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AM electromagnetic waves: 20 KHz modulation frequency onanastronomically-low carrier frequency
"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. onto a carrier via a non-linear process), at an envelope detector the two sidebands will be additive. But if you independe ntly place a carrier at frequency ( c ), another carrier at ( c-1 khz) and another carrier at (c+ 1 kHz), the composite can look like an AM signal, but it is not, and only by the most extreme luck will the sidebands be additive at the detector. They would probably cycle between additive and subtractive since they have no real relationship and were not the result of amplitude modulation. |
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: "Keith Dysart" wrote in message ps.com... On Jul 3, 2:07 pm, Keith Dysart wrote: On Jul 3, 12:50 pm, John Fields wrote: On Mon, 2 Jul 2007 23:03:36 -0700, "Ron Baker, Pluralitas!" wrote: "John Smith I" wrote in message ... Radium wrote: snip 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? snip What would it look like on a spectrum analyzer? | | | | | | --------+--------------------+-------+------+---- 100kHz 0.9MHz 1MHz 1.1MHz 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? snip Tricky!!! It looks like AM but it isn't, it's just the phases sliding past each other slowly and algebraically adding which creates the illusion. What would that look like on a spectrum analyzer? | | | | -----------------------------+--------------+---- 0.9MHz 1.1MHz -- JF But if you remove the half volt bias you put on the 100 kHz signal in the multiplier version, the results look exactly like the summed version, so I suggest that results are the same when a 4 quadrant multiplier is used. And since the original request was for a "1 MHz sine wave whose amplitude is multiplied by a 0.1 MHz sine wave" I think a 4 quadrant multiplier is in order. ...Keith- Ooops. I misspoke. They are not quite the same. The spectrum is the same, but if you want to get exactly the same result, the lower frequency needs a 90 degree offset and the upper frequency needs a -90 degree offset. And the amplitudes of the the sum and difference frequencies need to be one half of the amplitude of the frequencies being multiplied. ...Keith You win. :) When I conceived the problem I was thinking cosines actually. In which case there are no phase shifts to worry about in the result. I also forgot the half amplitude factor. 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. 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 |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
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 |
AM electromagnetic waves: 20 KHz modulation frequencyonanastronomically-low carrier frequency
On Thu, 5 Jul 2007 00:00:45 -0700, "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? --- The first example is amplitude modulation precisely _because_ of the multiplication, while the second is merely the algebraic summation of the instantaneous amplitudes of two waveforms. The circuit lists I posted earlier will, when run using LTSPICE, show exactly what the signals will look like using an oscilloscope and, using the "FFT" option on the "VIEW" menu, give you a pretty good approximation of what they'll look like using a spectrum analyzer. If you don't have LTSPICE it's available free at: http://www.linear.com/designtools/software/ -- JF |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
On Thu, 05 Jul 2007 00:06:02 -0700, isw wrote:
In article , John Fields wrote: On Wed, 04 Jul 2007 09:11:58 -0700, isw wrote: In article , "Ron Baker, Pluralitas!" wrote: You win. :) When I conceived the problem I was thinking cosines actually. In which case there are no phase shifts to worry about in the result. I also forgot the half amplitude factor. 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). --- That's not true. The human ear has a logarithmic amplitude response and the beat note (the difference frequency) is generated there. The sum frequency is too, but when unison is achieved it'll be at precisely twice the frequency of either fundamental and won't be noticed. Now you get to explain why the beat is measurable with instrumentation, and can can be viewed in the waveform of a high-quality recording. --- Simple. The process isn't totally linear, starting with the musical instrument itself, so some heterodyning will inevitably occur which will be detected by the measuring instrumentation. --- Then go on to show why all other multi-frequency-component signals (e.g. a full orchestra) don't produce similar intermodulation effects in ears under normal conditions. --- They do, and why don't you try being a little less of a pompous ass? -- JF |
AM electromagnetic waves: 20 KHz modulation frequencyonanastronomically-low carrier frequency
On Jul 5, 10:01 am, John Fields wrote:
On Thu, 5 Jul 2007 00:00:45 -0700, "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? --- The first example is amplitude modulation precisely _because_ of the multiplication, while the second is merely the algebraic summation of the instantaneous amplitudes of two waveforms. The circuit lists I posted earlier will, when run using LTSPICE, show exactly what the signals will look like using an oscilloscope and, using the "FFT" option on the "VIEW" menu, give you a pretty good approximation of what they'll look like using a spectrum analyzer. If you don't have LTSPICE it's available free at: http://www.linear.com/designtools/software/ -- JF Since your modulator version has a DC offset applied to the 1e5 signal, some of the 1e6 signal is present in the output, so your spectrum has components at .9e6, 1e6 and 1.1e6. To generate the same signal with the summing version you need to add in some 1e6 along with the .9e6 and 1.1e6. The results will be identical and the results of summing will be quite detectable using an envelope detector just as they would be from the modulator version. Alternatively, remove the bias from the .1e6 signal on the modulator version. The spectrum will have only components at .9e6 and 1.1e6. Of course, an envelope detector will not be able to recover this signal, whether generated by the modulator or summing. ....Keith |
