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#1
October 24th 03, 12:04 AM
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In article , Gary Schafer
writes: Speaking of AM modulation,, we all know that the carrier amplitude does not change with modulation. Or does it? Yes and no. It's a situation of subjective understanding of the basic modulation formulas which define the amplitude of an "RF" waveform as a function of TIME [usually denoted as RF voltage "e (t)" meaning the voltage at any given point in time]. With a REPETITIVE modulation waveform of a single, pure audio sinewave, AND the modulation percentage LESS than 100%, the carrier frequency amplitude does indeed remain the same. I put some words into all-caps for emphasis...those are required definitions for proof of both the math AND a bench test set-up using a very narrow bandwidth selective detector. One example witnessed (outside of formal schooling labs) used an audio tone of 10 KHz for amplitude modulation of a 1.5 MHz RF stable continuous wave carrier. With a 100 Hz (approximate) bandwidth of the detector (multiple-down-conversion receiver), the carrier frequency amplitude remained constant despite the modulation percentage changed over 10 to 90 percent. Retuning the detector to 1.49 or 1.51 MHz center frequency, the amplitude of the sidebands varied in direct proportion to the modulation percentage. That setup was right according to theory for a REPETITIVE modulation signal as measured in the FREQUENCY domain. But, but, but...according to a high-Z scope probe of the modulated RF, the amplitude was varying! Why? The oscilloscope was just linearly combining ALL the RF products, the carrier and the two sidebands. The scope "saw" everything on a broadband basis and the display to humans was the very SAME RF but in the TIME domain. But...all the above is for a REPETITVE modulation signal condition. That's relatively easy to determine mathematically since all that is or has to be manipulated are the carrier frequency and modulation frequency and their relative amplitudes. What can get truly hairy is when the modulation signal is NOT repretitive...such as voice or music. 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?? I don't blame you for being puzzled...I used to be so for many years long ago, too. :-) Most new commercial AM transmitters of today combine the "modulator" with the power amplifier supply voltage, getting rid of the old (sometimes mammoth) AF power amplifier in series with the tube plate supply. Yes, in the TIME domain, the RF power output does indeed vary at any point in time according to the modulation. [that still follows the general math formula, "e(t)"] You can take the modulation frequency and run it as low as possible. With AM there is no change in total RF amplitude over frequency (with FM and PM there is). If you've got an instantaneous time window power meter you can measure it directly (but ain't no such animal quite yet). If you set up a FREQUENCY domain test as first described, you will, indeed, measure NO carrier amplitude change with a very narrow bandwidth selective detector at any modulation percentage less than 100% using a REPETITIVE modulation signal. Actual modulation isn't "repetitive" in the sense that a signal generator single audio tone is repetitive. What is a truly TERRIBLY COMPLEX task is both mathematical and practical PROOF of RF spectral components (frequency domain) versus RF time domain amplitudes when the modulation is not repetitive. Please don't go there unless you are a math genius...I wasn't and tried, got sent to a B. Ford Clinic for a long term. :-) In a receiver's conventional AM detector, the recovered audio is a combination of: (1). The diode, already non-linear, is a mixer that combines carrier and sidebands producing an output that is the difference of all of them; (2). The diode recovers the time domain amplitude of the RF, runs it through a low-pass filter to leave only the audio modulation...and also allows averaging of the RF signal amplitude over a longer time. Both (1) and (2) are technically correct. With a pure SSB signal there is a constant RF amplitude with a constant-amplitude repetitive modulation signal, exactly as it would be if the RF output was from a Class C stage. Single frequency if the modulation signal is a pure audio tone. With a non-repetitive modulation the total RF power output varies with the modulation amplitude. The common SSB demodulator ("product detector") is really a MIXER combining the SSB input with a constant, LOCAL RF carrier ("BFO") with the difference product output...which recovers the original modulation signal. Question is, at what point does the carrier start to be effected? Beyond 100% modulation. The most extreme is a common radar pulse, very short in time duration, very long (relative) in repetition time. There's a formula long derived for the amplitude of the spectra of that, commonly referred to as "Sine x over x" when spoken. That sets the receiver bandwidth needed to recover a target return. I've gotten waist-deep