SSB Generation ?

[G8DLH]

Hi everyone!

My copy of "Solid State Design for the Radio Amateur", (1977), an ARRL publication, on page 184 states:

"It may be shown mathematically that a carrier which is amplitude modulated properly and frequency modulated simultaneously will yield a SSB output". No further comment is made. 

This interests me.    I can handle sufficient math to (hopefully) understand this, if  I could find the analysis somewhere! A search around the 'Net revealed nothing.  Any suggestions? Also, any non-math comments would be appreciated.

Regards,

Al / G8DLH

[W2JBL]

 go back a bunch of years and study Armstrong's origional FM exciter desgin. what you are looking for is in there, kinda sorta'...it can generate AM too.

[k4kyv]

Generate full carrier DSB AM, then shift the phase of the carrier 90°, and you end up with a phase modulated signal.

Armstrong's first FM rig was DSB suppressed  carrier, with the 90° phase shifted carrier re-inserted.    Then, to convert the phase modulated signal to FM, the appropriate audio pre-emphasis was used. Problem was, the deviation was very low, so the signal  had to be multiplied many, many times to produce broadcast quality FM, so the original signal started out in the VLF range.

SSB can be resolved to a combination of AM and PM.  There was one method of SSB amplification that was tried, in which the envelope of the SSB signal was detected, and used to modulate a class-C carrier amplifier.  The carrier was generated by severely limiting the SSB signal until all the amplification variations of the carrier were shaved off, leaving only the phase modulated component.  That signal was used to drive the class-C amplifier, and the  result was SSB.

But for it to work properly, the AM portion would have to respond flat down to zero ~.  Otherwise, what happens when the person stops talking and there is no more modulation?  Then comes the old question, what happens to the carrier during those silent periods, just as what happens to the carrier during periods of negative overmodulatin when the carrier completely disappears, as verified by the 'scope, but yet the carrier is supposed to remain steady with all the apparent amplitude variations resulting from its interaction with the sidebands.

A form of SSB, called "compatible SSB" has been used experimentally on the AM broadcast band, by adding the appropriate pre-distortion to the audio signal, isimultaneously with the appropriate phase modulation to the carrier, and the result is that most of the sideband products lie on one side of the carrier, but an ordinary diode type AM envelope detector receives the signal without the normal quadrature distortion associated with receiving one sideband plus carrier with an envelope detector.

The distortion associated with SSB plus carrier is exactly the inverse of the distortion of ordinary AM as received on a "square law" envelope detector.  Many of the early tube type AM broadcast receivers used triode detectors with the square law characteristic, and were well known for their peculiar type of distortion at high modulation percentages.  Supposedly, a square law detector will receive SSB + carrier just like ordinary AM with no BFO and without audio distortion.

The only reason those old detectors worked anywhere near halfway satisfactorily is that in the early days of broadcasting, 100% modulation of the carrier was rare.

[Ian VK3KRI]

Whilst the math is beyond me (school was too long ago) this is the premise behind Envelope elimination and Restorration (EER).
You generate a low level signal (AM or SSB) and split it two ways. One goes to an envelope detector to get the envelope.  The other goes to a hard limiter to give a phase/frequency modulated signal. This signal is amplified by your class C or even better class E amplifier  at high efficincy. You then modulate your final stage with the envelope that was perviusly extracted. Of course the phase resonse of the modulator will have to be quite good, so anything with iron in it is out,  I would assume a PWM modulator with sufficient bandwidth would work quite nicely.
                                                                                    Ian VK3KRI

 

[Bacon, WA3WDR]

EER would be complex, but amplifier efficiency would be higher than class B linear.

While I was experimenting with modulated oscillators, I noticed that when I received an AM signal with some FM on it, it did not tune symmetrically.  If I tuned the receiver on one side of the signal, the audio was loud; if I tuned the receiver on the other side of the signal, the audio was low.  I concluded that this was because slope detection of the FM was in phase with the AM on one side, and out of phase with the AM on the other side.  But this was not true SSB, just something that happened because of the slope of receiver selectivity.

