17-First Order Circuits 1

17-First Order Circuits 1 - First Order Circuits First...

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irst Order Circuits First Order Circuits © Fred Terry all, 008 Fall, 2008 1
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First Order Circuits • Only One Energy Storage Element (one L or one C) • Resistors, Independent and Dependent Sources • Result with be a First Order Ordinary, Linear Differential Equation in t – First Order since we have one circuit element with with a d/dt element constraint 2
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irst Order Ordinary inear Differential First Order Ordinary Linear , Differential Equations: The Short Story I Differential Equations of the form: dy ) () xy Qx = dx where ( ), ( ) are functions of x only (possibly even constants). he GENERAL solution is made up of a par cular solution ( ) Pxy Qx Px Qx x += The GENERAL solution is made up of a particular solution which solves the total p yx equation and a homogeneous solution ( ) which solves the homogeneous equation: h y x dy 0 dx So the full, general solution is: Pxy 3 ,g ph y x =+
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irst Order Ordinary inear Differential First Order Ordinary Linear , Differential Equations: The Short Story II The homogeneous solution ( ) to a 1st order, linear ODE will always have exactly 1 unknown constant, so the general solution: ) () h yx x y x + will also always have exactly 1 unknown constant. We elimin ph =+ ate that constant by matching to the initial condition (also called the boundary condition). We only match the solution to the initial condition.
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This note was uploaded on 01/31/2011 for the course EECS 215 taught by Professor Phillips during the Spring '08 term at University of Michigan.

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17-First Order Circuits 1 - First Order Circuits First...

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