AM electromagnetic waves: 20 KHz modulation frequencyonanastronomically-low carrier frequency
"John Fields" wrote in message ... On Thu, 5 Jul 2007 00:00:45 -0700, "Ron Baker, Pluralitas!" snip 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? --- The first example is amplitude modulation precisely _because_ of the Is there multiplication in DSB? (double sideband) multiplication, while the second is merely the algebraic summation of the instantaneous amplitudes of two waveforms. The circuit lists I posted earlier will, when run using LTSPICE, I think you did (sin[] + 1) * (sin[] + 1) not sin() * sin() show exactly what the signals will look like using an oscilloscope and, using the "FFT" option on the "VIEW" menu, give you a pretty good approximation of what they'll look like using a spectrum analyzer. If you don't have LTSPICE it's available free at: http://www.linear.com/designtools/software/ Yes, I have LTSPICE. It is pretty good. -- JF |
AM electromagnetic waves: 20 KHz modulationfrequencyonanastronomically-low carrier frequency
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...... (1 A) On scope will be a classical envelope showing what appears to be the carrier amplitude voltage varying from the effects of the sideband phases and voltages. It's an optical delusion, but is good for viewing linearity and % modulation. (1 B) The spectrum analyzer will show a carrier at 1 MHz, a carrier at 999.9 kHz (LSB), and a carrier at 1.1 MHz (USB). (1 C) Not asked, but needing an answer here, is "if the .1 MHZ modulation were replaced by a changing signal such as speech or music what would the analyzer show?" It would show an unchanging Carrier at 1 MHZ with frequency and amplitude changing sidebands extending above and below the unchanging carrier. (2 A) The scope would display a 1.1 MHz sine wave and a .9 MHz sine wave. They could be free-running or, depending on the scope features, either one or both could be used to sync a/the trace(s). (2 B) The spectrum analyzer will show a carrier at 1.1 MHz, and a carrier at .9 MHz. Don |
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 ... 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 |
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: 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 competently designed unit will not add any signals of its own to what it is being used to analyze. Isaac |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
In article ,
John Fields wrote: On Thu, 05 Jul 2007 00:06:02 -0700, isw wrote: In article , John Fields wrote: On Wed, 04 Jul 2007 09:11:58 -0700, isw wrote: In article , "Ron Baker, Pluralitas!" wrote: You win. :) When I conceived the problem I was thinking cosines actually. In which case there are no phase shifts to worry about in the result. I also forgot the half amplitude factor. 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). --- That's not true. The human ear has a logarithmic amplitude response and the beat note (the difference frequency) is generated there. The sum frequency is too, but when unison is achieved it'll be at precisely twice the frequency of either fundamental and won't be noticed. Now you get to explain why the beat is measurable with instrumentation, and can can be viewed in the waveform of a high-quality recording. --- Simple. The process isn't totally linear, starting with the musical instrument itself, so some heterodyning will inevitably occur which will be detected by the measuring instrumentation. That would suggest that there could be "low IM" instruments which would be very difficult to tune, since they would produce undetectably small beats; in fact that does not happen. It would also suggest that it would be difficult or impossible to create beats between two very-low-distortion signal generators, which is also not the case. Other than the nonlinearity of the air (which is very small for "ordinary" SPL, there's no mechanism to cause IM between two different instruments, although beats are still generated. The beat is simply a vector summation of two nearly identical signals; no modulation needs to take place. Or consider this: At true "zero beat" with the signals exactly 180 degrees out, no energy is avaliable for any non-linear process to act on. Then go on to show why all other multi-frequency-component signals (e.g. a full orchestra) don't produce similar intermodulation effects in ears under normal conditions. --- They do Well, no, mostly they don't, until you get to really high SPL. and why don't you try being a little less of a pompous ass? Exposing claims to conditions they have difficulty with is a good way to understand why those claims are invalid -- so long as the claimant actually explains what's going on, and doesn't just make up answers that fit the previously stated beliefs. Isaac |
AM electromagnetic waves: 20 KHz modulation frequencyonanastronomically-low carrier frequency
In article ,