The phasing method of SSB takes two DSB signals with 90 degree differences in carrier phase, and 90 degree difference in audio phase (across the entire audio spectrum).  This 90 degree shift was somewhat difficult back in the day of vacuum tube analog electronics (see "Wideband Phase Shift Networks" by R. B. Dome, Electronics, Vol. 19, No. 12, pages 112-115, December 1946, and "Design of RC Wide-Band 90-degree Phase Difference Networks," D. K. Weaver, Proc. IRE, Vol. 42, pages 671-676, April 1954.), but it can be easily done today using digital signal processing.

A 90-degree shifted carrier DSB signal is similar in many respects to a phase-modulated signal.  The difference is that the carrier is not suppressed in PM, and the sidebands are not exactly the same as DSB.  However, for experimental purposes they are close enough, at a modulation index of 0.5 or less.

So you could phase-modulate an AM signal with audio that is 90 degree shifted from the AM audio, and see if that gives you single-sideband AM.

It would be interesting to take two audio oscillators running at 1 KHz but with maybe 1/10 Hz difference between their frequencies, and amplitude modulate with one, and phase-modulate with the other, and watch what happens to the upper and lower sidebands over time.  You could adjust the relative amounts of AM and PM, and observe the effect.  The phase of the waveforms would slowly vary from 0 through 90 degrees, 180 degrees, 270 degrees, and back to 0 degrees, etc.

I have been thinking about simultaneous in-phase AM and PM, because this would be simple, it would almost double sideband power, and yet it would still demodulate nicely on an envelope detector.

[G8DLH]

Thank you for the replies everyone: very informative. 

[WA1GFZ]

That old solid state handbook was the best book ARRL ever printed.

[Ian VK3KRI]

That old solid state handbook was the best book ARRL ever printed.

Amen to That!

[Rob K2CU]

The first thing to ponder is this:  If it were practical, let alone possible, to use FM/PM combined with DSB AM to produce SSB then we would already be doing it!  And, mathmatically, the phasing method should produce zero alternate sideband.  And would you believe?.. I found three NIB phasitrons in my junk box!!!

For those wanting to brush up on their math, or just to bookmark it for reference purposes, check out:

http://mathworld.wolfram.com

and for the math of DSB AM:

http://mathworld.wolfram.com/WernerFormulas.html

The latter is used to produce double sidband suppressed carrier. Add 1 (DC term) to the modulating signal and you get a carrier out of the multiplication (modulation) process.

According to the ITT "Handbook for Radio Engineers", fourth edition (the bible), if the modulation index is kept below 0.2, then only one sideband pair is produced in FM modulation. These sidebands would have to be amplified as they would be low in amplitude if you wanted to combine them with a similar DSB AM signal to "phase out" one of the sidebands. The rub is that the amplitude of the sidebands is proportional to the modulation index which is, itself, inversely proportional to modulating frequency. IN DSB AM, the amplitude ofthe sidebands is not dependant on the frequency  of the modulating signal. You would need to predistort the frequency response curve of the FM modulating signal (pre-emphasis) in a frequency linear fashion to try and correct for this. This is just about as complex as making the audio phase shift network for the SSB phasing method. You would also have to reintroduce the unmodulated carrier at the right phase to null it out down stream.  There is also contradicting  information about whether the undesired sideband is out of phase between the two modulators to cancell each other in the first place.

As I said initially, if this method worked and was simple, we would be doing it to make SSB signals.

As to the square law detector, the simple diode detector actually has a natural logarithmic function to it. And, the logarithmic function   e^x can be approximated by a series expansion:

   (x)                              2             3
e        =  1 + x  +  (1/2 )x  + (1/6) x  + .....

The square term not only multiplies the two sidbands by the carrer to produce the desired demodulated signal, it also preoduces the cross product of the two sidebands which is 2nd harmonic distortion. the cubic and other terms produce additional harmonic distortion to a lesser degree.

