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)	Ae^λ₁t + Be^λ₂t	Ae^λ₁t + Be^λ₂t	Ae^λ₁t + Be^λ₂t
Damping Factor	$\zeta$	$\zeta ={R \over 2L}$	$\zeta ={1 \over 2RC}$
Resonant Frequency	$\omega _{o}$	$\omega _{o}={1 \over {\sqrt {LC}}}$	$\omega _{o}={1 \over {\sqrt {LC}}}$
Band Width	$\Delta \omega =2\zeta$	${R \over L}$	${1 \over CR}$
Quality factor	$Q={\omega _{o} \over \Delta \omega }={\omega _{o} \over 2\zeta }$	$Q={L \over R{\sqrt {LC}}}={1 \over R}{\sqrt {L \over C}}$	$Q={CR \over {\sqrt {LC}}}={R}{\sqrt {C \over L}}$

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