AM vs Beats: Why Do We Need a Carrier Wave?

[LLT71]

not sure if this is dumb question but I was reading something about "beats" and saw some similarities with AM so I got to a conclusion if you have just two waves (same phase) with similar frequencies etc. sin(x)+sin(1.1x)
you can maintain AM or...not? if not, why not? if yes than why do we need that "extra wave" (aka carrier wave)? when you mathemathicaly "decompose" simple AM you get these three things: carrier wave + two sidebands, and in my example you get same "AM shape" but with only two sidebands (?) without carrier wave. at the same time I do understand essence of having carrier wave but now this confused me. thanks in advance!

 

[Carrock]

not sure if this is dumb question but I was reading something about "beats" and saw some similarities with AM so I got to a conclusion if you have just two waves (same phase) with similar frequencies etc. sin(x)+sin(1.1x)
you can maintain AM or...not? if not, why not? if yes than why do we need that "extra wave" (aka carrier wave)? when you mathemathicaly "decompose" simple AM you get these three things: carrier wave + two sidebands, and in my example you get same "AM shape" but with only two sidebands (?) without carrier wave. at the same time I do understand essence of having carrier wave but now this confused me. thanks in advance!

All of these have been used to transmit audio etc:
carrier wave + two sidebands
carrier wave + one sideband
reduced or minimised carrier wave + two sidebands (double sideband suppressed carrier)
reduced or minimised carrier wave + one sideband (single sideband suppressed carrier)

The carrier is basically wasted power, but only the first two can be demodulated by a receiver with a simple diode detector.

 

[Averagesupernova]

We can eliminate the carrier and one sideband but this means we need to know at the receiving end what the original carrier frequency was if we want to decode the original information accurately.

 

[Carrock]

We can eliminate the carrier and one sideband but this means we need to know at the receiving end what the original carrier frequency was if we want to decode the original information accurately.

That depends on the modulation.
If it's speech, for example, you can use harmonics of different fundamental frequencies in the audio to calculate the carrier frequency.
Humans can easily tune ssb by ear.
Only in rare cases is some carrier necessary.

 

[Averagesupernova]

That depends on the modulation.
If it's speech, for example, you can use harmonics of different fundamental frequencies in the audio to calculate the carrier frequency.
Humans can easily tune ssb by ear.
Only in rare cases is some carrier necessary.

This is my point. Some knowledge of what is being sent is necessary no matter what, but MORE knowledge of what is being sent is necessary when we start leaving parts out. And of course I said ACCURATELY. As an amateur radio operator I know I can tune speech by ear, but I need to know if the transmitting station is transmitting the upper sideband or lower, or just try it by trial and error and it will almost never be accurate compared to true AM. But when we start sending an AFSK signal on SSB there is no way to determine by ear if we are tuning in the correct sideband.

 

[LLT71]

so in my case sin(x)+sin(1.1x) would mean: one of them is carrier another sideband and what do you mean by "carrier wave is wasted power"? btw thank you both for your comments!

 

[Carrock]

This is my point. Some knowledge of what is being sent is necessary no matter what, but MORE knowledge of what is being sent is necessary when we start leaving parts out. And of course I said ACCURATELY. As an amateur radio operator I know I can tune speech by ear, but I need to know if the transmitting station is transmitting the upper sideband or lower, or just try it by trial and error and it will almost never be accurate compared to true AM.

'MORE knowledge of what is being sent is necessary when we start leaving parts out'
Do you mean you have to know something about the modulation system that isn't described in your licence?

It would help if you defined 'accurately'.
SSB is intended to be low bandwidth and intelligible; an extreme equivalent of a low bandwidth phone call.
'True AM' is generally several times the bandwidth of SSB and fairly natural sounding if the S/N ratio is high enough.
Increasing to half the bandwidth of 'true AM,' with high enough quality equipment at tx and rx, SSB could be indistinguishable from 'true AM.'
Uneconomic and pointless of course...

But when we start sending an AFSK signal on SSB there is no way to determine by ear if we are tuning in the correct sideband.

As with SSB, you could derive the suppressed carrier from the audio.

AFSK is designed for simplicity and compatibility with audio links at the cost of high power and inefficient bandwidth usage.

