Phasors and Sinusoids

A sinusoid having period T and angular frequency can be represented as

A complex number

is associated with the sinusoid. F is called the phasor of f(t). The sinusoid is said to be represented by f(t) in the Time Domain and by F in the Frequency Domain.


This figure shows a phasor, F, in the Frequency Domain and corresponding sinusoid, f(t), in the Time Domain. Left click in the Frequency Domain with mouse to change the phasor. The Time Domain will change to show the sinusoid corresponding to the new phasor. (Each phasor is labeled using its real and imaginary parts: (real part, imaginary part).)

Some suggestions:

  1. Change the length, but not the direction, of the phasor.

  2. Change the direction, but not the length, of the phasor.

  3. Reverse the direction without changing the length of the phasor.

  4. Set the real part of the phasor to zero.

  5. Set the imaginary part of the phasor to zero.