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#151
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AM electromagnetic waves: 20 KHz modulationfrequencyonanastronomically-low carrier frequency
In article ,
Don Bowey wrote: On 7/5/07 10:27 PM, in article , "Ron Baker, Pluralitas!" wrote: "Don Bowey" wrote in message ... On 7/5/07 12:00 AM, in article , "Ron Baker, Pluralitas!" wrote: "Don Bowey" wrote in message ... On 7/4/07 8:42 PM, in article , "Ron Baker, Pluralitas!" wrote: "Don Bowey" wrote in message ... On 7/4/07 10:16 AM, in article , "Ron Baker, Pluralitas!" wrote: "Don Bowey" wrote in message ... On 7/4/07 7:52 AM, in article , "Ron Baker, Pluralitas!" wrote: snip cos(a) * cos(b) = 0.5 * (cos[a+b] + cos[a-b]) Basically: multiplying two sine waves is the same as adding the (half amplitude) sum and difference frequencies. No, they aren't the same at all, they only appear to be the same before they are examined. The two sidebands will not have the correct phase relationship. What do you mean? What is the "correct" relationship? One could, temporarily, mistake the added combination for a full carrier with independent sidebands, however. (For sines it is sin(a) * sin(b) = 0.5 * (cos[a-b]-cos[a+b]) = 0.5 * (sin[a-b+90degrees] - sin[a+b+90degrees]) = 0.5 * (sin[a-b+90degrees] + sin[a+b-90degrees]) ) -- rb When AM is correctly accomplished (a single voiceband signal is modulated The questions I posed were not about AM. The subject could have been viewed as DSB but that wasn't the specific intent either. What was the subject of your question? Copying from my original post: Suppose you have a 1 MHz sine wave whose amplitude is multiplied by a 0.1 MHz sine wave. What would it look like on an oscilloscope? What would it look like on a spectrum analyzer? Then suppose you have a 1.1 MHz sine wave added to a 0.9 MHz sine wave. What would that look like on an oscilloscope? What would that look like on a spectrum analyzer? So the first (1) is an AM question and the second (2) is a non-AM question...... What is the difference between AM and DSB? AM is a process. DSB (double sideband), with carrier, is it's most simple result. DSB without carrier (suppressed carrier dsb) requires using, at least, a balanced mixer as the AM multiplier. And requires, for proper reception, that a carrier be recreated at the receiver which has not only the amplitude of the original, but also its exact phase. Absent some sort of "pilot" to get things synchronized, this makes reception very difficult. Isaac |
#152
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AM electromagnetic waves: 20 KHzmodulationfrequencyonanastronomically-low carrier frequency
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#153
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AM electromagnetic waves: 20 KHz modulationfrequencyonanastronomically-low carrier frequency
isw wrote:
What is the difference between AM and DSB? AM is a process. DSB (double sideband), with carrier, is it's most simple result. DSB without carrier (suppressed carrier dsb) requires using, at least, a balanced mixer as the AM multiplier. And requires, for proper reception, that a carrier be recreated at the receiver which has not only the amplitude of the original, but also its exact phase. Absent some sort of "pilot" to get things synchronized, this makes reception very difficult. Isaac Try a Costas loop. |
#154
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AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
On Jul 5, 9:38 pm, John Fields wrote:
On Thu, 05 Jul 2007 18:37:21 -0700, Jim Kelley wrote: John Fields wrote: You missed my point, which was that in a mixer (which the ear is, since its amplitude response is nonlinear) as the two carriers approach each other the difference frequency will go to zero and the sum frequency will go to the second harmonic of either carrier, making it largely appear to vanish into the fundamental. Hi John - Given two sources of pure sinusoidal tones whose individual amplitudes are constant, is it your claim that you have heard the sum of the two frequencies? --- I think so. So if you have for example, a 300 Hz signal and a 400 Hz signal, your claim is that you also hear a 700 Hz signal? You'd better check again. All you should hear is a 300 Hz signal and a 400 Hz signal. The beat frequency is too high to be audible. (Note that if the beat frequency was a separate, difference signal as you suggest, at this frequency it would certainly be audible.) A year or so ago I did some casual experiments with pure tones being fed simultaneously into individual loudspeakers to which I listened, and I recall that I heard tones which were higher pitched than either of the lower-frequency signals. Subjective, I know, but still... Excessive cone excursion can produce significant 2nd harmonic distortion. But at normal volume levels your ear does not create sidebands, mixing products, or anything of the sort. It hears the same thing that is shown on both the oscilloscope and on the spectrum analyzer. Interestingly, this afternoon I did the zero-beat thing with 1kHz being fed to one loudspeaker and a variable frequency oscillator being fed to a separate loudspeaker, with me as the detector. My comments were based on my results in that experiment, common knowledge, and professional musical and audio experience. I also connected each oscillator to one channel of a Tektronix 2215A, inverted channel B, set the vertical amps to "ADD", and adjusted the frequency of the VFO for near zero beat as shown on the scope. Sure enough, I heard the beat even though it came from different sources, but I couldn't quite get it down to DC even with the scope's trace at 0V. Of course you heard beats. What you didn't hear is the sum of the frequencies. I've had the same setup on my bench for several months. It's also one of the experiments the students do in the first year physics labs. Someone had made the claim a while back that what we hear is the 'average' of the two frequencies. Didn't make any sense so I did the experiment. The results are as I have explained. jk |