"Ron Baker, Pluralitas!" wrote: "John Fields" wrote in message ... On Thu, 5 Jul 2007 00:00:45 -0700, "Ron Baker, Pluralitas!" snip 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? --- The first example is amplitude modulation precisely _because_ of the Is there multiplication in DSB? (double sideband) Yes, and in fact, that multiplication referred to above creates a DSB-suppressed-carrier signal. To get "real" AM, you need to add back the carrier *at the proper phase*. FWIW, if you do the multiplication and then add back a carrier which is in quadrature (90 degrees) to the one you started with, what you get is phase modulation, a "close relative" of FM, and indistinguishable from it for the most part. A true DSB-suppressed carrier signal is rather difficult to receive precisely because of the absolute phase requirement; tuning a receiver to the right frequency isn't sufficient -- the phase has to match, too, and that's really difficult without some sort of reference. A SSB-suppressed carrier signal is a lot simpler to detect because an error in the frequency of the regenerated carrier merely produces a similar error in the frequency of the detected audio (the well-known "Donald Duck" effect). Isaac |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-lowcarrier frequency
John Fields wrote:
On Wed, 04 Jul 2007 09:11:58 -0700, isw wrote: In article , "Ron Baker, Pluralitas!" wrote: The beat you hear during guitar tuning is not modulation; there is no non-linear process involved (i.e. no multiplication). --- That's not true. But it is true. The human ear has a logarithmic amplitude response and the beat note (the difference frequency) is generated there. The ear does happen to have a logarithmic amplitude response as a function of frequency, but that has nothing to do with this phenomenon. (It relates only to the aural sensitivity of the ear at different frequencies.) What the ear responds to is the sound pressure wave that results from the superposition of the two waves. The effect in air is measurable with a microphone as well as by ear. The same thing can be seen purely electrically in the time domain on an oscilloscope, and does appear exactly as Ron Baker described in the frequency domain on a spectrum analyzer. The sum frequency is too, but when unison is achieved it'll be at precisely twice the frequency of either fundamental and won't be noticed. The ear does not hear the sum of two waves as the sum of the frequencies, but rather as the sum of their instantaneous amplitudes. When the pitches are identical, the instantaneous amplitude varies with time at the fundamental frequency. When they are identical and in-phase, the instantaneous amplitude varies at the fundamental frequency with twice the peak amplitude. When the two pitches are different, the sum of the instantaneous amplitudes at a fixed point varies with time at a frequency equal to the difference between pitches. This does have an envelope-like effect, but it is a different effect than the case of amplitude modulation. In this case we actually have two pitches, each with constant amplitude, whereas with AM we have only one pitch, but with time varying amplitude. The terms in the trig identity are open to a bit of misinterpretation. At first glance it does look as though we have a wave sin(a+b) which is being modulated by a wave sin(a-b). But what we have is a more complex waveform than a pure sine wave with a modulated amplitude. There exists no sine wave with a frequency of a+b in the frequency spectrum of beat modulated sine waves a and b. As has been noted previously, this is the sum of two waves not the product. I think it can also help not to inadvertantly switch back and forth from time domain to frequency domain when thinking about these things. ac6xg |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
On Thu, 05 Jul 2007 10:00:33 -0700, isw wrote:
In article , John Fields wrote: On Thu, 05 Jul 2007 00:06:02 -0700, isw wrote: In article , John Fields wrote: On Wed, 04 Jul 2007 09:11:58 -0700, isw wrote: In article , "Ron Baker, Pluralitas!" wrote: You win. :) When I conceived the problem I was thinking cosines actually. In which case there are no phase shifts to worry about in the result. I also forgot the half amplitude factor. 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). --- That's not true. The human ear has a logarithmic amplitude response and the beat note (the difference frequency) is generated there. The sum frequency is too, but when unison is achieved it'll be at precisely twice the frequency of either fundamental and won't be noticed. Now you get to explain why the beat is measurable with instrumentation, and can can be viewed in the waveform of a high-quality recording. --- Simple. The process isn't totally linear, starting with the musical instrument itself, so some heterodyning will inevitably occur which will be detected by the measuring instrumentation. That would suggest that there could be "low IM" instruments which would be very difficult to tune, since they would produce undetectably small beats; --- Not at all. Since tuning is the act of comparing the acoustic output of a musical instrument to a reference, the "IM" of the instrument would be relatively unimportant, with a totally linear device giving the best output. For tuning, anyway. Then, the output of the instrument and the reference would be mixed, in the ear, with zero beat indicating when the instrument's output matched the reference. --- in fact that does not happen. It would also suggest that it would be difficult or impossible to create beats between two very-low-distortion signal generators, which is also not the case. --- That is precisely the case. Connect the outputs of two zero distortion signal generators so they add, like this, in a perfect opamp, (View in Courier) +-----+ +--------+ +---------+ +-----+ | SG1 |---[R]--+----[R]---+--| POWER |--| SPEAKER |--| EAR | +-----+ | | | AMP | +---------+ +-----+ | +V | +--------+ +-----+ | | | | SG2 |---[R]--+----|-\ | +----------+ +-----+ | --+--| SPECTRUM | +----|+/ | ANALYZER | | | +----------+ GND -V and the spectrum analyzer will resolve the signals as two separate spectral lines, while the ear will hear all four signals, if f1 + f2 is within the range of audibility. --- Other than the nonlinearity of the air (which is very small for "ordinary" SPL, there's no mechanism to cause IM between two different instruments, although beats are still generated. The beat is simply a vector summation of two nearly identical signals; no modulation needs to take place. --- I understand your point and, while it may be true, the incontrovertible fact remains that the ear is a non-linear detector and will generate sidebands when it's presented with multiple frequencies. What remains to be done then, is the determination of whether the beat effect is due to heterodyning, or vector summation, or both. --- Or consider this: At true "zero beat" with the signals exactly 180 degrees out, no energy is avaliable for any non-linear process to act on. --- Or any other process for that matter, except the conversion of that acoustic energy into heat. That is, with the signals 180° out of phase and precisely the same amplitude, didn't you mean? --- Then go on to show why all other multi-frequency-component signals (e.g. a full orchestra) don't produce similar intermodulation effects in ears under normal conditions. --- They do Well, no, mostly they don't, until you get to really high SPL. --- That's not true. Why do you think some harmonies sound better than others? Because the heterodyning occurring at those frequencies causes complementary sidebands to be generated which sound good, and that happens at most SPL's because of the ear's nonlinear characteristics. --- and why don't you try being a little less of a pompous ass? Exposing claims to conditions they have difficulty with is a good way to understand why those claims are invalid -- so long as the claimant actually explains what's going on, and doesn't just make up answers that fit the previously stated beliefs. --- I wasn't talking about making and/or debating claims, I was talking about your smartass "Now you get to explain" and "Then go on to show why" cracks. -- JF |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
On Thu, 05 Jul 2007 13:48:04 -0700, Jim Kelley
wrote: John Fields wrote: On Wed, 04 Jul 2007 09:11:58 -0700, isw wrote: In article , "Ron Baker, Pluralitas!" wrote: The beat you hear during guitar tuning is not modulation; there is no non-linear process involved (i.e. no multiplication). --- That's not true. But it is true. The human ear has a logarithmic amplitude response and the beat note (the difference frequency) is generated there. The ear does happen to have a logarithmic amplitude response as a function of frequency, but that has nothing to do with this phenomenon. --- Regardless of the frequency response characteristics of the ear, its response to amplitude changes _is_ logarithmic. For instance: CHANGE APPARENT CHANGE IN SPL IN LOUDNESS ---------+------------------ 3 dB Just noticeable 5 dB Clearly noticeable 10 dB Twice or half as loud 20 dB 4 times or 1/4 as loud --- (It relates only to the aural sensitivity of the ear at different frequencies.) What the ear responds to is the sound pressure wave that results from the superposition of the two waves. The effect in air is measurable with a microphone as well as by ear. The same thing can be seen purely electrically in the time domain on an oscilloscope, and does appear exactly as Ron Baker described in the frequency domain on a spectrum analyzer. The sum frequency is too, but when unison is achieved it'll be at precisely twice the frequency of either fundamental and won't be noticed. The ear does not hear the sum of two waves as the sum of the frequencies, but rather as the sum of their instantaneous amplitudes. When the pitches are identical, the instantaneous amplitude varies with time at the fundamental frequency. When they are identical and in-phase, the instantaneous amplitude varies at the fundamental frequency with twice the peak amplitude. --- 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. --- When the two pitches are different, the sum of the instantaneous amplitudes at a fixed point varies with time at a frequency equal to the difference between pitches. --- But the resultant waveform will be distorted and contain additional spectral components if that summation isn't done linearly. This is precisely what happens in the ear when equal changes in SPL don't result in equal outputs to the 8th cranial nerve. --- This does have an envelope-like effect, but it is a different effect than the case of amplitude modulation. In this case we actually have two pitches, each with constant amplitude, whereas with AM we have only one pitch, but with time varying amplitude. --- That's not true. In AM we have two pitches, but one is used to control the amplitude of the other, which generates the sidebands. --- The terms in the trig identity are open to a bit of misinterpretation. At first glance it does look as though we have a wave sin(a+b) which is being modulated by a wave sin(a-b). But what we have is a more complex waveform than a pure sine wave with a modulated amplitude. --- No, it's much simpler since you haven't created the sum and difference frequencies and placed them in the spectrum. --- There exists no sine wave with a frequency of a+b in the frequency spectrum of beat modulated sine waves a and b. As has been noted previously, this is the sum of two waves not the product. --- "Beat modulated" ??? LOL, if you're talking about the linear summation of a couple of sine waves, then there is _no_ modulation of any type taking place and the instantaneous voltage (or whatever) out of the system will be the simple algebraic sum of the inputs times whatever _linear_ gain there is in the system at that instant. Real modulation requires multiplication, which can be done by mixing two signals in a nonlinear device and will result in the output of the original signals and their sum and difference frequencies. --- I think it can also help not to inadvertantly switch back and forth from time domain to frequency domain when thinking about these things. --- Oh, well... -- JF |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
