AM Modulation

The upper, the lower sideband plus the carrier. Do a fourier transform of an AM modulation.

Rene

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Ing.Buero R.Tschaggelar - http://www.ibrtses.com
& commercial newsgroups - http://www.talkto.net

You see the carrier frequency, the carrierfreqiuency plus the modulation frequency, and the carrier frequency minus the modulation frequency.

When you modulate a carrier, you are essentially multiplying two sine waves toegther

sine A. sin B = 0.5 .(cos (A-B) - cos(A+B))

This implies that you shouldn't see the carrier frequency at all, but few modulators are perfect multipliers.

Single side band modulation schemes use 90-degree pahse shifters to generate cosine A and cosine B so that one can form the second product

cosine A. cosine B = 0.5.(cos (A-B) + cos (A+B)

which cn then be summed with the first to suppress the sum frequency (or - with very little more ingenuity) the difference frequency,

Electronics is really just a branch of trigometry .

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Bill Sloman, Nijmegen

The other reason the carrier doesn't disappear is that most AM stations don't run at 200% modulation.

John

The reason why most AM signals do have carrier is not because multipliers aren't as good as the designers would want. It is because they _want_ to transmit the carrier. And they want to transmit it because that simplifies the receiver. You can use a simple envelope detector (diode + capacitor + resistor) in your receiver, whereas without a carrier you would need coherent detection, which is more complex and expensive.

Best,

Or, to put things more precisely, the equation for AM is more like

v = sin(c*w*t) * (1 + m)

where m is the modulation signal, in the range +-1 for max (100%) modulation. The "1" is what preserves the carrier component, not the imperfection of the modulator.

John

(snip)

I couldn't get past the first sentence, "Amplitude modulation (AM) is a form of modulation in which the amplitude of a carrier wave is varied in direct proportion to that of a modulating"

Where does wikipedia get it's B.S?

Thanks for the useless reference.

Wiki is totally open; anybody can post, just like a newsgroup.

Not all engineers are articulate; for example, many have trouble distinguishing between "its" (possessive) and "it's" (contraction for "it is".)

John

Out of curiosity -- what don't you like about it? It's about as technically correct as you can fit into one sentence, and I doubt that I could make it any clearer while retaining the formal language that seems to prevail on wikipedia.

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Tim Wescott
Wescott Design Services

The stumbling block for understanding AM is the difference between the "carrier" and the envelope". They are not the same.

Imagine a spectrum analyzer with a very narrow filter. Imagine it can seperate or resolve all the components and that you will be able to see the "carrier" seperatley from the sidebands. In this case you will see that the carrier sits there unchanged all the time despite the modulation. The sidebands jump up and down but the carrier is unchanged.

If however, the spectrum analyzer is not narrow enough to resolve the carrer apart from the sidebands, then they will merge and you will be looking at the "envelope". The envelope is the picture we are all familiar with of AM on an oscilloscope. The ampliture of the ENVELOPE varies up and down in step with the modulation.

The sidebands combine with each other and with the carrier to vary the amplitude of the ENVELOPE. The carrier itself is unchanging.

Hope this helps.

Mark

the best understanding for the 3 freq. you can get if you make a small drawing like that: One vector representing the carrier wave. on the top of the carrier wave you draw 2 smaller vectors rotating clock and anticlockwise at the top of the carrier vector. Taking care that the resulting vector of the

2 smaller vectors is always in phase with the carrier vector. The rotating freq. represents the modulating freq. So the sum of the 3 vectors is a change in length of only one vector = modulated carrier. In the thread you can find the math. to that, namely the solving of the multiplication of the carrier freq. with the modulating freq (additions theorem for trig. functions).

rotating small vectors = the carrier freq.+ and - the modulating freq. \\ / \\/ | fixed vector = the carrier | | | if the small vectors are 50% of length of the carrier vector, as drawn, you get 100% modulation. If you delete the carrier vector and one small vector = the sideband you have SSB lower or upper sideband, depending which small vector you delete.

Rudi

He's too young and pig-headed to go look up "amplitude", "carrier wave", "varied", "direct proportion", things like that.

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Flap!
The Pig Bladder from Uranus, still waiting for that

It was hammered into my thick skull forty years ago and it still reverberates.

"... once you start modulating it no part of it is a sine wave.."

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Boris Mohar

** Shame that is NOT the formula for a normal AM wave. ** Because it is the wrong formula. ** Normal AM ones are certainly not.

Unless the signal is "double sideband, suppressed carrier".

** Horse manure.

"Electronics" was initially a branch of physics, then expanded to become a branch of engineering in its own right separate from "electrical engineering".

It is all about exploiting nature for human benefit.

Maths is just a tool to help achieve that end.

........ Phil

"Mark"

** When the modulation level falls to zero - they certainly are. ** I think it only deepens the mystery of AM for novices.

Carrier and envelope amplitude seem to be the same in practice.

Thinking in terms of the "frequency domain" is the problem.

....... Phil

As if Phil Allison knew the "right" formula - the cantankerous poseur would have posted it if he did.

If fact, given the range of applications for amplitude modulation, there is no one "right" formula. The one I posted is probably the right one to answer the OP's question, but that's a level of comprehension that Phil can't manage.

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Bill Sloman, Nijmegen

I noticed that everyone seems to be using trig to explain the addition of frequencies.

Having been deprived of trig, I prefer Euler's formula, which, IMO, is simply unforgettable:

e^jw=cosw +jsinw ---> cosw=1/2(e^jw+e^-jw)

You can express all your signals in this form so that not only do the resulting signals from modulation becomes easy compute, but you can

*see* the additions happening in the exponents.

-Le Chaud Lapin-

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Welcome back, Jim. :-)

Thanks ?:-)

...Jim Thompson

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|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |