Introduction and editor’s word

This can be a two-part collection the place DI authors Damian and Phoenix Bonicatto discover the IQ sign illustration and destructive frequencies. Half 1 explains the generally used SDR IQ sign illustration and destructive frequencies with out the complexity of math.

This closing half (Half 2) presents a tool that means that you can play with and show dwell SDR sign spectrums with destructive frequencies.

Wow the engineering world together with your distinctive design: Design Concepts Submission Information

Defining actual and imaginary alerts

Let’s begin off with one thing I disregarded on goal in Half 1, there are two extra phrases we’ll use: A “actual” sign is a time period used for the sign represented by the I knowledge. “Imaginary” sign is the time period used for the sign represented by the Q knowledge. I left them out till now as they add to the obfuscation of the dialogue. Simply take them at face worth as there’s nothing imaginary about an “imaginary” sign.

The “I/Q Explorer” design

Okay, so what we’re going to make is an Arduino Nano primarily based gadget that may generate “actual” and “imaginary” knowledge (I and Q samples) per your settings of frequency, amplitude, and section. Then it can show a spectrum exhibiting optimistic and destructive frequencies. We is not going to use the FFT function of your scope, we’ll generate the spectrum within the MCU and ship it out to the oscilloscope to type a hint within the form of the spectrum. In truth, we’ll generate a spectrum for the true sign, imaginary sign, and the magnitude of the mixture (that is the sq. root of the sum of the squares of the true and imaginary alerts).

We are going to confer with this design because the I/Q Explorer (Determine 1).

Determine 1 The ultimate I/Q Explorer design with an LCD for displaying menu gadgets and values and a toggle swap to change the scope between the time and frequency domains.

Let’s take a look at the schematic in Determine 2.

Determine 2 The schematic of the IQ Explorer gadget with an Arduino Nano, 4×20 LCD, two rotary encoders, a easy toggle swap, three analog outputs, three traces to go to the scope probes, a digital output, and BNC connectors.

You’ll be able to see the I/Q Explorer has a comparatively easy schematic. It’s primarily based on an Arduino Nano and makes use of a 4×20 LCD for displaying menu gadgets and values. The 2 rotary encoders are used to navigate by means of the menu and to alter values. A easy toggle swap is used to alter the scope view from the time area to frequency area. There are three analog outputs, created utilizing PWM outputs and single pole RC low-pass filters. The three traces go to the scope probes (you don’t want to attach all three in the event you don’t have a 4-channel scope). There’s additionally a digital output used as a set off to sync the scope to the analog outputs. The one different electrical elements are two BNC connectors which can be utilized if you wish to get alerts from a sign generator, as a substitute of the inner generated alerts.

The take a look at stand itself could be simply 3D printed (a hyperlink to the 3D information and Arduino code are on the finish of the article). The take a look at stand supplies a spot to mount the LCD, rotary encoders and the time/frequency swap. Two BNC connectors could be put in on the left facet. On the proper facet is a spot to put in 4 wires that shall be used to clip the scope probe on (you additionally have to clip one of many results in a floor). The remaining on the circuitry could be laid out on a small solderless breadboard. The breadboard then suits on the again of the take a look at stand. A doc exhibiting extra photos, BOM, and extra directions could be discovered within the obtain from the hyperlink on the finish of the article.

Utilizing the I/Q Explorer

Okay, what are you able to do with it now? First, the left facet of the take a look at stand has 4 naked wires which are used to attach the scope probes (additionally join one scope probe floor to digital floor on the breadboard. The highest wire is the true knowledge, the following one down is the imaginary knowledge, then the magnitude, and the underside one is the set off. Join the true, imaginary, and magnitude to the three inputs of your scope (in the event you solely have a two-channel scope, you’ll be able to join the true and imaginary solely, with out lacking a lot). The set off could be related to the final scope channel or to the exterior set off of your scope.

Now, set the Freq/Time swap to Freq. In your scope, set the vertical to 2v/div, for every of the inputs. Additionally set the sweep to 20ms/div.

Now you’ll be able to energy the system through the USB connection on the Arduino Nano. Unfold out the traces on the scope and set the scope to set off utilizing the set off enter. Now you can conceal the set off hint. The traces ought to appear like what we see in Determine 3.

Determine 3 The beginning spectrum from -2500 to +2500 Hz the place there’s sign vitality at each -1500 and +1500 Hz.

Now alter the horizontal place so the traces are centered. Ignore the time axis on the underside and the voltage axis on the proper facet—they’re irrelevant (flip them off in case your scope has such a function). The left-to-right axis is frequency with -2500 Hz on the left facet and +2500 Hz on the proper facet. DC or 0 Hz is the middle line. (On scopes with 10 main horizontal markings, every main marking measures off 500 Hz increments.) Vertical is simply a relative, auto-scaled, worth so it’s best to maintain the volts/div the identical for the true, imaginary, and magnitude traces. So, in Determine 3 you’ll be able to see we’ve got sign vitality at each +1500 Hz and -1500 Hz. (Observe, on boot up the true sign is 100 whereas the imaginary amplitude is 0.)

