# AM & FM modulation QUESTION

1. Jan 9, 2005

### Jake

Ok A question here about how AM & FM modulation works.

I know that AM trasmits the sound by varying the voltage of the radio signal, and FM varies the frequency itself of the signal, however, viable sound needs two things, varying frequency AND VARYING AMPLITUTE. So the modulation, whether FM or AM, transmits only 1 variation, so it needs to transmit one more for the volume of the sound, how does it transmit that?

Thanks!

2. Jan 9, 2005

### chroot

Staff Emeritus
Jake,

AM varies the amplitude of the radio signal, not the voltage. After all, the radio signal is a wave -- its voltage is always changing.

The reason this scheme works is that audio frequencies are very low -- only up to about 20 kHz or so. The radio frequencies used for AM broadcast are very high, over a megahertz. The original audio signal is used to modulate the amplitude of a fixed-frequency carrier. The radio receiver only has to look at how the envelope (amplitude) of the signal is changing to recover the original audio signal. Both frequency and amplitude information are recovered, because the receiver is really just recreating the entire original sound signal. FM works for the same reason; it just modulates frequency instead of amplitude.

Note that neither modulation would work in reverse; you could not use a lower-frequency carrier to encode information from a higher-frequency original signal.

- Warren

3. Jan 9, 2005

### Jake

Amplitude is the strength of the signal, which would translate to voltage when picked up by the antenna right? I thought that's how it worked.

Anyway, I'm still not getting how you can send both amplitute and frequency information of sound just by modulating the amplitute of a fixed-frequency electro-magnetic wave (or FM modulation for that matter). Here's my thinking: You take a frequency used in AM, and modulate its amplitute. Ok so as a result, the signal now has a fixed frequency with a varying amplitute which corresponds to the sound. That varying amplitute is the information. So here's the question: How can the single variation of amplitude carry the information for BOTH the FREQUENCY and AMPLITUTE of the actual sound signal? I'm just not getting that.

Thanks for the help :)

4. Jan 9, 2005

### Jake

Ok another quick question while we are on the subject of sound waves.

In the enclosed pic is a picture of waves recorded in a program. Waves vary by frequency and amplitute. But what I don't understand is how there are amplitude variations WITHIN amplitude variations. Meaning, see how the pic has the main wave, going up and down, but then there are mini spikes along the surface of THAT. What is that? Am I right in thinking that that is simply the frequency experiencing slight alterations but without ever returning to zero pressure? Like it keeps a constant pressure, but that varies etc.

Thanks again!

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5. Jan 9, 2005

### Cliff_J

Jake - think of frequency as simply a way to reflect the change versus time.

If we have a 20 Hz sine wave it will change 20 times in a second, a 400Hz changes 400 times a second. Using those numbers only allow you to tell you how quickly it is changing but the change is still made of the same wave behavior.

Modulate that on top of a radio wave that is varying 1 million times a second and now what was a signal that has a constant behavior during silence changes when there is an audio signal. The modulation means the radio wave will vary from the constant behavior and the circuitry pulls out that difference.

In your picture, you have some sort of large amplitude low frequency wave and a bunch of low amplitude higher frequency signals mixed in with that.

A sound wave has positive and negative pressures, meaning that the air pressure is increased, returns to zero, then is decreased, and finally returns to zero. This happens for each cycle. Each compression/rarefraction is part of how the energy is transferred through the air molecules. The slinky spring moved along its length back and forth is an easy demonstration of this effect. So I'm not sure what you mean by asking about returning to zero pressure but hopefully answered what you asked.

Continuing with our sine wave behavior it starts at zero. 1/4 of the way through its cycle it hits its positive peak. 1/2 way through it hits zero. 3/4 it hits its negative peak. At the end of the cycle it has returned to zero and starts over again. In your picture the low frequency wave is actually at 1/4 its cycle at the left of the picture (positive peak) and you can see how it continues on from there to complete the rest of this cycle and then start another.

Now to put this on radio waves. Lets use 10Hz, that means it takes 1/10 a second or 100 milliseconds to complete a cycle. I'll use an arbitrary level of 8 to illustrate. (ignore the periods, they are to maintain the spacing on the columns.

msec Level
0..........0
25........8
50........0
75.......-8
100......0

So with AM and an arbitrary starting level of 20 we can look at the same points in time:

msec Level
0..........20
25........28
50........20
75........12
100......20

So now the circuit simply subtracts off the level of 20 from the values and gets back the original signal. Now FM but its frequency and not level so its 1 MHz as the starting point.

msec freq
0..........1000000
25........1000008
50........1000000
75.........999992
100......1000000

Obviously this is oversimplified for purposes of explanation and you know that there would be many many steps in between each of the large steps I have graphed out. In fact, there would be millions of steps in between and each step happens much faster than the audio wave is changing, making it easy to tell the audio signal from the plain radio signal. Hopefullly you can see how the original wave could be extracted (demodulated) from the result and then amplified and sent on to some speakers as if it had never seen the radio carrier.

Cliff

Last edited: Jan 9, 2005
6. Jan 9, 2005

### GENIERE

The am modulation of the higher frequency carrier wave does alter the frequency of the carrier wave. In the receiver, the combined signals are passed through a filter that prevents the high frequency carrier wave from getting through but allows audible frequencies to pass. What is left is a signal varying in amplitude (loudness) and in frequency (low music note to high music note). In AM the modulating signal is by law limited to changing the carrier frequency to about 20,000hz, the allowable bandwidth. This modulation produces two side bands each has all the information, so only one side band is transmitted to save power.

In FM modulation, the RATE of CHANGE of carrier-wave-frequency determines the audio frequency at the receiver end, while the frequency change determines the volume. In other words if the frequency changes slowly, it would be a low music note. If the frequency changes to a much, much higher frequency slowly it will be a loud, low music note. As in AM only one side band is transmitted.

At least that is how this old brain remembers it.

 Your sine wave picture looks to be only high frequency noise riding on a relatively lower frequency wave, quite the reverse of AM modulation of a higher frequency carrier wave.

...

Last edited: Jan 9, 2005
7. Jan 9, 2005

### jdavel

Jake,

Create a table of values from t=0 to t=20 by increments of 0.1 (in Xcel or something) for this function:

sin(t)*sin(5*t)

Then make a graph of it. You'll see how the sin(t) (i.e., the signal) is modulating the amplitude of the the high frequency carrier (i.e., sin(5*t)).

8. Jan 9, 2005

### Jake

Ok thanks alot guys, I don't have a clue why I didn't understand it before...makes perfect sense now, doh!

Ok that's the AM/FM modulation aspect, however, still kinda shaky on the high requency-low amplitute riding on low frequency-high amplitute part. The question is. how would you reproduce that with a single speaker? I had said I thought it would simply be the air pressure (amplitute) not returning to zero pressure (IE rest state in a speaker, normal air pressure) before it increases and decreases a little bit. Is this a right way to understand it? Or am I completelly off base here. I'm just curious how you would reproduce a wave form like that with a single vibrating speaker...

Anyway thanks again guys for all the help

Last edited: Jan 9, 2005
9. Jan 10, 2005

### GENIERE

Lets assume the sine wave in your drawing represents a voltage waveform with a frequency of 2000hz which young ears hear, but my old ones don’t. The fuzzy stuff (that’s a technical term) on it is at much higher frequency and cannot be reproduced by the speaker except maybe a pop or audible static. What is presented to the speaker has nothing to do with AM or FM or any type of modulation. The small end of the speaker cone is attached to a small coil surrounded by a magnet. When the sine wave voltage is applied to the coil, a current flows through the coil. The electrical field interacts with the magnetic field causing the coil to move dragging along the speaker cone with it (think solonoid). From the mid point it moves one way with the positive part of the sine wave and vice-versa. The speaker then either compresses the air or rarifies it depending on which way it moved. The differences in pressure move at the speed of sound and impinge on your eardrums that vibrate tiny bones that vibrate tiny hairs (those of the correct length) that stimulate specific nerves that your brain interprets as sound at a given frequency.

...

10. Jan 10, 2005

### Cliff_J

Think of the waveform as the side profile of terrain that you would travel over with a bicycle or maybe even a remote controlled car. The low frequency could be the large hills/valleys and the high frequency would be the bumps you'd experience going up/down the hills.

Just like the tire in the physical example I just described, the speaker follows the waveform. At some point the mass of the speaker makes it difficult to follow the really high frequencies (and why high frequency speakers are very lightweight). There is no real limit for low frequencies in terms of speaker movement, but for it to create enough pressure to be audible at low frequencies the speaker must move a lot of air and that requires large speakers that can move back and forth more to move that amount of air. Our hearing may be from 20Hz-20,000Hz but it is not equal at all frequenices, look up Fletcher-Munson to see the curves where the sensitivity is best from 2k-4kHz or so and is less near the extremes.

Making a speaker large means large mass so they automatically suffer at high frequenices. In addition the size of the speaker versus the wavelength of the sound at that frequency changes the dispersion of the speaker so that is why most "loudspeakers" are a box made up of multiple speaker units that are each optimized for a certain range of frequencies. That or the performance is compromised to not cover a majority of the frequency range if a single speaker is used.

How close a speaker comes to accurately following a signal is another matter and is where Hi-Fi (High Fidelity) sound comes from. It is a cottage industry and gets horrendously expensive quickly.

Cliff

P.S. I'd hope the poster above meant something higher than 2KHz, otherwise understanding speech would be extremely difficult and a hearing assistance device would be warranted.

Last edited: Jan 10, 2005