#156
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AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
In article ,
"Ron Baker, Pluralitas!" wrote: "isw" wrote in message ... In article , "Ron Baker, Pluralitas!" wrote: "isw" wrote in message ... In article , "Ron Baker, Pluralitas!" wrote: snip While it might not be obvious, the two cases I described are basically identical. And this situation occurs in real life, i.e. in radio signals, oceanography, and guitar tuning. The beat you hear during guitar tuning is not modulation; there is no non-linear process involved (i.e. no multiplication). Isaac In short, the human auditory system is not linear. It has a finite resolution bandwidth. It can't resolve two tones separted by a few Hertz as two separate tones. (But if they are separted by 100 Hz they can easily be separated without hearing a beat.) Two tones 100 Hz apart may or may not be perceived separately; depends on a lot of other factors. MP3 encoding, for example, depends on the ear's (very predictable) inability to discern tones "nearby" to other, louder ones. I'll remember that the next time I'm tuning an MP3 guitar. The same affect can be seen on a spectrum analyzer. Give it two frequencies separated by 1 Hz. Set the resolution bandwidth to 10 Hz. You'll see the peak rise and fall at 1 Hz. Yup. And the spectrum analyzer is (hopefully) a very linear system, producing no intermodulation of its own. Isaac What does a spectrum analyzer use to arive at amplitude values? An envelope detector? Is that linear? I'm sure there's more than one way to do it, but I feel certain that any Which of them is linear? A well-designed filter running into a bolometer would be. You can make the filter narrow enough to respond to only one frequency component at the time, and a bolometer just turns the signal power into heat; nothing nonlinear there... Isaac |
#157
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AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
In article ,
"Ron Baker, Pluralitas!" wrote: "isw" wrote in message ... In article , "Ron Baker, Pluralitas!" wrote: "isw" wrote in message ... In article , "Ron Baker, Pluralitas!" wrote: "isw" wrote in message ... snip After you get done talking about modulation and sidebands, somebody might want to take a stab at explaining why, if you tune a receiver to the second harmonic (or any other harmonic) of a modulated carrier (AM or FM; makes no difference), the audio comes out sounding exactly as it does if you tune to the fundamental? That is, while the second harmonic of the carrier is twice the frequency of the fundamental, the sidebands of the second harmonic are *not* located at twice the frequencies of the sidebands of the fundamental, but rather precisely as far from the second harmonic of the carrier as they are from the fundamental. Isaac Whoa. I thought you were smoking something but my curiosity is piqued. I tried shortwave stations and heard no harmonics. But that could be blamed on propagation. There is an AM station here at 1.21 MHz that is s9+20dB. Tuned to 2.42 MHz. Nothing. Generally the lowest harmonics should be strongest. Then I remembered that many types of non-linearity favor odd harmonics. Tuned to 3.63 MHz. Holy harmonics, batman. There it was and the modulation was not multiplied! Voices sounded normal pitch. When music was played the pitch was the same on the original and the harmonic. One clue is that the effect comes and goes rather abruptly. It seems to switch in and out rather than fade in an out. Maybe the coming and going is from switching the audio material source? This is strange. If a signal is multiplied then the sidebands should be multiplied too. Maybe the carrier generator is generating a harmonic and the harmonic is also being modulated with the normal audio in the modulator. But then that signal would have to make it through the power amp and the antenna. Possible, but why would it come and go? Strange. Hint: Modulation is a "rate effect". Isaac Please elaborate. I am so eager to hear the explanation. The sidebands only show up because there is a rate of change of the carrier -- amplitude or frequency/phase, depending; they aren't separate, stand-alone signals. Since the rate of change of the amplitude of the second harmonic is identical to that of the fundamental, the sidebands show up the same distance away, not twice as distant. Isaac That doesn't explain why the effect would come and go. I don't understand what effect you're referring to here. But once again you have surprised me. Your explanation of the non-multiplied sidebands, while qualitative and incomplete, is sound. I'm a physicist/engineer, and have been for a long time. I have always maintained that if the only way one can understand physical phenomena is by solving the differential equations that describe them, then one does not understand the phenomena at all. If you can express a thing in words, such that a person with little mathematical ability can understand what's going on, *then* you have a good grasp of it. It looks to me that the tripple frequency sidebands are there but the basic sidebands dominate. Especially at lower modulation indexes. I don't understand what you are saying here either. And in my experience, the term "modulation index" is more likely to show up in a discussion of FM or PM than AM; are you using it interchangeably with "modulation percentage"? Isaac |
#158
