TF EIM Chapt3

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RLC circuit

An RLC circuit is a Resistor, an Inductors, and a Capacitor in series with an electromotive force.

TF EIM Lab5 RLC.png


Effective impedance

Xout=RL+XC+XL=RL+1iωC+iωL
|Xout|=[RL+i(1ωC+ωL)][Ri(1ωC+ωL)]
=R2L+(ωL1ωC)2

Gain

Loop Theorem

Vin=I(R+Xout)


Voltage Divider

VAB=Vout=XoutR+XoutVin


|VoutVin|=[XoutR+Xout][XoutR+Xout]

RL+i(ωL1ωC)

|VoutVin|=[RL+i(ωL1ωC)R+RL+i(ωL1ωC)][RL+i(ωL1ωC)R+RL+i(ωL1ωC)]
\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