Analogies exist to help you wrap your head around concepts that may not be obvious. Good analogies will offer insights to other behaviors besides. Many concepts in electronics are taught wrong at first, such as AM Modulation, then retaught once you get comfortable with the core concepts.

This came out of a thread in a different sub-forum, but can someone elaborate on what's the wrong (but pedagogically useful) model of AM modulation, and what's the right one?

This has got me wondering if I was taught the wrong model, and if I'm still in the dark about the right one...

M

 

The people who hold that opinion will have to weigh in. I only know a single explanation and it hasn't changed in over half a century.

 

OK, the quick skinny. When you are taught how AM is created, are you taught about the amplitude of the carrier being varied, or about sidebands?

The answer is it is in the sidebands, but until you have advanced to a point you can work with the concepts, it is taught that the amplitude is varied. It is almost true, true enough most people buy into it without thinking, but look into spectrum analyzers sometime.

If you like to play with computer graphics, take a 1Mhz sine wave, graph it about a 10 thousand cycles or so. Then add a 1.001Mhz sine wave, and look at the resultant waveform of the two added together. You will see a 1Khz AM modulation pattern, even though the 1Mhz signal is a constant amplitude. It is the sum and the difference of a heterodyned signal, the 1 Khz being heterodyned onto a 1 Mhz signal (but it can be created other ways, as in the two signals I set up).

Many times in electronics there are several ways of looking at problems. The different ways of looking at them can have two identical circuits used in entirely different ways, both valid.

 

Ah..to modulate you don't add two signals together you multiply them. When you know enough trigonometry to work out the multiplication of two sine waves you see the terms quite clearly. The output contains the original two frequencies and the sum and the difference. It's all in the mathematics.

 

When talking about sidebands and AM it is simply additive. When talking two different sine waves you add the instantaneous voltage of the waveforms, then plot the new points (remember the two frequencies, 1.000Mhz and 1.001Mhz, difference of 1Khz). The classic spectrum display of sum and difference is adding and subtraction, not multiplication.

I was able to demonstrate this using a simple basic program on a TRS80 in the late 70's, which is why I referred to a computer model.

To be honest, I don't know where you are going. I was referring to the fact when teaching AM modulation sidebands are not mentioned until the end of the semester, not the beginning. AM is simplistic, because there is a one to one correspondence between frequencies, which makes it much easier to demonstrate how sidebands are the modulation. The point is, sidebands are the basis for all modulation schemes.

 

When talking about sidebands and AM it is simply additive. When talking two different sine waves you add the instantaneous voltage of the waveforms, then plot the new points (remember the two frequencies, 1.000Mhz and 1.001Mhz, difference of 1Khz). The classic spectrum display of sum and difference is adding and subtraction, not multiplication.

I was able to demonstrate this using a simple basic program on a TRS80 in the late 70's, which is why I referred to a computer model.

To be honest, I don't know where you are going. I was referring to the fact when teaching AM modulation sidebands are not mentioned until the end of the semester, not the beginning. AM is simplistic, because there is a one to one correspondence between frequencies, which makes it much easier to demonstrate how sidebands are the modulation. The point is, sidebands are the basis for all modulation schemes.

Where I am going is that modulation is an inherently non-linear process. In the circuit we call a "mixer" two signals are combined by multiplication, not addition. Adding two sine waves of different frequencies together is interesting to be sure, but it is not modulation. It also does not produce signal components at the sum and the difference of the two input frequencies.

http://en.wikipedia.org/wiki/Amplitude_modulation

At least read the basic wiki article and tell me where it says that modulation is done with addition instead of multiplication. Seems pretty clear to me.

 

This is the way I presently look at it:

Describing the process of AM modulation as varying the amplitude of a carrier is perfectly valid and reasonable and describes how many modulators physically work. In describing the information contained in the resulting signal, it is "more" correct to talk about how the modulation of a pure carrier results in sidebands and this is where the information resides. But that doesn't make it "wrong" to describe the information as existing in the variations in the amplitude of the carrier. I think both are correct, just one is much more general and useful.

 

Ok, adding two sine waves together produces variations in amplitude. As I said before it is interesting but hardly qualifies as modulation. It also does not produce new frequencies. Do the FFT of a sum of two sine waves and tell me what you get.

 

Geez... I have no idea what you guys are talking about.

 

Ok, adding two sine waves together produces variations in amplitude. As I said before it is interesting but hardly qualifies as modulation. It also does not produce new frequencies. Do the FFT of a sum of two sine waves and tell me what you get.