SSB plus carrier (A3H) does not have produce the cross product and resultant 2nd harmonic distiortion. But, it sounds best with a true squarer detector. It also allows for twice the amplitude or four times the power in the one sideband over the power in each of the two in conventional DSB AM.  At full legal power you would have 350 W carrier and 350 W peak in the one sideband.  The Drake TR-7 makes AM this way, by reinserting carrier down stream of the SSB generator.  For rigs with a 1596 or similar multiplier for a product detector, just disable the BFO and feed the IF into the carrier input as well as the signal input...used to be called a homodyne detector, or autodyne, or synchrodyne, etc.   

Anyone interested in experimenting with A3H and true multiplying detectors let me know.

Slope detection of narrow band FM is easily percieved and visulaized that the swinging carrier is riding up and down the slope. The reciever is tuned to the side of the signal such that the carrier is down the slope a little bit. it is simple to visualize that as the carrier swings up the slope the detected voltage increases, and that as it swings downward a lower output is produced, the detected voltage thus following the modulating swing of the carrier.  In FM, the carreir is in quadrature (90 degrees) to the sidebands. Running it into an AM (multiplying) detector results in undesired resutls, mostly because sin x cos = 0.   By running the carrier down on the slope of the reciever's IF amp, the signal is in a situation where the phase is changing across the signal, and ideally, the carrier is at the 90 degree phase shift point. Then you will at least get some audio out of the thing. Basic PLL detectors work great for FM because at lock up, the VCO is locked at 90 degrees to the incoming carrier and the output of the phase detector (a multiplier) is pure recovered modulation.

nuff said.

[WA1GFZ]

"Just disable the BFO" That is exactly what Racal does with the AM demodulation then it gets a carrier from a MC1357 FM demodulator.

Max would be impressed

[Steve - WB3HUZ]

This AM/FM to get sideband is not the same as EER. The reason for using EER is to gain the use of a high efficiency final amp (Class C, D, etc.) I don't think it's complexity that's keeping it from being used. Modulation methods far more complex than EER are used every day. Take a look at your cell phone. There isn't a large demand for SSB in the comms market to begin with, so making it more efficient is not that important. But those Class E boys should check out the EER approach. They could use their Class E amps to run high efficiency slopbucket. Seems like a good use for those amps!

[Bacon, WA3WDR]

Phase modulation and AM could indeed be combined to produce SSB with suppressed carrier. 

Sort-of PM was generated with exciters such as the SB10 by unbalancing the "Q" channel balanced modulator and feeding audio to the "I" channel balanced modulator.  With in-phase audio, an AM signal would be the "I" channel, and a PM signal would be the "Q" channel.  If you put a 90-degree audio phasing network in between them, and balanced the modulation levels properly, and added the two signals together, with the carriers in inverse phase, you would get ssb with carrier suppressed.

This can not be done by PMing an AM signal.  The two signals have to be separately generated, because PM on an AM signal would be changed by the AM on it, if the combination was done that way.   The combination would be partially multiplicative, rather than purely additive.

In exciters like the SB10, it was easier to use two balanced modulators, fed with 90-degree shifted carrier.

[Steve - WB3HUZ]

Here ya go. Math away!

E_s(t) = α(t) cos[ω_ct + φ(t)]

Where, α(t) is the envelope or AM signal, and φ(t) the phase modulation.

[Bacon, WA3WDR]

I'm sure of it, but the PM is not exactly DSB with 90 degree shifted carrier because its amplitude is constant, and DSB with 90 degree shifted carrier has some amplitude variation.  So PM + AM with 90 degree shifted audio would make dirty SSB.  But it would be close enough to demonstrate the science.

The math for FM and PM is really complex.  I'll make a spreadsheet showing the results of the combination over the audio cycle of a sinewave, every 1/8 cycle.

<edit> A crude check using AM modulation levels of 100% shows a lot of garbage.  The lower the mod levels, the better the ssb.  That's because PM is not exactly the same as DSB with 90 degree shifted carrier.

[WU2D]

I wonder if there is way to make SSB by phasing two KW-1's together at the antenna terminals. 

Mike WU2D

[Steve - WB3HUZ]

It's really not complex at all.

Below are the spectra for AM and PM (low mod index, i.e. NBFM like).

Subtract the two and what do you get?

[Bacon, WA3WDR]

I'm working on how to put it onto a spreadsheet, because I understand things best that way.

What I'm realizing is the dynamics.  The carrier level of PM changes when you change the modulation index, but for a fixed sine wave, that will be constant, and I can certainly make SSB with suppressed carrier that way - although there will be a little bit of high order splatter.  Maybe adding a little bit of the right distortion to the AM or the PM audio can cancel that.

But with a varying amplitude waveform like speech or music, the carrier balance will be unstable.  Still, other than the bouncing carrier level, I believe that decent SSB is possible.  Probably by adjusting the PM carrier and deviation levels according to the modulation amplitude, this can be cancelled, but that's starting to get real complicated.

I've already reached the conclusion that it's a lot simpler to use I and Q balanced modulators.

<edit> OK, I got the spreadsheet going, and I expanded it to make a point every five degrees around an audio cycle (360 degrees).  A PM and an AM signal with modulation indices of 0.1 (10% mod AM, 0.1 radian PM) added together, with 90 degree audio phase shift between the AM and the PM, gives me pretty much a circle, centered on the origin, over a cycle of audio - which in this representation is an SSB suppressed carrier signal at + or - the modulating frequency from the carrier, frankly I'm not sure which.  However, I am sure that reversing the polarity of either the PM or the AM would reverse the sideband that was generated.  Since I added the signals at the same unmodulated carrier amplitude, I believe that the carrier balance would hold pretty well up to at least this amount of modulation at all modulating frequencies, at least up to a small fraction of the carrier frequency.

I am convinced.  However, (1) I was convinced before, and (2) this demonstration doesn't mean much.  It means that I can add and subtract sines and cosines and ones, strangely combined with 0.1 for the modulation indices, and arranged in a way that I believe represents AM and PM - and get a circle on a graph.  You'd have to accept and believe that my proof is a proof, that the ones and sines and cosines and 0.1 really represent AM and PM at a modulation index of 0.1, and that the circle really represents SSB, etc.

I have the modulation index controlled by a two cells (one for AM and one for PM), and I tried 1.0 and 0.5 modulation indexes.  YUCK!  It is really flat on one side at a modulation index of 1.0, and it's pretty distorted at a modulation index of 0.5.  It's not quite perfect at a mod index of 0.1, but it's pretty close.  As I said, PM is not exactly like DSB with 90 degree shifted carrier, and the difference gets bigger as the modulation index increases.

[WA1GFZ]

Yesterday I received an email from a guy in Germany who is going to do an article in QEX on modulating a class E final to do SSB. He was asking about my final and how we PDM them. gfz

[Bacon, WA3WDR]

I gotta read up on class E.  I don't know the difference between D, E, etc.  There's stuff here, and on the Window, and on the QIX site, I think.

[Bacon, WA3WDR]

If the modulation can be closely controlled, and RF bandwidth is adequate, which it certainly is for speech, you can use an amplitude-modulated amplifier to amplify any kind of signal.

For example, if you take an SSB signal, and limit it real heavily, you get something like FM or PM, although it's not going to sound like anything you'd want to listen to on an FM receiver.  But if you take that and use it as a "carrier", and you precisely restore the amplitude variations by amplitude-modulating it so that you restore it to what it originally was, then you can produce anything - SSB, DSB, M-ary, Piccolo, television, AM, or whatever - with a modulated amplifier.

I remember W3PHL Fred was talking about this basic technique back in 1967 for a high-level balanced modulator with a single RF tube.  He was trying to do the carrier polarity reversals in the RF driver stage, and feed full-wave rectified audio to the plate modulator.  The problem was timing, because any relative phase shift will introduce a bad glitches.

