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

$\frac{d^2}{d{t}^2}f(t)+\alpha \frac{d}{dt}f(t)+\beta =0$

• 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

$\omega =\sqrt{\frac{1}{LC}}atI=\frac{V}{R}$

$\delta \omega ={\omega }_2-{\omega }_{1}atI=\frac{V}{2R}$