A few people have asked for more info:The maths assumes a perfect multiplier, hence "Audio x Carrier = DSB output".

In hardware terms a perfect multiplier is a "four quadrant multiplier". This is a mixer with two differential (balanced) inputs, eg each input can handle dual polarity signals

(two x dual polarities = four combinations, hence "four quadrant").

If either input has zero applied, there is zero output. Four quadrant multipliers are expensive and usually have poor HF response, so are almost never used at RF.

More common is a "Two Quadrant" multiplier. An example is the NE602. One input is differential and can handle dual polarity signals, while the other input is single ended. This combination can only cover two quadrants, but is commonly used where a Double Balanced mixer (DBM) is required.

As a modulator it will output DSB, however if the bias is offset to give 50% carrier it will give true AM out.

The most common RF mixer is a "Single Quadrant" Mixer. An example would be a simple dual-gate FET with the Local Oscillator fed into one gate and the RF signal fed in the other.

When used as a Modulator, the FET is biased so that with no audio input the RF output will be at 50%. It can only output AM, it cannot be "balanced" to give DSB.

For a simple unbalanced modulator the maths is: Carrier x Audio + DC = DSB + Carrier

so in practical terms there is no need to "add in" the carrier, it would be completely redundant.

....... Zim