# How is the signal Multiplied with the Carrier in AM

In wireless transmission, via Amplitude modulation, we multiply the message signal by a carrier wave to get the modulated signal $$x(t) = m(t) \times cos(\omega t)$$ Where $m(t)$ is the original message, $\omega$ is the frequency of the carrier wave and $x(t)$ is the modulated signal.

My question is, how does this multiplication take place in Hardware?

I am aware of chips like the MPY 634 which use a Gilbert Cell-based Architecture to achieve Multiplication and have a transfer function of the form $$x_{out}=A\Big[\frac{(X_1-X_2)(Y_1-Y_2)}{SF}-(Z_1-Z_2)\Big]$$ Where the capitalised letters represent signals at 4 different terminals.

But this seems like an awfully complex, expensive and bulky solution for something that needs to be done often

• There are simpler designs for a two-quadrant multiplier that are, I believe, used in AM transmitters. I know I've seen a way to use just a single JFET to do it, though I don't know if that's how it's done in actual modulators. – Hearth Jul 21 '18 at 14:07
• It multiplies (and subtracts) differential signals, its transfer function isn't quite complex at all. If you tie X2, Y2, Z1, Z2 to ground, the equation will be much simpler. – Long Pham Jul 21 '18 at 14:25
• In frequency domain analysis, it is convolution ,not multiplication (as in time domain analysis), hence the iteration is not costly. – seccpur Jul 21 '18 at 16:50
• @seccpur but that would be true for a digital approach, right? I am not sure how we could think in terms of convolution in an Analog approach – ijuneja Jul 21 '18 at 17:04
• For just goofing around in the lab, you can do it with a chopper. Run the chopper at carrier frequency. Modulate the "VCC" of the chopper. So, basically, imagine an oscillator running from a VCC that is varied by the message signal. – mkeith Jul 21 '18 at 17:06