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)]
=R2L+(ωL1ωC)2(R+RL)2+(ωL1ωC)2
=R2L+(ω2LC1ωC)2(R+RL)2+(ωL1ωC)2

Phase shift