On Tue, 03 Jul 2007 22:42:20 -0700, isw wrote:
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. Have you ever actually observed this effect? Thanks, Rich |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-lowcarrier frequency
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? ac6xg |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
On Jul 5, 7:15 pm, John Fields wrote:
Regardless of the frequency response characteristics of the ear, its response to amplitude changes _is_ logarithmic. It seems clear that the brain's perception of amplitude changes is logarithmic. It is not so obvious that this means there exists a non-linear amplitude response in the ear such that harmonics are generated. I suggest the following alternative explanations: - the nerve signals from the ear to the brain could have a linear response but the low level driver in the brain converts it to a logarithmic response for later processing. - the nerves from the ear could have a logarithmic response - the AGC which limits the signal applied to the detectors in the ear by tightening muscles in the bones, could have a logarithmic response. The cycle by cycle response in the ear could be linear. The actual detector (if I recall my physiology correctly) consists of little hairs that actually detect different frequencies so that what is presented to the low level drivers is actually a spectrum, not the sound waveform. A non-linear amplitude response in these hairs would not produce inter-mod but would be preceived as non-linear. It is possible that the eardrum and bones connecting to the cochlea exhibit a non-linear response and are capable of generating inter-mod, but this is not proven just because the system has an apparent logarithmic response at the point of perception. Is there other evidence that the ear is non-linear before separating the signal into its component frequencies and therefore can generate inter-mod? "Beat modulated" ??? LOL, if you're talking about the linear summation of a couple of sine waves, then there is _no_ modulation of any type taking place and the instantaneous voltage (or whatever) out of the system will be the simple algebraic sum of the inputs times whatever _linear_ gain there is in the system at that instant. Real modulation requires multiplication, which can be done by mixing two signals in a nonlinear device and will result in the output of the original signals and their sum and difference frequencies. A 4 quadrant multiplier will leave no trace of the original two frequencies, only the sum and difference will be present in the spectrum. This could equally well have been generated by adding the two frequencies present in the spectrum. If the two frequencies in the spectrum are close, there will be an observable envelope that will be perceived as the sound rising and falling in amplitude. There is no need for a non-linear response for this to occur. Not that this proves there is not one, but the existence of the effect does not prove that there is one. ....Keith |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
"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. Frequency discrimination in the ear occurs through the resonant frequencies of the 20-30,000 fibers which make up the basilar membrane within the cochlea. Each fiber responds only to those tones which are at or very near its resonant frequency. While the response of each fiber to the amplitude of the signal is nonliner, no mixing occurs because each responds, in essence, only to a single tone. A model for the hearing process might be 30,000 or so non-linear meters, each seeing the output of a very narrow-band bandpass filter covering a specific frequency within the audio range. There is clearly no mixing, at least as the term is commonly used in electronics, going on in such a situation, even though there is non-linearity in some aspect of the system's response. Audible "beats" are perceived not because there is mixing going on within the ear, but instead are due to cycles of constructive and destructive interference going on in the air between the two original tones. Bob M. |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
In article ,
