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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

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    \$\begingroup\$ 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. \$\endgroup\$ – Hearth Jul 21 '18 at 14:07
  • \$\begingroup\$ 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. \$\endgroup\$ – Long Pham Jul 21 '18 at 14:25
  • \$\begingroup\$ In frequency domain analysis, it is convolution ,not multiplication (as in time domain analysis), hence the iteration is not costly. \$\endgroup\$ – seccpur Jul 21 '18 at 16:50
  • \$\begingroup\$ @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 \$\endgroup\$ – ijuneja Jul 21 '18 at 17:04
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    \$\begingroup\$ 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. \$\endgroup\$ – mkeith Jul 21 '18 at 17:06
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But this seems like an awfully complex, expensive and bulky solution for something that needs to be done often

Would you say the same about the Exclusive OR gate? It's a device that performs multiplication on digital signals and is the founding design for the Gilbert cell: -

enter image description here

Picture source.

Would you say that using a Gilbert cell for an EXOR gate is "an awfully complex, expensive and bulky solution for something that needs to be done often"?

Of course if you wanted a really simple AM modulator you could use a couple of diodes and a filter and get something that was quite linear enough for AM. You could extend this to a four quadrant mixer using more diodes or you could go the whole hog and use a gilbert cell and filter.

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  • \$\begingroup\$ Thank you this was insightful. Should I edit the question to remove the bias or let it stay? \$\endgroup\$ – ijuneja Jul 21 '18 at 17:09
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    \$\begingroup\$ My advice is let it stay because you might make my answer invalid with alterations. \$\endgroup\$ – Andy aka Jul 21 '18 at 17:17

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