Transmitter Modulators

[Robert Reed]

Hi MrAl
According to the magazine article, BSPK can send one bit per carrier sine wave. If I took this at face value, I would have to assume that a 10 MHz bit rate would produce a 10 MHz bandwidth on the carrier. Thats extraordinary and makes me think I read it wrong, but it does follow your professors lecture.I just need more info to be convinced as it seems to defy all laws of modulation.Thats where a display would make things clearer.(as they say, a picture is worth a thousand words ).
As to sidebands in angular modulation, yes they do drop off with increasing distance from the carrier, but probably not in the fashion you are thinking of. When a carrier is angle modulated and as we increase the deviation, the carrier amplitude starts to reduce and the sidebands start to increase in amplitude relative to each other and the carrier.At any given point in the modulation index, third and fourth order sidebands can be of greater amplitudes than first order and including the carrier itself. Further deviation , and the carrier actually disappears completely and all the power is now in the sidebands. This occurs at a Bessel Function of 2.405 ( which is also the modulation index number), and will repeatedly happen at some what regular intervals with even more deviation. Point being that at some modulation indexes all that is sent are the sidebands, so it stands to reason that at least a few low order bands are required. Post Filtering some of the sidebands reduces fidelity, but we are sending data bits, not studio quality audio here, so a fair amount of degradation is very permissible. I hope I am not confusing you, but like I said prior, Angle modulation is a very complex subject once you go beyond the basics.

[MrAl]

Hi Robert,

Well, once you have a waveshape it's not too hard to figure out the components. To analyze a modulated signal you can assume a particular message signal and then simply do a Fourier analysis on the waveshape. The real variable here is not what the harmonics are, we know they appear out to infinity, it's what harmonics they consider important enough to keep on sending the signal out. That's *all* that we dont know. If we assume that the previous readings we've done are true, then there can be only one conclusion: that the only important harmonic is the fundamental.

In many areas it helps to analyze circuits that are known to be used for that area. If you want to know how a toaster browns bread you analyze the internals of the toaster. When manufacturers want designers to use their product they often create reference designs for the designer to analyze and thus become familiar with the product. What we need is a reference design for a modulator and we can immediately put all the parts together. Without something like that we have little chance of understanding completely and have to take everybody's word for everything.
So the next step would be to acquire a reference design of a modulator.

[Robert Reed]

Or just a simple spectrum display of a transmission.Would tell all that I want to know.

[MrAl]

Hi Robert,

Yes if we could acquire an actual physical modulator that would of course be very nice too

What i was thinking was finding a schematic we can analyze to find out what is going on. I have a book somewhere that is two or three inches thick and bigger than a phone book that contains thousands of circuits, but unfortunately it predates this technology. If we could find something that had one of these circuits in it though we could see what was required without having to have an actual device.
Come to think of it, i dont know anything that uses this technology offhand.

ADDED:
I found a spectrum of the output of a BPSK circuit, and it shows a large hump in the center with smaller humps to either side. The first smaller hump (to either side) is about 1/2 of the center main hump, and the smaller ones trail off at a rate of about 66 percent of the preceding ones, so they get smaller and smaller. They show the output going to a power amp, then the output of the amp goes to an antenna. Whether this is a purely theoretical circuit or not though it's hard to say as they only show a block diagram.

[Robert Reed]

Yes, I have seen several of those in web searches. Resolution was quite poor and they were also "normalized". Look very much like simulated images, which I neither want nor trust. But mainly they did not have much info accompanying it. I am sure if we view the spectra for high speed data rates and that rate is probably constantly changing, all we will see is a hard to understand mess. For a good representation would require a steady state modulating signal to really define whats going on. Also, don't get hung up on those pictures of sidebands too much.What we were seeing is probably the modulating wave for one instant in time and in reality this display might constantly be changing quite rapidly- AND the sideband content along with it.
I have seen some block diagrams of the modulating process and seems to use a circuit called an NRZ ( Non Return to Zero). Theres a heap of other chips involved too! But again, the explanation starts to wander around and before you know it they are describing a different process. Never followed it through, as I had neither the time nor patience to follow them through for what might end in another dead end.

