# Modulation basics

I have a new interest in RF modulation and read the O'Reilly book electronics cookbook. I understand that in FM you start out with a carrier wave and then it is modulated but I don't understand if both waves are sent out or if it combines to make one wave.

To answer your question requires some definition of what it means to "send a wave". So let's look at the problem more rigorously, with math. First let's consider amplitude modulation, since it's mathematically simpler.

If the baseband signal (for example, audio from a microphone) is $$x(t)$$, and the carrier frequency is $$f$$, and time is $$t$$, then what's "sent out" is:

$$y(t) = [1 + x(t)] \cos(2\pi ft)$$

And by "sent out", I mean the voltage at the antenna terminals at any time will be proportional to $$y(t)$$. The antenna voltage at the receiver will also be proportional to $$y(t)$$, except weaker, and with added noise and interference.

You asked if one or both waves are sent out, but without a definition of what "a wave" is, this question can't really be answered. What we can say is $$y(t)$$ contains both a baseband signal term $$x(t)$$ and a carrier term $$\cos(2\pi ft)$$, but at any given time the antenna terminal voltage can have only one value.

Frequency modulation is no different, except the math is a little more complicated. Using the same terms as before but with the additional parameter $$f_{\Delta}$$ for the frequency deviation:

$$y(t)=\cos \left(2\pi ft +2\pi f_{\Delta} \int _{0}^{t}x(\tau )d\tau \right)$$

Again you can see the baseband signal is in there, as is the carrier wave, except now the baseband signal is changing the frequency of the carrier, instead of the amplitude.

By "both waves," I assume you mean both the unmodulated (carrier) wave and the modulated wave. Only the modulated wave is amplified and sent on to the antenna for outbound transmission. In the case of FM, the modulated wave includes some power dedicated to the carrier, which is also transmitted.

• I meant the carrier wave and the modulating wave not the modulated wave. – user14160 Feb 4 '19 at 23:24
• The "modulating" wave - typically the audio (voice/music) - is NOT transmitted as such. – mike65535 Feb 5 '19 at 14:01
• @user14160 You should edit your question and include this comment. – Mike Waters Feb 5 '19 at 18:36

In simple terms, modulated wave is sent out, which is what you get after modulating the carrier wave with the modulating wave.

Or some people also like to say that the carrier is sent with the message(modulating wave) modulated on it.

Neither of the carrier and modulating waves are transmitted in their pure forms, because pure carrier(which is just a sinusoidal signal) doesn't contain any information and pure modulating wave(or usually called message) is normally very low in the frequency spectrum(around DC(0 Hz) mostly), which makes it almost impossible to transmit over air for some practical reasons.