Phasor Representation

Phasor (phase vector) is a vector representing a sinusoidal function.

For the phasor:

• Magnitude is the rms value of the wave
• Angle is the angular position $\phi$, with respect to a reference direction

Can also be represented by a complex number. But $j$ is used as the imaginary unit becasue $i$ is used for time-varying current.

Representation

• Polar form
  $A=\lvert{A}\rvert\angle\phi$
• Cartesian or rectangular form
  $A=A_x+jA_y$

Here:

• $\lvert{A}\rvert=A_{\text{rms}}=\sqrt{A_x^2+A_y^2}$
• $A_x=\lvert{A}\rvert\cos{\phi}$
• $A_y=\lvert{A}\rvert\sin{\phi}$
• $j=\sqrt{-1}$
• $\tan{\phi}=\frac{A_y}{A_x}$