Solving circuits with differential equations is a pain. If we impose a discipline on ourselves and only consider input signals that look like sinusoids, a whole new method of AC analysis emerges.

AC analysis introduction part 1

AC analysis introduction part 2

Trigonometry review

Sine and cosine come from circles

Sine of time

Sine and cosine come from a rotating vector

Lead and Lag

Complex numbers

Multiplying by j is rotation

Complex rotation

Euler’s formula

Magnitude of a complex exponential

Complex exponentials spin

Euler’s sine wave

Euler’s cosine wave

AC superposition


Impedance vs frequency

ELI the ICE man

Impedance of simple networks

KVL in the frequency domain