[MrAl]

Hi Robert,


It took me quite a while to log in this time as i had to fight off all the tumbleweeds first

The plots i saw looked like they did actually vary because they were not clean looking pictures but had various levels of harmonics all in one picture. Sort of looked like several plots superimposed one on top of the other where ONLY the levels varied. I thought it might be significant that only the levels varied not the frequencies. This implies that for a changing transmission the frequencies stay the same but their relative amplitudes can change. That makes sense in a way because the raw wave always has the same shape, and the only thing that changes about it is the distance between transitions (ie 01000010 has greater distance between 0 to 1 and 1 to 0 transitions than 00010001 does).

[Robert Reed]

Hi MrAl
"I thought it might be significant that only the levels varied not the frequencies. "
In that display, were all levels changing in the same proportion or were they changing amplitude in relation to each other?

Just some food for thought-
If we assume that a constant stream of zeros provides no change in carrier (other than the state of constant phase that is in), then a constant stream of 1's should produce the same result (again holding steady but in a different phase). Now if we send a 101010 xxxxxxxx, this should be a square wave with its given odd harmonic set. Next we send a 011111110xxxxxxxxxx,and this would be a rectangular wave with a whole new set of fundamental and harmonics content. It would seem that we are sending different frequency patterns as the data (1's & 0's) change patterns. What do ya think?

PS - Tumbleweed? Are you East coasters experiencing some of the wild weather thats been going around?

[MrAl]

Hi Robert,


If we send 01010101 for example we dont send a set of square waves, that would be what modulates the phase of a sine wave. What we would end up with is maybe a full sine wave followed by an abrupt change in phase for the next sine wave followed by another abrupt change in phase, etc. So we'd see that strange pattern that looks like a bunch of sine waves that suddenly switch phase after each cycle. So i think the way we could generate this (to give a better picture of this) is to have say a center tapped (secondary) transformer with the center leg grounded, and two relays, one relay on output 1 and the other relay on output 2 (output 1 is 180 degrees out of phase with output 2) and the output of the two relays connected together (our final output), with the primary driven with the carrier sine wave. To generate a '1' we would energize only the #1 relay and that would give us a sine wave out with zero phase shift (relative to when we start) and to generate a '0' we energize only the #2 relay and that would give us a 180 degree phase shifted sine wave out. So a 1010 pattern for this setup would mean we would see an output that is first a complete single cycle of a sine wave with 0 degrees phase shift followed by a sine wave that is 180 degrees shifted (one complete cycle) followed by another 0 degree cycle followed by another 180 degree shifted cycle. So the output would look like single cycle sine waves that abruptly change and are either 0 degrees or 180 degrees phased. This would looks pretty strange but if we flipped the phases of all the 0 degree sine cycles for example we would see a normal sine wave that did not change phase from start to finish. [Note that we only allow a change in phase after a complete cycle of the carrier so we always get a complete sine wave from 0 to 360 degrees relative output, but it may not be the same absolute phase as the previous cycle, and so we never allow any relay change during a complete cycle but only after a full cycle has completed]. The attachment shows the result of the modulation.



So the frequency components are not really odd like the square wave modulator, but end up being even with odd too. I think what else happens is we end up with a sub harmonic too because the periodicity of the two out of phase sine waves is 1/2 of the carrier frequency. The sub harmonic will be lower in frequency than the fundamental. And if we generate a 1100 pattern i think we would end up with an even lower sub harmonic that would be 1/4 the frequency of the carrier.
The other harmonics would not change frequency but their amplitudes could change.

The plot that i saw looked like a plot of the output with some pattern (which generates harmonics of a given frequency) with another plot right on top of it with a different pattern which would have to give the same harmonics but they might vary in amplitude.
The lower sub harmonics are not shown in the plots so for the two examples above we would not see those 1/2 and 1/4 frequency components.

