ABSTRACT
The circuit response resulting from some initial conditions in the circuit is the natural response of the circuit. In the case of first-order circuits, which essentially contain only a single energy-storage element, the impulse response and the natural response are one and the same because the effect of the impulse is to establish an initial condition in the given energy-storage element. The definition of terms used in describing the responses of first-order and second-order circuits, such as time constant, damping factor, damped natural frequency, etc. The response of a linear time-invariant (LTI) circuit to an arbitrary input can be considered as the superposition of responses to sufficiently narrow pulses, each having an amplitude determined by the input. Convolution with step and impulse functions is particularly simple, and functions consisting of linear segments and step discontinuities, when differentiated, yield a combination of impulse and step functions.
