Difference between revisions of "TF EIM Chapt3"

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:<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>\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>\left | \frac{V_{out}}{V_{in}}\right | = \sqrt{\left [ \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}\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>
  
 
=== Phase shift===
 
=== Phase shift===

Revision as of 03:45, 2 February 2011

RLC circuit

An RLC circuit is a Resistor, an Inductors, and a Capacitor in series with an electromotive force.

TF EIM Lab5 RLC.png


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]


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]

Phase shift