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#1
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Avery Fineman wrote:
There isn't any corresponding similarity of FM and PM to AM for the repetition of sidebands' information when looking at the spectral content. Umm... last I looked the spectrum of FM and PM was symmetrical about the carrier frequency? (Well, the lower sideband is 180 degrees out of phase with the upper, but that's true of AM as well.) Looking at a single sine wave input to an FM or phase modulator, this comes about from the Bessel function expansion of the sidetones and J-n(x)=-Jn(x)? I know you're far more experienced in this area than I am, however, so I'll let you explain what I'm misinterpreting here! ---Joel Kolstad |
#2
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In article , "Joel Kolstad"
writes: Avery Fineman wrote: There isn't any corresponding similarity of FM and PM to AM for the repetition of sidebands' information when looking at the spectral content. Umm... last I looked the spectrum of FM and PM was symmetrical about the carrier frequency? (Well, the lower sideband is 180 degrees out of phase with the upper, but that's true of AM as well.) Looking at a single sine wave input to an FM or phase modulator, this comes about from the Bessel function expansion of the sidetones and J-n(x)=-Jn(x)? Yes. More or less. I know you're far more experienced in this area than I am, however, so I'll let you explain what I'm misinterpreting here! Noooo...I'm not going to. About a million subjective years ago I had to slog through a solution and series expansion with the only "help" I got being a suggestion to use Bessel Functions of the First Kind. In doing so - AND thinking about it in the process - I learned quite a bit about the math AND the modulation process. Very useful later on. ALL learning takes place in one's own noggin...doesn't matter whether one is in a formal class or alone being "lectured" by print on paper through the eyeballs. Over on the Agilent website, I would suggest downloading their free Application Note 150-1. That is really a subtle selling thing for their very fine spectrum analyzers but it is also a darn good treatise on modulation and modulation spectra for all the basic types. It should (unless altered there) include that nice little animated display of sidebands versus modulation index. I've always admired those H-P appnotes, valuing most as nice little tutorials on specialized subjects. Richard Slater in the mentioned January '77 HR article was trying to explain a combination of FM and AM. In order to get a proper "feel" for that (in my opinion), one needs the experience of juggling those series terms in the expanded equation form. There IS one hint and that is the not-quite symmetry (in numeric values) of FM and PM spectra as compared to AM spectra. True "single-sideband" has a possibility only on true symmetry. FM and PM spectra, by themselves, don't have that symmetry in the expanded form. I'm not going to discuss that one since it should be apparent. If you want some source code on calculating the numeric values of Bessel Functions of the First Kind, I'll be happy to post it here under some thread. It's short and not complicated and a #$%^!!! faster than slugging through 5-place tables with slide rule and/or four-function mechanical calculator. Been there, done too much of that. Computers aren't just for chat rooms, are very nice for numeric calculations of the large kind. :-) Len Anderson retired (from regular hours) electronic engineer person |
#3
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The amplitudes of the sideband components are symmetrical (at least for
modulation by a single sine wave), but the phases aren't. The phases of all the upper sideband components are in phase with the carrier; in the lower sideband, the odd order components (and only the odd order ones) are reversed in phase. With multitone modulation, things get a whole lot more complex. Unlike AM, FM is nonlinear, so there are sideband components from each tone, plus components from their sum, difference, and harmonics. The inability to use superposition makes analysis of frequency modulation with complex waveforms a great deal more difficult than AM. Note also that unlike AM, whatever fraction of the carrier that's left when transmitting FM also contains part of the modulation information. Of course, at certain modulation indices with pure sine wave modulation, the carrier goes to zero, meaning that all the modulation information is in the sidebands. But this happens only under specific modulation conditions, so you'd certainly have an information-carrying carrier component present when modulating with a voice, for example. Roy Lewallen, W7EL Joel Kolstad wrote: Avery Fineman wrote: There isn't any corresponding similarity of FM and PM to AM for the repetition of sidebands' information when looking at the spectral content. Umm... last I looked the spectrum of FM and PM was symmetrical about the carrier frequency? (Well, the lower sideband is 180 degrees out of phase with the upper, but that's true of AM as well.) Looking at a single sine wave input to an FM or phase modulator, this comes about from the Bessel function expansion of the sidetones and J-n(x)=-Jn(x)? I know you're far more experienced in this area than I am, however, so I'll let you explain what I'm misinterpreting here! ---Joel Kolstad |
