Electrical engineering
Magnetism, motors, control
Faraday, motors, filters, feedback.
Basics
Electromagnetic induction
A changing flux through a coil induces an emf. Lenz: induced current opposes the change. Generators and (AC) transformers use this. Motors: a current in a magnetic field feels F=Iℓ×B.
Filters
RC low-pass: capacitor to ground bypasses highs. High-pass: capacitor in series. At the cutoff, power is halved (−3 dB). LC resonance can select more sharply.
Feedback
Negative feedback stabilizes gain and improves distortion and bandwidth (op-amps). Oscillation when loop gain is 1 with the right phase. PID control uses proportional, integral, and derivative of error.
Formulas
Faraday's law
N turns, flux Φ. The sign is Lenz.
Symbols
-
ℰinduced emf -
Φ_Bmagnetic flux (Wb)
Lorentz force (wire)
Maximum when I and B are perpendicular. Start of motor torque.
Symbols
-
Bmagnetic field (T)
RC cutoff
Frequency where |V_out/V_in| is 1/√2.
Symbols
-
f_ccutoff frequency
Non-inverting gain (ideal)
Ideal op-amp with negative feedback. Input current ≈0, differential voltage ≈0.
Symbols
-
R_ffeedback resistor -
R_gground-leg resistor
In this field
DC circuits
Ohm, Kirchhoff, series/parallel, power.
Capacitors, inductors, AC
Charge/discharge, reactance, impedance, resonance.
Power, semiconductors, digital
Transformers, three-phase, diodes, gates.
Signals and logic
Fourier sketch, sampling, Boolean algebra.
Semiconductors
Carriers, diodes, a MOSFET sketch.
Measurements and electrical safety
Multimeters, RMS versus peak, transformer ratio, and electrical safety.
Op-amps and filters
The ideal op-amp, inverting and non-inverting gain, RC low- and high-pass, cutoff frequency.
Digital logic
Boolean algebra, gates, flip-flops, and timing.
Three-phase power
Line versus phase, Y and Δ, √3 power, and a motor sketch.
Batteries and photovoltaics
Capacity and C-rate, series/parallel packs, PV I–V curves, and the maximum-power point.