Transmitter Modulators

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Robert Reed
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Transmitter Modulators

Post by Robert Reed » Tue Feb 21, 2012 9:06 pm

I last worked in commercial radio systems about 12 years ago and Trunked Simulcast systems were then the rage (also fairly complex). In the ensuing years, I have read tech sheets of incredible modulation spread in very limited bandwidths, to the point of defying laws of electronics. Recently I read a rather detailed article on the latest methods of modulation and made this phenomenon more understandable (although still seems like smoke and mirrors). One type of modulation caught my interest though and that being BPSK (Binary Phase Shift Keying). This method makes a 180 degree shift in the carrier (or sub carrier) at the rise and fall segment of a binary pulse. It would seem that the sideband content would be extremely narrow using this method (a good thing). The explanation was fairly clear, but did not follow up on some important details. What I would like to know is what a spectrum analyzer presentation would look like with center frequency being the carrier of course and in particular the adjacent sidebands. Any one out there had experience with this or seen these displays?

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Re: Transmitter Modulators

Post by MrAl » Wed Feb 22, 2012 7:27 am

Hi there Robert,

Where did you read about this? I ask because you seemed to have formed the idea that the output bandwidth would be very limited and i'd like to see how you got to that. The images i have seen on the web (and i havent studied them it great detail yet) all show a sine wave that shifts phase abruptly. Any time a sine wave shifts like that it requires an infinite bandwidth which is impossible to generate in real life. What happens is an analysis has to be done about the true limitation in real life bandwidth that a real circuit would cause to find out how bad the errors will be and what impact they will have on the overall operation.
But you were asking about the sidebands. It could be that the sidebands are low content, but i dont see the overall bandwidth being low unless a large error can be tolerated. Would be nice to read the article though to get a better idea what is happening.
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Re: Transmitter Modulators

Post by Robert Reed » Wed Feb 22, 2012 9:13 pm

MrAl
The phase shift of the carrier at the proper time occurs at the zero crossing point. At that time there is an immediate 180 degree reversal which is fixed until the next binary pulse state occurs.Why would that require an infinite band width? I am having a hard time wrapping my mind around this as compared to modulation index calculations for simple analog phase shift modulation (voice transmission being the one I am familiar with).
Trying to visualize where and what these side bands would occur in the frequency domain.Obviously the higher the data rate, the wider the bandwidth.
The last article I read on this was written by Lou Frenzel and was published in Electronic Design Magazine - Feb.9, 2012 issue.I may be able to look up its website for you.

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Re: Transmitter Modulators

Post by MrAl » Thu Feb 23, 2012 9:22 am

Hi Robert,

If there is a jump discontinuity, even at zero, it means an infinite bandwidth is required to exactly reproduce that signal. Infinite bandwidth however does not mean that all of the harmonics have to be of the same amplitude, and often the higher we go the lower the level becomes. But this is still theoretically called infinite bandwidth because it really does require harmonics that reach to infinity to exactly reproduce the signal.
One of the loopholes here is found in the keyword, "exactly". In cases like this what often happens is we find we can reproduce the signal to an acceptable degree of accuracy without actually using an infinite bandwidth. The result is some measurable harmonic distortion in the reproduced signal. The goal then is to decided if this amount of distortion is tolerable or not. If it is, then the system is go, but if not, of course it has to be improved somehow.
If we knew the intended demodulation scheme we might be able to judge just what we could call acceptable and what not. If there is a demod scheme that can work even with a high harmonic distortion, then a smaller bandwidth would work ok.

I've read that the phase shift could be at 90 degrees too, but im not sure if that's the same kind of system you are talking about. If i could see the article you were referring too i might be able to understand this better too. I dont think i've ever looked into this kind of modulation before, but i've looked into other types including a fairly in depth look at ultrasonic audio air transmission modulation schemes, which also runs into this infinite bandwidth issue in some forms, and one of those forms involves a 180 degree phase shift.

For a couple examples:
Im sure you know that a square wave requires an infinite bandwidth, but so does a full wave rectified sine wave even though the discontinuities occur at zero volts, and the full wave signal is equivalent to a 180 degree phase shift except we never see the negative half cycles.
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Re: Transmitter Modulators

Post by Robert Reed » Thu Feb 23, 2012 9:48 pm

Way back in engineering 101, I learned that there is only ONE waveform in electronics and that being a pure SINE wave. All the other lopsided, distorted and so on wave shapes we see (square waves included) are a presentation of amplitude versus time in which a certain combination of sine wave frequencies and amplitudes when algebraically added together will result in that wave shape in the time domain.
I have always used this as a basis for analysis of some odd ball occurrences in past designs. Also having used high end spectrum analyzers many times have always proved that this is actually so. However I have never considered a pure sine wave changing state ( phase in this case) as being nothing other than still a pure sine wave with the same frequency and amplitude.Its sort of like turning off a generator at the zero crossing point of a negative transition and then restarting that generator at the zero crossing starting point of a positive going transition. This is where I get confused. But in continuous operation that transition does qualify as a distorted wave so there must be other sine waves occurring at that instant to make up that momentary wave form. Then according to standard FM and PM theory, a side band would be created at a given distance from the carrier frequency and a group of harmonics of lessening amplitude on down the road.My familiarity with this is transmitting audio, music with FM or PM and lo-speed data with FSK. These methods either swing the carrier frequency or abruptly shift it to another frequency for a period of time.Generally at least up to the third harmonic sideband must be sent through for minimum fidelity The BPSK is only a glitch so to speak and there in lies the rub as to what the required Tx traffic pattern would look like. It was instituted for its high data rate per bandwidth function so its obviously far superior to the types I have just described. One screen shot from a spectrum analyzer would make it very clear as to whats actually going on. I will see if I can find the article on the web and give the URL if I find it. Maybe you will read in something that I missed.

Try This- http://electronicdesign.com/channels/co ... eless.aspx

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Re: Transmitter Modulators

Post by MrAl » Fri Feb 24, 2012 8:59 am

Hi Robert,

Here's a little report of the Fourier analysis of a pure sine wave, the Fourier components of a full wave rectifier sine with base frequency 100Hz, and the same full wave rectified sine with a base frequency of 200Hz.

Here is also a scope picture of a full wave rectifier circuit output (red) compared to the first three Fourier components added together (blue). We can see that the first three components get close but to reproduce the signal exactly we'd need more and more harmonics. Maybe they dont need all those harmonics for the reception.
So what this means is that we would need more information to determine how they are decoding the received signal, and most important, what kind of output filter they use on the transmitter. I took a look at the article but it is just too brief.

Image

The 100Hz sine components are only here to show that there is a small error using LT Spice, but it is very small.
The 100Hz based components show the Fourier components just the way they are.
The 200Hz based components show the components relative to 200Hz, which means multiply the harmonic number by 2 to get the real harmonic number. I did this because there are only even harmonics in the wave.

Code: Select all

Pure 100Hz sine wave:
Harmonic	Frequency	 Fourier 	Normalized	 Phase  	Normalized
 Number 	  [Hz]   	Component	 Component	[degree]	Phase [deg]
    1   	1.000e+02	1.000e+00	1.000e+00	   -0.00°	    0.00°
    2   	2.000e+02	6.925e-07	6.925e-07	 -110.30°	 -110.30°
    3   	3.000e+02	7.341e-07	7.341e-07	  -83.82°	  -83.82°
    4   	4.000e+02	7.895e-07	7.895e-07	 -127.49°	 -127.49°
    5   	5.000e+02	6.211e-07	6.211e-07	  -77.59°	  -77.59°
    6   	6.000e+02	9.004e-07	9.004e-07	 -139.60°	 -139.60°
    7   	7.000e+02	4.904e-07	4.904e-07	  -65.12°	  -65.12°
    8   	8.000e+02	1.011e-06	1.011e-06	 -148.01°	 -148.01°
    9   	9.000e+02	3.641e-07	3.641e-07	  -39.35°	  -39.35°
   10   	1.000e+03	1.096e-06	1.096e-06	 -154.08°	 -154.08°
   11   	1.100e+03	3.592e-07	3.592e-07	    2.24°	    2.24°
   12   	1.200e+03	1.152e-06	1.152e-06	 -158.50°	 -158.50°
   13   	1.300e+03	5.318e-07	5.318e-07	   31.18°	   31.18°
   14   	1.400e+03	1.173e-06	1.173e-06	 -162.63°	 -162.63°
   15   	1.500e+03	7.827e-07	7.827e-07	   45.59°	   45.59°
   16   	1.600e+03	1.146e-06	1.146e-06	 -165.46°	 -165.46°


