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First Order Circuits

# First Order Circuits - First Order Circuits First Order...

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1 First Order Circuits, First Order Differential Equations EECS 215 Jamie Phillips A first order circuit will contain one energy storage element (capacitor or inductor), where the circuit response will be represented by a first order differential equation. A general configuration for such a circuit is given by the following schematic. Note that the voltage source v s may be time dependent. Also note that any linear circuit (combination of independent sources, dependent sources, and resistors) attached to a capacitor may be “converted” into the circuit below through determination of the Thevenin equivalent (a powerful technique!). Similar analysis may be done for a first order circuit with an inductor, current source, etc. C R v s (t) v + - 1. Set up differential equation From KCL, the differential equation for this circuit is RC t v RC v dt dv s ) ( = + The solution is f n v v v + = , where v n and v f are the natural (unforced, homogeneous) and forced (particular) solutions, respectively.

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