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General Category => General Radio Discussion => Topic started by: YesterdayMan on November 10, 2024, 1802 UTC
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I thought I understood AM modulation, but now I have to question my understanding, since I've found several sources that explain the bandwidth of SSB transmission differently than what I think it should be.
Please allow me to present an example that conveys my confusion:
Suppose a carrier signal of 20kHZ is used to transmit a 3kHZ sinewave. The receiver can reconstruct the sinewave from the amplitude of the carrier signal. Therefore, the bandwidth consists of only one frequency, 20kHZ. If we consider the 3kHZ sinewave that's being superimposed upon the carrier wave, we could say that in addition to the 20kHZ carrier wave, there is also a 3kHZ sinewave imposed upon the top of the carrier signal and a mirror image signal that's imposed upon the bottom. However, both the top and the bottom signals that are imposed upon the carrier frequency would be a 3kHZ sine wave, not 23kHZ. This 3kHZ sinewave, if it were transmitted with a higher frequency carrier wave, say 40kHZ, would have greater definition, but the same frequency, 3kHZ. The frequency of the transmitted signal is independent of the carrier frequency.
What I envision is 2 signals that compose the transmission. A 20kHZ carrier frequency, and the 3kHZ signal. There is nothing being transmitted at 10kHZ for instance. However, in the scenario I described above, if we were transmitting a 3kHZ signal on a 20kHZ carrier wave, using SSB, I believe the conventional wisdom is that the bandwidth would be 23kHZ. This doesn't make sense to me. We're not using 23kHZ of bandwidth. We're using one frequency only. If we want to express the bandwidth to represent the entire spectrum of frequencies that include both the signal and the carrier wave, then that would be 20kHZ - 3kHZ = 17kHZ.
Can someone help me make sense of this?
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Long time lurker, first time poster here. Hopefully the admins don't mind our noise. :)
It's a bit hard to understand what you're trying to convey, but I think I'm following what you're pondering about. The first key is defining bandwidth. Let's start there.
> if we were transmitting a 3kHZ signal on a 20kHZ carrier wave, using SSB, I believe the conventional wisdom is that the bandwidth would be 23kHZ
This is wrong in the sense that if you had a 3khz tone on a SSB signal, then the bandwidth would 3khz. If you had a simultaneous 1khz, 2khz, and 3khz tone on a SSB signal, then the bandwidth would still be 3khz. If that SSB was located at 1Mhz, it'd be 3khz wide. If it was located at 5mhz, it'd be 3khz wide. If it were at 7.200mhz, it'd be 3khz wide with wackos talking. So what gives?
The word bandwidth is conveying the width of a signal. That's measured by noting where a transmission's RF energy is above and below a center frequency. Taking the difference between those two points is the bandwidth.
Let's work with your 20khz example. Assume you have an AM transmitter with a 20khz carrier wave modulated with a 3khz sine wave. What you'll see is RF at 20 - 3 and 20 + 3 khz. Mark those two points, being 17 and 23, and take the difference: 23 - 17 = 6. That AM signal has a 6khz bandwidth. Doing the same at 40khz: 43 - 37 khz = 6khz. Taking the difference is why the bandwidth of a signal is independent of the signal's center frequency.
What makes SSB special are the points in which you'll find that RF energy around a center frequency. By removing the carrier and opposing side band, the difference between the lowest and highest frequency in which you measure RF power is going to be half that of AM. For example, a USB signal with 3khz wide audio transmitted at 20khz would have RF energy at 20khz through 23khz, hence 23 - 20 = 3khz bandwidth.
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If you go to any of the online SDR radios, you can see exactly this.
KiwiSDR: http://kiwisdr.com/public/
KiwiSDR Map: http://rx.linkfanel.net/
WebSDR: http://websdr.org/
https://www.receiverbook.de/
You can tune to the amateur bands where there is usually plenty of SSB and a little AM. If 11m is open, you can see this difference easily on the CB channels. Ch 1-35 are typically AM and 36-40 (and above ch 40) are usually SSB (LSB is common, some use USB).
Down on the AM broadcast band, you'll find stations that differ in their bandwidth. Some are wide, some not so much. When you listen to them, you can hear the difference in quality.
And then there's FM, which is an entirely different animal.
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I think you're overthinking it.
The bandwidth is determined by the audio regardless of the frequency of the carrier. A 3 kHz tone is 3 kHz wide in SSB and 6 in DSB or AM.
Or maybe I'm underthinking it :-\
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Guys, thanks for the help. What you're describing is the way I've always understood bandwidth and AM signals. But there MUST be something I'm missing, because I don't understand how there's a signal at all without the carrier signal. When I read that the carrier signal is removed from SSB transmission, I thought they were mistaken, but I couldn't find anything that said they were wrong. That sent me into the mind-bend that produced the post above, as I second guessed everything I ever though I knew about AM transmission.
