# Why modulate the data sinusoid onto a transmitter sinusoid?

• Niko Bellic
In summary: Finally, you can use higher frequencies where shorter waves are blocked by buildings and other obstructions. There is a physical component at the end of the cable called a 'transmitter' which can be resonant at certain frequencies and amplify the signal sent through it.
Niko Bellic
Why modulate the "data" sinusoid onto a "transmitter" sinusoid?

(Sorry about the simple question but this stuff isn't exactly my specialty)

From howstuffworks.com ...

In amplitude modulation, the amplitude of the sine wave (its peak-to-peak voltage) changes. So, for example, the sine wave produced by a person's voice is overlaid onto the transmitter's sine wave to vary its amplitude.

Why can't you just send the sine wave produced by a person's voice directly through the air (or whatever channel you are using) instead of encoding the voice onto transmitter sinusoid? I am guessing it is because the sinusoid of a higher frequency can travel farther without attenuation. If so, why is this?

Also, unrelated...

The advantage to FM is that it is largely immune to static.

What exactly is "static" and why is FM immune to it?

Thanks!

Niko Bellic said:
Why can't you just send the sine wave produced by a person's voice directly through the air (or whatever channel you are using) instead of encoding the voice onto transmitter sinusoid? I am guessing it is because the sinusoid of a higher frequency can travel farther without attenuation. If so, why is this?
The U.S. Navy used to send radio signals to submarines at frequencies in the 10kHz range which is in the audio spectrum. At those frequencies the signals could penetrate the Earth and the oceans. The reason audio is not transmitted directly is that for an antenna to be efficient it must be resonant. Even at 10kHz the antennas were miles long and the signals were transmitted at very high power levels. Audio, consisting of a wide range of frequencies would need a bunch of very long antennas, each a different length.

By encoding the audio onto a higher frequency, antennas of a reasonable size can be used.

Niko Bellic said:
What exactly is "static" and why is FM immune to it?

Thanks!

Static especially on AM radios is noise that adds or subtracts from the amplitude of the carrier. Since the receiver uses the amplitude of the carrier to detect the audio signal, any nearby noise is received as static.

FM transmissions don't use the amplitude of the carrier to contain the information. Instead they use the variation of the frequency over a narrow range for the information. FM receivers cut off the top and bottom of the carrier to remove the noise. Radio noise has much less effect on the frequency of the carrier than on its amplitude.

Beautiful answer. Thank you!

What if you're not sending the signal through the air to an antenna but are instead using, say, a coaxial cable? Will modulating the signal onto a higher frequency sinusoid have any benefit in this case? Is there something at the end of a coaxial cable connection that is analogous to an "antenna" in that it has a resonant frequency?

Niko Bellic said:
I am guessing it is because the sinusoid of a higher frequency can travel farther without attenuation. If so, why is this?
A big advantage of medium- and short- wave radio is that it can achieve incredible reach by exploiting a characteristic of the ionosphere, to bounce the signal around the globe. Not totally reliable, and dependent on the sun's influence and time of day, this nevertheless allows you to listen to foreign radio stations. I doubt that the ionosphere would be similarly reflective to a band of audio frequencies directed towards it.

In addition to requiring large transmitting antennae, as skeptic2 mentioned, the receiving antennae would similarly need to be scaled up in size and height.
What exactly is "static" and why is FM immune to it?
Before the introduction of digital TV transmission, the older analog method used AM for transmitting the picture information, and FM to send the audio. So while an approaching thunderstorm might light up the sky and rattle the house, there would be no static on the audio. But static on the AM picture showed up as fleeting white streaks or dots on the picture, and explained by AM not being immune to electrical interference.

If you are in a country still using analog TV (and plagued by ghosting and shadowing, etc.), then you should be able to notice this.

Niko Bellic said:
Beautiful answer. Thank you!

What if you're not sending the signal through the air to an antenna but are instead using, say, a coaxial cable? Will modulating the signal onto a higher frequency sinusoid have any benefit in this case? Is there something at the end of a coaxial cable connection that is analogous to an "antenna" in that it has a resonant frequency?

There are many advantages of modulating a 'carrier' frequency with your wanted signal. You do not need to send very low frequency or DC components on the cable, which would be susceptible to Mains Hum and ubiquitous low frequency amplifier noise. You can send more than one set of signals down one wire - just use a number of different carriers. Decades ago, Telecommunications Engineers found that they could send thousands of voice channels down one 'trunk' line where they would have been stuck with one conversation per line.
At the receive end of the line, you have a receiver - similar to what you would connect to an antenna, which you can tune (with a filter) to whichever of the carrier signals you want.

How does this 'carrier system' work? There are many different systems for doing this - culminating with the digital systems used today. Amplitude Modulation just varies the amplitude of the carrier according to the instantaneous value of the programme or data signal. The AM signal, when viewed on an oscilloscope, looks like a band of green with its width (the envelope) looking just the same as the original data / sinewave etc..
Frequency modulation varies the frequency of the carrier about a nominal undeviated value. The signal just looks a total mess and unintelligible on an oscilloscope. BUT it has an enormous advantage in that the information can be spread over a very wide range of the RF spectrum and this gives you a large signal out of your receiver which 'dilutes' the effect of any channel noise or interference - the so-called FM Advantage.
There is no end to this . . . . . . .

Wow thanks sophiecentaur!

I can't believe I forgot that you could superimpose multiple different "channels" onto the same coaxial cable.

Am I right to say that in AM modulation, a specific channel resides on a single (very narrow) frequency in the RF spectrum, whereas in FM modulation, a channel resides on a wider band of frequencies centered around a frequency in the RF spectrum?

NikoBellic said:
Wow thanks sophiecentaur!

I can't believe I forgot that you could superimpose multiple different "channels" onto the same coaxial cable.

Am I right to say that in AM modulation, a specific channel resides on a single (very narrow) frequency in the RF spectrum, whereas in FM modulation, a channel resides on a wider band of frequencies centered around a frequency in the RF spectrum?

You can't possibly imagine it can be as straightforward as that. FM can actually be used in a narrow band mode, which takes up no more spectrum than AM. No 'FM advantage' but the transmitter is a lot cheaper to engineer. The receiver is more complex than a 'cat's whisker' but that's not a problem these days and narrow band FM is in common use for low quality comms - around the VHF bands for taxis, boats and the gas man. (and radio hams, of course)

Not so long ago, TV links (and analogue satellite TV) used FM with a modest amount of deviation. Much easier to transmit with the equipment available to put up there.

NikoBellic said:
I can't believe I forgot that you could superimpose multiple different "channels" onto the same coaxial cable.
Not unlike being able to superimpose multiple different channels through the same "ether".

NikoBellic said:
Am I right to say that in AM modulation, a specific channel resides on a single (very narrow) frequency in the RF spectrum, whereas in FM modulation, a channel resides on a wider band of frequencies centered around a frequency in the RF spectrum?
That is not correct. An AM channel width depends on the bandwidth of the signal modulating the carrier. For instance the video portion of an analog AM television channel in the U.S. takes up about 3.5 MHz and even then one of the sidebands is mostly chopped off. With FM it is the modulation that creates the bandwidth of the channel. Without the modulation the FM carrier would be as narrow as an unmodulated AM carrier.

Hmmm... I'm failing to understand this.

Let's say you tune into the 680 channel on the AM dial. What you are doing is tuning into a 680 kHz carrier signal with the sound sinusoid encoded into it by varying the carrier amplitude in the same pattern as the sound sinusoid. Isn't this 680 channel technically 0 Hz "wide" since it is located exactly at the 680 kHz frequency, and does not include a wide band of frequencies? If you tune into 681 or 679 you are still far away from that super-thin, single frequency "band" of 680. On the other hand, since FM modulation means you are varying the frequency of the carrier signal in order to encode the sound sinusoid into the carrier, your channel is going to be a wider band of frequencies spread out around a central frequency.

Isn't that right? Thanks

Niko Bellic said:
Hmmm... I'm failing to understand this.

Let's say you tune into the 680 channel on the AM dial. What you are doing is tuning into a 680 kHz carrier signal with the sound sinusoid encoded into it by varying the carrier amplitude in the same pattern as the sound sinusoid. Isn't this 680 channel technically 0 Hz "wide" since it is located exactly at the 680 kHz frequency, and does not include a wide band of frequencies? If you tune into 681 or 679 you are still far away from that super-thin, single frequency "band" of 680. On the other hand, since FM modulation means you are varying the frequency of the carrier signal in order to encode the sound sinusoid into the carrier, your channel is going to be a wider band of frequencies spread out around a central frequency.

Isn't that right? Thanks
This is technically correct but narrow band FM uses a low deviation and the occupied bandwidth is hardly different from that of a similar quality AM signal. The channel spacing for narrow band FM is as low as 7.5kHz - which makes my point.
The reason for using wider deviation is simply to improve SNR. This is something that AM can't do.
If you look at the spectrum of low deviation FM with a sinusoid, you actually just get two significant sidebands (same spacing as for AM and indistinguishable to look at on a spectrum analyser). The difference is that the phase of one sideband is just 180 degrees different from the corresponding AM sideband.

Niko Bellic said:
Hmmm... I'm failing to understand this.
That's not surprising. Until you have studied the mathematics of Fourier analysis it is going to remain a bite hazy.
Let's say you tune into the 680 channel on the AM dial. What you are doing is tuning into a 680 kHz carrier signal with the sound sinusoid encoded into it by varying the carrier amplitude in the same pattern as the sound sinusoid. Isn't this 680 channel technically 0 Hz "wide" since it is located exactly at the 680 kHz frequency, and does not include a wide band of frequencies?
Listening to a single frequency (i.e., the carrier in a ~0Hz bandwidth) becomes just a tiny bit monotonous after about, oh, 10 seconds. If you want to send/receive intelligence on that AM carrier, then you have to allow a bandwidth proportional to the frequencies in that intelligence. So to transmit music (say a bandwidth of 33kHz) using plain old AM, you need to accommodate a range of frequencies = carrier ± 33KHz.

There is nothing stopping you from listening to an AM radio station using your own custom-built narrow-band receiver that's tuned to a bandwidth of ~0Hz, but the only information you will hear is whether the station is on the air or not, according to the presence or absence of the carrier. You won't hear any speech or music, because that information is contained within the sidebands.

I'll cover a few things here that just might be misleading. It is my opinion that AM is actually a misnomer. The amplitude of the carrier itself is not chaning in amplitude at all. It appears that way on a scope but this is because you are viewing a composite signal of the carrier and the upper and lower sidebands. The higher the frequency of the modulating signal, the wider the bandwidth of the signal. I suspect the OP is probably not familiar with sidebands.
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Now for the issue of FM. The bandwidth of an FM signal is also reliant on the frequency of the modulating signal. It is not possible to have an FM signal with a deviation of 5 Khz when the modulating signal is 50 Khz and expect a bandwidth of 10 Khz (5 Khz of devaition*2). Sidebands of an FM signal appear as multiples of the modulating signal. In the case above, there would be no sidebands until 50 Khz away from the carrier.
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There have been a number of threads on this forum about modulation. It would pay to do a search. Lots of stuff to learn.

@Averagesupernova
I don't think one needs to worry too much about what's really going on with AM. The spectrum is a result of varying the amplitude of a carrier. It's what you actually do with an AM transmitter- just the same as if you wiggled a knob around on the gain control - it's just that you are doing it faster. If you looked with a very narrow band detector at the amplitude of carrier with modulation and without, the value would change from unity to half as the power is shoved out into the sidebands at 100% Mod.

I agree that the whole business of modulation takes some getting used to - particularly with FM. Many people think they've got it then they haven't - then they have. Like QM, but on a more trivial level. On that subject, I wonder when someone will try to 'explain' FM signals in terms of photons -haha.

Hmmmmm. I'm not so sure sophie. I don't think the amplitude of the carrier ever changes going from 0% mod to 100% mod. The power that the transmitter consumes will double and the total power in all three frequencies combined will double. But I don't think the carrier itself ever changes. I'd have to dig and crunch some number to come to a better conclusion but I believe what I say is correct.

Averagesupernova said:
I don't think the amplitude of the carrier ever changes going from 0% mod to 100% mod. The power that the transmitter consumes will double and the total power in all three frequencies combined will double. But I don't think the carrier itself ever changes. I'd have to dig and crunch some number to come to a better conclusion but I believe what I say is correct.

An alternative way of looking at AM is with a phase diagram. Imagine a diagram with the carrier at 0 deg at a radius of 1. Now modulate the carrier with a 1 kHz signal. This introduces two sidebands each with a radius of 0.5. Note that the amplitude represents voltage, not power.

The upper sideband, being higher than the carrier, is advancing in phase at 2*pi*1000 radians per second. The lower sideband is losing 2*pi*1000 radians per second. On the phase diagram the upper sideband is rotating counterclockwise and the lower sideband is rotating clockwise. When all three vectors are lined up at 0 deg, they add together with a resultant amplitude of 2. 0.5 ms later the two sidebands are in phase with each other but out of phase with the carrier. The sum of the 3 signals is now 0. Looking at it this way, the carrier doesn’t change amplitude.

The phase diagram for FM is similar. The carrier is still at 0 deg. but the sidebands, instead of being in phase with the carrier are 90 deg out of phase. The 2 sidebands would be in phase with each other at 90 deg and 270 deg. The resultant vector of the sidebands and carrier produce a carrier whose phase shifts back and forth.

In fact, there is a method a creating FM by using a balanced modulator to generate double sidebands and injecting the carrier 90 deg phase shifted. The resulting FM signal has the advantage of being as narrow as an AM signal, yet still having a decent deviation index. It is also a way of getting good deviation from a crystal oscillator without needing a lot of frequency multiplication.

Averagesupernova said:
Hmmmmm. I'm not so sure sophie. I don't think the amplitude of the carrier ever changes going from 0% mod to 100% mod. The power that the transmitter consumes will double and the total power in all three frequencies combined will double. But I don't think the carrier itself ever changes. I'd have to dig and crunch some number to come to a better conclusion but I believe what I say is correct.

Yes, you're right there about the power at the carrier frequency.
As for the power in the sidebands - their amplitude, at 100% mod index of each sideband, is half that of the carrier. So the power of each s/b is 1/4, giving a half of the power (total) turning up in the sidebands. I know that because the mod amplifier never needs to be as beefy as the RF power amplifier in a conventional AM broadcast transmitter.

Not sure about the sidebands on AM. I was thinking that each sideband was 50% of the main carrier power and not 25% at 100% modulation. I haven't had anything to do with AM for a while so I am getting rusty.

50% amplitude - 25% power

I had no idea how deep this rabbit hole is. I'm going to go do some independent research and then come back because I'm determined to figure this whole business out. Good discussion so far.

## 1. Why is it necessary to modulate data onto a transmitter sinusoid?

Modulation is necessary because it allows us to transmit information over long distances without losing the data signal. The data signal is combined with a carrier sinusoid, which enables the signal to travel further and be less susceptible to noise and interference.

## 2. What are the benefits of modulating data onto a transmitter sinusoid?

The main benefit of modulating data onto a transmitter sinusoid is that it allows for efficient use of the available bandwidth. By combining the data signal with a carrier signal, multiple signals can be transmitted simultaneously without overlapping or interfering with each other.

## 3. How does modulation affect the quality of the transmitted data?

Modulation can improve the quality of the transmitted data by allowing for better signal-to-noise ratio. The carrier signal helps to amplify the data signal, making it less susceptible to noise and interference that could distort the data. This results in a clearer and more reliable transmission of the data.

## 4. Are there different types of modulation that can be used for transmitting data?

Yes, there are several different types of modulation that can be used for transmitting data, including amplitude modulation, frequency modulation, and phase modulation. Each type has its own advantages and is used in different applications depending on the specific needs and requirements.

## 5. How does the modulation process work?

The modulation process involves combining the data signal with a carrier sinusoid using a modulator. The modulator varies the amplitude, frequency, or phase of the carrier signal according to the characteristics of the data signal. The resulting modulated signal is then transmitted through a medium, such as air or a cable, to a receiver where it is demodulated to retrieve the original data signal.

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