[CeaSaR]

Here's the question I have:

How is the phase determined?

Is it by comparing it to a reference frequency set by a phase lock initiation protocol at the
beginning of the transmission? If that were the case, mixing the 2 would result in a sine wave
of the reference frequency (which is also the transmission frequency) for a phase of 0 (zero)
deg. and a non-existent (as much as it can be accomplished) sine wave for a phase of 180
deg. All you would need then is a timer and to divide that result by the frequency to find the
number of 1's or 0's as the case may be.

Or is it that once the signal sync is established, all you need to detect is the phase change
signaled by the doubling of the frequency? Then you need the timer/division circuit above to
decode the 1's and 0's, as determined by the time between the doubled frequency bursts.

Or once again, am I totally off track?

No, I have not read the treatise on how it is done and really, I don't want to go down that road.
I just want to know where you guys are on it to see if the scant amount I have seen is enough
to follow along. Usually I don't need a ton of info to glean the workings of things, but this may
be a case where, if I get the info I need, it may help "you" get the info "you" need.

CeaSaR

P.S. - As for the sidebands, since the transmission is really only concerned with the phase of the
main carrier and the doubled frequency, wouldn't they be concerned with only the even sidebands,
maybe out to the second or third, just to insure that the phase change point was accurately received?
That's what it seems to me, but, like my tag says: Hey, what do I know? (Hence, my questions.)

[MrAl]

Hi Ceasar,

Thanks again for joining the discussion.

My guess is that yes there would be some protocol to follow at the beginning of the transmission and for each packet. This would allow the receiver to lock on to the phase and frequency.

BTW just after you posted your message i included a diagram of a typical short transmission not including the protocol though.

You gave me an idea here. We could simulate the wave in the diagram i posted above (previous post, hand drawn more or less) and then look at the output after it gets passed through a bandpass filter with reasonable (but not perfect) response. It would be interesting to see the output.
Im going to have to do this next as soon as possible. I'll post the result.

[CeaSaR]

I saw your post before I put mine up (the infamous "another post has come before yours, would you like to read it first?",
or whatever it said) and I put mine up as is. Looking at the graphic, wouldn't the phase change be a doubling instead of
a "halving" of the frequency? You have 2 half waves on the same side of "0" in the space of what would be 1 complete
wave of the base frquency. I am thinking that this is where the harmonics really come into play ("evens", no doubt).

Anyway, I am glad to chime in, and I see that my question has spurred your thought processes as well. My intent exactly.

I'll be checking in tomorrow (later this morning) to see what you've come up with.

CeaSaR

[MrAl]

Hi Ceasar,

Well yes it does mean doubling of the frequency and that's where some of the harmonics are, but it also means that in order to generate the pattern we have to use a frequency that is one half of the carrier. This is plain to see when the output is low pass filtered. The output looks like a slightly distorted sine that is at 1/2 the carrier frequency.

I did the bandpass filtering test and interesting the harmonics never go away completely because there's always some remnants with an imperfect filter. The output looks like it has larger lobes that follow the phase even though they are decreased in amplitude. There are also thin lobes too though.
In other words, the phase changes dont seem to be lost.

[note you have to click on this preview as it is not shown right as a smaller pic here]

[CeaSaR]

Okay, after looking at your plot, this particular scenario has a data period of ~0.75 of 1 full reference cycle, meaning
that the data is on a frequency of ~25% higher than the original signal, with the phase change signal taking up the
remaining amount. What would it look like if you were to modulate 001100110011... or 000111000111..., so forth and
so on? And then, when you throw in the mix of actual data 010010110111001..., what would it look like?

Me thinks I am beginning to see Robert's dilemma and why he wants to see an actual screenshot from a spectrum
analyzer. It might be less confusing.

