Difference between revisions of "TF EIM Chapt3"

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:<math>X_{L} = \omega L = 2 \pi \nu L = \frac{L}{\sqrt{LC}} = \sqrt{\frac{L}{C}} = \sqrt{\frac{33 \times 10^{-6} H}{1 \times 10^{-6}F}} = 5.7 \Omega</math>
 
:<math>X_{L} = \omega L = 2 \pi \nu L = \frac{L}{\sqrt{LC}} = \sqrt{\frac{L}{C}} = \sqrt{\frac{33 \times 10^{-6} H}{1 \times 10^{-6}F}} = 5.7 \Omega</math>
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;Bandwith: The most common definition for the Bandwidth of this circuit is the frequency range over which the output decreases by 3 dB
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[[Forest_Electronic_Instrumentation_and_Measurement]]
 
[[Forest_Electronic_Instrumentation_and_Measurement]]

Revision as of 05:52, 2 February 2011

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