Full wave, harmonics from 100Hz:
Harmonic	Frequency	 Fourier 	Normalized	 Phase  	Normalized
 Number 	  [Hz]   	Component	 Component	[degree]	Phase [deg]
    1   	1.000e+02	6.759e-06	1.000e+00	  -38.86°	    0.00°
    2   	2.000e+02	4.229e+01	6.256e+06	  -90.00°	  -51.14°
    3   	3.000e+02	4.195e-06	6.207e-01	  -93.02°	  -54.16°
    4   	4.000e+02	8.421e+00	1.246e+06	  -90.00°	  -51.14°
    5   	5.000e+02	3.978e-06	5.885e-01	 -109.24°	  -70.38°
    6   	6.000e+02	3.592e+00	5.314e+05	  -90.00°	  -51.14°
    7   	7.000e+02	3.787e-06	5.603e-01	 -122.26°	  -83.40°
    8   	8.000e+02	1.985e+00	2.936e+05	  -90.00°	  -51.14°
    9   	9.000e+02	3.705e-06	5.482e-01	 -127.58°	  -88.72°
   10   	1.000e+03	1.255e+00	1.857e+05	  -90.00°	  -51.14°
   11   	1.100e+03	3.095e-06	4.579e-01	 -132.35°	  -93.49°
   12   	1.200e+03	8.635e-01	1.278e+05	  -90.00°	  -51.14°
   13   	1.300e+03	2.160e-06	3.196e-01	 -130.72°	  -91.86°
   14   	1.400e+03	6.287e-01	9.302e+04	  -90.00°	  -51.14°
   15   	1.500e+03	8.454e-07	1.251e-01	 -138.04°	  -99.18°
   16   	1.600e+03	4.771e-01	7.059e+04	  -90.00°	  -51.14°


200Hz as fundamental:
Harmonic	Frequency	 Fourier 	Normalized	 Phase  	Normalized
 Number 	  [Hz]   	Component	 Component	[degree]	Phase [deg]
    1   	2.000e+02	4.229e+01	1.000e+00	  -90.00°	    0.00°
    2   	4.000e+02	8.421e+00	1.991e-01	  -90.00°	    0.00°
    3   	6.000e+02	3.592e+00	8.493e-02	  -90.00°	    0.00°
    4   	8.000e+02	1.985e+00	4.693e-02	  -90.00°	    0.00°
    5   	1.000e+03	1.255e+00	2.969e-02	  -90.00°	    0.00°
    6   	1.200e+03	8.636e-01	2.042e-02	  -90.00°	    0.00°
    7   	1.400e+03	6.288e-01	1.487e-02	  -90.00°	    0.00°
    8   	1.600e+03	4.772e-01	1.129e-02	  -90.00°	    0.00°
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Re: Transmitter Modulators

Post by CeaSaR » Fri Feb 24, 2012 9:12 am

Louis E. Frenzel's ED article, Jan. 23, 2012

Looking at the explanation, and especially the graphic, your spectrum analyzer should
see a steady frequency with either positive or negative peaks of twice (2x's) the base
frequency at the data transition points. According to the aforementioned graphic, positive
spikes are transitions from a 0 to a 1 state, while negative spikes are transitions from a
1 to a 0 state. So you would need to find the transitions, and measure the period between
to see how many of that particular value are stored there (see the double 0 in the graphic).

