Andrew Carter

Electrical Engineer

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Studying the Phasor Diagram

Posted Feb 22, 2012 at 12:12 pm

A phase vector or phasor in physics and engineering signifies a sine wave whose amplitude and frequency are time-variant. The behavior of a sinusoid is decomposed by phasors into three independent factors that relay phase information, frequency and amplitude. To visualize complex constants and variables, electrical engineers, aircraft engineers, electronic engineering technicians and electronics engineers all use phasor diagrams.

Figure 1 Phasor Diagram

A phasor can be seen as a rotating vector and the sine wave can be understood as the projection onto the real axis of a rotating vector on the complex plane. The modulus of this vector is the amplitude of the oscillations and the phase constant represents the angle that the complex vector forms.

Figure:1 Click on the image to see the animation

Figure 2 Click on the image to see the animation

The image below shows the sum of phasors as addition of rotating vectors. Since the sum of sine waves with the same frequency is also a sine wave with that frequency, the sum of multiple phasors produces another phasor.

Figure 3 Click on the image to see the animation

It is sometimes helpful to treat the phase as if it defined a vector in a plane. The usual reference for zero phase is taken to be the positive x-axis and proportional to the magnitude of the quantity represented is the length of the phasor. Its angle represents its phase relative to that of the current. The main value of phasor diagrams is that they can be used, not only to represent waveform diagrams, but also in carrying out calculations involving ac waves. The calculations involve any of the common values such as peak values, phase angles, RMS, etc. it is much easier and quicker than performing the calculations on waveform diagrams.

Figure 4

As shown in the image above, phasor diagrams are similar to an analog clock face. To keep track of time, we use the rotating hands in such a clock. Time is a one dimensional progression like a time line for an average man but for mechanical convenience, a circular clock face is used to keep track of time because in rotating circular devices, the repeating motions are easiest to construct.

A set of phasors is defined as the three complex cube roots of unity, graphically represented as unit magnitudes at angles of 0, 120 and 240 degrees in analysis of 3-phase AC power systems. Balanced circuits can be simplified and unbalanced circuits can be treated as an algebraic combination of symmetrical circuits by treating polyphase AC circuit quantities as phasors. These approaches greatly simplify the work required in electrical calculations of voltage drop, power flow and short-circuit currents. To understand the phasor diagram for the voltages or currents is the key to understanding three-phase.

Figure 5

Shown below are the phase relationships of the three elements including resistor, capacitor and inductor. The basic relationship in electrical circuits is between the current through an element and the voltage across it. The phase angle, the difference in phase between the voltage and the current in an AC circuit, is the phase angle associated with the impedance Z of the circuit.