First_Order_Circuits_Example

First_Order_Circuits_Example - Find the Transfer Function...

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Find the Transfer Function, ( ) : Combine and the capacitor, , into a single equivalent impedance, . Note that the two impedances are in parallel. Calculate the current flowing around the closed loop: ( )
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The output voltage, , is equal to the product of the current, ( ) , and : ( ) ( ) ( ) ( ) ( ) ( ) The transfer function of the circuit is therefore given by: ( )
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Find ( ) for ( ) ( ) : In the Laplace domain: ( ) ( ) ( ) ( ) ( ( ) ( ) ) ( ( ) ( ) ) ( ( ) ( ) ) ( ( ) ( ) ) Referring to the tables of Laplace Transforms, the first term resembles: { } ( ) while the second term is of the form: { ( ) } ( ) ( ) To get in the same form (i.e., to isolate ), multiply through by:
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