In-phase and quadrature components

Lore & Background

In vector analysis, a vector with polar coordinates can be represented as the sum of orthogonal components, analogous to the trigonometric angle sum identity. When the angle is a linear function of time, these components are sinusoids and are orthogonal functions. A phase-shift of π/2 changes the identity, making one component the in-phase component. In an angle modulation application with carrier frequency, the left-hand side of the equality is the amplitude/phase form, and the right-hand side is the quadrature-carrier or IQ form. Because of modulation, the components are no longer completely orthogonal functions, but when I and Q are slowly varying compared to the carrier frequency, the assumption of orthogonality is common, often called a narrowband assumption or narrowband signal model.

Reader's Guide

I/Q data is a stream of information about how to amplitude-modulate the I and Q phases of a sine wave. By amplitude-modulating these two 90°-out-of-phase sine waves and adding them, it is possible to produce the effect of arbitrarily modulating a carrier in amplitude, phase, and frequency. For received signals, determining how much in-phase carrier and quadrature carrier is present allows representation of that signal using I and Q components. I/Q data has extensive use in radio modulation, software-defined radio, audio signal processing, and electrical engineering. It is a two-dimensional stream, treated by some as a complex number (I as real, Q as imaginary) and by others as distinct pairs, a 2D vector, or separate streams. The data rate of I/Q is largely independent of the signal frequency; I/Q data can be generated at a relatively slow rate and used to modulate a faster carrier. I/Q data is also used to represent signals from receivers, in designs such as digital down converters, and for spectrum monitoring, allowing capture of radio traffic in an RF band with a reasonable amount of data irrespective of the monitored frequency. Vector signal generators and analyzers typically use I/Q data, and many modulation schemes, such as quadrature amplitude modulation, rely heavily on I/Q.

Did You Know?

• The two amplitude-modulated sinusoids are known as the in-phase (I) and quadrature (Q) components.
• A sinusoid with modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are in quadrature phase.
• I/Q data can be generated at a relatively slow rate (e.g., millions of bits per second) and used to modulate a carrier frequency that may be faster (e.g., Gigahertz).
• In alternating current circuits, when the phase difference is such that the in-phase component is zero, the current and voltage sinusoids are said to be in quadrature and no average electrical power is consumed.