Colby.fullerton: Created page with 'Find the Thevenin equivalent impedance seen looking into the terminals of the following circuit: center To find the Thevenin equivalent…'

2010-11-08T00:07:40Z

Created page with 'Find the Thevenin equivalent impedance seen looking into the terminals of the following circuit: thumb|400px|center To find the Thevenin equivalent…'

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Find the Thevenin equivalent impedance seen looking into the terminals of the following circuit:
[[File:Lna hw8 diagram1.jpg|thumb|400px|center]]

To find the Thevenin equivalent impedance I will need to take the Laplace transform of each branch of the circuit and add them in series.

The Laplace transform of a resistor is
<math>\mathcal{L}\{resistor\} = R</math>

The Laplace transform of an inductor is
<math>\mathcal{L}\{inductor\} = sL</math>

The Laplace transform of a capacitor is
<math>\mathcal{L}\{\mbox{capacitor}\} = \frac{1}{sC}</math>

Taking the Laplace transform of the original circuit gives the following.
[[File:Lna hw8 diagram2.jpg|thumb|400px|center]]

The Thevenin equivalent impedance of this circuit is given by the equation
:<math>Z = \frac{1}{\frac{1}{R1+\frac{1}{sC}}+\frac{1}{R2+sL}} \Omega</math>

Substituting the values for R1, R2, C and L into the equation gives
:<math>Z = \frac{1}{\frac{1}{50+\frac{1}{.002s}}+\frac{1}{100+.5s}} \Omega = \frac{1}{\frac{s}{50(s+10)}+.5(s+200)} \Omega = \frac{2(s+10)}{s^2+210.04s+2000} \Omega</math>

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Colby.fullerton: Created page with 'Find the Thevenin equivalent impedance seen looking into the terminals of the following circuit: center To find the Thevenin equivalent…'