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)]∗
- \left | \frac{V_{out}}{V_{in}}\right | = \sqrt{\left [ \frac{R_L + i \left ( \omega L - \frac{1}{\omega C}\right)}{R + R_L + i \left ( \omega L - \frac{1}{\omega C}\right)}\right ]\left [ \frac{frac{R_L^2+ \left ( \omega L - \frac{1}{\omega C}\right)^2}{R + R_L + i \left ( \omega L - \frac{1}{\omega C}\right)}\right ]^*}
- \left | \frac{V_{out}}{V_{in}}\right | = \sqrt{ \frac{R_L^2+ \left ( \omega L - \frac{1}{\omega C}\right)^2}{R + R_L R_L^2+ \left ( \omega L - \frac{1}{\omega C}\right)^2}
Phase shift