Also, in ref. to the modulating freq. being 1/2 the carrier (for 10101010...), wouldn't it be the same as the carrier
because it changes phase after each 360 deg. of sine wave? 1/2 should be for 11001100...and 1/3 should be for
111000111000.. so forth and so on. But we know in a real data situation, the modulation will be all over the place
due to the variability of data.

I've included your original plot here:

and my hand-updated version adding in the Raw unmodulated signal, which I think is necessary to include
when looking at such a system:

Both are shown for easy comparison.

I know that right now this is basically all conjecture with some theory thrown in for good measure. It would be
nice if someone who knew the real mechanics of BPSK would join in and point the way. Isn't Lou Frenzel an
author on N&V? Maybe he would like to share some of his expertise, since he was the one author specifically
named by Robert (near the beginning of this thread).

CeaSaR

[MrAl]

Hi Ceasar,

You know between the three of us we might figure this out yet

Actually for the data 10101010 the reason we see a sub harmonic 1/2 the frequency of the carrier can be reasoned like this...
If you look at the pattern 10 that means we send one COMPLETE cycle at say 0 degrees and the next COMPLETE cycle at 180 degrees. Now if we did the pattern 11 instead, we'd send TWO complete cycles of the same frequency as the carrier. So there has to be a difference. That difference can be observed by looking at the plot i posted, the green raw modulated carrier. What do we see. We see two humps negative followed by two humps positive, where one hump is 180 degrees (of the carrier) wide. this means two humps are 360 degrees. We have two humps negative and two humps positive, and this forms a strange wave with base frequency of 1/2 the carrier.
It actually does show up in a Fourier analysis too as a one half frequency component.

The spectrum of a modulated carrier modulated with a random data pattern instead of a fixed data pattern shows harmonics stable in frequency but varying in amplitude. The spectrum of the modulated carrier with fixed pattern shows the same harmonics but they are fixed in amplitude. So the overall shape of the spectrum stays the same as it is always missing some harmonics. This looks like bumps that start out highest in the center, then tapers off as the frequency increases. For one data pattern we would have a fixed height on all the humps, and if we switched the data pattern to something else we would have the same humps in the same places but they would be of a different amplitude.
Picture this:
Most human hands have the longest finger in the middle. Hold your hand up in front of you as if to push something with the palm of your hand, you'll be looking at the back of your hand. With the middle figure highest it looks like the center hump, then the other fingers form the harmonic humps. That's one data pattern spectrum. Next, curl all your fingers so that they all look shorter from the same viewing angle. That's another data pattern spectrum.

[Robert Reed]

Hi MrAl
Wow, a lot of stuff going on here since I last logged in. There is some confusion on my end though. You may have misinterpreted my last post - or- I didn't explain clearly. The square wave/rectangular wave patterns I was referring to were describing the MODULATING WAVE (Data) and not the MODULATED WAVE (Carrier). I was merely trying to point out that various changes in the data rate or pattern might possibly affect the frequency content the MODULATING wave.
Your graphs show us the time domain, but the frequency domain is more of concern here as that ultimately will determine the RF carriers bandwidth required.
Also there is no way we could legally cut the carrier wave frequency in half or modulate it in such a way as to accomplish that. FCC would have convulsions and send in the SWAT team to our transmitting location. Also, no final amplifiers would be able to transmit that wide a spread.
As to angle modulated waves and it's spectra , lets say with a simple square wave for example, it would appear as:
Carrier at the center frequency
first sideband pair will be spaced equidistant each side of the carrier
All other sideband pairs spaced at even increments either side of the carrier
and spreading out further and further from the carrier.
Each sideband pair would include all frequency components that the MODULATING WAVE imposed on it. When you mention harmonics I am not sure what you mean. The MODULATING WAVE contains harmonics. The MODULATED WAVE ( carrier) contains side bands and no harmonics.

Now since I can only relate this subject to normal modulation practices from my own actual field experience, I cannot say for sure whats really going on with the BPSK mode of transmission.
I like Caesar's comment about Lou Frenzel. Wouldn't it be great if we could get him in to our little "coffee clutch".