I would expect you to get a spike at the two frequencies. You would NOT get a spike at the "difference" frequency of 0.999MHz. Modulate the amplitude and you should get both.

 

Both approaches work for me. The amplitude spectra [not shown] are identical.

 

Both approaches work for me. The amplitude spectra [not shown] are identical.

But the claim, if I understood it correctly, was that just summing the carrier and the carrier plus modulating waveform was sufficient to produce the same spectra. You added both sidebands explicitly (which I would expect to yield the same result).

Now, my understanding is that AM modulation is a bit more involved because you can't just take a modulating sine wave, for instance, and multiply the carrier amplitude by it since you can't distinquish between positive and negative amplitudes. So don't you normally apply a DC offset to the modulating signal so that it never goes negative (and, in practice, always stays somewhat positive to provide margin).

Maybe I'm missing something, because I am just now starting to look at this stuff with a fine-tooth comb and I'm sure I have a lot of misconceptions that I will be finding and correcting as I go.

 

Yes - I was a little puzzled by Bill's statement. I thought maybe he had actually added both the sum and difference sidebands but had neglected to make that clear. What is interesting is the result of a single sideband plus the carrier addition does look like an AM signal, albeit with a lower modulation index - even though [strictly speaking] it does not have the same spectrum as the true AM signal. Presumably one could therefore demodulate the SSB+Carrier signal in an AM receiver without any difficulty.

 

Yes - I was a little puzzled by Bill's statement. I thought maybe he had actually added both the sum and difference sidebands but had neglected to make that clear. What is interesting is the result of a single sideband plus the carrier addition does look like an AM signal, albeit with a lower modulation index - even though [strictly speaking] it does not have the same spectrum as the true AM signal. Presumably one could therefore demodulate the SSB+Carrier signal in an AM receiver without any difficulty.

This is called SSB, although I think the carrier is usually suppressed as well. Demondulating it is possible, but I believe you first have to remodulate it with a local carrier to generate the missing sideband. I don't know if you can do it more directly with an IQ demodulator or not. Ain't there yet.

 

Both approaches work for me. The amplitude spectra [not shown] are identical.

Oh, I meant to ask what software you used for this.

Thanks.

 

Amplitude modulation is the modulation of an AC signal by an AC signal with different frequency.

If you looks at a typical graphical plot it appears as if the carrier signal is indeed multiplied by the modulating signal. 10% modulation for instance relate to a multiplication between 1 and 0.9

sin(x) - blue - carrier
sin(5*x)*0.2 - red - modulator

sin(x) + (sin (5*x) * 0.2) - additive product (modulated carrier)

sin(x) * (sin (5*x) * 0.2) - multiplication - ??

http://www.mathe-fa.de/en

 

Oh, I meant to ask what software you used for this.

Thanks.

It's called "Powersim". Primarily developed for power / power electronics sims but useful for other things as well.

 

This is called SSB, although I think the carrier is usually suppressed as well. Demondulating it is possible, but I believe you first have to remodulate it with a local carrier to generate the missing sideband. I don't know if you can do it more directly with an IQ demodulator or not. Ain't there yet.

I think one could readily recover the modulating signal using a simple envelope detector. I don't think you would need to re-instate the 'missing' sideband in a typical bog standard AM receiver.

 

One of the reasons I dispute the model where you vary the carrier amplitude is the carrier does not actually vary amplitude, it is the sidebands that do all the varying. To achieve 100% modulation you do not vary the RF carrier, but the side band amplitude.

A statement was made that AM is not linear, in an ideal system I would dispute that too. The sidebands are spectrally identical to the audio. You don't need both side bands either, upper or lower sidebands work equally well by themselves, nor do you need to suppress the carrier, though this is done to reduce the real radiated power in a real world setup. Power is money, the watts sent into the void are not free.

AM is used for more than commercial broadcasts, which explain some of the statements I made in the previous paragraph that may seem off. Commercial broadcasts choose to leave the carrier intact, to act as a simple reference and simplify a whole class of receivers. Crystal radios existed long before a lot of fancier electronic systems, it was the original radio receiver. Crystal radios were used before there was audio modulation too, it came as quite a shock to the hobbiests listening to Morse signals when there was music in a medium where it had not been conceived that could do this by a majority of people.