If someone could just explain to me how the carrier signal could possibly be removed from the transmission in AM signals, I would be forever grateful. It just doesn't compute. The carrier signal IS the signal. There's nothing else transmitted.
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Modulation is a mixing phenomena. When we send two signals through a non-linear device, additional frequencies (called modulation products) are generated.
If I transmit a carrier at 1 MHz, you would only see a carrier at 1 MHz. If I then modulate that carrier with a 1 kHz tone, I am in fact mixing the 1 MHz signal with a 1 kHz signal. What you then see is a carrier at at .999 MHz (the lower sideband), the original carrier at 1 Mhz, and another carrier at 1.001 MHz (the upper sideband).
The mixing of the 1 kHz tone and the 1 MHz carrier has produced three RF carriers.
If you want to replace the 1 kHz tone with some audio from (going 0 to 3 kHz for example), what you get is that 3 kHz wide chunk of audio duplicated above and below the carrier (the upper and lower sidebands). Those sidebands look just like the original audio waveform - but they are now at RF frequencies. This is where the information is….and the upper and lower sidebands carry identical information. You don’t really need both of them, so in SSB we remove one of them. Also, once we have accomplished the mixing phenomena to generate the sidebands, we no longer need the carrier, so in SSB or DSB, we remove it.
It’s difficult to explain this without drawing pictures.
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What you're describing is what I picture for FM modulation. For AM modulation, I understood there to be a carrier wave that is typically much higher frequency than the signal being sent, and a message signal that modulates the amplitude of the carrier so that the shape of the carrier wave has the shape of the message signal. This way, without the carrier, there is no signal.
The situation where the message signal bandwidth is present above and below the carrier frequency sounds like FM modulation to me. I found images to share, but I don't know if I can share images here without some kind of repercussions, so I have a link.
https://reviseomatic.org/help/2-modulation/Amplitude%20Modulation.php
if you look at the second image on this page, you'll see how I understand it to be. And you'll see that without a carrier wave, there's no signal at all.
Please comment back.
Thanks,
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I think you've got a good sense of understanding with those charts. Now you're running into the limits of what these charts can show you.
The issue with these charts is they are in the time domain. That is time advances as you read them left-to-right while showing the absolute value of a signal at a particular point in time. All's well until the signal becomes more complex than a continuous wave or amplitude modulated audio.
When we start looking at more signals with more nuanced modulation, we reach for the frequency domain. Signals charted in the frequency domain show the amount of energy at a particular frequency. Sometimes frequency domain charts use color to show energy at a frequency, with a new line of colors added every few milliseconds. That kind of frequency domain chart is a waterfall chart, but now with time as a third dimension (power-frequency-time).
Understanding the frequency domain is why skeezix was suggesting using a web based SDR. They'll often have a waterfall that can help get you that intuitive feeling of modulation in the frequency domain.
I have three videos in mind that might get you started. First up is a ham radio related one that directly addresses your struggle:
Dave Casler - Why We don't look at Single Side Band in the Time Domain: https://www.youtube.com/watch?v=F5zuLi19ar4 (https://www.youtube.com/watch?v=F5zuLi19ar4)
While not RF related, getting an intuitive understanding of sine waves can be helpful. I think Posy did a great job in visually, and interestingly, breaking it down.
Posy - Every sound is SINE: https://www.youtube.com/watch?v=UrBZsUBibtk (https://www.youtube.com/watch?v=UrBZsUBibtk)
This last one may seem a bit thick, but trust me in that it's completely approachable and that you don't have to do the math yourself. Understanding Fourier series at a very high level is a good way of getting a better grasp of frequency domain charts.
3blue1brown - But what is a Fourier series? From heat flow to drawing with circles | DE4: https://www.youtube.com/watch?v=r6sGWTCMz2k (https://www.youtube.com/watch?v=r6sGWTCMz2k)
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https://reviseomatic.org/help/2-modulation/Amplitude%20Modulation.php
if you look at the second image on this page, you'll see how I understand it to be. And you'll see that without a carrier wave, there's no signal at all.
That picture that shows the amplitude of the RF wave going up and down….that is in the time domain and the waveform you see is actually the SUM of the LSB, the carrier, and the USB signals. It is what you would see if you had an oscilloscope connected to the transmitter output. It is seeing all the energy (carrier, LSB, and USB) at once.
The three of them are all on slightly different different frequencies, so they go in phase and out of phase with each other. Sometimes they add and sometimes they subtract….so you see the amplitude going up and down.
