# Phasor Diagrams

A work in progress

Phasors are a very useful technique for conceptualizing sinusoidally oscillating electrical quantities.  A phasor is simply a vector in the complex plane usually defined by its magnitude and phase.  One of the first techniques used is to represent voltage, current and impedance as phasors.  Students often have a hard time visualizing what a phasor represents.

This document describes a MatLab® tool for visualizing phasors.  The user provides two of the three necessary phasors (either current&voltage or current&impedance or impedance&voltage).  The program then calculates the third (unspecified) phasor and displays all three phasors.  It will also animate the rotating current and voltage phasors.  The time domain representation is also displayed (which is simply the real part of the rotating phasors).

Download the two files below and put them in the same directory

Now run the GUI by either

• putting that directory in the MatLab path and typing:  >>phasors

• or, open the "phasors.m" file from MatLab, and go to Debug->Run.

A window similar to the one below will appear.   Only the upper left graph is originally complete, and it shows the voltage, current and impedance phasors in red, blue and magenta, respectively.

To show the current and voltage phasors in action, hit the "Go!" button at the bottom of the page. The projection on the real axis (denoted by a small, filled, circle)  is the "real" response of the circuit.  The voltage and current phasors are displayed, in real time, in the upper right graph.  The real response is displayed as a function of time in the lower graph.  After the animation is complete, the image looks like the one below.

We can also change parameters and visualize a different set of phasors.  Let's change the voltage and impedance phasors as well as the frequency as shown.

To calculate the resulting current phasor, hit the "Calculate I" button.  To animate the display hit the "Go!" button and the program will use the voltage and current phasors to calculate a new current phasor.  the end of the animation, the display looks like the one shown below.

Note that the values for the magnitude and phase of the current phasor are now updated.

You can also specify current and voltage and calculate impedance (the "Calculate Z" button), or specify current and impedance and calculate voltage (the "Calculate V" button).  Try to keep all three phasors about the same length since they are all displayed at the same scale.

 ← Comments or Questions? Erik Cheever Engineering Department Swarthmore College