Practical Electronics/Parallel RLC

Summary

Network	Symbol	Series RLC	Parallel RLC
Network
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	$\zeta$	$\zeta =\frac{R}{2L}$	$\zeta =\frac{1}{2RC}$
Resonant Frequency	${\omega }_o$	${\omega }_o=\frac{1}{\sqrt{LC}}$	${\omega }_o=\frac{1}{\sqrt{LC}}$
Band Width	$\mathrm{\Delta }\omega =2\zeta$	$\frac{R}{L}$	$\frac{1}{CR}$
Quality factor	$Q=\frac{{\omega }_o}{\mathrm{\Delta }\omega }=\frac{{\omega }_o}{2\zeta }$	$Q=\frac{L}{R\sqrt{LC}}=\frac{1}{R}\sqrt{\frac{L}{C}}$	$Q=\frac{CR}{\sqrt{LC}}=R\sqrt{\frac{C}{L}}$