TF EIM Chapt3

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gain

Loop Theorem

V=I(R+Xtot)=I(R+iωL1ω2ω2LC)

or

I=V0eiωt(R+iωL1ω2ω2LC)
Notice
When ωωLC=1LC then the AC signal is attenuated.

Looking at the Voltage divider aspect of the circuit

VAB=Vout=XtotR+XtotVin
|VoutVin|=[XtotR+Xtot][XtotR+Xtot]
=[iωL1ω2ω2LC(R+iωL1ω2ω2LC)][iωL1ω2ω2LC(R+iωL1ω2ω2LC)]
=ω2L2ω4LCR2(ω2LCω2)2ω2L2ω4LC
=ω2C2R2(ω2LCω2)2ω2
=ω21ω2RC(ω2LCω2)2ω2



L=33μH and C=1μF and R=200 Ω
TF EIM LC paral Gain.png
ω=174077.66 rad/s or ν=ω2π=27705 Hz

Q and Bandwidth

In the above circuit

ν=ω/2π=12πLC=27705Hz

The inductors reactance at this resonance frequency is

XL=ωL=2πνL=LLC=LC=33×106H1×106F=5.7Ω


Bandwith
The most common definition for the Bandwidth of this circuit is the frequency range over which the output decreases by 3 dB


Forest_Electronic_Instrumentation_and_Measurement