into "matched filter" signals, such as using a 1 MHz bandwidth filter to recover 1 microSecond RF pulses. (bandwidth is equivalent to the inverse of on-time of signal, hence the term "matched" for the filter) Most folks, me included, were utterly amazed at the filtered RF output envelope when a detector was tuned off to one side by 1, 2, or 3 MHz. Not at all intuitive. The math got a bit hairy on that and I just accepted the late Jack Breckman's explanation (of RCA Camden) since it worked on the bench as predicted. It's all a matter of how the observer is observing RF things, time domain versus frequency domain...and whether the modulation is repetitive single frequency or multiple, non-repetitive. The math for a repetitive modulation signal works out as the rule for practical hardware that has to handle non-repetitive, multi-frequency modulation signals. When combining two basic modulation forms, things get so hairy its got fur all over. So, like someone explain how an ordinary computer modem can send 56 Kilobits per second over a 3 KHz bandwidth circuit? :-) Len Anderson retired (from regular hours) electronic engineer person |
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#3
October 25th 03, 04:52 AM
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In article , Gary Schafer
writes: I understand all of the points that you have made and agree that looking at a spectrum analyzer with a modulated signal, less than 100% modulation, shows a constant carrier. I also agree that looking at the time domain with a scope shows the composite of the carrier and side bands. I understand that AM modulation and demodulation is a mixing process that takes place. My question of "at what point does the carrier start to be effected" I was referring to low frequency modulation. Meaning when would you start to notice the carrier change. As long as the AM is less than 100% there won't be any change. The qualifier there is the MEASURING INSTRUMENT that is looking at the carrier. With low and very low modulation frequencies, the sidebands created will be very close to the carrier frequency. If the measuring instrument cannot select just the carrier, then the instrument "sees" both the carrier and sidebands...and that gets into the time domain again which WILL show an APPARENT amplitude modulation of the carrier (instrument is looking at everything). I don't know how you would observe the carrier in the frequency domain with very low frequency modulation as the side bands would be so close to the carrier. DSP along with very narrow final IF filtering can do it, but that isn't absolutely necessary to prove the point. Using "ordinary" narrowband filtering like a very sharp skirt 500 Hz BW filter and variable frequency audio modulation from about 1 KHz on up to some higher, one can separately measure the carrier and sideband amplitudes. It will also show that the sidebands and carrier do not change amplitude for a change in modulation frequency, which is predicted by the general AM equations. Ergo, decreasing the modulation frequency will not change amplitude but one bumps into the problem of instrument/receiver selectivity. That problem is one of instrumentation, not theory. In my scenario of plate modulating a transmitter with a very low modulation frequency (sine or square wave), on the negative part of the modulation cycle the plate voltage will be zero for a significant amount of time of the carrier frequency. The modulation frequency could be 1 cycle per day if we chose. In that case the plate voltage would be zero for 1/2 a day (square wave modulation) and twice the DC plate voltage for the other half day. During the time the plate voltage is zero there would be no RF out of the transmitter as there would be no plate voltage. It's a problem of observation again. Even with a rate of 1 cycle per day, the sidebands are still going to be there and the observing instrument is going to be looking at carrier AND sidebands at the same time. That would be right at 100% modulation, has to be if the carrier envelope is observed to go to zero. At 99.999% (or however close one wants to get to 100 but not reach it) modulation, the theory for frequency domain still holds. Above that 100% modulation, another theory has to be there. For greater-than-100% modulation, an extreme case would be on- off keying "CW." Sidebands are still generated, but those are due to the very fast transition from off to on and on to off. Those sidebands definitely exist and can be heard as "clicks" away from the carrier. In designs of on-off keyed carrier transmitters, the good rule is to limit the transition rate, to keep it slower rather than faster. [that's in the ARRL Handbook, BTW] Slowing the transition rate reduces the sidebands caused by transient effects (the on-off thing). Modulation indexes greater than 100% fall under different theory. For on-off keyed "CW" transmitters, the transient effect sideband generation is much farther away from the carrier than low-frequency audio at less than 100% modulation. It can be observed (heard) readily