Amplitude Modulation and Bandwidth...

[Michael Lawton]

     Over the years I have heard a lot of discussions about bandwidth in AM radio. Thinking about the basics of amplitude modulation, I never quite understood what all this fuss was about, or exactly HOW these "sidebands" ended up being generated. After all, AM is merely the increasing and decreasing of the carrier wave strength based on the fluctuation of an audio wave form. The detection of the signal merely consists of the rectification of that carrier wave, and the smoothing out of the result so only the audio frequency remains. Simple enough. So where do these "sidebands" come in? How come they exist? Why are they important at all? It seems that as long as the carrier strengthens and weakens in accordance with the audio wave form all should work fine.

     A discussion of this subject came up over on the Philco Phorum, and I expressed my puzzlement about its importance. I got a number of answers, but mostly they amounted to "Because the books say so, and the books have magical mathematics formulae to prove it." I have never accepted these kinds of explanations, so I began to do research. I was sure there was a simple explanation.

     After doing considerable searching and reading through both the books in my own engineering library and also searching on line, I FINALLY figured out a decent explanation as to how the sidebands on either side of the carrier are generated. The books all too often just say "This is so" and give some mathematical formula, but don't give any clear explanation as to the HOW these sidebands come about. There is a simple, one word explanation, HETERODYNE. It is the same principle used to generate the IF in a superheterodyne radio. Just as when you mix two RADIO frequencies, you produce image frequencies both above and below the tuned carrier frequency by the sum and difference of the local oscillator frequency; when you combine an AUDIO frequency with a carrier frequency, you produce image frequencies both above and below the carrier frequency by the sum and difference of the two frequencies. Since speech and music consist of MULTIPLE frequencies, each of these frequencies which mix with the carrier frequency produce images above and below the carrier. This multiplicity of images forms what are known as the upper and lower sidebands. If you just remember the word HETERODYNE, and what it means, then sidebands make sense.

[David C. Poland]

Forget about the notion of side bands for audio quality.

I think of it this way with regard to the IF amplifier.  The audio signal is a low frequency amplitude signal (with an audio range of maybe 80 to 4000 HZ of maybe 50 to 8000 Hz) which is riding on the higher AM radio frequency. A really sharply tuned IF amp will have a very narrow peak for the IF frequency. Such a sharply tuned IF will allow only a narrow range of audio frequencies through - a low fidelity result for your ear. Why? the higher audio frequencies (music notes, for example) are outside of the center of the sharply tuned IF frequency. The radio design engineer has determined the audio quality in the choices of parts. Don't expect decent fidelity from a 5 tube table radio. To enable the higher musical notes to reach the speaker, the IF frequency must not be too sharply peaked. The IF amp of a high quality radio may be designed to produce two peaks very close to each other - staggered peaks if you will - for higher fidelity reception.. Say, the 1st iF at 456 KC and the 2nd IF a hair higher. Or maybe the primary of each IF at 456 and the each secondary a tad higher. Or may switch in a another IF coil or two. An oscilloscope can show the resulting IF peak(s).

The high fidelity Scott AW-23 and Scott Philharmonic have a variable selectively control. It is a bank of small tuning caps, one per IF amp coil, on a separate control shaft below the IF coils. The small tuning caps are arranged on the control shaft so that when advancing the control for higher fidelity audio, these small tuning caps detune the IF peak, thus broadening  the IF peak. These Scott models will receive as much as 30 to 16,000 Hz audio  with very good fidelity if the audio signal range is truly that wide, pretty rare now, but in the mid1930s, there were experimental stations broadcasting a high fidelity like that above 1500KC on the dial. (Before FM began in 1940). High fidelity AM is fine with a strong/local station putting out a higher fidelity program. But otherwise, you just pick up more noise and static.

[Michael Lawton]

Yes, David, I understand that principle, basically what the small caps do is DE-TUNE the IF transformer, thus broadening the passed band of frequencies, and reducing the selectivity. What I was always hazy about was the WHY of the sidebands, WHY did they exist, HOW did they come about. I have never been one to accept the "Because I say so", or in this case because some book says so, not even when it is backed up with magical, mystical equations. Nope, ya gotta give it to me clear and simple. I wracked my brain over this with my research, and then it hit me. It is simply a matter of HETERODYNE. The sounds being used to modulate the carrier constitute many different frequencies, each of which will heterodyne with the carrier frequency, and produce an image above and below the carrier frequency equal to the sum or difference of THAT PARTICULAR FREQUENCY. Because there are many different ones, they make an entire band above and below the carrier frequency, and, the higher the frequency which one wishes to modulate the carrier, the greater the deviation of those images will be. SIMPLE ! HETERODYNE ! So... why don't the electronics texts just explain it that way and make it understandable instead of cloaking it in a load of over technical mumbo jumbo? SHEESH !

[Igor Golioto]

Just another take-

The answer is in the mathematics of a modulated AM signal.  Without a lengthy treatise of the equations, when an audio signal of let's say 5 kHz bandwidth (realistically containing audio signal from 40 Hz to 5 kHz) is modulated with an example carrier frequency of 1000 kHz (the frequency of a carrier signal is the frequency you tune to on the radio dial)- the resulting waveform contains energy between -5 kHz and +5 kHz from that center carrier frequency in a traditional dual sideband AM signal.  If this signal were to pass through a  bandpass filter, it should ideally have a width of 10 kHz, centered at 1000 kHz in this example.

The long and short of the equations is that when multiplying waveforms 1 and 2, when they can both be described as being sinusoidal functions having frequencies 1 and 2, the function that describes the resulting waveform is the sum of two sinusoids, with one part having a frequency that is the sum of the two original frequencies and the second part having a frequency that is the difference of the two frequencies. 

The IF frequency is something that happens after the mixer/converter stage does it's thing, taking that 1000 kHz signal in the example above and converting it using the hetrodyning principal to the IF frequency, i.e. 455 kHz is some receivers.  Again, this principal is best explained with the mathematical equations associated with the mixing of two waveforms- which is actually like a mathematical multiplication of the signal at the local oscillator and the RF frequency.  This signal that passes onto the IF transformers is centered at 455 kHz ( in this example)- but just as before it contains energy between 450 and 460 kHz

[Michael Lawton]

Yes, Igor, that is pretty much what I said, however perhaps in simpler words. The principle is THE SAME with both AF amplitude modulation of an RF carrier frequency, and the combination a received RF signal with a local oscillator signal to produce the IF to be amplified in a superheterodyne radio. Where you are talking about a "band" of AF, I make the distinction that the "band" consists of many different distinct audio frequencies which fall within a range, the "band" you refer to. Each if these DISTINCT frequencies produce an image frequency above and below the carrier frequency by their sum or difference from the carrier. If you looked at an actual tracing of the whole sidebands, you would see that they are actually constantly changing along with the audio modulation. Were the modulation from a single sine wave frequency, you would see a single, very narrow spike at the plus and minus area of the tracing. For each frequency added there would be more spikes. With the complexity of frequencies in music and speech there would be so many of these spikes that it would look like a sort of hill on either side of the carrier frequency, and that the shape and nuances of the top of that "hill" are constantly changing with the sounds being imposed on the carrier. The production of these image frequencies which make up the sideband is exactly the same as the principle used to create the IF frequency, which is that the combining of two frequencies produces image frequencies the sum and difference above and below the original frequency. That principle is known as 'HETERODYNING" . As long as we remember that, and how it works, we can understand where the upper and lower sidebands in AM radio come from, and how they are produced.