You will note a menu on the I/Q Explorer LCD. Rotating the left rotary encoder will mean you can transfer up and down within the menu. The correct rotary encoder means that you can change the values of the menu merchandise subsequent to the flashing cursor (second line from the highest of the LCD). Within the menu you’ll be able to change the frequency, amplitude and the section of the true (I knowledge) or imaginary (Q knowledge) alerts.) Observe that altering the frequency of both the true or imaginary will change the opposite—they should be on the similar frequency.) The menu additionally has gadgets to print knowledge, plot knowledge, activate/off windowing, activate/off a mixer, and alter the supply for the FFT from the inner generated knowledge to exterior sign from a sign generator.

As a sanity test, Determine 4 is a plot of the true output from a simulation package deal utilizing the identical alerts, pattern charge, and variety of samples. These are as follows: The true sign used has an amplitude of 100 and the imaginary sign has an amplitude of 0. The frequency of each is 1500 Hz. The pattern charge is 5000 samples/second and the variety of samples used within the FFT is 64.

Determine 4 Actual FFT simulation utilizing the identical settings the place the true sign has an amplitude of 100, the imaginary sign has an amplitude of 0, the frequency of each is 1500 Hz, the pattern charge is 5000 samples/second, and the variety of samples used within the FFT is 64.

You’ll be able to see that the true sign matches properly.

Adjusting actual and imaginary sign settings

Let’s change the imaginary sign so it has the identical amplitude as the true sign. Set the imaginary amplitude to 100. Now we get the next in Determine 5.

Determine 5 The FFT when imaginary and actual amplitudes are the identical (set to 100).

You’ll be able to see we solely have a sign at +1500 Hz…there isn’t a destructive frequency element.

If we flip the Freq/Time to “Time” it is possible for you to to see the time area samples used to generate the FFT, with out adjusting something on the scope.

Mixer mode

Now let’s strive quadrature (complex-to-complex) mixing. Transfer down within the menu and activate “Mixer” (extra on transferring and adjusting settings within the obtain). This can do the combination utilizing the true and imaginary alerts you’ve units, and a hard and fast sign having its actual and imaginary setting of 1000 Hz, and amplitudes of 100 and phases set to 0. What you’ll at first is proven in Determine 6.

Determine 6 Quadrature mixing of 1500 Hz with 1000 Hz exhibiting the sign at 500 Hz and a picture created at 2000 Hz.

You’ll be able to see two issues. First, the sign is now at 500 Hz, the distinction of 1500 Hz from our sign and the 1000Hz from the combination sign. Second, there’s a picture created at 2000 Hz (1500 Hz + 500 Hz) but it surely has been eliminated by the arithmetic of the mixer.

Subsequent change the frequency of the true or imaginary sign (bear in mind one will change the opposite) to 500 Hz. Additionally word, as you flip the dial, the FFT frequency will slide down as you method 500 Hz. And as you go previous 1000 Hz you will notice the FFT within the destructive frequency space. Whenever you get to 500 Hz you will notice this in Determine 7.

Determine 7 Quadrature (complex-to-complex) mixing of 500 Hz with 1000 Hz.

You now have generated a destructive frequency—so simple as that.

Observe which you could additionally see the plot, of any of the displayed FFTs, on the PC through the use of the “Serial Plot” choice. You can too get a view of the numerical knowledge through the use of the “Serial Print Knowledge” choice.

Extra enjoyable IQ manipulation

So now that you just’ve seen a couple of examples, you’ll be able to discover I/Q knowledge and quadrature mixing by altering issues just like the amplitude of the true and/or imaginary alerts. Additionally, strive altering the section of alerts. After you get a grasp of that strive altering the section of both. To get an actual deal with on this, see in the event you can manipulate the trig equations to raised perceive the way you get to that FFT. The system additionally has a windowing operate, you’ll be able to play with, that adjusts amplitudes of the info factors earlier than the FFT is calculated (for individuals who know these items, it’s a Hann window). 

Bear in mind, it’s also possible to use precise exterior alerts, reminiscent of these from a two-channel sign generator, to carry out the identical checks. You’ll word although, the FFTs are usually not fairly as secure. There’s extra data on that within the downloadable notes.

One final thought; you’ll discover numerous dialogue on whether or not destructive frequencies are actual (within the conventional sense) or not. My two cents is they don’t seem to be bodily actual as they can’t be transmitted as a single waveform, however they’re a really good mathematical assemble that permits us to govern the alerts that we will obtain. Let the arguing start.

To obtain 3D printable information and doc containing extra working data, a BOM, and further picture, go to: https://makerworld.com/en/fashions/1013533#profileId-993290

The Arduino Nano code could be discovered at: Arduino Nano code could be discovered at: https://github.com/DamianB2/IQ_Explorer

Damian Bonicatto is a consulting engineer with a long time of expertise in embedded {hardware}, firmware, and system design. He holds over 30 patents.

Phoenix Bonicatto is a contract author.

 Associated Content material

• A newbie’s information to energy of IQ knowledge and fantastic thing about destructive frequencies – Half 1
• Exploring software-defined radio (with out the annoying RF) – Half 1
• Exploring software-defined radio (with out the annoying RF)—Half 2
• SDR Fundamentals Half 3: Transmitters
• The digital actuality of 5G – Half 2 (measurements)
• Extremely-wideband I/Q demodulator improves receiver efficiency

The publish A newbie’s information to energy of IQ knowledge and fantastic thing about destructive frequencies – Half 2 appeared first on EDN.

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