with a strong signal. This is where I get into trouble visualizing the "carrier staying constant with modulation". As the above scenario, there would be zero output so zero carrier for 1/2 a day. The other 1/2 day the plate voltage would be twice so we could say that the carrier power during that time would be twice what it would be with no modulation and that the average carrier power would be constant. (averaged over the entire day). But we know that the extra power supplied by the modulator appears in the side bands and not the carrier. What is happening? A lack of a definitive terribly-selective observation instrument is what is happening. Theory predicts no change in sideband amplitude with AM's modulating frequency and practical testing with instruments proves that, right down to the limit of the instruments. So, lowering the modulation frequency to very low, even sub-audio, doesn't change anything. The instruments run out of selectivity and start measuring the combination of all products at the same time. Instrumentation will observe time domain (the envelope) instead of frequency domain (individual sidebands). There's really nothing wrong with theory or the practicality of it all. The general equations for modulated RF use a single frequency for modulation in the textbooks because that is the easiest to show to a student. A few will show the equations with two, possibly three frequencies...but those quickly become VERY cumbersome to handle, are avoided when starting in on teaching of modulation theory. The simple examples are good enough to figure out necessary communications bandwidth...which is what counts in the practical situation of making hardware that works for AM or FM or PM. In the real world, everyone is really working in time domain. But, the frequency domain theory tells what the bandwidth has to be for all to get time domain information. In SSB with very attenuated carrier level, that single sideband is carrying ALL the information needed. We can't "hear" RF so the very amplitude stable receiver carrier frequency resupply allows recovery of the original audio. With very very stable propagation and a constant circuit strength, the original audio could go way down in frequency to DC. The SSB receiver could theoretically recover everything all the way down to DC...except the practicality of minimizing the total SSB bandwidth and suppressing the carrier puts the low frequency cutoff around 300 to 200 Hz. The carrier isn't transmitted, and it is substituted in the receiver at a stable amplitude in a SSB total circuit. Yet, theoretically it would be possible to get a very low modulation rate but nobody cares to do so. There ARE remote telemetering FM systems that DO go all the way down to DC...but most communications applications have a practical low-frequency cutoff. Theory allows it but practicality dictates other- wise. The same in instrumentation recording/observing what is happening...that also has practical limitations. If most folks stop at the "traditional" AM modulation envelope scope photos, fine. One can go fairly far just on those. To go farther, one has to delve into the theory just as deeply, perhaps moreso. Staying with the simplistic AM envelope-only view is what made a lot of hams angry in the 1950s when SSB was being adopted very quickly in amateur radio. They couldn't grasp phasing well; it didn't have any relation to the "traditional" AM modulation envelope concept. They couldn't grasp the frequency domain well, either, but that was a bit simpler than phasing vectors and caught on better than phasing explanations. :-) Basic theory is still good, still useable. Nothing has been violated for the three basic modulation types. Practical hardware by the ton has shown that theory is indeed correct in radio and on landline (the first "SSB" was in long-distance wired telephony). BLENDING two basic modulation types takes a LOT more skull sweat to grasp and nothing can be "proved" using simplistic statements or examples (like AM from just RF envelope scope shots) either for or against. I like to use the POTS modem example...getting (essentially equivalent) 56 K rate communications through a 3 KHz bandwidth circuit. That uses a combination of AM and PM. Blends two basic types of modulation, but in a certain way. Nearly all of us use one to communicate on the Internet and it works fine, is faster than some ISP computers, heh heh. So, the simplistic explanations of "one can't get that fast a communication rate through a narrow bandwidth!" falls flat on its 0 state when there are all these practical examples showing it does work. It isn't magic. It's just a clever way to blend two kinds of modulation for a specific purpose. It works. In the "single-sideband FM" examples, one cannot use the simplistic rules for FM in regards to bandwidth or rate. Those experiments were combining things in a non-traditional way. It isn't strictly single sideband, either, but many are off-put by the name given it. Len Anderson retired (from regular hours) electronic engineer person |
