Transmitter Modulators

[Bob Scott]

I have a simple explanation for describing the modulation products of the signals Robert described.

The type of modulation is double sideband suppressed carrier. On positive portion of the modulating signal the carrier is in phase with the supplied carrier. On negative portions of the modulating signal the carrier is inverted. This is illustrated in most good explanations of sideband transmission.

Now for the sidebands and bandwidth required......
A square wave is a mixture, or a sum of the amplitude of several of sine waves. A square wave of any particular amplitude contains a sum of the odd harmonics of the frequency of the square wave. It contains 1X amplitude of the fundamental square wave frequency plus 1/3 of the third harmonic plus 1/5 of the fifth harmonic, 1/7 of the seventh harmonic, etc, etc, ad infinitum. Yes it indeed requires infinite bandwidth. Every harmonic modulates the carrier and produces sum and difference frequencies to be transmitted. If your bandwidth is limited, harmonics will be missing from the demodulated signal. The demodulated waveform will be less "square". The rising edges of the demodulated square wave will be less sudden. They will be sloped, and the square wave will have slight ripples due to missing harmonics.

The phase of the harmonics of a square wave is such that they must all have a zero crossing point from negative to positive at the same instant in time that the fundamental crosses zero from negative to positive. You can imagine how with every missing harmonic, the leading edge of the quare wave becomes a little less square and a little more sloped.

This pertains to 50% duty cycle square waves. If the modulation is not 50%, the the products will also contain even order harmonics.

If the modulation is just a single transition of DC, then its like ringing every bell in sight with a single blow.

I hope this helps.

[MrAl]

Hi Bob,


The odd harmonics come up with waves that are the same to the right of zero as to the left of zero except to the left of zero it is negative. Even harmonics come up with waves that are completely symmetrical about the Y axis.

The biggest question that came up for me was what the demodulator is capable of. If we look at the second waveform i posted where the original was sent through a low pass filter, we still see a similar wave but the points are not as sharp. Thus, i wonder if the correct demodulator would be able to discern between the two different phases even when missing a lot of the upper harmonics. This would mean less bandwidth needed to transmit. So the question is just how good is the demodulator. If we look at the low pass filtered wave we would be able to tell where a zero and where a one had occurred, so i suspect that the right demodulator could too (like a phase comparison type demodulator). What i dont know is how much effort or technology they intend to put into the demodulator. A simple diode and capacitor (ha ha) or a micro controller using DSP?
My guess is that by now there is some type of optimized system where certain standards are adopted and that gives good results. What they can get away with on the transmitter end i dont know yet as i havent found any good enough references to this type of modulation yet.

[Robert Reed]

EDITED 4/04/2012
MrAl
"How are you defining modulation index here?"
In a nutshell without getting in too deep -- Mod Index:
FM Deviation ratio/highest modulating frequency
PM Mod index = Radians (Ex. Mod index of 1 = 1 radian of phase)
This is going from memory!

REQUIRED BANDWIDTH:
AM Double sideband highest mod frequency x 2
AM Single sideband Highest mod frequency x 1
FM Highest mod frequency + deviation x 2
PM Basically the same as above ( except Delta phase + Delta
amplitude = deviation ) x2



These products are referenced to the carrier and are the actual spectrum needed
for transmission.
Linear amplifiers are only used where amplitude fidelity must be preserved. This is one advantage to FM & PM as they can use more efficient class C finals.In all transmitters past and present, there are two main filters, one for the modulating signal (sometimes called a splatter filter) for constraining the composite signal within a given bandwidth,
and one Pre antenna filter inserted between the Final and the matching network. This is to kill upper carrier harmonics that would interfere with other radio services, not to mention almost certainly an FCC requirement for acceptance. Now we have reduced fidelity some what, but its all in what you can get away with and still have a respectable signal. Even transmitted high speed logic pulses may resemble more of a sine wave but high speed logic chips down stream in the receiver will shape that signal to satisfy any binary application. My point being is yes there is a lot of filtering going on and that is acceptable.

Bob
No single sideband here,this post is strictly about Phase modulation - PM.

Caesar
There you go with the time domain again. Was it something you inferred from my later posts?

