Natural and forced responses

NATURAL AND FORCED RESPONSES

On applying KCL and KVL to a network containing R, L and C, we obtain a linear differential equation with constant coefficients. The solution of this differential equation represents the response of the network. The response or behaviour of the network is governed by its internal stored energy and external energy supplied by the source.

The response determined by the internal energy stored in the network is called natural response. It depends upon the type of elements, their size, the inter connection of the elements. This response is independent of the source. In a network, energy may be stored internally in the electric field of a capacitor or in the magnetic field of an inductor. A natural response dies out gradually. That is, it approaches zero as time becomes infinite. The natural response is also known as transient response.

The response or behavior determined by the application of external energy source is called forced response. A forced response may be maintai. ed indefinitely if energy is supplied continuously to make up losses. The complete or total response of a network is the sum of the natural response and forced response.

The external energy source or forcing function may be any type. For example it may be direct voltage or current, sinusoidal source, an exponential function, a ramp function.

The complete solution of linear differential equation with constant coefficients describing the network consists of two parts.

(a) The particular integral, (b) Complementary function

The particular integral represents the forced response due to the particular driving source. It satisfies differential equation but not the initial conditions. The forced response depends on both the network elements and source.

The complementary function is the solution of the differential equation with forcing function set to zero. Therefore, the complementary function represents the source-free response. This response is also called the natural response or transient response.