“The modulator (or mixer) also has two inputs, but the signal input is linear, while the carrier input contains a limiting amplifier, or is driven with a sufficiently large signal limited by it. In either case, the carrier signal becomes a square wave, so its amplitude is relatively unimportant—as long as it is large enough and its noise or amplitude variation does not appear at the output.

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Why can’t I use the multiplier as a modulator or mixer? Aren’t they the same thing?

No, it’s important to understand the difference between them.

The multiplier has two analog inputs and the output is proportional to the product of the magnitudes of the two inputs (Note 1).

V_{OUT} = K × V_{IN1} ×V_{IN2}

where K is a constant of dimension 1/V. In theory, a signal can be input to either input and the output will not be affected.

The modulator (or mixer) also has two inputs, but the signal input is linear, while the carrier input contains a limiting amplifier, or is driven with a sufficiently large signal limited by it. In either case, the carrier signal becomes a square wave, so its amplitude is relatively unimportant—as long as it is large enough and its noise or amplitude variation does not appear at the output. The formula becomes:

VOUT = K × VSIGNAL × sgn(VCARRIER)

Multipliers are used for analog calculations. An example is calculating power in a circuit. A signal proportional to the instantaneous voltage and current is applied to the input of the multiplier, and its output is proportional to the instantaneous power.

Like a modulator, a multiplier encodes the amplitude of the signal input to the signal at the carrier input, but unlike a modulator, changes in the amplitude of the carrier signal also appear at its output. In communications applications employing modulators, this change is undesirable. Assuming two sinusoidal (Note 2) waves are fed into a multiplier, its simplified (Note 3) formula is:

VOUT

Simple descriptions of modulators often use the above formula, but the clipping of the carrier signal to a square wave means that it contains odd harmonics. The simplified formula for a square wave is the odd harmonic Fourier series:

V

These odd harmonics are also modulated by the carrier, so the modulator output contains not only the desired fundamental product, but also the products of the odd harmonics:

V

In many applications, these harmonic products are filtered out and ignored, but must be included in the correct functional description of the modulator. Sometimes they work, sometimes they overlap with the fundamental product, leading to unexpected results.

Therefore, before choosing a multiplier, modulator or mixer, you should consider what your purpose is and which device will produce the least error.

Note 1: Inputs and outputs can be voltage or current, depending on the device. This example uses voltage.

Note 2: Input and output amplitudes are normalized for simplicity.

Note 3: The formula uses the cosine function which is easier to handle. The end result is the same.

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