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If The I And Q Of Software Defined Radio Are Your Nemesis, Read On

For those of us whose interests are in radio, meeting our first software-defined radio should seem universal as a miracle. Here’s a surprisingly simple device, a substantially intelligent mixer, and a set of analog-to-digital or digital-to-analog converters that can import all the complex and sophisticated parts of a traditional radio to a computer where all signal processing can be done with using software.

Quadrature mixer.  Jugandi (public domain).
Quadrature mixer. Juganda (Public domain).

When your curiosity overwhelms you and you start to look at the work of software-defined radio, you come across something you have never seen in traditional radio. There are two mixers, powered by two local oscillators of the same frequency, but with a phase shift of 90 degrees, and in the receiver the resulting mixing products are fed into two separate ADCs. You meet the letters I and IN in terms of these two signaling paths and wondering what the hell that means.

What you just saw is a quadrature mixer. Quadrature refers to everything mathematical that includes a quarter circuit, in this case the phase shift of 90 degrees between the two local oscillators. This 90-degree phase shift has the ability to reveal not only the frequency and amplitude information in the signal that you would be familiar with from a mixer in a traditional radio, but also the phase information in it that the two 90 degrees are out of phase. I (In phase) and Q (Quadrature) the component signals retain.

I and Q data as a side view of a spiral.  Mikael Q Kuisma, I / Q data for mannequins.
I and Q data as a side view of a spiral. Mikael Q Kuisma, I / Q data for mannequins.

A significant amount of math needs to be mastered if you want to fully understand how this works, which is probably best for directing the curious. for a longer explanation. For a quick understanding, however, it is best to imagine the sine wave amplitude view of a signal that you can only see on an oscilloscope as a two-dimensional side view of a signal, which is actually a 3D spiral because it also has a phase component. If this side view of the spiral was yours I component, then a similar 2D view at the top of the spiral would be yours IN component, the same signal, but with a phase difference of 90 degrees. Of these two I and IN the signals can be reconstructed throughout the original signal, including its complex phase connections, rather than just the two-dimensional view of the amplitude you can see on an oscilloscope.

Production of 90 degree phase change with flip flops.
Production of 90 degree phase change with flip flops.

Fortunately, this is not one of those things that only exists as part of a theory in a textbook, you can easily build a simple SDR receiver based on the square mixer diagram above your bench. If you are willing to limit the receiver’s bandwidth to that of your computer’s audio card, often in the 50 kHz band, you can use the left and right audio inputs as I and IN respectively, and run one of the many SDR applications. Linrad is just one example.

In terms of hardware, mixers and the associated low pass filter can be extremely easy to build, for example you can try to lift this design using a CMOS analog switch. And while you can imagine that creating a 90-degree phase shift would be a problem, in fact, it can also be easily done with a pair of flip-flops. Add a logic level oscillator and then it is possible to make a software-defined radio interface almost entirely from logic chips, with the exception of a few operational amplifiers. It won’t perform much more than RF (shortwave) frequencies, but even if you only use it to browse local AM radios, it can still give you a practical understanding of SDR hardware.

Sometimes it seems that SDRs are magical black boxes surrounded by a cloud of marketing courtship. And with the exception of the famous USB TVs with RTL chipset, they seem to attract a price that matches the ad. But the reality is that from a hardware point of view, they can be surprisingly simple. Why not take out a model and hack a simple one!

Image of the title: Bob K. [CC0].

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