Dumb question

[wa2dtw]

I've often wondered about the phase relationship between the carrier and the two sidebands.  My understanding always was that the two sidebands are 180 degrees out of phase with eachother, with each 90 degrees out of phase with the carrier.   But is this really correct?  Does it apply to the RF wave only, the audio content of the sidebands, or both?


73
Steve WA2DTW

[Steve - WB3HUZ]

The phasor animation at the link below may make it more clear. Use the slider control to change the display and stop at various instants in time. The carrier is red, one sideband is green, the other yellow. The display is referenced to the carrier, so only the sideband phasors are rotating. It's like using a strobe light to stop motion (like on a timing belt) and the strobe is synced to the carrier.

As you can see, the sidebands are rotating in opposite directions. This is because the angular velocity of the each of the sideband phasors is either greater and less than the angular velocity of carrier's phasor by the modulating signal’s angular velocity (rotation rate or angular velocity is related to frequency by v = 2*pi*freq) . This means they are just slightly different from the carrier's velocity because the modulating signal is such a low frequency compared to the carrier. You can think of the upper sideband as always slightly gaining on the carrier and the lower sideband as slightly losing angular velocity with respect to the carrier.

Their phases relative to the carrier are constantly changing. Each will add/subtract with the carrier to produce the familiar envelope pattern shown. The black bar in the envelope shows the portion of the envelope produced by the vector addition of the phasors at that particular time.

http://www.amwindow.org/misc/av/phwenvanim.mov

The display is for one modulating tone/frequency. For voice, there would be many, many rotating vectors, all rotating at slightly different rates, with different amplitudes.

Hope this helps.

[k4kyv]

If you replaced the two sideband vectors with one sideband vector of twice the amplitude, you would see that the resultant vector contains both amplitude modulated (the resultant vector varies in length) and phase modulated (the vector swings periodically to the left and right, across the carrier vector) components, and the amplitude component waveform of the resultant vector is very different from the case of DSB AM.  The resultant output vector drops to zero as the negative modulation peak hits 100% just the instant that the tip of the vector brushes by the baseline.

This demonstrates that one sideband plus carrier is not the same thing as true AM.

[Ed WA4NJY]

     K4KYV:
                " This demonstrates that one sideband plus carrier is not the same thing as true AM."


       Isn't this what Drake TR-7 and Ten-Tec ParagonII use for AM transmit. I have a chance to
      buy a VERY nice Paragon II and would be interested in comments about AM performance.

                                                                    Ed Purvis
                                                                    Bradenton, Fl

[wa2dtw]

Many thanks to Steve, Don and Ed.  But I am still confused.   
I thought that the basis for the old "phasing" method of SSB generation and also the current IQ detectors was a fixed  phase separation between the two sidebands, so that when superimposed they would cancel one another.  Is that incorrect?
73
Steve WA2DTW (not an engineer)

[Steve - WB3HUZ]

The sidebands are out of phase, they are rotating in opposite directions. If they were in phase, they would rotate in the same directions. If they were phase locked, their rotations would be identical.

[flintstone mop]

Just think!!! It took someone to figure that all out mathematically. It wasn't an accident that you throw a big audio amplifier through a transformer in series with the plate of the final. FM must have been a real humdinger!!!

Crazy Fred

[Bacon, WA3WDR]

I would say that AM sidebands are in phase alignment with the carrier.  Because they are on opposite sides in frequency, they rotate in opposite directions on the carrier-referenced diagram.  When the sidebands are combined, the combination is precisely in phase or precisely out of phase with the carrier, producing positive and negative amplitude modulation, respectively.

In PM and FM, the sidebands are in phase quadrature to the carrier. Like the AM sidebands, they rotate in opposite directions on the carrier-referenced diagram, because they are on opposing sides of the carrier.  But the combination of the sidebands (called sidecurrents in FM) is primarily in phase quadrature with the carrier, and many higher order sidecurrents in phase alignment and phase quadrature appear as well, such that the composite carrier-sidecurrent amplitude does not change with modulation.  FM/PM is very complex in this regard.

This was all discovered pretty much by accident.  Amplitude was modulated, sidebands were noticed, and theory explained the phenomenon.  Frequency was modulated, sidecurrents were observed, and again theory explained the phenomenon.

[AB2EZ]

Steve

The upper and lower sidebands are at different frequencies... so it is a little confusing to try to think of them as "in phase" or "out of phase".

The formula for AM is s(t) = [1+ m(t)] [cos (2pift)];

where s(t) is the transmitted signal,
m(t) is the modulating (audio) signal, f is the carrier frequency and t is time.

The formula for DSB is s(t) = m(t) [cos (2pift)]; where the absence of the "1" corresponds to the absence of the carrier.

If the modulating (audio) signal m(t) is a sine wave at frequency u (Hz), then the corresponding DSB signal is s(t) = sin (2piut) [cos(2pift)]. From trigonometry, we can rewrite this as s(t) = sin [2pi(f+u)t] + sin[2pi(f-u)t], which correspond to the upper and lower sidebands.

To make a USB single sideband signal, using the phasing method, we need to create a double sideband signal as per the above formula, plus a second double sideband signal of the form s(t) = sin [2pi(f+u)t] - sin [2pi(f-u)t]. When you add this second double sideband signal to the first double sideband signal... the upper sidebands add, and the lower sidebands cancel. To create this second double sideband signal, you need to shift the modulating frequency by 90 degrees, and use it to double sideband modulate a carrier that is also shifted by 90 degrees. I.e., the second double sideband signal is s(t)= cos(2piut)[sin(2pift)]

Best regards
Stu

[wa2dtw]

Stu
Many thanks.  That completely answers my question.
73
Steve WA2DTW