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AM electromagnetic waves: 20 KHz modulation frequencyonanastronomically-low carrier frequency
On Thu, 05 Jul 2007 00:00:45 -0700, Ron Baker, Pluralitas! wrote:
Suppose you have a 1 MHz sine wave whose amplitude is multiplied by a 0.1 MHz sine wave. What would it look like on an oscilloscope? This is close, but not to scale: http://en.wikipedia.org/wiki/Amplitude_modulation The animation shows the "envelope". What would it look like on a spectrum analyzer? One vertical "spike" at 1 MHz with smaller spikes at .9 and 1.1 MHz. The height of the two side spikes, depends on the depth of modulation. In this case, the carrier is in the middle, and the sidebands are on the sides. Then suppose you have a 1.1 MHz sine wave added to a 0.9 MHz sine wave. What would that look like on an oscilloscope? whatever 0.9 MHz superimposed on 1.1 MHz looks like. ;-) What would that look like on a spectrum analyzer? One spike at each input frequency, 0.9 and 1.1 MHz. If they're mixed nonlinearly, then you get modulation, as above. Hope This Helps! Rich |
#159
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AM electromagnetic waves: 20 KHzmodulationfrequencyonanastronomically-low carrier frequency
On 7/6/07 12:15 PM, in article
, "isw" wrote: In article , Don Bowey wrote: On 7/6/07 9:36 AM, in article , "isw" wrote: In article , Don Bowey wrote: On 7/5/07 10:27 PM, in article , "Ron Baker, Pluralitas!" wrote: "Don Bowey" wrote in message ... On 7/5/07 12:00 AM, in article , "Ron Baker, Pluralitas!" wrote: "Don Bowey" wrote in message ... On 7/4/07 8:42 PM, in article , "Ron Baker, Pluralitas!" wrote: "Don Bowey" wrote in message ... On 7/4/07 10:16 AM, in article , "Ron Baker, Pluralitas!" wrote: "Don Bowey" wrote in message ... On 7/4/07 7:52 AM, in article , "Ron Baker, Pluralitas!" wrote: snip cos(a) * cos(b) = 0.5 * (cos[a+b] + cos[a-b]) Basically: multiplying two sine waves is the same as adding the (half amplitude) sum and difference frequencies. No, they aren't the same at all, they only appear to be the same before they are examined. The two sidebands will not have the correct phase relationship. What do you mean? What is the "correct" relationship? One could, temporarily, mistake the added combination for a full carrier with independent sidebands, however. (For sines it is sin(a) * sin(b) = 0.5 * (cos[a-b]-cos[a+b]) = 0.5 * (sin[a-b+90degrees] - sin[a+b+90degrees]) = 0.5 * (sin[a-b+90degrees] + sin[a+b-90degrees]) ) -- rb When AM is correctly accomplished (a single voiceband signal is modulated The questions I posed were not about AM. The subject could have been viewed as DSB but that wasn't the specific intent either. What was the subject of your question? Copying from my original post: Suppose you have a 1 MHz sine wave whose amplitude is multiplied by a 0.1 MHz sine wave. What would it look like on an oscilloscope? What would it look like on a spectrum analyzer? Then suppose you have a 1.1 MHz sine wave added to a 0.9 MHz sine wave. What would that look like on an oscilloscope? What would that look like on a spectrum analyzer? So the first (1) is an AM question and the second (2) is a non-AM question...... What is the difference between AM and DSB? AM is a process. DSB (double sideband), with carrier, is it's most simple result. DSB without carrier (suppressed carrier dsb) requires using, at least, a balanced mixer as the AM multiplier. And requires, for proper reception, that a carrier be recreated at the receiver which has not only the amplitude of the original, There is no need at all to match the carrier amplitude of the original signal. You can use an excessively high carrier injection amplitude with no detrimental affect, but if the injected carrier is too little, the demodulated signal will be over modulated and sound distorted. but also its exact phase. Exact, not required. The closer the better, however. Well, OK, the phase must at least bear a constant relationship to the one that created the signal. If you inject a carrier that has a quadrature relationship to the one that created the DSB signal, the output will be PM (phase modulation). In between zero and 90 degrees, the output is a combination of the two. If the injected carrier is not at precisely the proper frequency, the phase will roll around and the output will be unintelligible. Not unintelligible.... Donald Duckish. On a more practical side, however, most receiver filters for ssb will essentially remove one sideband if there are two, and can attenuate a carrier so the local product detector can do it's job resulting in improved receiving conditions. But this is more advanced than the Ops questions. Don Isaac |
#160
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AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
On Thu, 05 Jul 2007 20:02:15 -0600, Bob Myers wrote:
"John Fields" wrote in message You missed my point, which was that in a mixer (which the ear is, since its amplitude response is nonlinear) as the two carriers approach each other the difference frequency will go to zero and the sum frequency will go to the second harmonic of either carrier, making it largely appear to vanish into the fundamental. Sorry, John - while the ear's amplitude response IS nonlinear, it does not act as a mixer. "Mixing" (multiplication) occurs when a given nonlinear element (in electronics, a diode or transistor, for example) is presented with two signals of different frequencies. But the human ear doesn't work in that manner - there is no single nonlinear element which is receiving more than one signal. Sure there is - the cochlea. (well, the whole middle ear/inner ear system.) What would the output look like if you summed a 300Hz tone and a 400Hz tone and sent the sum to a log amp and spectrum analyzer/fft? Thanks, Rich |
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