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Daqarta for DOS
Data AcQuisition And Real-Time Analysis
Shareware for Legacy Systems

From the Daqarta for DOS Help system:


The modulation rate is controlled by AM Hz, and the percent of modulation (depth) is controlled by AM Pct. Since AM results in the overall level of the wave going above (and below) the baseline Level, AM can't be used when the Level is set to maximum. If AM Pct is set above zero in this case, Level will be automatically reduced to half of full scale.

AM Hz can be set anywhere from 0 to 65535 Hz in 1 Hz steps, while AM Pct allows 16 power-of-2 steps from 0 to 100%... plus a special range called MULT which is "below" zero. Direct entry of AM Pct will result in the nearest power-of-2 value, but to reach the MULT range you will need to enter a negative value (any value) or use cursor adjustment to go below zero. The modulating frequency is always sinusoidal, regardless of whether the carrier Wave is Sine, Ramp, Square, or Triangle.

When viewing the AM waveform, it will look "bubbly" because it is synchronized to the carrier and not the modulator. (See AM Triggering.)

Try the FFT mode with the carrier frequency (Freq) set to 5000 Hz and AM Pct set to 50. As you increase AM Hz, you will see two discrete AM sidebands appear, one on either side of the carrier and separated from it by the value of the modulating frequency. At low modulating frequencies, the carrier line appears to be rather bouncy, and larger than the original Level setting. As you increase the modulation frequency it steadies out at exactly the preset value and is independent of further changes. The height of the sidebands is proportional to the percent of modulation.


Try bringing up the Trigger control menu with CTRL-T and set Source to AM. Now if you view the waveform, the outline looks stable and shows the expected modulation waveform, while the carrier rolls by unsynchronized (unless it happens to be and exact multiple of the modulator). If you view the FFT at low AM Hz modulation rates, the carrier no longer bounces.

Fine-tune the modulating frequency for maximum carrier size, which will be with AM Hz around 15 for 512 points at a 20 kHz sample rate. Flip back to view the waveform, and you can see what is going on: Since we are now locked to the modulator, at this low modulation frequency we are only getting a portion of a modulation cycle per N-points sweep.

If the Trigger Slope is set to Positive and the Trigger Level to zero, then this will be the positive half-cycle of the modulator, which starts from zero modulation (which is the normal carrier amplitude) and grows to maximum amplitude and just starts back down before the end of the trace. Here is where we have the biggest average value of carrier over the N-points width of the trace, which is all that the FFT knows about.


In waveform mode with AM triggering, set AM Hz to see a few modulation cycles on the trace. Move AM Pct between 0 and 100 percent modulation. At 0 percent, you see just the normal carrier amplitude (though it may be unsynchronized due to triggering on the modulator instead of the carrier). Look at only the top edge of the carrier as you increase the modulation, and you will see the modulator sine wave grow larger and larger. As it grows, the positive part of the modulator sine makes the carrier get larger, and the negative part makes the carrier grow smaller. Finally, at 100% modulation, the negative peak takes the carrier just to zero. Daqarta doesn't allow you to go past 100% here, but if it did we would expect to see the negative peak "break through" zero and actually invert the carrier.

The process of amplitude modulation is really just the multiplication of the carrier wave by the sum of one plus the depth-scaled modulator wave. When modulation depth is zero, we just get the normal carrier. When modulation depth is 100%, the modulator and carrier are equal.

sin(carrier) × [1 + depth × sin(modulator)]


When AM Pct is set below 0, a special setting called MULT becomes active. This gives the straight multiplication of the carrier by the modulator (here fixed at 100% of full-scale), with no unity constant added. This is also known as Ring Modulation to old-timers from the pre-digital stone age of electronic music, named after an early circuit that performed multiplication using a (square) ring of 4 diodes connected head to tail.

Multiplication looks superficially similar to 100% AM when viewing waveforms. Try setting AM triggering, and use a carrier Freq of 2500 with AM Hz set to 50. Now scroll AM Pct between 100% and MULT and you will see (besides an obvious size change) that the MULT waveform appears to have twice as many modulation cycles as 100% AM. There is also a shape change, with the 100% AM just "kissing" zero, while the MULT plunges into it. Reduce Freq to 500 and look carefully at the individual carrier cycles as the modulation goes past zero... you should be able to see that in the MULT case the polarity of the carrier reverses at the zero crossing.

To see what's happening, think of a single cycle of the modulator. It starts at zero, so of course zero times the carrier gives zero. It then climbs to a positive peak, so the product of this rising value times the carrier rises as well. It then passes the peak and heads back down to zero, with the product following suit. Now as the modulator goes negative, we get a rising product... the carrier is just inverted. So the modulator's negative half-cycle looks pretty much like the positive one, other than the inversion. Where the 100% AM wave had only one peak and valley per cycle, the multiplier gives two, one for each phase.

But the most interesting difference between multiplication and AM is in the spectra. With AM Pct = 100, flip to FFT and move the carrier up to 5000. Move AM Hz up until you see the AM sidebands move out from the carrier, then run AM Pct down into MULT. Presto! The carrier vanishes, and we are left with only the sidebands. This has practical applications for radio transmission, since the carrier contains a lot of the transmitter power but none of the information used to modulate it. Why waste power that does you no good? In fact, with some clever circuitry it is possible to generate only a single sideband (SSB), since the two sidebands are redundant copies of the same information.

To understand the multiplier operation, dig out that old trigonometry book and look up the formula for multiplying two sines together:

sin(A) × sin(B) = 1/2 × [cos(A-B) - cos(A+B)]

The product of two sines gives two cosines (which look like sines when you don't know the starting point). But the angles (frequencies) of these two cosines are not those of either of the two starting sines... they are the sum and difference, namely our two sideband frequencies!

As we will see under Sine Wave Analysis, this simple formula is the heart of Fourier Transform Theory.


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