Modes in Linear Circuits

The purpose of this review paper is to show that the concept of modes does apply to any linear time invariant circuit. This is accomplished by reducing the network equations to the standard vector form . In particular, it is shown that 1) any free oscillation of a linear circuit can be thought of as a superposition of non-interacting modes, 2) in the case of free oscillations, the amount of excitation of each mode can easily be expressed in terms of the initial conditions, 3) any forcing function excites each mode independently, and finally, 4) the resonance phenomenon is easily interpreted and the importance of the proper type of excitation is made obvious. Vector notation is used throughout. Examples of RC, RLC and active circuits are included.