Perhaps someday I'll try to improve the AAC book, this particular aspect of electronics is one of my strengths, it is what I chose in college to study. Digital was around in the late 70's, but it was not the big dog in electronics it has become since. Telephony has become a tail of digital and internet, but before the internet became the primary telephone carrier it was Upper SSB AM (Single Side Band AM) Suppressed Carrier that was the primary way of carrying many telephone channels on a base band (BB) signal. Understand, every bit of this is analog, and was used to carry digital signals in analog fashion. A typical BB signal had a very low frequency response (some of the equipment I worked on with Collins Radio actually went down to DC) up to 14 Mhz or more with a very flat frequency response, and the BB signal was FM modulated onto a 70Mhz IF frequency. If it was telephone it was sliced into 4Khz segments, starting from 300hz up to the 14Mhz I mentioned, each 4Khz USSB signal being one voice channel. Telephone specs for this technology was 300Hz-3.4Khz, the 3.5Khz to 4Khz was used as guard frequencies to prevent cross talk between voice channels.

The reason I say if it was telephone is the same 70Mhz FM carrier was used for video signals with early satellites. Once you had a BB signal, there was very little difference in how it was treated by the phone or satellite company. Land line IF equipment and satellite electronics was interchangeable in many cases. A lot of engineers and techs at Collins would buy surplus or rejected racks and make some very high tech satellite receivers. I doubt management (those who weren't doing it themselves) would have approved, but they could not have stopped it if they tried.

Many of the concepts you guys are already aware of, so when I start explaining the basics I am talking to people who may never have really studied it in depth, nor put much thought into it. The old tech was very complete, and worked well. Much of it was developed in WWI, as those wires strung across battlefields were bought with blood, and they wanted to get as much use from those wires as they could.

Take a spectrum of a complex audio waveform.

Now lets take a look when you modulate this onto a 1Mhz carrier at approximately 50% index.

If you were to overlap the audio and RF sidebands you would find they are proportionally identical. This is why AM is such a good system to teach with, it is relatively simple to explain mathematically. FM is superior in every way, but is a major nightmare to describe with math. Edwin Armstrong, who invented FM and much, much more, was a genius of the 1st magnitude, and should be up there with Tesla in my opinion. As with Tesla, most of his inventions were stolen by big business of the time, who settled with his widow after his suicide. It was a popular business model, and unfortunately, it worked. It is interesting to me how politics and business can drive technical developments in electronics in many cases.

AM, and just about every RF technology afterwards, revolves around the concept of heterodyne. When you heterodyne two signals together, you are heterodyning them. Heterodyne is not simply mixing two signals together, though semantics gets tricky here, as many cases heterodyning two signals together is referred to as mixing. Just be aware there are two distinct types of mixing signals together.

Linear mixing two signals is straightforward. You mix them, you have the same two signals afterwards. Useful perhaps, but no big deal.

When you feed two signals into a nonlinear device such as a diode, something interesting happens, you get the sum and the difference of both frequencies. You now have 4 frequencies where you used to have two. Over the years electronics has developed Balanced Mixers, where the two original frequencies are nulled out and all you are left with is the sum and the difference frequencies.

Now here is where the true core concept of AM comes in. When you modulate a RF carrier with audio, you are actually heterodyning the two frequency sets. This is the real basis of AM. The resultant output has the RF carrier along with the sum and differences of the audio/RF. These are the sidebands.

The model taught beginners is a very compelling analogy. It is simple,easy to understand, models well, and can actually help come up with new concepts that are valid. It will never go away. Only with a deeper understanding does it show its flaws, but by that time you see the flaws you don't need that model. You have advanced to the point you can work without it, and with something a lot closer to reality.

Electronics is full of cases like this, though this is one of the most prominent. So even if you think it is wrong (as I do) it is so dang useful only an idiot would not use it to help beginners understand some really new concepts that can be quite challenging. If the beginners continue studying and reach a better level of understanding later then it can be abandoned, but for the moment, it works.

 

I have build an AM transmitter some time ago. It works even if just on the margin. At some point inside the circuit, I have the audio, and I have the 560KHz signal. And I have wired this in a way the amplitude of the RF is somehow put in dependence of the audio signal.

I must admit I did not care much about the actual waveform, sidebands, or if this is called heterodyning.

If a circuit like this really works 1:1 like in the model, you would get one sharp response, or even no response at all. Indeed you get a range where the radio set will response, including some weird noise as well.

I have never had any need to deal with radio circuits, besides to build a small AM transmitter, rather for hobby purpose.

This does not however mean that I am thinking a concept from a book would be true 1:1 in reality. It has something to do with it, but there are limits. And that is not just because all the hidden capacitors and small wire inductances.

All models are just an approximation to understand the subject, to understand it more, or even to understand it at all.