More than seven years ago I first uttered the phrase: “I/Q”, and palmed it off to future me with “we should look at that [at] some other time”. Since then I’ve referred to it several more times and all but vaguely waved my hands about.
Today I’m going to poke the bear called “I/Q” and to be clear, this is a signal term meaning “In-phase and Quadrature” not “Intelligence Quotient”.
Most explanations I’ve seen jump into the mathematics of this concept, but none ever spoke to me at any fundamental level.
Ultimately, a simple phenomenon underlies all of the magic that hides behind the concept of an “I/Q” signal. So, let’s explore.
When you digitise a signal, you essentially record a voltage each time you take a sample, which can happen many millions of times per second. The aim of this process is to create a digital representation of an analogue signal for the purpose of doing something with it, like decode it. This process happens in billions of devices across the planet.
In its simplest form a signal is a sine wave that starts at zero and oscillates between one and minus one. You might recall that a sine wave is associated with degrees in a circle and that each angle shares the same sine value with another. For example, the sine of 30 degrees and 150 degrees are the same, 0.5.
This means that the value of 0.5 could represent 30 degrees, but it could also represent 150 degrees, which means that our digital representation of a sine wave is incomplete.
A cosine wave has all the attributes of a sine wave. If you were to draw them together you’d notice that its shape is identical but shifted in time and because we’re talking about angles, it’s delayed, or phase shifted, by 90 degrees.
What if you sampled both waves … at the same time?
Doing so removes all angle ambiguity. By convention, the I in “I/Q” represents the In-Phase or cosine signal and the Q in “I/Q” represents the Quadrature or sine signal. And while we’re in the business of naming things, signals that are separated in phase by 90 degrees are “in quadrature”.
So, what does this buy you, or why does it matter?
As it happens, you can represent any radio modulation as an I/Q signal. While until now I’ve talked about digital signals, all this applies to analogue signals, and it applies to transmitted signals as well.
Final piece of the puzzle. To create any modulation from an I/Q signal, all you need is to vary the amplitude of each of the I and Q signals, which means that you can do this with analogue circuits as well as in software using cheap hardware.
If you’ve looked at this phenomenon before, you might wonder why I haven’t said anything about “complex numbers” yet and if you haven’t, those words might scare you off. The concept of “complex” really refers to the idea of embracing two numbers within, for example, it can represent an arrow with a length and a direction. Our I/Q signal, which consists of two numbers for each sample, can also be represented as a complex number and it’s one of several ways to represent an I/Q signal.
One final comment. You can create an I/Q stream from an RF signal by mixing it with a so-called quadrature mixer, one that outputs two signals, 90 degrees out of phase.
Now, I will add that I had porridge for breakfast and I’m operating on five and a half hours of sleep, but I’m fairly confident that I covered the foundations of an I/Q signal in less than four minutes and I even had time to tell you what I had for breakfast.
For my next trick, I’m going to tell you how to make pancakes with just a banana and an egg.
I’m Onno VK6FLAB