#4
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Roy Lewallen wrote:
The amplitudes of the sideband components are symmetrical (at least for modulation by a single sine wave), but the phases aren't. The phases of all the upper sideband components are in phase with the carrier; in the lower sideband, the odd order components (and only the odd order ones) are reversed in phase. I certainly didn't realize that until you pointed it out; I was generalzing from the narrowband FM situation where only the first sideband components are necessarily maintained and incorrectly assuming the same phase differences applied to the general case. However... Say you start with a baseband FM signal. Let's call the two sides of its Fourier transform L and R for the 'left' and 'right' halves. Now we mix up to the desired carrier frequency. At -f_c we have L at even greater negative frequencies and R at smaller negative frequencies. Ditto at f_c. If we now apply a low pass filter to select the lower sideband, we end up with R and L -- No information has been lost! (Likewise, with a high pass filter you have L and R left -- Same deal.) Fundamentally mixing ANY signal followed by SSB filtering shouldn't lose information. Yes, in practice we'll be talking about VSB instead of SSB, but I still think we're OK. Speaking of narrowband FM (NBFM)... and at the risk of splitting this topic... I had a discussion today with someone over the ability to use an envelope detector to recover narrowband FM signals. The output of the envelope detector is approximately 1+0.5*cos^2(2*pi*f*t), where f was the original modulating signal. The '1' will be killed by a capacitor, but that leaves the cosine squared term... which seems impossible to easily change back into cosine, since sqrt(x^2)=abs(x) and therefore it would appear that we've irreversably lost information. Comments? ---Joel Kolstad ....ambitious novice who'll be licensed shortly... ....and I still think C-QUAM AM stereo is quite clever... |
#5
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Joel Kolstad wrote:
. . . Say you start with a baseband FM signal. Let's call the two sides of its Fourier transform L and R for the 'left' and 'right' halves. Now we mix up to the desired carrier frequency. At -f_c we have L at even greater negative frequencies and R at smaller negative frequencies. Ditto at f_c. If we now apply a low pass filter to select the lower sideband, we end up with R and L -- No information has been lost! (Likewise, with a high pass filter you have L and R left -- Same deal.) Fundamentally mixing ANY signal followed by SSB filtering shouldn't lose information. Yes, in practice we'll be talking about VSB instead of SSB, but I still think we're OK. I'm afraid you lost me with the "baseband" FM signal. Would you provide a carrier frequency, modulation frequency, and deviation or modulation index as an example? The lower and upper sidebands of an FM signal do contain the same information when the modulation is a single sine wave, even though the sidebands aren't identical. But when you modulate with a complex waveform, you might find that some of the information which is adding in one sideband is subtracting in the other, and you might not be able to recover the modulating waveform from only one or the other -- sort of like you can't get two separate stereo channels from just the sum signal. I don't know if that's true, but it wouldn't surprise me. And, as I pointed out in another posting, the entire modulation information isn't even contained in *both* sidebands except under very special conditions -- some is in the carrier. Another question, of course, is whether you can get close enough to be useful. Perhaps with NBFM, at least, you could. Speaking of narrowband FM (NBFM)... and at the risk of splitting this topic... I had a discussion today with someone over the ability to use an envelope detector to recover narrowband FM signals. The output of the envelope detector is approximately 1+0.5*cos^2(2*pi*f*t), where f was the original modulating signal. The '1' will be killed by a capacitor, but that leaves the cosine squared term... which seems impossible to easily change back into cosine, since sqrt(x^2)=abs(x) and therefore it would appear that we've irreversably lost information. Comments? Cos^2(x) = abs(cos(x)) = 1/2 * (1 + cos(2x)). As you've noted, the DC term can be blocked with a capacitor, so you'd end up with a cosine wave at twice the frequency. But I've never heard of trying to detect NBFM directly with an envelope detector like you'd detect AM. The trick we used in ye olden tymes was called "slope detection". You tuned the signal so it was on the edge of the IF filter. The filter slope converted the FM to AM, which was then detected with the normal AM envelope detector. If you tuned directly to the carrier frequency, you didn't hear any modulation to speak of. Roy Lewallen, W7EL |
#6
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Joel Kolstad wrote:
. . . Say you start with a baseband FM signal. Let's call the two sides of its Fourier transform L and R for the 'left' and 'right' halves. Now we mix up to the desired carrier frequency. At -f_c we have L at even greater negative frequencies and R at smaller negative frequencies. Ditto at f_c. If we now apply a low pass filter to select the lower sideband, we end up with R and L -- No information has been lost! (Likewise, with a high pass filter you have L and R left -- Same deal.) Fundamentally mixing ANY signal followed by SSB filtering shouldn't lose information. Yes, in practice we'll be talking about VSB instead of SSB, but I still think we're OK. I'm afraid you lost me with the "baseband" FM signal. Would you provide a carrier frequency, modulation frequency, and deviation or modulation index as an example? The lower and upper sidebands of an FM signal do contain the same information when the modulation is a single sine wave, even though the sidebands aren't identical. But when you modulate with a complex waveform, you might find that some of the information which is adding in one sideband is subtracting in the other, and you might not be able to recover the modulating waveform from only one or the other -- sort of like you can't get two separate stereo channels from just the sum signal. I don't know if that's true, but it wouldn't surprise me. And, as I pointed out in another posting, the entire modulation information isn't even contained in *both* sidebands except under very special conditions -- some is in the carrier. Another question, of course, is whether you can get close enough to be useful. Perhaps with NBFM, at least, you could. Speaking of narrowband FM (NBFM)... and at the risk of splitting this topic... I had a discussion today with someone over the ability to use an envelope detector to recover narrowband FM signals. The output of the envelope detector is approximately 1+0.5*cos^2(2*pi*f*t), where f was the original modulating signal. The '1' will be killed by a capacitor, but that leaves the cosine squared term... which seems impossible to easily change back into cosine, since sqrt(x^2)=abs(x) and therefore it would appear that we've irreversably lost information. Comments? Cos^2(x) = abs(cos(x)) = 1/2 * (1 + cos(2x)). As you've noted, the DC term can be blocked with a capacitor, so you'd end up with a cosine wave at twice the frequency. But I've never heard of trying to detect NBFM directly with an envelope detector like you'd detect AM. The trick we used in ye olden tymes was called "slope detection". You tuned the signal so it was on the edge of the IF filter. The filter slope converted the FM to AM, which was then detected with the normal AM envelope detector. If you tuned directly to the carrier frequency, you didn't hear any modulation to speak of. Roy Lewallen, W7EL |
#7
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Speaking of AM modulation,, we all know that the carrier amplitude
does not change with modulation. Or does it? Here is a question that has plagued many for years: If you have a plate modulated transmitter, the plate voltage will swing down to zero and up to two times the plate voltage with 100% modulation. At 100% negative modulation the plate voltage is cutoff for the instant of the modulation negative peak. How is the carrier still transmitted during the time there is zero plate voltage? If we lower the modulation frequency to say 1 cps or even lower, 1 cycle per minute, then wouldn't the transmitter final be completely off for half that time and unable to produce any carrier output?? Question is, at what point does the carrier start to be effected? 73 Gary K4FMX On Wed, 22 Oct 2003 20:39:20 -0700, Roy Lewallen wrote: The amplitudes of the sideband components are symmetrical (at least for modulation by a single sine wave), but the phases aren't. The phases of all the upper sideband components are in phase with the carrier; in the lower sideband, the odd order components (and only the odd order ones) are reversed in phase. With multitone modulation, things get a whole lot more complex. Unlike AM, FM is nonlinear, so there are sideband components from each tone, plus components from their sum, difference, and harmonics. The inability to use superposition makes analysis of frequency modulation with complex waveforms a great deal more difficult than AM. Note also that unlike AM, whatever fraction of the carrier that's left when transmitting FM also contains part of the modulation information. Of course, at certain modulation indices with pure sine wave modulation, the carrier goes to zero, meaning that all the modulation information is in the sidebands. But this happens only under specific modulation conditions, so you'd certainly have an information-carrying carrier component present when modulating with a voice, for example. Roy Lewallen, W7EL Joel Kolstad wrote: Avery Fineman wrote: There isn't any corresponding similarity of FM and PM to AM for the repetition of sidebands' information when looking at the spectral content. Umm... last I looked the spectrum of FM and PM was symmetrical about the carrier frequency? (Well, the lower sideband is 180 degrees out of phase with the upper, but that's true of AM as well.) Looking at a single sine wave input to an FM or phase modulator, this comes about from the Bessel function expansion of the sidetones and J-n(x)=-Jn(x)? I know you're far more experienced in this area than I am, however, so I'll let you explain what I'm misinterpreting here! ---Joel Kolstad |
