Electronics Handbook/Circuits/Summary of RLC Series

Normal
RL and RC both pocess the same character


 * Differential equation of first ordered in the form
 * $$\frac{d}{dt}f(t) + \frac{1}{T} = 0$$


 * Which can only has one real root in the form
 * $$f(t) = A e^(-\frac{t}{T})$$
 * $$A = e^c$$

LC and RLC both pocess the same character


 * Differential equation of second ordered in the form
 * $$\frac{d^2}{dt^2}f(t) + \alpha \frac{d}{dt}f(t) + \beta = 0$$


 * Which can only has one real root in the form
 * $$f(t) = A (e^\omega t +e^-\omega t ) $$
 * $$A = e^\alpha t$$
 * $$\omega = \sqrt{\alpha^2 - \beta^2}$$

Resonance
At resonance
 * LC will generate Oscillation of Standing Sin Wave of frequency
 * $$\omega = \sqrt{\frac{1}{LC}}$$


 * RLC will act as Resonant Tuned Selected Bandpass Filter
 * $$\omega = \sqrt{\frac{1}{LC}} at I = \frac{V}{R}$$
 * $$\delta \omega = \omega_2 - \omega_1 at I = \frac{V}{2R} $$