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#4
October 26th 03, 10:30 PM
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#5
October 27th 03, 02:22 AM
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In article , Gary Schafer
writes: Let's start at the other end and see what happens; If we have a final amp with 1000 dc volts on the plate and we want to plate modulate it to 100% or very near so, we need 1000 volts peak to peak audio to do it. On positive audio peaks the dc plate voltage and the positive peak audio voltage will add together to provide 2000 volts plate voltage. On negative audio peaks the negative audio voltage will subtract from the dc plate voltage with a net of zero volts left on the plate at that time. (or very nearly zero volts if we do not quite hit 100%) How does the tube put out any power (carrier) at the time there is near zero plate voltage on it? The negative audio cycle portion is going to be much longer than many rf cycles so the tank circuit is not going to maintain it on its own. Why does the carrier stay full? Gary, you are trying to mix the frequency domain and time domain information...and then confusing steady-state conditions in the time domain with repetitive conditions. The "carrier amplitude is constant" holds true over repetitive audio modulation. In conventional AM, with repetitive modulation from a pure tone, there are three RF spectral products. If you deliberately notch out the carrier component in a receiver, and then reinsert a steady-state, synchronized carrier frequency component in its place, you will recover the original modulation audio. The receiver demodulator sees only a steady, constant-amplitude carrier frequency component. There is absolutely no carrier amplitude variation then. But the original modulation audio is demodulated exactly as if it were the done with the original transmitted carrier. SSB reception is done all the time that way (except the carrier amplitude is so low it might as well be zero). That's a practical test proving only that the carrier amplitude does not have any change insofar as demodulation is concerned. As a practical test of just the transmitter, let's consider your basic old-style AM description...Class-C RF PA with linear plate volts v. power output characteristic, modulation by the plate voltage. That plate voltage is 1 KV steady-state. In steady-state, RF output has a single RF component, the carrier frequency. One. RF spectral component will follow the general time-domain RF equations with no modulation. [easy math there] Apply modulation to the plate voltage with a pure tone. Plate voltage swings UP as well as DOWN equally. [theoretical perfect linear situation] Same rate of UP and DOWN. [start thinking dv/dt] Look at the spectral components with this pure tone modulation. Now we have THREE, not just one. Any high resolution spectrum analyzer sampling the RF output will provide practical proof of that. So, if you want to examine the total RF in a time-domain situation, you MUST examine it as amplitude versus an infinitely-thin slice of TIME. You cannot take a finite time chunk out of the RF envelope and "prove" anything...anymore than you can justify the existance of three RF components, not just TWO. [if this were the real classroom, you would have to prove that on the whiteboard and justify it in full public view...and maybe have to show the class the spectrum analyzer output]. Remember that the modulation signal also exists in a time domain and is constantly changing. If the "carrier sinewave goes to zero and thus power output is zero," how do you justify that, a half repetition time of the modulation signal later, "carrier sinewave goes to twice amplitude and power output is double"? You are trying an analogy that has a special condition, by neglecting the RATE of the modulation. It is always changing just as the carrier frequency sinewave is changing. You want to stop time for the modulation to show repetitive RF carrier sinusoids and that is NOT modulation. It is just adjustment of the RF output via plate voltage. No modulation at all. The basic equation of an AM RF amplitude holds for those infinitely- small slices of TIME. The series expansion of that basic equation will show the spectral components that exist in the frequency domain. Nothing has been violated in the math and practical measurements will prove the existance and nature of the spectral components. For those that like the vector presentation of things, trying to look at a longer-than-infinitely-small slice of time or just the negative or positive modulation swings is the SAME as removal of the modulation signal vector. Such wouldn't exist in that hypothetical situation. It would be only the RF carrier vector rotating all by itself. In basic FM or PM, there's NO change in RF envelope amplitude with a perfect source of FM or PM. "The carrier swings from side to side with modulation," right? Okay, then how come for why does the carrier spectral frequency component go to ZERO with a certain modulation/deviation level and STAY there as long as