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Hi Jerry

Thanks for the nice explanation. Though QMX wasn't first... EER techniques are I believe, used commericially. In amateur radio:

In 2017 the Polar Explorer was explained in a QEX article:

See also the Polar Explorer website:

?

I visited the booth at the 2019 Dayton Hamvention.?

Next was the uSDX transceiver by Guido PE1NNZ which evolved from the QRP Labs QCX transceiver. Several people developed versions of uSDX, including many Chinese produced implementations on AliExpress and eBay; Manuel DL2MAN and Guido PE1NNZ run the (tr)uSDX project which is a closed-source version of uSDX distributed by authorized producers only.?

Polar Explorer is rather complex and hasn't evolved into a commercial product. And uSDX/(tr)uSDX performance doesn't really qualify it as a serious or reasonable SSB transceiver, as a result of the limited hardware resources (CPU and the rest of the design).?

It's fair to say QMX/QMX+ is the first serious successful amateur radio SSB product. But it's very important to recognize the predecessors and remember that we stand on the shoulders of giants! In particular Guido's project really demonstrated and showed the way, we should be forever grateful.?

73 Hans G0UPL

On Mon, Oct 14, 2024, 18:59 Jerry Gaffke via <jgaffke=[email protected]> wrote:

After years of reading about the filter and phasing methods of SSB generation, EER can seem mysterious and magical.? How can a single oscillator generate all the needed component frequencies of an SSB signal?
The wire from your antenna at any instant in time has a particular voltage, all signals that the antenna is sensitive to come through that single wire.? Looking at it with an oscilloscope will show the voltage jumping about randomly, this would be impossible to recreate with a single oscillator.
Now assume we send the signal from your antenna through a very good filter, only allowing through one two-tone SSB test signal that is 2000 Hz wide.? This signal is very simple, perhaps the sum of two sine waves of equal amplitude at 7200 and 7202 KHz. ?
From secondary school algebra, the sum of two sine waves of equal amplitude is given by: ? ?sin(a)+sin(b) = 2*sin((a+b)/2) * cos((a-b)/2)
So the result of our sine waves at 7000 and 7002 KHz summed together is a sine wave of 7001 KHz multiplied by (modulated by) a cosine wave (a sine wave with a 90 degree phase shift) of 1 KHz, as shown in the images at ?
If we have a third sine wave in the mix, that can be added to the waveform resulting from the sum of the first two.? Varying amplitudes make an exact solution impossible, but the summation can be accomplished numerically.? This is repeated for as many component sine waves as we wish. ?
Any SSB signal can be broken down into component sine waves through a Fourier transform, and we now know that the sum of those components will be a sine wave of varying amplitude and slightly varying frequency (or phase).? The variations in frequency and amplitude required are quite slow, determined by the audio bandwidth.? Therefore, a single oscillator of which we can control the amplitude and the frequency is sufficient to create an SSB signal.
The theory behind EER was first proposed by Kahn in 1952, the computations required were not then practical but are now within easy reach of a processor such as the STM32F446.? Much to my astonishment, Hans has demonstrated that the frequency of the Si5351 can be controlled accurately and quickly enough to meet the phase requirements of a clean SSB signal, making the QMX the first practical EER SSB transmitter that I am aware of.? EER allows a very efficient final amplifier and a minimal hardware design if we can ignore the millions of transistors and thousands of lines of code inside that $5 processor.? Of course, a $10 broadcast band receiver on Ebay can have a few million transistors in it these days.

?

Jerry, KE7ER