At 100% modulation, 50% of the transmitted power is present in the carrier, 25% is in the LSB and 25% is in the USB. At some points the two sidebands will be out of phase with the carrier and the display on your scope will go to zero. At other times everything will be in phase and you will see the scope display show twice what it does with the carrier alone. It might appear that the signal goes to zero but if you were looking in the frequency domain (that is what a waterfall display in a SDR shows) you would see that NONE of them….the sidebands or the carrier…actually go away.
Do you have a recent copy of the ARRL Handbook? It discusses this in Chapter 11, including drawings.
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pc486 and NJQA, thank you for the responses. I'm sorry for not having the time to get back to you sooner. I just read your posts now. Give me some time to read the resources you suggested and soak it in, and I'll get back with you.
I did allot with Fourier Transforms when I was in school, but that was a long time ago. I was pretty good at the math back then, but I'm sure that's not the case today. However, I remember the gist of it - transferring a signal from the time domain to the frequency domain. Although I thought I understood the concept, I don't deny that there could be more for me to learn.
3blue1brown is one of my favorite YouTube channels. I watch it with my daughter from time to time. That kid amazes me. I wish I had half the mathematical intuition that he has.
Thanks again - I'll get back to you soon, I hope.
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I think I get it.
I would describe it as follows:
Keeping in mind that any waveform can be broken down into specific set of component sinewaves, the SSB process can be understood as follows:
1. Perform amplitude modulation upon the carrier frequency with the signal waveform, resulting in a time-domain waveform that looks like the carrier frequency with the shape of the signal waveform represented by its amplitude.
2. Picture this amplitude modulated signal as a specific set of component sinewaves.
3. Once the signal is created, remove the carrier frequency and every frequency below it in the frequency domain and transmit the rest.
4. On the receiving end, provide the same carrier frequency and add it to the received set of component sinewaves to rebuild half of the original signal.
Please don't tell me I'm wrong. This finally makes sense to me. :)
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I think you are getting there. The way I think of the process is that it is all about frequency translation of my audio signal. And the way we do this is by mixing the audio signal with another signal (the RF signal). The math of doing this shows we then generate sum and difference signals, and we can then filter out the ones we don’t want and are left with the one we do want to transmit. On the other end we reverse the process by mixing the received signal with a carrier signal and the mixing now gives us a signal back at audio frequencies.
I struggled with this myself years ago, especially with why on AM the waveform I would see on an oscilloscope would go to zero at 100% modulation, yet it was obvious that I was still transmitting power. The Ah-hah moment was when I realized the oscilloscope picture was the composite of the carrier, usb, and lsb all together. The sum of the signals could go to zero, but that didn’t mean that the individual signals were zero….they were just phased differently.
I thought I knew all of this stuff cold when I got my BSEE. Later when I got my MSEE I realized I knew nothing. Teaching is just a process of telling smaller and smaller lies. You make everything sound simple at the beginning and then when the students get their heads wrapped around the basic concept, you start introducing the complexities. It’s easy to say that in amplitude modulation we modulate the carrier. If you look at it on an oscilloscope that is exactly what appears to be happening. Yet the real story is much different. Years ago the tools to see things in the frequency domain were very esoteric; today any SDR lets you see do this. And the simple lies that worked well enough in the mid-twentieth century aren’t enough anymore.
Theoretical physicists seem to have a good grasp of this problem as they attempt to explain how the universe works. One of them said “Not only is the universe stranger than we know, it may very well be stranger than we CAN know”. That’s pretty sobering. But as engineers we know that we only need to know it well enough so that we can build things.
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I'm pretty sure I understand this now. For one thing, I understood exactly what you were saying in you last post :) .
I had all the parts in my toolbox already, but I was stuck on the notion that AM didn't mess with the frequencies. Maybe I was never told, and maybe I missed it, but I wasn't aware that the carrier was re-introduced to the signal at the receiving end. I probably just missed it, since I couldn't get past the part about sending a signal on a carrier wave that had been removed.
NJQA, I'm going to remember two of your statements from you last post - they're quotable:
1. Teaching is just a process of telling smaller and smaller lies.
2. As engineers we know that we only need to know it well enough so that we can build things.
Great and true statements.
I want to thank everyone on this post for their help. It's allot to ask people to take the time to type up a response to someone's question who seems to have no idea what he's talking about. You never know if you're helping to fill in a hole, or throwing dirt into a bottomless pit. But you guys took the time to push some dirt in the hole until I was able to climb out, and it's a great feeling to resolve the matter of whether I'm not quite smart enough to understand a concept or just looking at things the wrong way.
By the time I finished watching PC486's first link I understood what I was missing.