the modulation is held at that level? RF envelope amplitude will remain constant. Good old spectrum analyzer has practical proof of that. [common way of precise calibration of modulation index with FM] The FM is "just swinging frequency up and down" is much too simple an explanation, excellent for quick-training technicians who have to keep ready- built stuff running, not very good for those who have to use true basics for design, very bad for those involved with unusual combinations of modulation. If you go back to your original situation and have this theoretical power meter working with conventional AM, prove there are ANY sidebands generated from the modulation of plant voltage...or one or two or more. :-) Going to be a difficult task doing that, yet there obviously ARE sidebands generated with conventional AM and each set has the same information. Lose one and modulation continues. Prove it solely from the time-domain modulation envelope. Prove the carrier component amplitude varies or remains constant. Hint: You will wind up doing as another Johnny Carson did way back in 1922 (or thereabouts) when the basic modulation equations were presented on paper. [John R. Carson, I'm not going to argue the year, that's in good textbooks for the persnickety] With conventional AM the CARRIER FREQUENCY COMPONENT amplitude remains the same for any modulation percentage less than 100. Period. I not gonna argue this anymore. :-) Len Anderson retired (from regular hours) electornic engineer person |
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#6
October 27th 03, 03:48 AM
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Avery Fineman wrote:
So, if you want to examine the total RF in a time-domain situation, you MUST examine it as amplitude versus an infinitely-thin slice of TIME. You might want to remind everyone that the mathematical Fourier transform of a signal is an integral that extends from time=minus infinity to plus infinity. Since Real Spectrum Analyzers (or network analyzer) need to produce results in something, oh, less than infinite time (probably less than the time between now and the next donut break), they're necessarily limited in the low frequency detail they can provide. True, if Gary's transmitter is transmitting a zero at the moment he connects a spectrum analyzer, he won't see anything at all on the display, but as you point out -- this is an equipment problem, not a mathematical one. I'm still a believer in SSB-FM, BTW. :-) But I have enough respect for you that I won't attempt to argue it further without first finding the time to prepare a few drawings to demonsrate why! ---Joel Kolstad |
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#7
October 27th 03, 04:38 AM
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In article , "Joel Kolstad"
writes: Avery Fineman wrote: So, if you want to examine the total RF in a time-domain situation, you MUST examine it as amplitude versus an infinitely-thin slice of TIME. You might want to remind everyone that the mathematical Fourier transform of a signal is an integral that extends from time=minus infinity to plus infinity. The series expansions of the basic modulation type RF time-domain expression don't use Fourier series. The series expansions show the sprectral content are still equivalent to that infinitely-thin slice of time as the function of amplitude. I think that Panters "Signals, Modulation, and Noise" text has it worked out in there (by memory, don't have that one handy here). The "Landee" text I mentioned is an old one and not that familiar to most. Since Real Spectrum Analyzers (or network analyzer) need to produce results in something, oh, less than infinite time (probably less than the time between now and the next donut break), they're necessarily limited in the low frequency detail they can provide. True, if Gary's transmitter is transmitting a zero at the moment he connects a spectrum analyzer, he won't see anything at all on the display, but as you point out -- this is an equipment problem, not a mathematical one. No, it's an argument problem. :-) There's no infinitely-fast RF power meter in existance. Yet. I'm still a believer in SSB-FM, BTW. :-) But I have enough respect for you that I won't attempt to argue it further without first finding the time to prepare a few drawings to demonsrate why! I'm not arguing that "single-sideband FM" won't work. I just don't like the name. The technique DOES work from all the explanations of experiments, is reproducible. [it isn't the "cold fusion" thing. :-) ] I've not seen any convincing case that the single-whatever FM thingy has any practical applications. For narrowband voice, SSB AM is just dandy and a phasing system using the Gingell-Yoshida polyphase network is quite easy and error-tolerant to make a good phasing exciter. It can be used in "reverse" to get an easy-to-select sideband demod or an ordinary AM detector that yields false stereo (one sideband to each ear), already done with simple CW receivers. Len Anderson retired (from regular hours) electronic engineer person |