I would think they would have a sync protocol for double redundancy so that the frequencies
could be compared to make sure they are seeing the same exact waveform. Just think how
bad it would be if the receiver based everything off of a 180 deg. signal! ;)

Just my simple layman's view. Hope I didn't confuse your view.

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Re: Transmitter Modulators

Post by Robert Reed » Sat Feb 25, 2012 5:48 pm

Started a lengthy research on the web and still didn't answer my question. Also there seems to be some discrepancies on the definition of BPSK. I did come across some Fourier patterns, but they were simulated. Not very good, as the resolution was horrible and the scan data was very minimal.The gloppy mess that was presented could just as well been a familiar analog PSK transmission - a declining sideband pattern with the first set being of higher amplitude than that of the carrier showing that it was headed in the direction of carrier null by virtue of Bessel function. All well and good but definitely no where near clear enough to learn anything from. After about 2 hours of "research", the math was getting so mind boggling I couldn't stay awake anymore and gave up and went to bed.

MrAl -
Nice presentation and jogged my memory to the RFI rectifiers can cause in high voltage supplys and why many shunt those rectifiers with 1000pf caps for suppression.

Caesar
When you mention positive and negative glitches, you may be still thinking in the time domain. There are no glithes in the frequency domain - only sine waves that are symmetrical on a zero axis.

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Re: Transmitter Modulators

Post by CeaSaR » Sat Feb 25, 2012 9:22 pm

Robert Reed wrote:Caesar
When you mention positive and negative glitches, you may be still thinking in the time domain. There are no glithes in the frequency domain - only sine waves that are symmetrical on a zero axis.
Yes, you will see a sine wave as you say, but there should be a short burst of 2x's the
base frequency whenever a transition occurs because of the immediate doubling of the
particular pulse (positive or negative, whichever the case was at the time of transition).
I thought about it and you won't see a spike up or down, but a really dense spot on the
display of the spectrum analyzer.

To put it another way, at transition, you get 2 half cycles in the same direction from the
zero axis, and this happens in the space of what would have been 1 full cycle. Now these
2 half cycles can be treated as 2 complete "distorted" cycles because they have frequency
relative to the rest of the sine wave. So, any time a "2x's base frequency" is detected, a
transition has occurred and you know that the base wave has changed phase and is the
opposite phase (0 or 180 deg) from the previous one. Another thing to think about is that
there is only 1/2 the amplitude of the original waveform, so you have another thing to look
for to verify if a transition has occurred.

Example:
Frequency - 100 Hz, amplitude - 10 mV sine wave carrier or base wave. At transition, you
should see (2) 5 mV amplitude peaks/troughs that can be described as a frequency of 200 Hz
Yes, I am mixing both domains, but I see things in multiple ways when I visualize them.

As I stated above, this is my layman's view. If anyone can explain any misconceptions I
have, please do so that I may have a clearer understanding as well as all involved.

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Re: Transmitter Modulators

Post by Robert Reed » Sat Feb 25, 2012 9:57 pm

Hi Caesar
"Example:
Frequency - 100 Hz, amplitude - 10 mV sine wave carrier or base wave. At transition, you
should see (2) 5 mV amplitude peaks/troughs that can be described as a frequency of 200 Hz
Yes, I am mixing both domains, but I see things in multiple ways when I visualize them."

What you have just described is the same image of the carrier going through it's phase shifts like the article shows(only at a lower frequency for simplicity). You are still in the time domain. But I agree with you that a momentary "doubling"of the carrier sine wave would produce a doubling of the frequency. Look at MrAl's post above and you will also see many other component frequencies in the package which is due to the non true sine wave nature of that instantaneous wave form. My mental image of an SA scan would be this group of components (sideband) separated from the carrier (or sub carrier) by the data rate frequency and then multiple side bands diminishing in amplitude.What I have just described is a pretty standard display for PSK modulation. However, this method is supposed to have a MUCH lower modulation index in spite of increased data band width. This is the point that confuses me. It seems that it would require a very small deviation of the carrier in order to obtain that low of a modulation index.