[MrAl]

Hi Robert,


Actually what i was asking really was how do you define modulation index for phase modulation where it's binary but you did mention for PM.

What you said for PM is it is basically the delta phase, but that means that the mod index could be 180 or 0, or pi or 0 in rads.
What i was thinking was that it was either 1 or 0, 1 being 180 and 0 be 0 or vice versa. So when we say the modulation index is less than 1 that means it's not as good as it could be right?

[CeaSaR]

I'm sorry Robert, I must have misinterpreted what I read/saw in the linked article.
As I stated, I am just a layman, no work or anything in the field. Just a person with
a desire to understand. I feel I don't quite understand yet... at this point I defer.

CeaSaR

[Robert Reed]

Caesar
No apology necessary. I have worked in the radio field on two different jobs and have experienced first hand on whats happening on this subject. But I am far from being an expert on it. Trouble is, with this subject, the more you delve into it-the more complex and confusing it becomes. At some point the only explanation is with very complicated mathematical formulas ( my weak point). It seems like there is a new form of modulation coming out every year and its too hard to keep up with. The major reason for this is that Radio Spectrum is at an all time premium and just about milked to the max for current technology. Most certainly this is a bi-product of TV, cell phones,hi-speed data transmission and so on. Pity, since much of this is wasted spectrum to satisfy teeny boppers twittering and such. But the spectrum use goes where the money is, regardless of sanity! I was just curious about BPSK in a spectrum analyzer display. As they say a pix is worth 1K words.

[Robert Reed]

MrAl
I just reread my last post to you and by golly I was thinking one thing and typing another (Late night response).
I have edited that post so you can reread it.You asked about PM in binary and for that I have no answer. All I can come up with is that it may be required to follow the same rules as analog such as all the component frequencies to make that pulse are included in the modulation package(?).
I can only relate to you of what I know in analog methods since that is all I am familiar with. FM and PM are very similar in their transmitted spectrum and can actually be received with the same receiver detection circuitry. FM modulation requires changing the OSCILLATOR frequency at the modulating rate and amplitude while PM modulation requires varying the reactance of a post oscillator AMPLIFIERS tank circuit component. From that point on its all the same circuitry. Sorta six one way and a half dozen the other. I suspect that PM has only one advantage over FM and that being where the TX uses a very tight high stability oscillator which would be difficult and undesirable to pull off frequency. In this digital age, the Tx process may be quite different for BPSK, but still has to somewhat conform to electronic law. The only thing I have heard about receiver detection is that the demod is self adjusting to phasing of the original carrier and this might be done with periodic error correction circuitry.
We could get into quite a lengthy forum on all the aspects of BPSK, but I am not too interested in all the system workings, only curious as to the transmission pattern and the spectrum space it would take up at a given data rate. Just wondering how much space they save compared to older traditional PM.

[MrAl]

Hi again Robert,


I guess what i am trying to do here is understand what you meant when you said something like you wanted to know how they could get away with a modulation index that was less than 1.

The way i understand it, 1 would mean 100 percent modulation, 0.5 would mean 50 percent modulation, etc. So having a modulation index less than 1 doesnt make any sense when that is stated as some sort of 'quality' of the type of transmission. If instead someone said, "and they can get a modulation index very close to 1", then i would be impressed Having a modulation index less than 1 is was plagues some modulation schemes because they cant go over a certain percent modulation [cant remember which one(s) offhand].

So i dont know what you are trying to understand here really because i dont understand why you said what you did, unless you had some other reason of course.

For phase modulation if 180 degrees was the maximum allowed with a given setup then i would think the modulation index would be 1 if we could vary the phase from 0 to 180 degrees, but only 0.5 if we could only go 0 to 90 degrees. If however the theory was 360 degrees then 180 degrees would only be a mod index of 0.5, and if for some other reason we were limited to 180 in that case we would have to say that modulation technique is limited to 50 percent modulation.

Does this make sense, and is my question understandable?

[MrAl]

Hi again Robert,

I made another post rather than edit the previous one because this post will be very different.

I ran across an old lecture by Rob Maunder of the University of Southampton and he had something like this to say about BPSK, although he did not delve into the math behind it too much...

