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

Multiply by j is rotation

Complex rotation

Euler’s formula

Magnitude of a complex exponential

Complex exponentials spin

Euler’s sine

Euler’s cosine

Euler’s sine and cosine

AC superposition


Impedance vs frequency

ELI the ICE man

Impedance of simple networks

KVL in the frequency domain