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Re: Transmitter Modulators

Post by MrAl » Thu Mar 01, 2012 2:18 pm

Hi again,

Here is a simulation of a 100Hz sine wave changing phase every two cycles. It changes by 180 degrees after each two cycle set.
So the wave starts out with 180 deg phase shift, then two cycles later switches phase by 180 degrees to 0 degrees, then two cycles later it switches back to 180 degrees (another 180 degrees).

In addition to that simulation, i think what else would be interesting would be to run this sine pattern through a low pass filter and see what comes out of the output. The low pass filter could be set to cut 3db say at 200Hz or something. Since the low pass filter cuts more for higher frequencies, if there were no higher frequency content in the wave then the waveform would pass without much change. But if there were higher order harmonics involved, the waveform would definitely change shape because it would loose some of its higher order components which are necessary to exactly produce the wave.
[Done, see second picture. This makes it look like the lower harmonics are more important]

In the simulation shown the Fourier components came out like this:

I think what is interesting is there is 50Hz component showing up. This is probably because the wave switches phase in a regular pattern every two cycles. That would correspond to a regular bit pattern.

Code: Select all


Fourier components of V(vo1)
DC component:1.48797e-007

Harmonic	Frequency	 Fourier 	Normalized	 Phase  	Normalized
 Number 	  [Hz]   	Component	 Component	[degree]	Phase [deg]
    1   	5.000e+01	8.479e-01	1.000e+00	  -90.00°	    0.00°
    2   	1.000e+02	8.989e-04	1.060e-03	    0.09°	   90.09°
    3   	1.500e+02	5.087e-01	6.000e-01	   90.00°	  180.00°
    4   	2.000e+02	3.356e-07	3.958e-07	  123.57°	  213.57°
    5   	2.500e+02	1.211e-01	1.429e-01	   90.00°	  180.00°
    6   	3.000e+02	1.421e-06	1.676e-06	   99.82°	  189.82°
    7   	3.500e+02	5.652e-02	6.666e-02	   90.00°	  180.00°
    8   	4.000e+02	4.345e-07	5.124e-07	  147.45°	  237.45°
    9   	4.500e+02	3.303e-02	3.896e-02	   90.00°	  180.00°
Total Harmonic Distortion: 62.158376%

Image


Low pass filtered:
Image
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Re: Transmitter Modulators

Post by MrAl » Thu Mar 01, 2012 2:56 pm

MrAl wrote:Hi again,

Here is a simulation of a 100Hz sine wave changing phase every two cycles. It changes by 180 degrees after each two cycle set.
So the wave starts out with 180 deg phase shift, then two cycles later switches phase by 180 degrees to 0 degrees, then two cycles later it switches back to 180 degrees (another 180 degrees).

In addition to that simulation, i think what else would be interesting would be to run this sine pattern through a low pass filter and see what comes out of the output. The low pass filter could be set to cut 3db say at 200Hz or something. Since the low pass filter cuts more for higher frequencies, if there were no higher frequency content in the wave then the waveform would pass without much change. But if there were higher order harmonics involved, the waveform would definitely change shape because it would loose some of its higher order components which are necessary to exactly produce the wave.
[Done, see second picture. This makes it look like the lower harmonics are more important]

In the simulation shown the Fourier components came out like this:

I think what is interesting is there is 50Hz component showing up. This is probably because the wave switches phase in a regular pattern every two cycles. That would correspond to a regular bit pattern.