John Fields wrote: On Thu, 05 Jul 2007 10:00:33 -0700, isw wrote: In article , John Fields wrote: On Thu, 05 Jul 2007 00:06:02 -0700, isw wrote: In article , John Fields wrote: On Wed, 04 Jul 2007 09:11:58 -0700, isw wrote: In article , "Ron Baker, Pluralitas!" wrote: You win. :) When I conceived the problem I was thinking cosines actually. In which case there are no phase shifts to worry about in the result. I also forgot the half amplitude factor. 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). --- That's not true. The human ear has a logarithmic amplitude response and the beat note (the difference frequency) is generated there. The sum frequency is too, but when unison is achieved it'll be at precisely twice the frequency of either fundamental and won't be noticed. Now you get to explain why the beat is measurable with instrumentation, and can can be viewed in the waveform of a high-quality recording. --- Simple. The process isn't totally linear, starting with the musical instrument itself, so some heterodyning will inevitably occur which will be detected by the measuring instrumentation. That would suggest that there could be "low IM" instruments which would be very difficult to tune, since they would produce undetectably small beats; --- Not at all. Since tuning is the act of comparing the acoustic output of a musical instrument to a reference, the "IM" of the instrument would be relatively unimportant, with a totally linear device giving the best output. For tuning, anyway. Then, the output of the instrument and the reference would be mixed, in the ear, with zero beat indicating when the instrument's output matched the reference. --- in fact that does not happen. It would also suggest that it would be difficult or impossible to create beats between two very-low-distortion signal generators, which is also not the case. --- That is precisely the case. Connect the outputs of two zero distortion signal generators so they add, like this, in a perfect opamp, (View in Courier) +-----+ +--------+ +---------+ +-----+ | SG1 |---[R]--+----[R]---+--| POWER |--| SPEAKER |--| EAR | +-----+ | | | AMP | +---------+ +-----+ | +V | +--------+ +-----+ | | | | SG2 |---[R]--+----|-\ | +----------+ +-----+ | --+--| SPECTRUM | +----|+/ | ANALYZER | | | +----------+ GND -V and the spectrum analyzer will resolve the signals as two separate spectral lines, And when the two frequencies are very close to being equal, the spectrum analyzer will only be able to resolve one frequency, and it will vary between a maximum of amplitude and zero at a rate which is precisely related to the difference between the two frequencies. If you get an analyzer with finer resolution, I can always reduce the difference frequency sufficiently to produce the described effect, which does not in any way require a nonlinear process. Other than the nonlinearity of the air (which is very small for "ordinary" SPL, there's no mechanism to cause IM between two different instruments, although beats are still generated. The beat is simply a vector summation of two nearly identical signals; no modulation needs to take place. --- I understand your point and, while it may be true, the incontrovertible fact remains that the ear is a non-linear detector and will generate sidebands when it's presented with multiple frequencies. OK, but off subject. We were discussing whether a "zero beat" while tuning an instrument requires a non-linear process (i.e. "real" modulation. It does not. What remains to be done then, is the determination of whether the beat effect is due to heterodyning, or vector summation, or both. Yup. And since the beat is easily observable using instrumentation of measurably high linearity, whether or not ears have some IM is of no matter. In fact, I agree that IM is produced in ears; just not at significant levels for anything short of pathological SPL -- upwards of 120 dB, say. Or consider this: At true "zero beat" with the signals exactly 180 degrees out, no energy is avaliable for any non-linear process to act on. --- Or any other process for that matter, except the conversion of that acoustic energy into heat. That is, with the signals 180° out of phase and precisely the same amplitude, didn't you mean? Yes. The 180 degree situation is just a special case that very obviously produces a change in output level in a linear environment. IOW it shows that a linear combination of two nearly equal tones will cause a "beat" in amplitude. Then go on to show why all other multi-frequency-component signals (e.g. a full orchestra) don't produce similar intermodulation effects in ears under normal conditions. --- They do Well, no, mostly they don't, until you get to really high SPL. --- That's not true. Why do you think some harmonies sound better than others? Because the heterodyning occurring at those frequencies causes complementary sidebands to be generated which sound good, and that happens at most SPL's because of the ear's nonlinear characteristics. For your argument to be true, there should be harmonies that can be shown to "sound better" when played at a lower SPL (or better, auditioned through a passive acoustical attenuator). Avoiding pathological sound levels, I am not aware of any such thing ever being demonstrated. Do you have any examples? In fact, I believe it is the case that in "musical frequency space" virtually every IM product of significance, regardless of where it arises, is considered unpleasant. and why don't you try being a little less of a pompous ass? Exposing claims to conditions they have difficulty with is a good way to understand why those claims are invalid -- so long as the claimant actually explains what's going on, and doesn't just make up answers that fit the previously stated beliefs. --- I wasn't talking about making and/or debating claims, I was talking about your smartass "Now you get to explain" and "Then go on to show why" cracks. And I still don't think you have adequately explained the things I was referring to. Do you have any references? Isaac |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
In article ,
