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I am not sure if it is valid to conclude that a mixer produces a difference/sum of frequencies at output ,while multiplier produces multiples of frequency at its output. I am keen to know how far I have got it right. Is there something else that I should know? please post with simple e.g.

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    $\begingroup$ The word "mixer" has two meanings: summer and multiplier. $\endgroup$ – endolith Apr 21 '16 at 18:57
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    $\begingroup$ In my experience, 'mixer' is usually a circuit that multiplies its two inputs. In other words, saying 'mixer' instead of 'multiplier' emphasizes the implementation over the math. $\endgroup$ – MBaz Apr 21 '16 at 19:12
  • $\begingroup$ @MBaz Hmm, my experience (more in a software context) is that a mixer makes a linear combination (i.e. weighted sum) of its inputs. I would (and do) find it surprising that you view it as synonymous with a multiplier. I would use the term "modulator" or more likely just "multiplier" if that's what I meant. That said, if you have a variable mixer (i.e. you can control the weighting of the mixture with yet another signal) then the "control" signal is modulating (multiplying) the mixed signals. $\endgroup$ – Derek Elkins Apr 22 '16 at 0:15
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    $\begingroup$ @DerekElkins Instead of "In my experience" I should have said "In communications". See for example en.wikipedia.org/wiki/Frequency_mixer. To a communications engineer, a "multiplier" is ideal, whereas a (frequency) mixer is a circuit that somehow implements the multiplication (such as the diode mixer in the page I linked). Since the OP asked about modulation, I thought this definition was the most relevant. $\endgroup$ – MBaz Apr 22 '16 at 0:57
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For most purposes a mixer is a multiplier.

The issue regarding sum / difference frequencies is that when you multiply two signals of different frequencies, $\omega_1$ and $\omega_2$ say, then you get one component at the sum of the two frequencies and one component at the difference of the two frequencies: $$ \cos(\omega_1 t) \cdot \cos(\omega_2 t) = \frac{1}{2} \left\{ \cos([\omega_1+\omega_2]t) + \cos([\omega_1 - \omega_2]t) \right \}$$


Response to comment

A frequency multiplier is a completely different kettle of fish. These are often highly nonlinear systems that take a signal $\cos(\omega_1 t)$ and produce $$\sum_{k=1}^{N} \cos(k \omega_1 t + \phi_k)$$

For example, a frequency tripler can be had by driving a transformer into saturation (so that it outputs something like a square wave) and low-pass filtering the result.

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  • $\begingroup$ K, What if ,I am being very specific, it is mixer vs. frequency multiplier? Mixer certainly works on the maths that you have produced. How does output frequency change wrt input in both cases ? This question is purely related to communication, but for those who have explained it keeping other fields in view I appreciate..Thank you $\endgroup$ – user20119 Apr 22 '16 at 4:32
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A mixer is often synonymous with a crossfader.

A crossfader is made of two amplitude multipliers, in mathematics a liner interpolator of values from 0-1 multiplying one signal and 1-0 multiplying the other signal. there can be mixers for multiple, 3-15 signals using the same control, which are called multiplexers.

Strictly speaking, modulating a signal relates to a variation in an applied effect on a signal, whereas mixing is not generally related to effects, it's signal and volume control.

A multiplier is used also for ring modulation where one sound/osc is multiplied with another.

A serge wave multiplier is an analogue trick where a wave is amplified and sent through some rectifiers/mirrors that bounce it backwards from values above 1, thereby increasing the side bands of the original oscillator in a way powerful and economic relative to the electronic components used. it is best applied to a sine wave.

A mixer is also jargon for a mixing console.

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