Practical Electronics/Parallel RLC

Summary

Network	Symbol	Series RLC	Paralle RLC
Network			200
Impedance	Z	$Z = (j\omega)^2 + (j\omega)\frac{R}{L} + \frac{1}{LC}$	$Z = (j\omega)^2 + (j\omega) \frac{1}{RC} + \frac{1}{LC}$
Roots	λ	λ = $- \zeta \pm \sqrt{\zeta^2 - \omega_o^2}$	λ = $- \zeta \pm \sqrt{\zeta^2 - \omega_o^2}$
I(t)	Aeλ1t + Beλ2t	Aeλ1t + Beλ2t	Aeλ1t + Beλ2t
Damping Factor	$\zeta$	$\zeta = {R \over 2L}$	$\zeta = {1 \over 2RC}$
Resonant Frequency	$\omega_o$	$\omega_o = {1 \over \sqrt{L C}}$	$\omega_o = {1 \over \sqrt{L C}}$
Band Width	$\Delta \omega = 2 \zeta$	${ R \over L}$	${ 1 \over CR}$
Quality factor	$Q = {\omega_o \over \Delta \omega } = {\omega_o \over 2\zeta }$	$Q = {L \over R \sqrt{LC}} = {1 \over R} \sqrt{L \over C}$	$Q = {CR \over \sqrt{LC}} = {R} \sqrt{C \over L}$