Far simpler to use frequency shift keying and if needed convert from/to AFSK at the tx and rx rather than selecting one AFSK sideband to (in effect) convert AFSK to FSK and then insert carrier at the rx.

 

[Carrock]

so in my case sin(x)+sin(1.1x) would mean: one of them is carrier another sideband and what do you mean by "carrier wave is wasted power"? btw thank you both for your comments!

I said 'The carrier is basically wasted power.'

Most of the time a (suppressed) carrier can be regenerated in the rx from redundant information in the modulation so the information it provides (frequency and phase) is not needed and the power to generate it is 'wasted'. (but it does make rx design simpler.)

With sin(x)+sin(1.1x) you would need both frequencies as there is no redundant information.

When you're sending information there's always some redundancy; it can often be used to regenerate the carrier.

 

[LLT71]

I said 'The carrier is basically wasted power.'

Most of the time a (suppressed) carrier can be regenerated in the rx from redundant information in the modulation so the information it provides (frequency and phase) is not needed and the power to generate it is 'wasted'. (but it does make rx design simpler.)

With sin(x)+sin(1.1x) you would need both frequencies as there is no redundant information.

When you're sending information there's always some redundancy; it can often be used to regenerate the carrier.

sorry mate I am still at the "beginner level" in modulations and trying to figure out basics. I have no clue what you are saying to me atm. I guess this will have to wait haha

 

[Merlin3189]

I don't know if I've missed the point of your question (I don't understand what you mean by, "... you can maintain AM ..."), because I can't understand the answers (or even the intent of the answers) others have given! But I'll add a few comments below, which I hope may help.

not sure if this is dumb question but I was reading something about "beats" and saw some similarities with AM so I got to a conclusion if you have just two waves (same phase) with similar frequencies etc. sin(x)+sin(1.1x)
you can maintain AM or...not? if not, why not? if yes than why do we need that "extra wave" (aka carrier wave)? when you mathemathicaly "decompose" simple AM you get these three things: carrier wave + two sidebands, and in my example you get same "AM shape" but with only two sidebands (?) without carrier wave. at the same time I do understand essence of having carrier wave but now this confused me. thanks in advance!

First, I don't think you do get "the same AM shape". If you look at the graph of your function, it does not look like AM. It is a sinewave whose amplitude is modulated, but not in the same sinusoidal way as AM.
The envelope of an AM signal (made from a pure audio tone and a pure carrier) is the shape of the complete audio wave. The top envelope is a complete sinewave and the bottom envelope is the antiphase complete sinewave.
When you make beats between two pure frequencies, the shape of the envelope is like a full wave rectified sine wave, or a sequence of half wave pulses.

Second, AM is not the addition of two waves, it is the product of two waves. So mathematically, when you add two (sine) waves, you get two waves: when you multiply two (sine) waves, one way of expressing the result is as the sum of three waves, but there is no way of expressing it as the sum of two (sine) waves.

Third, the frequencies you get in the mix are different. AM gives carrier plus USB at the sum frequency and LSB at the difference frequency. Beats between two sines gives you the mean frequency, modulated (NOT sinusoidally) at the difference frequency. In fact it is multiplied by half the difference frequency, so that the magnitude of the modulation has its main component at the difference frequency.

If you search the past threads, you should find this dealt with before. I'll see if I can find the diagrams and maths I posted then.

You could simply draw (using whatever software you have - I use Excel) a beat waveform and an AM waveform and see the difference.

You may also like to think about why people use traditional AM radio. If you simply added an RF signal to an audio signal and applied the result to an antenna, only the constant RF would be radiated to any significant degree*. When you modulate the two signals, you generate 3 RF frequencies, all of which get radiated and can then be received and demodulated.
(*It might be interesting to see if you could produce a beat wave current in an antenna cut for half the RF frequency. If so, I guess you might be able to transmit this and eventually receive a distorted version of your audio? But this is just a wild possibility I thought of when checking my comment above. )

 

[LLT71]

I don't know if I've missed the point of your question (I don't understand what you mean by, "... you can maintain AM ..."), because I can't understand the answers (or even the intent of the answers) others have given! But I'll add a few comments below, which I hope may help.