First, he says the bandwidth is equal to the symbol rate:
B=Rs
(Apparently the true bandwidth isnt needed, but he never went into why that might be at all, no proofs of any kind where included)
(The true bandwidth here being the infinite bandwidth required to perfectly reproduce those pointed tips in the actual modulated waveform)

As an example, audio has a bandwidth of 20kHz typically sampled at 44.1k samples per second.
32 bits are typically used for stereo, giving a bit rate of 1411.2k bits per second.
Using BPSK, k=log2(M)=1 bit per symbol (M=2 because there are two symbols for binary).
This gives a symbol rate and signal bandwidth of 1411.2kHz (keep in mind this is over 1MHz and it's just for audio!).
As the M factor goes up the bandwidth goes down proportionally, so M=4 would mean half the bandwidth.
By contrast, double sideband suppressed carrier requires a bandwidth of only 2*fmax=40kHz.
To achieve this same bandwidth (as low as that) would require M=2^32, that's over 4e9.
Alternately, MP3 compression can be used to reduce the bit rate to 128k bits per second which only needs M=8.

I had forgotten all about these lectures as i was helping someone work through some of these communication problems about a year ago. I've been through 2000 other subjects and circuits since then however so i forgot all about it. It's just too bad that he didnt go into detail about why the so called bandwidth is what he says it is as that would have been nice to know too. Maybe it has something to do with the demodulation techniques typically used.

[Robert Reed]

Hello MrAl
"The way I understand it, 1 would mean 100 percent modulation, 0.5 would mean 50 percent modulation, etc. So having a modulation index less than 1 doesnt make any sense when that is stated as some sort of 'quality' of the type of transmission. If instead someone said, "and they can get a modulation index very close to 1", then i would be impressed Having a modulation index less than 1 is was plagues some modulation schemes because they cant go over a certain percent modulation [cant remember which one(s) offhand]."

What you have described here would be an index for AM modulation although usually referred to as % of modulation. AM is a fairly simple process and easily described.
However angular modulation (FM or PM) is a far more complex subject and its equations require calculus and Bessel function for support , something I do not want to get into as it gets deeper and deeper. Angular has no modulation limits so there is no 100% involved here. The only relationship 100% has in this realm is what the designer deems adequate for the application or the FCC allows for that particular service.
A single tone Angularly modulating a carrier produces side bands to infinity.But it has been proven that only sidebands above 1% in spectral power are needed for good fidelity (called significant sidebands and usually includes up to the seventh sideband). Due to this, Angular modulation actually requires more bandwidth than AM for a given modulating signal. Increasing fidelity subsequently increases the Modulation Index number. As an example, the Narrow band Land Mobile Radio Service uses a Modulation Index (MI) of 1.7 for low grade voice communication whereas Commercial FM broadcast uses MI's of 5 or 6 for high grade music transmission. MI's can run any where from 0.0 (carrier only) to into the 100's. Higher MI's would require more bandwidth.
Back to the original article about BPSK. Since this was generally about reducing bandwidth while sending higher and higher data transmissions, I would assume that the modulating signal has a very high frequency component, not to mention all the supporting frequencies needed for fidelity. This indicates that a high number modulation index is required here for all the required sidebands to preserve that signal. That is my confusion as to their reference of an MI of one (1). But that aspect is only a side question as the actual spectral display is what I would like to see.
When I worked System level Microwave links, My employer required I take an 8 week course in Microwave transmission Theory & Principles.It was a good course but that was 17 years ago and I have since moved on to different fields. So I have forgotten some of the details in that time and like you, I have laid down many circuit designs between then and now so my mind is in a different place at present.
But going from memory, I think I have the basics right (I think ).

[Robert Reed]

Hello again MrAl
In my last post, I forgot to answer one question you had. That was in reference to my stating that a low Modulation index was a good thing. It is good in regards to reducing bandwidth and conservation of spectrum, but at the expense of deteriorating signal fidelity. As in all electronic architecture its a juggling of trade offs for the Optimum system design.

[MrAl]

Hi Robert,

Maybe the quality they are talking about comes from the increase of the number of symbols, which also reduces the bandwidth (relative to a lower number of symbols). That would make a lot of sense.

