// fundamentals track
Fundamentals
Build the foundation. Circuits, math, physics, components.
Math Foundations
The mathematical language of circuits. Complex numbers are essential for AC analysis, trig for waveforms and phasors. Revisit if your fundamentals are shaky — everything builds on this.
- Manipulate complex numbers in rectangular and polar form
- Apply trig identities to simplify expressions
- Perform vector operations
- Complex numbers
- Trig identities
- Unit conversions
How circuits change over time. Derivatives describe capacitor/inductor behavior, integrals calculate energy and charge. Differential equations model real circuit dynamics.
- Differentiate and integrate common functions
- Solve first-order differential equations
- Apply calculus to analyze changing quantities
- Differentiation
- Integration
- ODEs
Enables systematic circuit analysis. Matrix methods solve complex multi-loop circuits, eigenvalues appear in stability analysis. Critical for signals, systems, and control theory later.
- Perform matrix operations and find inverses
- Solve systems of linear equations
- Calculate and interpret eigenvalues
- Matrix operations
- Determinants
- Eigenvalues
Circuit Fundamentals
Your first real circuits. Master voltage, current, and resistance relationships. Kirchhoff's laws let you analyze any circuit; Thevenin/Norton simplify complex networks into simple equivalents.
- Apply Ohm's law to calculate V, I, R
- Use KVL and KCL to analyze multi-loop circuits
- Find Thevenin and Norton equivalents
- Calculate power dissipation
- Ohm's Law
- KVL & KCL
- Thevenin & Norton
Real-world power is AC. Phasors turn differential equations into algebra, impedance extends Ohm's law to capacitors and inductors. Foundation for power systems and signal processing.
- Convert time-domain signals to phasors
- Calculate impedance of RLC combinations
- Analyze resonant circuits
- Calculate real, reactive, and apparent power
- Phasors
- Impedance
- Resonance
- Power factor
Electromagnetism
Understand how charges create fields and how fields create forces. Coulomb's law, electric potential, and capacitance all stem from this. Essential for understanding how capacitors store energy.
- Calculate electric field from charge distributions
- Relate electric potential to field
- Apply Gauss's law to symmetric geometries
- Calculate capacitance of simple structures
- Coulomb's law
- Electric potential
- Gauss's law
Magnetic forces drive motors, Faraday's law explains transformers and generators. Inductance is just stored magnetic energy.
- Calculate magnetic force on moving charges and currents
- Apply Faraday's law to find induced EMF
- Use Lenz's law to determine induced current direction
- Calculate inductance of simple geometries
- Magnetic force
- Faraday's law
- Lenz's law
- Inductance
The complete picture — four equations that unify all electromagnetic phenomena. Essential for RF, antennas, and understanding why circuits behave differently at high frequencies.
- State Maxwell's equations in differential and integral form
- Derive the electromagnetic wave equation
- Explain how changing E-fields create B-fields and vice versa
- Differential form
- Integral form
- Wave equation
Passive Components
The simplest component, but details matter. Learn to read color codes, choose appropriate power ratings, and understand tolerance. Know when to use precision vs. general-purpose.
- Read resistor values from color codes
- Calculate power dissipation and select appropriate wattage
- Choose resistors based on tolerance requirements
- Understand SMD package sizes
- Color codes
- Power ratings
- Resistor types
Store energy in electric fields. Different types (ceramic, electrolytic, film) have different behaviors — ESR affects filtering, voltage ratings prevent explosions. Decoupling is an art.
- Select appropriate capacitor type for application
- Understand ESR and its effect on performance
- Design basic decoupling and filtering circuits
- Read capacitor markings and datasheets
- Capacitance
- Dielectrics
- Capacitor types
Store energy in magnetic fields. Saturation limits current handling, mutual inductance enables transformers. Turns ratio determines voltage transformation in power supplies.
- Calculate inductance and stored energy
- Understand core saturation and its limits
- Apply transformer turns ratio for voltage conversion
- Select inductors for filtering applications
- Inductance basics
- Core materials
- Inductor types
First step into semiconductors. One-way current flow enables rectification (AC→DC). Zener diodes regulate voltage, LEDs convert current to light. The PN junction concept underlies all semiconductors.
- Analyze circuits with forward/reverse biased diodes
- Design basic rectifier circuits
- Use Zener diodes for voltage regulation
- Calculate LED current limiting resistors
- PN junction
- Diode characteristics
- Diode types
Measurements & Lab
Your most-used tool. Measures voltage, current, resistance — but technique matters. Learn proper probe placement, when to use AC vs DC ranges, and how to safely measure current in-circuit.
- Measure DC and AC voltage accurately
- Measure current without blowing fuses
- Test resistance and continuity
- Identify common measurement errors
- Voltage measurement
- Current measurement
- Resistance measurement
- Diode and continuity
See what's actually happening. Voltage vs. time reveals signal integrity, noise, and timing issues invisible to multimeters. Master triggering to capture the waveform you need.
- Set up timebase and vertical scale appropriately
- Use triggering to capture stable waveforms
- Measure frequency, amplitude, and rise time
- Identify signal integrity issues
- Time domain basics
- Probes
- Measurements
Rapid prototyping without soldering. Understand the internal connections, keep wires short and organized. Most debugging is just finding the loose connection or wrong row.
- Understand breadboard internal connections
- Build organized, debuggable circuits
- Identify and fix common breadboard issues
- Know breadboard limitations (current, frequency)
- Breadboard layout
- Wiring techniques
- Common problems
- Prototyping workflow
Permanent connections done right. Good joints are shiny and concave. Learn proper iron temperature, flux usage, and desoldering for mistakes. SMD opens up modern component access.
- Create reliable through-hole solder joints
- Identify and fix cold joints
- Desolder components without damage
- Attempt basic SMD soldering
- Iron tips
- Flux
- Desoldering
- SMD basics
// topic connections