Rich Grise wrote: On Tue, 03 Jul 2007 22:42:20 -0700, isw wrote: 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. Have you ever actually observed this effect? Sure. (In a previous life, I designed AM and FM transmitters for RCA). Just get a short-wave radio, locate yourself fairly close to a standard AM transmitter, and tune to the harmonics. you'll find, in every case, that the audio sounds just the same as if you were listening to the fundamental. Works for FM, too, but the situation is somewhat more complex. Isaac |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
In article ,
John Fields wrote: On Thu, 05 Jul 2007 13:48:04 -0700, Jim Kelley wrote: John Fields wrote: On Wed, 04 Jul 2007 09:11:58 -0700, isw wrote: In article , "Ron Baker, Pluralitas!" wrote: The beat you hear during guitar tuning is not modulation; there is no non-linear process involved (i.e. no multiplication). --- That's not true. But it is true. The human ear has a logarithmic amplitude response and the beat note (the difference frequency) is generated there. The ear does happen to have a logarithmic amplitude response as a function of frequency, but that has nothing to do with this phenomenon. --- Regardless of the frequency response characteristics of the ear, its response to amplitude changes _is_ logarithmic. For instance: CHANGE APPARENT CHANGE IN SPL IN LOUDNESS ---------+------------------ 3 dB Just noticeable 5 dB Clearly noticeable 10 dB Twice or half as loud 20 dB 4 times or 1/4 as loud --- (It relates only to the aural sensitivity of the ear at different frequencies.) What the ear responds to is the sound pressure wave that results from the superposition of the two waves. The effect in air is measurable with a microphone as well as by ear. The same thing can be seen purely electrically in the time domain on an oscilloscope, and does appear exactly as Ron Baker described in the frequency domain on a spectrum analyzer. The sum frequency is too, but when unison is achieved it'll be at precisely twice the frequency of either fundamental and won't be noticed. The ear does not hear the sum of two waves as the sum of the frequencies, but rather as the sum of their instantaneous amplitudes. When the pitches are identical, the instantaneous amplitude varies with time at the fundamental frequency. When they are identical and in-phase, the instantaneous amplitude varies at the fundamental frequency with twice the peak amplitude. --- 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. --- When the two pitches are different, the sum of the instantaneous amplitudes at a fixed point varies with time at a frequency equal to the difference between pitches. --- But the resultant waveform will be distorted and contain additional spectral components if that summation isn't done linearly. This is precisely what happens in the ear when equal changes in SPL don't result in equal outputs to the 8th cranial nerve. --- This does have an envelope-like effect, but it is a different effect than the case of amplitude modulation. In this case we actually have two pitches, each with constant amplitude, whereas with AM we have only one pitch, but with time varying amplitude. --- That's not true. In AM we have two pitches, but one is used to control the amplitude of the other, which generates the sidebands. --- The terms in the trig identity are open to a bit of misinterpretation. At first glance it does look as though we have a wave sin(a+b) which is being modulated by a wave sin(a-b). But what we have is a more complex waveform than a pure sine wave with a modulated amplitude. --- No, it's much simpler since you haven't created the sum and difference frequencies and placed them in the spectrum. --- There exists no sine wave with a frequency of a+b in the frequency spectrum of beat modulated sine waves a and b. As has been noted previously, this is the sum of two waves not the product. --- "Beat modulated" ??? LOL, if you're talking about the linear summation of a couple of sine waves, then there is _no_ modulation of any type taking place and the instantaneous voltage (or whatever) out of the system will be the simple algebraic sum of the inputs times whatever _linear_ gain there is in the system at that instant. Absolutely correct. And as that "simple algebraic sum" varies with time, which it will as the phases of the two signals slide past each other, it produces the tuning "beat" we've been talking about. Totally linear. Isaac |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
In article ,
"Bob Myers" wrote: Bob M. (Personal message; sorry, but e-mail wouldn't work.) Hi, Bob. It's been a long time since we used to correspond on rec.audio. Nice to hear from you. Isaac |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
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. 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... A microphone with an amplitude response following that of the human ear might do better. 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. 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. Close, though, and as it turned out it wasn't the zero output amplitude as shown by the scope which made the difference, it was the amplitude of the signals which got to my ear(s). As fate would have it, I have two ears, with some distance between them, so perfect cancellation in one left some uncancelled signal in the other, obviating what otherwise might have been perfect silence. Except, perhaps, for the heterodynes. Anyway, I'm off to the 75th reunion of the Panama Canal Society and the 50th reunion of the Cristobal High School Class of '57 in Orlando, so I'll see y'all when I get back on Sunday, GLW. -- JF |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