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#8
October 27th 03, 04:38 AM
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In article , "Joel Kolstad"
writes: Avery Fineman wrote: So, if you want to examine the total RF in a time-domain situation, you MUST examine it as amplitude versus an infinitely-thin slice of TIME. You might want to remind everyone that the mathematical Fourier transform of a signal is an integral that extends from time=minus infinity to plus infinity. The series expansions of the basic modulation type RF time-domain expression don't use Fourier series. The series expansions show the sprectral content are still equivalent to that infinitely-thin slice of time as the function of amplitude. I think that Panters "Signals, Modulation, and Noise" text has it worked out in there (by memory, don't have that one handy here). The "Landee" text I mentioned is an old one and not that familiar to most. Since Real Spectrum Analyzers (or network analyzer) need to produce results in something, oh, less than infinite time (probably less than the time between now and the next donut break), they're necessarily limited in the low frequency detail they can provide. True, if Gary's transmitter is transmitting a zero at the moment he connects a spectrum analyzer, he won't see anything at all on the display, but as you point out -- this is an equipment problem, not a mathematical one. No, it's an argument problem. :-) There's no infinitely-fast RF power meter in existance. Yet. I'm still a believer in SSB-FM, BTW. :-) But I have enough respect for you that I won't attempt to argue it further without first finding the time to prepare a few drawings to demonsrate why! I'm not arguing that "single-sideband FM" won't work. I just don't like the name. The technique DOES work from all the explanations of experiments, is reproducible. [it isn't the "cold fusion" thing. :-) ] I've not seen any convincing case that the single-whatever FM thingy has any practical applications. For narrowband voice, SSB AM is just dandy and a phasing system using the Gingell-Yoshida polyphase network is quite easy and error-tolerant to make a good phasing exciter. It can be used in "reverse" to get an easy-to-select sideband demod or an ordinary AM detector that yields false stereo (one sideband to each ear), already done with simple CW receivers. Len Anderson retired (from regular hours) electronic engineer person |
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#9
October 27th 03, 03:48 AM
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Avery Fineman wrote:
So, if you want to examine the total RF in a time-domain situation, you MUST examine it as amplitude versus an infinitely-thin slice of TIME. You might want to remind everyone that the mathematical Fourier transform of a signal is an integral that extends from time=minus infinity to plus infinity. Since Real Spectrum Analyzers (or network analyzer) need to produce results in something, oh, less than infinite time (probably less than the time between now and the next donut break), they're necessarily limited in the low frequency detail they can provide. True, if Gary's transmitter is transmitting a zero at the moment he connects a spectrum analyzer, he won't see anything at all on the display, but as you point out -- this is an equipment problem, not a mathematical one. I'm still a believer in SSB-FM, BTW. :-) But I have enough respect for you that I won't attempt to argue it further without first finding the time to prepare a few drawings to demonsrate why! ---Joel Kolstad |
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#10
October 27th 03, 02:22 AM
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In article , Gary Schafer
writes: Let's start at the other end and see what happens; If we have a final amp with 1000 dc volts on the plate and we want to plate modulate it to 100% or very near so, we need 1000 volts peak to peak audio to do it. On positive audio peaks the dc plate voltage and the positive peak audio voltage will add together to provide 2000 volts plate voltage. On negative audio peaks the negative audio voltage will subtract from the dc plate voltage with a net of zero volts left on the plate at that time. (or very nearly zero volts if we do not quite hit 100%) How does the tube put out any power (carrier) at the time there is near zero plate voltage on it? The negative audio cycle portion is going to be much longer than many rf cycles so the tank circuit is not going to maintain it on its own. Why does the carrier stay full? Gary, you are trying to mix the frequency domain and time domain information...and then confusing steady-state conditions in the time domain with repetitive conditions. The "carrier amplitude is constant" holds true over repetitive audio modulation. In conventional AM, with repetitive modulation from a pure tone, there are three RF spectral products. If you deliberately notch out the carrier component in a receiver, and then reinsert a steady-state, synchronized carrier frequency component in its