Unformatted text preview: btained from the forcing function. It is normally of the same functional form as the forcing function and its derivatives. A table containing various forcing functions and their corresponding particular solutions are readily available. The complementary solution does not depend on the forcing functions and is also called the natural response of the circuit as it depends on the passive circuit elements. Rearranging the homogenous equation we get, 74 EE1002 Introduction to Circuits and Systems dxc (t ) dt 1 xc (t )
Integrating both sides, we get: ln xc (t ) t c where c is the constant of integration. Thus, xc (t ) ec e t Ke t . The given initial conditions can then be used to find the value of K . Final solution then will be x(t ) x p (t ) xc (t ) . Example: Second order circuits A circuit containing a dc source and R,L, C in series as shown in the figure: vc (t ) t0 - + L C R i (t ) Vs(t) Writing KVL equation, we have t L di (t )
1 Ri (t ) i (t )dt vc (0) vs (t ) dt
C0 By differentiating again with respect to time, we remove the integrals and convert it to a purely differential equation. We get d 2i (t ) R di (t ) 1
1 dvs (t ) i (t ) 2
L dt Solution of the second‐order equation General second order differential equation...
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- Winter '14