Difference between revisions of "TF EIM Chapt3"

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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
+
;Bandwith: The most common definition for the Bandwidth of this circuit is the frequency range over which the output decreases by 3 dB.  This correspond to the frequency at which the circuits power is cut in half from the resonance frequency.
 +
 
 +
:<math>P = I^2 R</math>
 +
:<math>P_{1/2} = (\sqrt{2}I)^2 R</math>
  
 
[[File:TF_EIM_BandWidthDef_LC.gif | 200 px]]
 
[[File:TF_EIM_BandWidthDef_LC.gif | 200 px]]
  
 
[[Forest_Electronic_Instrumentation_and_Measurement]]
 
[[Forest_Electronic_Instrumentation_and_Measurement]]

Revision as of 05:56, 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. This correspond to the frequency at which the circuits power is cut in half from the resonance frequency.
P=I2R
P1/2=(2I)2R

TF EIM BandWidthDef LC.gif

Forest_Electronic_Instrumentation_and_Measurement