Difference between revisions of "TF EIM Chapt3"

Revision as of 03:54, 2 February 2011

Phase shift

Forest_Electronic_Instrumentation_and_Measurement

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-==RLC circuit==
-An RLC circuit is a Resistor, an Inductors, and a Capacitor in series with an electromotive force.
+=== Phase shift===
-[[File:TF_EIM_Lab5_RLC.png| 200 px]]
-===Effective impedance===
-:<math>X_{out} = R_L + X_C + X_L = R_L + \frac{1}{i \omega C} + i \omega L</math>
-:<math>\left | X_{out} \right | =  \sqrt{\left [ R_L + i \left (\frac{-1}{\omega C} +  \omega L\right ) \right ]\left [ R - i \left (\frac{-1}{\omega C} + \omega L\right ) \right ]^*}</math>
-:: <math>=  \sqrt{ R_L^2 +  \left ( \omega L -  \frac{1}{\omega C} \right )^2}</math>
-=== Gain===
-Loop Theorem
-: <math>V_{in} = I (R+ X_{out})</math>
+[[Forest_Electronic_Instrumentation_and_Measurement]]
-Voltage Divider
-:<math>V_{AB}=V_{out} = \frac{X_{out}}{R + X_{out}}V_{in}</math>
-:<math>\left | \frac{V_{out}}{V_{in}}\right | = \sqrt{\left [ \frac{X_{out}}{R + X_{out}}\right ]\left [ \frac{X_{out}}{R + X_{out}}\right ]^*}</math>
-<math>R_L + i \left ( \omega L - \frac{1}{\omega C}\right)</math>
-:<math>\left | \frac{V_{out}}{V_{in}}\right | = \sqrt{\left [ \frac{R_L + i \left ( \omega L - \frac{1}{\omega C}\right)}{R + R_L + i \left ( \omega L - \frac{1}{\omega C}\right)}\right ]\left [ \frac{R_L + i \left ( \omega L - \frac{1}{\omega C}\right)}{R + R_L + i \left ( \omega L - \frac{1}{\omega C}\right)}\right ]^*}</math>
-::<math> = \sqrt{\frac{R_L^2 + \left ( \omega L - \frac{1}{\omega C}\right)^2}{(R + R_L)^2 +  \left ( \omega L - \frac{1}{\omega C}\right)^2}}</math>
-::<math> = \sqrt{\frac{R_L^2 + \left ( \frac{\omega^2 LC - 1}{\omega C}\right)^2}{(R + R_L)^2 +  \left ( \frac{\omega^2 LC - 1}{\omega C}\right)^2}}</math>
-Let
-:<math>\omega_0 = \sqrt{\frac{1}{LC}}</math>
-Then
-:<math>\left | \frac{V_{out}}{V_{in}}\right |  = \sqrt{\frac{R_L^2 + \left ( \frac{\omega^2 - \omega_0^2}{\omega_0^2 \omega C}\right)^2}{(R + R_L)^2 +  \left ( \frac{\omega^2- \omega_0^2}{\omega_o^2 \omega C}\right)^2}}</math>
-When<math> \omega = \sqrt{{1}{LC}} = \omega_0</math>
-Then
-:<math>\left | \frac{V_{out}}{V_{in}}\right |  =\frac{R}{R+R_L}</math>
-=== Phase shift===

Difference between revisions of "TF EIM Chapt3"

Revision as of 03:54, 2 February 2011

Phase shift

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