Practical Electronics/Series RLC

Summary

Network	Symbol	Series RLC
Network
Impedance	Z	$Z=(j\omega )^{2}+(j\omega ){\frac {R}{L}}+{\frac {1}{LC}}$
Roots	λ	$\lambda =0.I=e^{-}\alpha t$ $\lambda >0.I=e^{-}\alpha t[e^{\omega }t+e^{\omega }t$ $I=e^{-}alphat[e^{j}\omega t+e^{-}j\omega t$
I(t)	I	Ae^λ₁t + Be^λ₂t
Damping Factor	$\zeta$
Resonant Frequency	$\omega _{o}$
Band Width	$\Delta \omega =2\zeta$
Quality factor	$Q={\omega _{o} \over \Delta \omega }={\omega _{o} \over 2\zeta }$	$Q={L \over R{\sqrt {LC}}}={1 \over R}{\sqrt {L \over C}}$

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