RLC電路中的諧振

The Impedance of serial RLC circuit:
$$Z_m = R_m + j\omega L_m + {1\over j\omega C_m}$$

$$= R_m + j(\omega L_m - {1\over \omega C_m})$$

The resonance frequency ($f_r$):
$$ f_r = {1\over 2\pi \sqrt {L_mC_m}} (Hz) $$

Quality factor (Q):
$$ Q = {\omega_r L_m\over R_m} = {1\over {\omega_r C_mR_m}} $$
$$ = {1\over R_m}\sqrt{L_m\over C_m} = \frac{{\omega}_r}{BW} $$
$BW$: bandwidth

The Impedance of parallel RLC circuit:
$$Y_p = G_p+{1\over j\omega L_p}+j\omega C_p$$
$$Z_p = {1\over Y_p} = {{\frac{1}{R_p} - j(\omega C_p - {1\over \omega L_p})}\over {{\frac{1}{R_p}}^2 + (\omega C_p - {1\over \omega L_p})^2}}$$

The resonance frequency ($f_r$):
$$ f_r = {1\over 2\pi \sqrt {L_pC_p}} (Hz) $$

Quality factor (Q):
$$ Q = {R_p\over {\omega_r L_p}} = {\omega_r C_pR_p} $$
$$ = R_p\sqrt{C_p\over L_p} = \frac{{\omega}_r}{BW} $$
$BW$: bandwidth