TF EIM Chapt2 - Revision history

Foretony: /* Gain */

2015-02-05T16:51:48Z

Gain

2015-02-04T18:57:32Z

Quick Solution

2015-01-29T19:09:30Z

Inductor Reactance

2015-01-29T19:02:29Z

Inductor/Choke

2015-01-29T18:40:58Z

Q and Bandwidth

2015-01-29T18:39:23Z

Q and Bandwidth

2015-01-29T18:38:06Z

Q and Bandwidth

2015-01-29T18:11:04Z

gain

2015-01-29T18:10:23Z

parallel LC circuit (Band Stop/Notch Filter/ tank circuit)

2015-01-29T18:10:12Z

parallel LC circuit (Band Stop/Notch Filter/ tank circuit)

← Older revision		Revision as of 16:51, 5 February 2015
Line 681:		Line 681:
	:<math>\left \| \frac{V_{out}}{V_{in}}\right \| =\frac{R}{R+R_L}</math>		:<math>\left \| \frac{V_{out}}{V_{in}}\right \| =\frac{R}{R+R_L}</math>

		+	[[File:TF_EIM_RLC.png \| 200 px]]

	=== Phase shift===		=== Phase shift===

@@ Line 244: / Line 244: @@
 then
-:<math>\frac{V_{out}}{V_{in}} =  \frac{1}{\sqrt{1 + \left ( \frac{\omega}{\omega_b}\right )^2}}</math>
+:<math>\frac{V_{out}}{V_{in}} =  \frac{1}{\sqrt{1 + \left ( \frac{\omega}{\omega_b}\right )^2}}= \frac{1}{\sqrt 2}</math>
 [[File:TF_EIM_LowPassVoutVin-vs-omega.png|200px]]

@@ Line 480: / Line 480: @@
 : <math>\Rightarrow I(t) = V_0 \frac{sin(\omega t)}{\omega L}  + I(0)</math>
-Assum I(0) =0 and rewrite <math>\sin</math> in terms of a phase shifted <math>\cos</math>
+Assume I(0) =0 and rewrite <math>\sin</math> in terms of a phase shifted <math>\cos</math>
 : <math>\Rightarrow I(t) = \frac{V_0}{\omega L} cos(\omega t - \pi/2) </math> : V and I are 90 degrees out of phase

@@ Line 462: / Line 462: @@
 So in essence the inductor acts "like" a resistor which resists the current flow according to the amount of current is changing.
-There is an effective impedance <math>Z_{L}</math> for inductors as there was one for capacitors
+There is an effective reactance <math>X_{L}</math> for inductors as there was one for capacitors
 == Inductor Reactance==

@@ Line 605: / Line 605: @@
 :The Band Width is a measurement of the two frequencies which will decrease the resonance voltage by 30 %.
-[[File:TF_EIM_BandWidthDef_LC.gif | 200 px]]
+[[File:TF_EIM_BandWidthDef_LC.gif | 400 px]]
 ;Quality Factor

← Older revision		Revision as of 18:39, 29 January 2015
Line 597:		Line 597:


−	~~This correspond~~ to the frequency at which the circuits power is cut in half from the resonance frequency.	+	A 3dB drop corresponds to the frequency at which the circuits power is cut in half from the resonance frequency.

	:<math>P = I^2 R</math>		:<math>P = I^2 R</math>

← Older revision		Revision as of 18:38, 29 January 2015
Line 585:		Line 585:


−	;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.	+	;Bandwith: The most common definition for the Bandwidth of this circuit is the frequency range over which the output decreases by 3 dB.
		+
		+	;Decibels
		+	:The decibel system is a logarithmic scale for the ratio of two quantities
		+
		+	;For power
		+	:dB = <math>10 \log_{10} \left ( \frac{P_{in}}{P_{out}}\right )</math>
		+
		+	;For amplitude (Voltage)
		+	:dB = <math>20 \log_{10} \left ( \frac{V_{in}}{V_{out}}\right )</math>
		+
		+
		+	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 = I^2 R</math>

@@ Line 568: / Line 568: @@
 |<math>L = 33 \mu H</math> and   <math>C = 1 \mu F </math> and R=200 <math>\Omega</math>
 |-
-|[[File:TF_EIM_LC_paral_Gain.png | 200 px]]
+|[[File:TF_EIM_LC_paral_Gain.png | 400 px]]
 |-
 |<math>\Rightarrow \omega = 174077.66</math> rad/s  or <math>\nu = \frac{\omega}{2 \pi} = 27705</math> Hz

@@ Line 496: / Line 496: @@
 ==parallel LC circuit (Band Stop/Notch  Filter/ tank circuit)==
-[[File:TF_EIM_Parallel_RLC.png| 400 px]]
+[[File:TF_EIM_Parallel_RLC.png| 200 px]]
 The above circuit has a resistor in series with an inductor and capacitor in parallel.