Code: Select all


Fourier components of V(vo1)
DC component:1.48797e-007

Harmonic	Frequency	 Fourier 	Normalized	 Phase  	Normalized
 Number 	  [Hz]   	Component	 Component	[degree]	Phase [deg]
    1   	5.000e+01	8.479e-01	1.000e+00	  -90.00°	    0.00°
    2   	1.000e+02	8.989e-04	1.060e-03	    0.09°	   90.09°
    3   	1.500e+02	5.087e-01	6.000e-01	   90.00°	  180.00°
    4   	2.000e+02	3.356e-07	3.958e-07	  123.57°	  213.57°
    5   	2.500e+02	1.211e-01	1.429e-01	   90.00°	  180.00°
    6   	3.000e+02	1.421e-06	1.676e-06	   99.82°	  189.82°
    7   	3.500e+02	5.652e-02	6.666e-02	   90.00°	  180.00°
    8   	4.000e+02	4.345e-07	5.124e-07	  147.45°	  237.45°
    9   	4.500e+02	3.303e-02	3.896e-02	   90.00°	  180.00°
Total Harmonic Distortion: 62.158376%

Image


Low pass filtered (and inverted):
Image
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Re: Transmitter Modulators

Post by Robert Reed » Thu Mar 01, 2012 6:10 pm

MrAl
Interesting Sims! Well we know now that two things occur with every event - a momentary aberration in the steady sine wave stream and an immediate shift in that carrier of 180 degrees - back and forth. So we have created a set of Fourier waves at the change over points , and immediately following that we have shifted the carrier phase. BPSK detectors apparently looks for those aberrations, as that is when it reacts and then does nothing (even though we are phase shifted 180 degrees) until the next aberration at which time it reacts again (producing a rise and fall of a binary pulse). So it would appear that we cannot escape carrying at least a few sidebands per event on the carrier for fidelity purposes. These side band clusters would appear on the carrier at the data rate being transmitted and the higher the data rate, the higher frequency of occurrence.The modulation index is primarily composed of two variables - data rate in Hertz per second and carrier deviation either by phase or actual frequency. I just can't get it through my thick skull how they achieve modulation indexes of less than one in actual operation. Can you think of something I am overlooking?
BTW - In researching this on the web, there were several references to strict requirement of a LINEAR amplifier for the Tx final stage, which means that there must also be some amplitude modulation occurring there - maybe in the doubling area?

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Re: Transmitter Modulators

Post by CeaSaR » Thu Mar 01, 2012 10:14 pm

So you do have to look at it in both Time and Frequency domains in order to get the whole signal.
And you also would still need a frequency locked reference signal to compare it to in order to know
which part of the signal is 180 degrees and which is 0 degrees. The "aberrations" are there just to
tell the decoder when to switch states. Also, you need a counter of some type to determine how
many of one state is present in the current phase. Reference the article to see that they show a
binary data of 100101, where the 00 is shown as twice as many cycles as either a standard 1 or 0.
As for how they can get the modulation index so low, perhaps they are using a form of frequency
counting, one for the base frequency and one for the "change state" frequency. Anything not within
either of those ranges is discarded.

I'm not sure how close I am to that last statement, but it is how I would do it (if I knew enough to
do it :mrgreen: ). As I said, just a layman here with my take looking at only the graphic. Comments???

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Re: Transmitter Modulators

Post by MrAl » Fri Mar 02, 2012 7:14 am

Hi again,


Robert:
How are you defining modulation index here?
It seems to me that the maximum deviation for a phase modulation is 180 degrees, and apparently they use that for a '0' and 0 degrees for a '1' (or vice versa).

In my last post i should have created a third plot drawing, where the second drawing was superimposed over the first drawing to show what happens to the sharp points in the first drawing when the signal is passed through a low pass filter. Note that the points in the first drawing go to zero, but in the second drawing (low pass filtered) the points only make it down to within 0.3v of zero, which is about 25 to 30 percent difference. That's significant although how significant it is might also depend on the demodulation scheme.

Here's another view...

If the normalized carrier is:
Vc=sin(wt)

then the phase modulated signal is:
Vs=sin(wt+m(t))

where m(t) is the message signal. Since the message signal can be just about any signal, i would expect this to show up in Vs. If m(t) is sinusoidal, i would expect a smooth transition between phase changes, but if it is abrupt that would cause switching transients which have lots of harmonic content.

A linear amplifier would simply amplify all of the harmonics without change. A non linear would create new harmonics, while a switcher would introduce more high order components (without filtering). What they might be implying is that the harmonics in the signal are important.
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