I think it was the 1978 ARRL Handbook that used this technique as a speech compressor.  It took a speech waveform and clipped it to a total square wave, and then it took the original amplitude variations and remodulated them back onto the square wave.  The amplitude variations in that design were AC-coupled to the modulator, and the result was that the average amplitude was constant.  Probably the same thing can be done to an amplifier like that at RF - by AC coupling, the unit will act as a compressor.  It's not real good peak-controlling ALC, it's just average AGC.  The AC coupling time constant becomes the compression time constant, but it introduces phase shift at the low end.  I think that this relative phase shift issue can be minimized with a phase-shifting all-pass network, though.

It seems to me that a very good peak-controlling compression can be applied to such an amplifier by baseband processing of the amplitude variation information.  Linearity errors can also be corrected in analog with level-dependent loading based on diode breakpoints, or digitally with a digital lookup table for the corrective curvature, and then off to the modulator.  A precision rectifier could be used to measure the incoming signal amplitude, and delay lines can correct for relative timing errors. Such a design could be a very superior RF linear amplifier.

[Steve - WB3HUZ]

What you describe sounds like the Envelope Elimination and Restoration (EER) method of high efficiency SSB amplification. Lots of info on this on the IEEE site. Even some linear ICs out there for this method. More wideband comms equipment, including cell phones are going to this method - saves on batteries.

[WA1GFZ]

I hooked my German contact to Steve's site to see if he can make it work. I don't know what will happen to the phase delay through the pdm filter integrator.....
but I are not dat smart.
5kw slop bucket at high efficiency anyone.....

[Bacon, WA3WDR]

I think it was the 1978 ARRL Handbook that used this technique as a speech compressor.  It took a speech waveform and clipped it to a total square wave, and then it took the original amplitude variations and remodulated them back onto the square wave.  The amplitude variations in that design were AC-coupled to the modulator, and the result was that the average amplitude was constant.  Probably the same thing can be done to an amplifier like that at RF - by AC coupling, the unit will act as a compressor.  It's not real good peak-controlling ALC, it's just average AGC.  The AC coupling time constant becomes the compression time constant, but it introduces phase shift at the low end.  I think that this relative phase shift issue can be minimized with a phase-shifting all-pass network, though.

Oops, that wasn't exactly right.  If I remember correctly, the baseband level information was digitized with a variable-delta modulator, and demodulated by a non-variable delta demodulator... that actually did the compression.  I suppose that the entire square wave-remodulation portion of the design was superfluous, which may be why it was dropped from the handbook the next year. It was certainly interesting, though.

I didn't know that somebody has already picked up on this concept (EER) for SSB amplification.  It's a cool idea.  With a little design trickery, these cool transmitters can be designed as linear amplifiers with great ALC.

If the PDM integrator filter frequency is high enough, it can probably be treated as a simple delay.  An all-pass network could probably tweak any remaining delay twist.  I think it would need a bandwidth several times that of the SSB signal to be clean, though.  I think I was hearing about a 9 KHz top end for some of the new digital modulators - that might be tight, but probably it will work with careful tweaking of response and phasing.

The amplitude variations might look like DSB - full wave rectified sine wave stuff.  The sharp bounces at the baseline need to be accurately reproduced, and that takes modulator bandwidth.  Possibly a QIX technique like going linear at this low-power point could work around that, with careful adjustment of the amount of limiting of the incoming sgnal, and a flattening of the negative peaks of modulation.

[Steve - WB3HUZ]

Lots of interesting high efficiency and high linearity designs out there, many used as we speak in the microwave bands. Some good reading the book below. Was reading about one today using a Class E output amp, PDM modulated with NO filter on the PDM. How about that!?!

High-Linearity RF Amplifier Deisgn, Peter B. Kennington, Artech House, 2000, ISBN 1-58053-143-1