First, I don't think you do get "the same AM shape". If you look at the graph of your function, it does not look like AM. It is a sinewave whose amplitude is modulated, but not in the same sinusoidal way as AM.
The envelope of an AM signal (made from a pure audio tone and a pure carrier) is the shape of the complete audio wave. The top envelope is a complete sinewave and the bottom envelope is the antiphase complete sinewave.
When you make beats between two pure frequencies, the shape of the envelope is like a full wave rectified sine wave, or a sequence of half wave pulses.

Second, AM is not the addition of two waves, it is the product of two waves. So mathematically, when you add two (sine) waves, you get two waves: when you multiply two (sine) waves, one way of expressing the result is as the sum of three waves, but there is no way of expressing it as the sum of two (sine) waves.

Third, the frequencies you get in the mix are different. AM gives carrier plus USB at the sum frequency and LSB at the difference frequency. Beats between two sines gives you the mean frequency, modulated (NOT sinusoidally) at the difference frequency. In fact it is multiplied by half the difference frequency, so that the magnitude of the modulation has its main component at the difference frequency.

If you search the past threads, you should find this dealt with before. I'll see if I can find the diagrams and maths I posted then.

You could simply draw (using whatever software you have - I use Excel) a beat waveform and an AM waveform and see the difference.

You may also like to think about why people use traditional AM radio. If you simply added an RF signal to an audio signal and applied the result to an antenna, only the constant RF would be radiated to any significant degree*. When you modulate the two signals, you generate 3 RF frequencies, all of which get radiated and can then be received and demodulated.
(*It might be interesting to see if you could produce a beat wave current in an antenna cut for half the RF frequency. If so, I guess you might be able to transmit this and eventually receive a distorted version of your audio? But this is just a wild possibility I thought of when checking my comment above. )

thank you for clearing things up! about that "maintain" part I saw some similarities and instantly thought "well, ok than you can maintain AM just by using two waves with two similar frequencies" (now I know it's not true, but you got the point). now I see the differences "full wave rectified sine wave" vs "envelope of modulated AM wave".

I want to ask you this one more question. why do we need "1+ part" in:
y(t)=[1+m(t)]*c(t)
where c(t) is carrier wave and m(t) modulation waveform (Wikipedia, Simplified analysis of standard AM).

can we "maintain" modulation by just multiplying y(t)=m(t)*c(t) or we have to "model" our function in such way so that envelope of that function represents signal we want to send?

 

[Averagesupernova]

As with SSB, you could derive the suppressed carrier from the audio.

AFSK is designed for simplicity and compatibility with audio links at the cost of high power and inefficient bandwidth usage.

Far simpler to use frequency shift keying and if needed convert from/to AFSK at the tx and rx rather than selecting one AFSK sideband to (in effect) convert AFSK to FSK and then insert carrier at the rx.

If you feed AFSK into a SSB transmitter you will have the sideband shifting back and forth between two frequencies which are the same number of hertz apart that the original two tones were in the AFSK signal. The RF signal completely resembles FSK. Can you tell which sideband the signal was transmitted on? If you inject carrier on the wrong side of the signal to recover the audio the high and low tones will reversed. This is not an issue with actual AM.
-
Many hams get on RTTY or another digital mode using AFSK fed into the microphone connector. Nothing new or unusual about that.
-
Yes I realize this has gotten off topic.

 

[Carrock]

If you feed AFSK into a SSB transmitter you will have the sideband shifting back and forth between two frequencies which are the same number of hertz apart that the original two tones were in the AFSK signal. The RF signal completely resembles FSK. Can you tell which sideband the signal was transmitted on? If you inject carrier on the wrong side of the signal to recover the audio the high and low tones will reversed. This is not an issue with actual AM.

From
http://n1mm.hamdocs.com/tiki-index.php?page=General+RTTY+and+PSK+Information

If you are using SSB for AFSK, MMTTY expects the radio to be in LSB on all bands, whereas Fldigi expects the radio to be in USB on all bands. Both of these engines have means to operate on the "other" sideband, using a "Reverse" ("Rev" or "Rv") button

I never thought anyone would do this for real...the black box operators have taken over.
I suppose this is something you would have to know about the modulation system that isn't described in your licence.
And there's surely a few lids out there who're transmitting the wrong sideband.
So you have a point.

AFSK is designed for simplicity and compatibility with audio links at the cost of high power and inefficient bandwidth usage.

(I was assuming DSB with full carrier.)

...-
Many hams get on RTTY or another digital mode using AFSK fed into the microphone connector. Nothing new or unusual about that.
-...

Are we in agreement here?

LLT71: Merlin3189's and my posts are independent and any common ground is coincidental.

I can only suggest you read the topics at the bottom of the page ie Similar Discussions: Amplitude Modulation vs Beats

 

[sophiecentaur]

AM ('Ancient Modulation') was the only form of transmission that was available to early broadcasters and it is suitable for very simple radio receivers. Broadcast transmitters are large sweaty beasts and the AM network is a very inefficient user of spectrum space. It is still with us simply because the international agreements on spectrum use have to satisfy everyone and there are still a lot of people who can only receive AM broadcasts. Strangely enough, Digital Mobile Phone and Satellite Broadcast technology leapfrogged all those systems that were developed, over the years, in the "west" and the digital data networks can deliver nearly all the programmes needed to nearly everyone in the world. At least, it is rapidly heading that way.

There are many many pictures of waveforms all over the Web. Google (images) AM waveform and google Suppressed Carrier AM. The difference between the two waveforms is striking. AM has an 'envelope' around the high frequency carrier. That envelope looks identical to the modulating waveform. (A sine wave on either side, is the simplest). Looking at Double sideband (two equal amplitude signals) you get a 'string of beads' waveform in which there is a 'sort of envelope' which crosses through zero at the beat frequency. A very messy looking waveform - sounds messy too!

 

[Merlin3189]

I want to ask you this one more question. why do we need "1+ part" in:
y(t)=[1+m(t)]*c(t)

Good question. I had actually forgotten about this until I tried to explain AM to someone in a previous thread. I had just remembered the general principle of (amplitude) modulation as multiplication.
I think back to how one did AM in old valve transmitters (yes, I'm that old!) We used to take the power amplifier valve, with its high +ve voltage on the anode and use a transformer in series with the high voltage supply. By applying the audio signal to the primary of the transformer, the audio voltage was added to the high voltage via the secondary. So If the valve had a quiescent voltage of say +100V and you applied 50V (AC) of audio, the anode voltage varied between +150V and +50V as the audio voltage varied between +50V and -50V.
The anode voltage determined the amplitude of the RF output, so the RF output was proportional to the audio voltage added to the quiescent high voltage. The 1+ part of the formula represents this quiescent (or average, or standing) high voltage applied to the anode and the m(t) represents the audio voltage added to it by the modulation transformer. The sum of these is the instantaneous anode voltage, which determines the output amplitude of the c(t) carrier signal.

(1+m(t))*c(t) , when m(t)=0 you have unmodulated RF ( ie c(t) ).

When the amplitude of m(t) =1 or the same as c(t) you have 100% modulation

and the envelope is 1+m(t), (here a sinewave)

You could increase the audio drive up towards 100V (AC) causing the anode voltage to vary between 0V and +200V. If you increased the audio drive beyond that, the the anode voltage would become negative for part of the audio cycle, which would make the valve "cut off", since it only functions with a positive voltage on the anode.
So the amplitude of the audio signal was not allowed to exceed the quiescent anode voltage. In the formula this quiescent voltage is factored out, so that it is represented by 1 and the magnitude of m(t) is always less than 1. (Since in practical terms you don't actually get a valve or transistor to operate to 100% modulation, because there would be no voltage on the anode, collector, drain or whatever.)
If the amplitude of m(t) is greater than that of c(t), then you have over-modulation, causing distortion.

This shows the calculated (1+m(t))c(t) and the envelope no longer reproduces the sinewave. In a transmitter, the part where (1+m(t)) is negative would cut off the PA device and the graph would be flat here rather than inverted.
If there were no 1+ in the formula, then any amplitude of m(t) would produce negative values of (0+ m(t)) and you would never get a clean envelope.
The value has to be 1 simply because that represents the amplitude of c(t) and the maximum allowable amplitude of m(t).BTW. The wild comment at the end of my previous post (about maybe transmitting a beat signal rather than a modulated one, is rubbish! ( It was very late, blah, blah, etc.) What I'd not thought of was, that you won't even get beats unless the frequencies are close - which will never be the case for audio and RF. (I'd just accepted without thinking, the proposition that you got beats between any frequencies.) With close frequencies you get half the sum (mean) modulated by (sort of) the difference (frequencies.) Once the frequencies become too far apart, the difference frequency is bigger than the mean frequency, so the result looks nothing like one modulating the other.
Now if you have two radio frequencies which are close, they do indeed produce beats, which were heard as annoying whistles in AM receivers. And they were used, as musicians use audio beats, to adjust two transmitters to the same frequency by listening for zero beat.

 

[Merlin3189]

Thinking about Sophie's comment on DSB (suppressed carrier) I realized I can get this on my spreadsheet by removing the 1

so you can see the string of beads.
And this does indeed look like beats between the two constant sideband frequencies.
When you add in a constant carrier, say in phase with the RF in the first bead, it will double* the amplitude of that bead and cancel the next inverted-phase bead, restoring the envelope back to a clean sinewave. (No point in a picture of that, because it then looks exactly like 100% AM.) If you don't add enough carrier, it still looks like an overmodulated AM, and when you add too much, it just becomes undermodulated AM (ie. normal AM! Since AM should be 100% modulated only on the absolute peaks of the audio signal. Though amateurs, who wanted power rather than clarity, did turn up the modulation and try to filter out the worst of the harmonic distortion in order to get more of their limited power into the sidebands - effectively transmitting a sort of DSB (slightly) Reduced Carrier.).

*[Edit: should say raise rather than double]

 

[sophiecentaur]

This shows the calculated (1+m(t))c(t) and the envelope no longer reproduces the sinewave.

Where the 'envelope' crosses the axis, the carrier changes phase by 180°.
I tried to figure out what the equivalent to transmitting two nearby tones would involve if you wanted to transmit a complicated waveform (say audio). The answer would have to be the two sidebands from a normal AM signal. They would need to be spaced correctly if the demodulated signal is to be undistorted. But of course, producing two SSB signals and then combining them would be 'fiddly' and not very efficient use of transmitter power.

 

[Merlin3189]

...The answer would have to be the two sidebands from a normal AM signal. They would need to be spaced correctly if the demodulated signal is to be undistorted. But of course, producing two SSB signals and then combining them would be 'fiddly' and not very efficient use of transmitter power.

Of course the way of generating SSB used to be to produce AM (or DSB suppressed carrier) then filter off one sideband. So you'd be making two sidebands twice, filtering off opposite sidebands from the two pairs, then adding them together. I think perverse is more the word than fiddly.

As for power, once we got into SSB, all the fiddling to generate the signal is done at low power, then the final signal is raised to whatever power is wanted by linear amplifiers. And now the fiddly bit is probably all done by a DSP chip at micropower levels, so it doesn't matter how fiddly it is. A bit different from the old AM where the final signal was actually created in the PA stage and up to half the output power had to be provided by the audio driver.

 

[tech99]

not sure if this is dumb question but I was reading something about "beats" and saw some similarities with AM so I got to a conclusion if you have just two waves (same phase) with similar frequencies etc. sin(x)+sin(1.1x)
you can maintain AM or...not? if not, why not? if yes than why do we need that "extra wave" (aka carrier wave)? when you mathemathicaly "decompose" simple AM you get these three things: carrier wave + two sidebands, and in my example you get same "AM shape" but with only two sidebands (?) without carrier wave. at the same time I do understand essence of having carrier wave but now this confused me. thanks in advance!

Amplitude modulation is different to just having two signals present together such that they create beats.
The lower frequency signal is the modulating signal, and the higher frequency signal is the carrier.
The AM modulation circuit causes the amplitude of the carrier to be proportional to the amplitude of the modulating signal. This is sometimes achieved by causing the modulating signal to alter the gain of an RF amplifier.
The resulting AM can be looked at either as an amplitude-varying signal, or alternatively, as a carrier and sidebands when looked at in the frequency domain.

 

[LLT71]

thanks everyone for helping understand this concept better!