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

$f(t)=Ae^{(}-{\frac {t}{T}})$

$A=e^{c}$

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

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

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