On Linearity, Phasors and Steady-State Response of Electrical Circuits

This note addresses the widespread and often unquestioned assumption that a linear circuit supplied by a sinusoidal input (voltage or current) always results in a sinusoidal output (current or voltage). Likewise, it is generally assumed that only nonlinear circuits can generate harmonic distortion. Based on the linearity assumption, the analysis of power systems properties is usually carried out using Fourier analysis and phasors. Such analyses typically neglect the transients and initial conditions. Two elementary examples are exploited to show that linearity alone is not sufficient to guarantee a sinusoidal steady- state response. It is necessary to invoke some additional assumptions. However, these assumptions contradict the underlying philosophy of phasors or are difficult to accomplish physics-wise.