Quadrature Phase

Two periodic waveforms whose phase difference is of their output period are said to have a quadrature phase relationship. The term is also used in communication systems to describe one of the components of orthogonal decomposition.

A composite signal described by its envelope-and-phase form can be decomposed to an equivalent quadrature-carrier (IQ) form as:

$\begin{align} &A(t)\cdot \sin \\ \equiv {} &A(t)\cdot \left(\sin\cos + \cos\sin \right) \\ \equiv {} &I(t)\cdot \sin(2\pi ft) + Q(t)\cdot \cos(2\pi ft) \\ \equiv {} &I(t)\cdot \sin(2\pi ft) + Q(t)\cdot \sin\left(2\pi ft + \frac{\pi}{2}\right) \end{align}$

where represents a carrier frequency, and:

$\begin{align} I(t) &\equiv A(t) \cdot \cos\\ Q(t) &\equiv A(t) \cdot \sin \end{align}$

and represent possible modulation of a pure carrier wave: . The modulation alters the original component of the carrier, and creates a (new) component, as shown above. The component that is in phase with the original carrier is referred to as the direct or in-phase component. The other component, which is always 90° ( radians) out of phase, is referred to as the quadrature component.

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