# 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. Commented Jul 21, 2018 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. Commented Jul 21, 2018 at 14:25
• In frequency domain analysis, it is convolution ,not multiplication (as in time domain analysis), hence the iteration is not costly. Commented Jul 21, 2018 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 Commented Jul 21, 2018 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. Commented Jul 21, 2018 at 17:06