Transforming the Circuit Math So That Time Disappears

Exploring the Relationship Between Sine Waves and Phasors in DC Circuit Analysis

Abstract

We know that every function can be written as a series ofsine waves of various frequencies and magnitudes added together. The entireworld can be constructed from sin waves. Here, one sine wave islooked at, the repeating nature () is stripped away. Whatsleft is a phasor. Since time is made of circles, and if we consider just one ofthese circles, we can move to a world where time doesn't exist and circles are"things". Instead of the word "world", use the word"domain" or "plane" as in two dimensions. Math in thePhasor domain is almost the same as DC circuit analysis. What is different isthat inductors and capacitors have an impact that needs to be accounted for.The transform into the Phasors plane or domain and transforming back into timeis based upon Euler's equation. It is the reason we studied imaginary numbersin past math class.