#8
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You have to be careful in what you call the "carrier". As soon as you
start modulating the "carrier", you have more than one frequency component. At that time, only the component at the frequency of the original unmodulated signal is called the "carrier". So you have a modulated RF signal, part of which is the "carrier", and part of which is sidebands. General frequency domain analysis makes the assumption that each frequency component has existed forever and will exist forever. So under conditions of modulation with a periodic signal, you have three components: A "carrier", which is not modulated, but a steady, single frequency, constant amplitude signal; and two sidebands, each of which is a frequency shifted (and, for the LSB, reversed) replica of the modulating waveform. You can take each of these waveforms, add them together in the time domain, and get the familiar modulated envelope. So, the short answer is that the carrier, which is a frequency domain concept, is there even if you're modulating at 0.001 Hz. But to observe it, you've got to watch for much longer than 1000 seconds. You simply can't do a meaningful spectrum analysis of a signal in a time that's not a lot longer than the modulation period. Roy Lewallen, W7EL Gary Schafer wrote: Speaking of AM modulation,, we all know that the carrier amplitude does not change with modulation. Or does it? Here is a question that has plagued many for years: If you have a plate modulated transmitter, the plate voltage will swing down to zero and up to two times the plate voltage with 100% modulation. At 100% negative modulation the plate voltage is cutoff for the instant of the modulation negative peak. How is the carrier still transmitted during the time there is zero plate voltage? If we lower the modulation frequency to say 1 cps or even lower, 1 cycle per minute, then wouldn't the transmitter final be completely off for half that time and unable to produce any carrier output?? Question is, at what point does the carrier start to be effected? 73 Gary K4FMX |
#9
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So what you are saying is that the carrier of a modulated signal is
ONLY a frequency domain concept? That would mean that it really does turn on and off in the time domain at the modulation rate. 73 Gary K4FMX On Thu, 23 Oct 2003 10:49:46 -0700, Roy Lewallen wrote: You have to be careful in what you call the "carrier". As soon as you start modulating the "carrier", you have more than one frequency component. At that time, only the component at the frequency of the original unmodulated signal is called the "carrier". So you have a modulated RF signal, part of which is the "carrier", and part of which is sidebands. General frequency domain analysis makes the assumption that each frequency component has existed forever and will exist forever. So under conditions of modulation with a periodic signal, you have three components: A "carrier", which is not modulated, but a steady, single frequency, constant amplitude signal; and two sidebands, each of which is a frequency shifted (and, for the LSB, reversed) replica of the modulating waveform. You can take each of these waveforms, add them together in the time domain, and get the familiar modulated envelope. So, the short answer is that the carrier, which is a frequency domain concept, is there even if you're modulating at 0.001 Hz. But to observe it, you've got to watch for much longer than 1000 seconds. You simply can't do a meaningful spectrum analysis of a signal in a time that's not a lot longer than the modulation period. Roy Lewallen, W7EL Gary Schafer wrote: Speaking of AM modulation,, we all know that the carrier amplitude does not change with modulation. Or does it? Here is a question that has plagued many for years: If you have a plate modulated transmitter, the plate voltage will swing down to zero and up to two times the plate voltage with 100% modulation. At 100% negative modulation the plate voltage is cutoff for the instant of the modulation negative peak. How is the carrier still transmitted during the time there is zero plate voltage? If we lower the modulation frequency to say 1 cps or even lower, 1 cycle per minute, then wouldn't the transmitter final be completely off for half that time and unable to produce any carrier output?? Question is, at what point does the carrier start to be effected? 73 Gary K4FMX |
#10
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Gary Schafer wrote:
So what you are saying is that the carrier of a modulated signal is ONLY a frequency domain concept? Yes. That would mean that it really does turn on and off in the time domain at the modulation rate. "It" only exists in the frequency domain. Talking about the carrier in the time domain makes no more sense than talking about the sidebands in the time domain, or the envelope in the frequency domain. Roy Lewallen, W7EL |
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