As to the phase modulation limitation, it would seem that if we modulate by more than 360 degrees it would lead back to 0 degrees, so i would think that we would have to have a limit of 360 degrees at the very least. Are you saying that some demodulators can detect a phase modulation of more than 360 degrees? Usually they dont do that and if you look at the phase diagrams they always contain the complete set of symbols within 0 to 360 degrees no matter how many symbols they go to (4, 8, 16, etc.). They never show an angle higher than 360 degrees which does make sense.

So what was your take on the Professor's lecture? Does it make sense to you that the bandwidth should be equal to the symbol rate?

[Robert Reed]

MrAl
I thought symbols related to the quantity of information possible in one cycle of carrier wave. I am not at all familiar with that aspect of modulating carriers, However I have seen various constellation diagrams and BPSK supposedly can send one (1) bit per Hertz. To send more per Hertz requires 4PSK,8PSK,16PSK and I think it may go to 64PSK. Would these be symbols? At any rate BPSK is a less complex form of modulation and has lower limits than the above. As to PM modulation as I recall it can use the whole 360 degree package. I don't know what its limits are but in my past work, it has been every bit as high as FM modulation. When either carrier is scoped in time domain, you cannot see the difference, practically identical. In the frequency domain,only small differences at lower mod rates - none at higher mod rates. There are equations that explain why this is. Altering the phase from 360 to fractional degrees can cover a LOT of territory in the frequency spectrum,and when I said in last post that there were no limits,I was speaking figuratively as every thing has limits in one way or another.

"So what was your take on the Professor's lecture? Does it make sense to you that the bandwidth should be equal to the symbol rate?"
I just don't have enough knowledge on that subject to even make an intelligent guess. I am still struggling with BPSK, which is supposed to be a more basic style

[MrAl]

Hi Robert,

BPSK uses two symbols, 0 and 1, which might be represented by 0 degrees and 180 degrees, and might be also called 2PSK.
Adding more symbols beyond that gives us more information for one cycle, so 4PSK would have four symbols: 00, 01, 10, 11
and would be represented by phases 0, 90, 180, and 270 degrees.
For 8PSK we'd have more symbols: 000,001,010,011,100,101,110,111
which would have to be represented by units of 45 degrees each, so 000 would be 0 deg, 001 would be 45 deg, 010 would be 90 deg, etc.
What this means is that NOW when we send a phase shift of 180 degrees we are actually sending three bits at once, and the bit pattern is: 100
If we wanted to send other data for those three bits we could use a different phase shift, but it always takes one cycle for those three bits.
With 2PSK when we send 180 degrees we are only sending one bit (that's all we are allowed) and it is a '1'
So it would take three cycles to send 010: 0 deg followed by 180 deg followed by 0 deg.
Obviously the data gets sent three times faster with 8PSK.
Taking the professor's lecture without proof, that would mean three times the bandwidth would be required. So yes there must be some approximation going on here so the full infinite bandwidth isnt needed. Note also that infinite bandwidth doesnt necessarily mean that all the harmonics are the same amplitude either, and some might drop quite low very fast.

But also i think worth mentioning is that just because the bandwidth of some sort of modulated transmission is low it doesnt necessarily mean some sort of better quality. I can send audio with a 2kHz bandwidth but it will take 10 times longer (or more) than real time to send.

[Robert Reed]

I remember some systems back a ways use amplitude and phase combinations to achieve multi symbol systems. I think this is still the common use today.
Angular Mod sidebands are constantly changing amplitudes in relation to the carrier and each other with increases in deviation. When the mod index is 2.405 (bessel function) , the carrier actually disappears. At other Bessel functions The sidebands are popping up and down like a bunch of prairie rats out of their holes.The sidebands are always changing amplitudes and some lower order bands at times are of more amplitude than any others.

"But also i think worth mentioning is that just because the bandwidth of some sort of modulated transmission is low it doesnt necessarily mean some sort of better quality. I can send audio with a 2kHz bandwidth but it will take 10 times longer (or more) than real time to send."

I don't understand this paragraph. Why would a lower bandwidth indicate higher quality to begin with? Also isn't all radio transmission in real time?