# In amplitude modulation is the carrier wave multiplied by the radio signal wave to form the equation of the resultant wave to be transmitted?

I understand how to add sinusoidal waves. They use the priciple of superposition and the original waves are not affected. However in amplitude modulation the radio wave that is transmitted is a result of a modulation of a carrier wave and a signal wave. However I do not understand how these waves are "blended" together. I am struggling with different articles.

Are they multiplied together perhaps? But how? It appears remarkable to me that electrical signals would multiply together. Perhaps someone understands the math behind this and could offer a clue.

• TL/DR yes. Search for "analog multiplier" IC datasheets and you will usually find AM multipliers in the examples or app notes.
– user16324
Feb 22, 2021 at 15:27
• Amplitude modulation in its simplest form is simply multuiplying the carrier and the message. Mathmatically easy. Electronically somewhat tricky.
– JRE
Feb 22, 2021 at 15:32
• Yes. They are multiplied. Feb 22, 2021 at 15:38
• It appears remarkable to me that electrical signals would multiply together. It can be done using an "analog multiplier circuit" which can be as simple as a single stage amplifier which is biased at a certain current. As the gain depends on that bias (more bias=> more gain) that means the circuit behaves as a multiplier and can do AM modulation. Feb 22, 2021 at 15:44
• Don't think of over unity multiplication like 5V * 12V is going to give you 60V. Think of it like 5V * .5V is going to give you 2.5V. Feb 22, 2021 at 15:55

I think you are overthinking it.

Imagine that both the carrier and the signal are sinusoidal functions. This means that at time t, each has a value you could read off a graph. For all values of t those numbers are multiplied to get the "new" signal at time t.

What you end up with looks like https://www.tutorialspoint.com/analog_communication/analog_communication_amplitude_modulation.htm

BTW, frequency modulation is quite a bit harder to envision. But AM is pretty straightforward.

• ...Nice tutorial ... I like the math derivation. Much better than Wikipedia...at least for me. Thank you Feb 23, 2021 at 18:20

It appears remarkable to me that electrical signals would multiply together

Think of an audio 1 kHz tone going through an amplifier to a loudspeaker. Then, when you adjust the volume control up or down, the speaker output gets louder or softer. That is precisely what multiplication is in AM broadcast transmissions. The 1 kHz tone represents the carrier wave and, the relatively slower changes in the movement of the volume control represent the modulation signal.

And, in reality, that's pretty much what a broadcast AM transmitter uses - a voltage controlled amplifier where the control voltage is the modulating signal and the input is the carrier frequency. That is multiplication (2 quadrant type).

There are more esoteric types of modulation but grasp this first and you are well on your way.

• Good Information. The link above your answer has a nice tutorial on signal processin..I think I got it now. . It is remarkable that the math fits so nice..... Feb 25, 2021 at 18:27

In amplitude modulation, the message signal(of lower frequency) is multiplied with the carrier signal(of higher frequency). The multiplication is governed by the modulation index. The modulation index is used to determine the type of modulation. The multiplication can be understood using sinusoidal signals. The sinusoidal signals can be multiplied (using trigonometric identities). You can find the derivation of the amplitude modulation on the internet.