place, you will recover the original modulation audio. The receiver demodulator sees only a steady, constant-amplitude carrier frequency component. There is absolutely no carrier amplitude variation then. But the original modulation audio is demodulated exactly as if it were the done with the original transmitted carrier. SSB reception is done all the time that way (except the carrier amplitude is so low it might as well be zero). That's a practical test proving only that the carrier amplitude does not have any change insofar as demodulation is concerned. As a practical test of just the transmitter, let's consider your basic old-style AM description...Class-C RF PA with linear plate volts v. power output characteristic, modulation by the plate voltage. That plate voltage is 1 KV steady-state. In steady-state, RF output has a single RF component, the carrier frequency. One. RF spectral component will follow the general time-domain RF equations with no modulation. [easy math there] Apply modulation to the plate voltage with a pure tone. Plate voltage swings UP as well as DOWN equally. [theoretical perfect linear situation] Same rate of UP and DOWN. [start thinking dv/dt] Look at the spectral components with this pure tone modulation. Now we have THREE, not just one. Any high resolution spectrum analyzer sampling the RF output will provide practical proof of that. So, if you want to examine the total RF in a time-domain situation, you MUST examine it as amplitude versus an infinitely-thin slice of TIME. You cannot take a finite time chunk out of the RF envelope and "prove" anything...anymore than you can justify the existance of three RF components, not just TWO. [if this were the real classroom, you would have to prove that on the whiteboard and justify it in full public view...and maybe have to show the class the spectrum analyzer output]. Remember that the modulation signal also exists in a time domain and is constantly changing. If the "carrier sinewave goes to zero and thus power output is zero," how do you justify that, a half repetition time of the modulation signal later, "carrier sinewave goes to twice amplitude and power output is double"? You are trying an analogy that has a special condition, by neglecting the RATE of the modulation. It is always changing just as the carrier frequency sinewave is changing. You want to stop time for the modulation to show repetitive RF carrier sinusoids and that is NOT modulation. It is just adjustment of the RF output via plate voltage. No modulation at all. The basic equation of an AM RF amplitude holds for those infinitely- small slices of TIME. The series expansion of that basic equation will show the spectral components that exist in the frequency domain. Nothing has been violated in the math and practical measurements will prove the existance and nature of the spectral components. For those that like the vector presentation of things, trying to look at a longer-than-infinitely-small slice of time or just the negative or positive modulation swings is the SAME as removal of the modulation signal vector. Such wouldn't exist in that hypothetical situation. It would be only the RF carrier vector rotating all by itself. In basic FM or PM, there's NO change in RF envelope amplitude with a perfect source of FM or PM. "The carrier swings from side to side with modulation," right? Okay, then how come for why does the carrier spectral frequency component go to ZERO with a certain modulation/deviation level and STAY there as long as the modulation is held at that level? RF envelope amplitude will remain constant. Good old spectrum analyzer has practical proof of that. [common way of precise calibration of modulation index with FM] The FM is "just swinging frequency up and down" is much too simple an explanation, excellent for quick-training technicians who have to keep ready- built stuff running, not very good for those who have to use true basics for design, very bad for those involved with unusual combinations of modulation. If you go back to your original situation and have this theoretical power meter working with conventional AM, prove there are ANY sidebands generated from the modulation of plant voltage...or one or two or more. :-) Going to be a difficult task doing that, yet there obviously ARE sidebands generated with conventional AM and each set has the same information. Lose one and modulation continues. Prove it solely from the time-domain modulation envelope. Prove the carrier component amplitude varies or remains constant. Hint: You will wind up doing as another Johnny Carson did way back in 1922 (or thereabouts) when the basic modulation equations were presented on paper. [John R. Carson, I'm not going to argue the year, that's in good textbooks for the persnickety] With conventional AM the CARRIER FREQUENCY COMPONENT amplitude remains the same for any modulation percentage less than 100. Period. I not gonna argue this anymore. :-) Len Anderson retired (from regular hours) electornic engineer person |
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