# In Amplitude Modulation transmission, why do we need to mix (multiply) rather than just add the carrier and base-band?

Why is it necessary to mix the carrier with the message signal to create the sum and difference of the frequencies when you can just add both signal? Not only is it much easier to achieve but it would also just contain only the carrier and message frequency harmonics.

I think the reason is because only the high frequency harmonic would be able to get transmitted am I correct?

• Your goal is to add frequency, so you have to multiply amplitude. See: mathworld.wolfram.com/ModulationTheorem.html if you add amplitude the frequency is unchanged. – user1850479 Jan 28 '20 at 1:54
• If all you did was add, then only the carrier would make it through all the RF tuned circuits between that stage and the receiver output. – user_1818839 Jan 28 '20 at 12:42

If you just added, then all the baseband energy would still be in the baseband. 0 - 5 kHz or so, assuming we're talking about analog. So it wouldn't be transmitted by an antenna that works at 531 - 1602 kHz.

It also wouldn't be separated from the signal of any other channel operating on the same system.

you don't want baseband + carrier.

you do want carrier plus two sidebands of equal power that have phases rotating in opposite directions, so all phase variation cancels out, leaving only amplitude information.

This is mainly to have a way to transmit multiple baseband information through the same medium(air, a cable, optic fiber)

Imagine you have two audios (e.g rock, jazz) as there is people who like rock, there is whose who like jazz, nevertheless they share the same medium(air), so in order to no have a wire running to anyone of them what you do is use these audios to modify a well known reference signal (one for rock, one for jazz), then add together the modified signals and throw them into the air JAYYY!

but wait!

How do rock people distinguish their music from others?!! everything is weirly blended together!! well not quite...

then...

When you get the all blended signal, you know the reference used for rock so you just have to check the difference between what you got and your own reference and that difference is the audio signal.

But wait!(again)

jazz is there too .... mmm somewhere(?) in the all blended signal doesn't it interfere? well... yes but no, it's complex, just limit the amount of difference you will accept, Ok?

Easy, isn't it?

well now the real Sh t, Ok no, first the ideal Sh t,

taking a reference signal , sine/cosine it does't mater, you have to change it acording of the input audio (e.g ) one way is by changing the reference's amplitude (AM: amplitude modulation) other is by slightly changing the frecuency

now let's give things a name: Your reference signal is called "carrier" because it is a mean of info transportation your audio signal is called "modulation" signal

Here is a form of AM: double side band AM

this means 1 by your carrier equals your carrier, so you will be sending a carrier only signal, then your audio by the carrier, using this identity: