Understanding carrier waves?

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Hello. I am trying to teach myself some information about radio engineering. I keep getting stuck on the concept of carrier waves. I understand their uses and what they look like, but I do not understand what causes them or why they are needed. Any clarification or analogies would help. I only have 1 year of calculus so far, so try to keep and formulas to single integrals if possible :]

Thank you very much in advance!


Science Advisor
A carrier wave is nothing more than the fundamental signal on which the information is impressed, or carried. An unmodulated carrier is (ideally) a sine wave. Nothing "causes" them in the sense they're a byproduct of a process, but rather a carrier is intentionally generated by some sort of oscillator. When you tune your radio to 102.7 FM to listen to your favorite tunes, you're tuning in to the carrier frequency of 1,027,000 Hz (102.7 MHz) and the radio's circuitry demodulates the signal to effectively "strip out" the carrier leaving the desired signal--the music. They are needed because directly sending low-frequency EM signals in the audio-frequency range is highly problematic not least because antenna lengths at those frequencies become ginormous (that's the technical term for really, really long); modulating a high-frequency carrier allows the transmitting and receiving equipment to use smaller antennas--especially useful for portable radios and TVs.


Science Advisor
I do not understand what causes them or why they are needed.

what causes them
Carrier waves are produced by a high frequency oscillator in a transmitter. It is usually just a sinewave AC voltage and it may not be generated on the final output frequency but it ends up as a sinewave on the same frequency as the transmitter. It needs to be stable so it may be generated by a crystal oscillator and it may be locked to an atomic standard frequency controller.

why they are needed.
AC voltages in wires radiate from the wire more readily if the frequency is high enough. So, you may not get much radiation from an audio signal in some speaker wires, but if you have a much higher frequency, like 1000000 Hz or higher, there will be a lot of radiation from the wire.

Since radiation is the purpose of building a transmitter, such a high frequency is needed to get radiation.

Just radiating a carrier is useless though, so there are various ways of putting information on the carrier. One is amplitude modulation where the size of the voltage in the output of the transmitter is altered according to voice amplitude or picture brightness if it is television.

Receivers are built to expect such signals and to remove the carrier and recover the voice, music or picture information.

Please don't try to teach yourself this though. The best way to learn it is to get into a hobby class and have someone explain it properly to you.
here, maybe I should add some more context to my question. I was reading the second edition of "Radio Engineering" by Terman (it is rather ancient), and for AM radio he modifies the equation: E=Eo + mEosin2[pi](fs)t, in which E is the amplitude at a given time, Eo is the average amplitude, fs is the frequency of the signal, if it were a sine wave(not the source wave, but the frequency of the signal should it happen to be sinusoidal). M is a ratio that he says represents the average amplitude relative to the average variation from the average. He then uses some trig identities to show how E equals three trigonometric expressions added together. He calls one the carrier wave (This one has no fs, which he uses to show that the carrier always has the same amplitude). The other two waves are similar mathematical expressions that depend on the difference and sum between the signal frequency and the source frequency.

So I am trying to understand what is happening here on a more theoretical level- Why exactly is the carrier wave needed? Like, I see that it has to occur, but I suppose I am getting caught when I try to think about how exactly it is used- if I picked a given frequency to tune my receiver to (assume AM), then why not just receive some modulated waves? why is the constant carrier wave important? Is it just so that it can get "subtracted out" [terrible word choice, I'm thinking in terms of graph shifts] of the modulated wave so all that one ends up with is the signal variation and not the source waves?

As you can tell, I am sort of a newbie, so my apologies if some of this post was incoherent. Thank you for your help!


Science Advisor
When you amplitude modulate a carrier, there are two sidebands produced which are the sum and difference of the carrier and the audio frequencies.
So, there are two sidebands with exactly the same information on them.

Also, as you point out, there is a carrier which does nothing except make reception simpler.

So, with some extra complexity at both ends, the transmitter can be made to transmit only one sideband and to not transmit the carrier at all.
This requires a fairly expensive filter to do this and this adds to the cost of the transmitter.
However, you can then have a transmitter that uses very little power if you are not talking and has a lot greater coverage for the same power as an AM transmitter.

Such signals are commonly used on Amateur Radio bands below 30 MHz and for long distance communication above 30 MHz.

Terman's book is still a classic despite being written nearly 70 years ago. But it is not suitable for beginners and it is not up to date with modern techniques. There was a 1954 version which is a bit better, but that is still a long time ago.

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