phasors indicate power flow and system stability. Telecommunications: analog modulations The rotating frame picture using phasor can be a powerful tool to understand analog modulations such as amplitude modulation (and its variants) and frequency modulation. where the term in brackets is viewed as a rotating vector in the complex plane. The phasor has length , rotates anti-clockwise at a rate of revolutions per second, and at time makes an angle of with respect to the positive real axis. The waveform can then be viewed as a projection of this vector onto the real axis. A modulated waveform is represented by this phasor (the carrier) and two additional phasors (the modulation phasors). If the modulating signal is a single tone of the form , where is the modulation depth and is the frequency of the modulating signal, then for amplitude modulation the two modulation phasors are given by, , and . The two modulation phasors are phased such that their vector sum is always in phase with the carrier phasor. An alternative representation is two phasors counter rotating around the end of the carrier phasor at a rate relative to the carrier phasor. That is, , and . Frequency modulation is a similar representation except that the modulating phasors are not in phase with the carrier. In this case the vector sum of the modulating phasors is shifted 90° from the carrier phase. Strictly, frequency modulation representation requires additional small modulation phasors at etc, but for most practical purposes these are ignored because their effect is very small. See also In-phase and quadrature components Constellation diagram Analytic signal, a generalization of phasors for time-variant amplitude, phase, and frequency. Complex envelope Phase factor, a phasor of unit magnitude Footnotes References Further reading External links Phasor Phactory Visual Representation of Phasors Polar and Rectangular Notation Phasor in Telecommunication Electrical circuits AC power Interference Trigonometry