# IQ Phasor Addition

- Author:
- Chuck Faber

The term “I/Q” is an abbreviation for “in-phase” and “quadrature.” “In-phase” and “quadrature” refer to two sinusoids that have the same frequency and are 90° out of phase. By convention, the I signal is a cosine waveform, and the Q signal is a sine waveform. As you know, a sine wave (without any additional phase) is shifted by 90° relative to a cosine wave. Another way to express this is that the sine and cosine waves are

*in quadrature*. The first thing to understand about I/Q signals is that they are always amplitude-modulated. I/Q modulation involves multiplying I/Q waveforms by modulating signals that can have negative voltage values, and consequently the “amplitude” modulation can result in a 180° phase shift. I and Q signals on their own are not very interesting. The interesting thing happens when I and Q waveforms are added. It turns out that any form of modulation can be performed simply by varying the amplitude—only the amplitude—of I and Q signals, and then adding them together. If you take I and Q signals of equal amplitude and add them, the result is a sinusoid with a phase that is exactly between the phase of the I signal and the phase of the Q signal. In other words, if you consider the I waveform to have a phase of 0° and the Q waveform to have a phase of 90°, the summation signal will have a phase of 45°. If you want to use these I and Q signals to create an amplitude-modulated waveform, you simply amplitude modulate the individual I and Q signals at the same time. Phase modulation, in the form of phase shift keying, is an important technique in modern RF systems, and phase modulation can be conveniently achieved by varying the*amplitude*of I/Q signals. Increasing the amplitude of one of the waveforms relative to the other causes the summation signal to shift toward the higher-amplitude waveform. This makes intuitive sense: if you eliminated the Q waveform, for example, the summation would shift all the way over to the phase of the I waveform, because (obviously) adding the I waveform to zero will result in a summation signal that is identical to the I waveform.