful.
FundamentalsSuperposition Theorem: Principle and Worked Examples
Learn the superposition theorem for linear circuits: how to kill sources, solve independently, and sum results, with a complete two-source example.
Analysis Methods
Nodal Analysis Step by Step
A complete guide to nodal analysis: identify nodes, choose a ground, write KCL equations, handle voltage sources with supernodes, and solve.
Analysis MethodsMesh Analysis Step by Step
Master mesh analysis: define mesh currents, write KVL equations, handle current sources with supermeshes, and solve a complete example.
Analysis MethodsModified Nodal Analysis (MNA): The Algorithm Behind Circuit Solvers
Understand how MNA extends nodal analysis to handle voltage sources, learn the stamp approach, and see how CircuitMath builds the A*x = z system.
Analysis MethodsTransfer Functions in Circuit Analysis
Learn what H(s) represents, how to derive transfer functions from nodal analysis, identify poles and zeros, and work through an RC example.
Amplifiers
BJT Small-Signal Model: Hybrid-Pi Explained
Understand the hybrid-pi model for NPN and PNP BJTs: r_pi, g_m, r_o, and how CircuitMath substitutes them automatically.
AmplifiersMOSFET Small-Signal Model for Circuit Analysis
Learn the MOSFET small-signal equivalent circuit: g_m, r_o, and how to analyze common-source, common-gate, and common-drain configurations.
AmplifiersCommon Emitter Amplifier: Gain, Input and Output Impedance
Analyze the common emitter amplifier step by step using the hybrid-pi model, deriving voltage gain, input impedance, and output impedance.
AmplifiersCommon Source Amplifier: Analysis and Design
Step-by-step analysis of the common source MOSFET amplifier: small-signal gain, impedance, and the effect of source degeneration.
AmplifiersCascode Amplifier: Analysis and Design
Analyze the cascode amplifier configuration: improved bandwidth, higher output impedance, and step-by-step small-signal analysis.
Filters
RC Low-Pass Filter: Transfer Function and Frequency Response
Derive the RC low-pass filter transfer function, find the cutoff frequency, and plot the Bode magnitude and phase.
FiltersRL High-Pass Filter: Analysis and Applications
Analyze the RL high-pass filter circuit, derive H(s), and compare with the RC high-pass topology.
FiltersRLC Resonance: Series and Parallel Circuits
Understand resonance in RLC circuits: resonant frequency, quality factor, bandwidth, and impedance behavior at resonance.
Practical Topics
Thevenin and Norton Equivalent Circuits
Find Thevenin and Norton equivalents step by step: open-circuit voltage, short-circuit current, and equivalent resistance.
Practical TopicsDependent Sources in Circuit Analysis
Learn how VCVS, VCCS, CCVS, and CCCS dependent sources change nodal and mesh analysis, with worked examples.
Practical TopicsHow to Read Circuit Schematics: A Beginner Guide
Learn to read schematic diagrams: component symbols, node connections, reference designators, and how to trace current paths.
Practical TopicsHow to Use CircuitMath: Getting Started Guide
A step-by-step guide to using the CircuitMath editor: drawing circuits, adding components, running analysis, and reading results.
Practical TopicsUsing LaTeX Circuit Equations for Homework
Learn how to copy CircuitMath LaTeX equations into your homework, lab reports, and technical documents.