"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. But once again you have surprised me. Your explanation of the non-multiplied sidebands, while qualitative and incomplete, is sound. It looks to me that the tripple frequency sidebands are there but the basic sidebands dominate. Especially at lower modulation indexes. |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
"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? competently designed unit will not add any signals of its own to what it is being used to analyze. Isaac |
AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
On Thu, 5 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. --- Sorry, Bob, If the ear's amplitude response is nonlinear, it has no choice _but_ to 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. --- Not true. Just look at the tympanic membrane, for example. Consider it a drumhead stretched across a restraining ring and it becomes obvious that the excursion of its center with respect to the pressure exerted on its surface won't be constant for _any_ range of sound pressure levels it experiences. Consequently, when it's hit with two different frequencies, its displacement will vary non-linearly with the pressures they exert and sidebands will be generated. --- Frequency discrimination in the ear occurs through the resonant frequencies of the 20-30,000 fibers which make up the basilar membrane within the cochlea. Each fiber responds only to those tones which are at or very near its resonant frequency. While the response of each fiber to the amplitude of the signal is nonliner, no mixing occurs because each responds, in essence, only to a single tone. A model for the hearing process might be 30,000 or so non-linear meters, each seeing the output of a very narrow-band bandpass filter covering a specific frequency within the audio range. There is clearly no mixing, at least as the term is commonly used in electronics, going on in such a situation, even though there is non-linearity in some aspect of the system's response. Audible "beats" are perceived not because there is mixing going on within the ear, but instead are due to cycles of constructive and destructive interference going on in the air between the two original tone --- Not necessarily. More on Sunday. -- JF |
AM electromagnetic waves: 20 KHz modulationfrequencyonanastronomically-low carrier frequency
"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 electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency
In message , isw
writes In article , Rich Grise wrote: On Tue, 03 Jul 2007 22:42:20 -0700, isw wrote: 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. Have you ever actually observed this effect? Sure. (In a previous life, I designed AM and FM transmitters for RCA). Just get a short-wave radio, locate yourself fairly close to a standard AM transmitter, and tune to the harmonics. you'll find, in every case, that the audio sounds just the same as if you were listening to the fundamental. Works for FM, too, but the situation is somewhat more complex. Isaac Yes, I think I'm missing something obvious here. Let me have another think (aloud).... If you FM modulate a 1MHz carrier with a 1kHz tone, you get a spectrum consisting of a 1MHz carrier in the middle, plus a family of sidebands harmonically spaced at 1kHz, 2kHz, 3kHz etc (to infinity). [One obvious difference between the FM spectrum and that of an AM signal is that the AM spectrum only has sidebands at 1kHz, and the amplitude of the carrier does not vary with modulation depth. With the FM signal, the amplitudes of the carrier and each pair of sideband do vary with the amount of modulation.] So, if you FM modulate a 1MHz carrier with a 1kHz tone, you get a 1Mhz carrier and the family of 1kHz 'harmonic' sidebands. Demodulated it, and you hear a 1kHz tone. Now double the signal to 2MHz. You might expect the sidebands to appear at 2, 4, 6kHz etc. However, if you demodulated the signal, you still hear the original 1kHz tone (which should now be double the amplitude of the original 1MHz signal). You definitely don't hear 2kHz. This at least proves that the original 1kHz FM modulation is preserved during the doubling process. So, would it be simplistically correct to consider that, during the doubling process, the original family of 1kHz sidebands also mix with the new 2MHz carrier, and create a family of 1kHz sidebands centred on 2MHz? Or, alternatively, does the original family of 1kHz sidebands (on the 1MHz signal) mix with the original 1MHz carrier to produce a family of baseband 1kHz 'harmonic' signals, and these then mix with the new 2MHz carrier to create the family of 1kHz sidebands centred on 2MHz? Or are both equally valid (invalid)? A possible flaw in my simplistic 'explanations' is that I would have thought that, while the doubling process occurs as a result of 2nd-order intermodulation, surely the two-step process in both 'explanations' is really 4th-order intermodulation? However, my explanations work equally well (?) for FM and AM. Am I wrong, or am I wrong? Ian. -- |
AM electromagnetic waves: 20 KHzmodulationfrequencyonanastronomically-low carrier frequency
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. |
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 |
AM electromagnetic waves: 20 KHzmodulationfrequencyonanastronomically-low carrier frequency
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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. |
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 |
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 |
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 |
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 |
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 |
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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