# Electronics Fundamentals/Electronic Oscillator/Sinusoidal Wave Oscillator

## Sinusoidal Wave Oscillator

Sinusoidal Wave Oscillator is an Electronics device that generate Sinusoidal Wave Oscillation

### Configuration

LC connected in series has the capability to generate Sinusoidal Wave Oscillation at equilibrium

### Mathematical Analysis

$L \frac{d}{dt} i + \frac{1}{C} \int i dt = 0$
$\frac{d}{dt} i + \frac{1}{LC} \int i dt = 0$
$s^2 + \frac{1}{LC} = 0$
$s = \pm j \sqrt{\frac{1}{LC}} t$
$s = \pm j \omega t$
$i = e^(j \omega t) + e^(-j \omega t)$
$i = A Sin \omega t$

## Summary

LC series has the capabilty to generate oscillation of sinusoidal wave oscillate at frequency

$\omega = \sqrt{\frac{1}{LC}}$