Sinusoid & Phasor

Introduction

Any (non-pathological) function can be represented by an appropriate superposition of sine waves of

different frequencies, either as a Fourier series or as a Fourier integral. The response of a linear network toa composite sinusoidal signal can be determined for each sinusoidal term separately, and the overall

response then obtained by superposition. This is in part the basis of the fundamental importance of the

analysis of the response of a linear circuit to a single sinusoid of

 arbitrary frequency. Circuit behavior for

composite signals can be inferred from knowledge of this sinusoidal response. Hence what is considered

in this course primarily is the analysis of a linear circuit with an arbitrary

single-frequency sinusoidal

excitation.

We now begin the analysis of circuits in which the source voltage or current is time-varying. In this chapter, we are particularly interested in sinusoidally time-varying excitation, or simply, excitation by a sinusoid. 

  

A sinusoid is a signal that has a form of the sine or cosine function.

v(t) = Vm sinωt

Vm=the amplitude of the sinusoid

ω=the angular frequency in radians/s

ωt=the argument of the sinusoid

A periodic function is one that satisfies v(t) = v(t+nT), for all 

t and for all integers n.

While...

A phasor is a complex number that represents the amplitude and phase of a sinusoid.

Arithmetic With Complex Numbers