Practical Electronics/Parallel RLC

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Summary[edit]

Network Symbol Series RLC Paralle RLC
Network
RLC series circuit v1.svg
RLC parallel circuit v1.svg
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}