RLC circuit
An RLC circuit is a Resistor, an Inductors, and a Capacitor in series with an electromotive force.
Effective impedance
- Xout=RL+XC+XL=RL+1iωC+iωL
- |Xout|=√[RL+i(−1ωC+ωL)][R−i(−1ωC+ωL)]∗
- =√R2L+(ωL−1ωC)2
Gain
Loop Theorem
- Vin=I(R+Xout)
Voltage Divider
- VAB=Vout=XoutR+XoutVin
- |VoutVin|=√[XoutR+Xout][XoutR+Xout]∗
RL+i(ωL−1ωC)
- |VoutVin|=√[RL+i(ωL−1ωC)R+RL+i(ωL−1ωC)][RL+i(ωL−1ωC)R+RL+i(ωL−1ωC)]∗
- =√R2L+(ωL−1ωC)2(R+RL)2+(ωL−1ωC)2
- =√R2L+(ω2LC−1ωC)2(R+RL)2+(ωL−1ωC)2
Phase shift