Frequency Mixer

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In telecommunication, a mixer is a nonlinear electrical network or device that accepts as its input two different frequencies and presents at its output a mixture of signal (information theory)s at several frequency:

the sum of the frequencies of the input signals

the difference between the frequencies of the input signals

both original input frequencies — these are often considered parasitic and are electronic filter out.

The manipulations of frequency performed by a mixer can be used to move signals between channel (communications)s, or to encode and decode them. One other application of a mixer is as a product detector.

Mathematical description The input signals are, in the simplest case, sinusoidal voltage waves, representable as v_i(t) = A_i \sin 2\pi f_i t\, where each A is an amplitude, each f is a frequency, and t represents time. (In reality even such simple waves can have various phase (waves)s, but that does not enter here.) One common approach for adding and subtracting the frequencies is to multiply the two signals; using the trigonometric identity \sin(A) \cdot \sin(B) \equiv \frac{1}{2}\left we have v_1(t)v_2(t) = \frac{A_1 A_2}{2}\left 2\pi(f_1-f_2)t-\cos 2\pi(f_1+f_2)t\right where the sum (f_1 + f_2) and difference (f_1 - f_2) frequencies appear. This is the inverse of the production of acoustic beat (acoustics)s.

Multiplication implementation There are various ways of multiplying voltages, many of them quite sophisticated. However, as an example, a simple technique involving a diode can be described. The importance of the diode is that it is non-linear (or non-Ohm's law), which means its response (current) is not proportional to its input (voltage). The diode therefore does not reproduce the frequencies of its driving voltage in the current through it, which allows the desired frequency manipulation. Certain other non-linear devices could be utilized similarly.

The current I through an ideal diode as a function of the voltage V across it is given by I=I_\mathrm{S} \left( e^{qV_\mathrm{D} \over nkT}-1 \right) where what is important is that V appears in e's exponent. The exponential can be Taylor series as e^x = \sum_{n=0}^\infty \frac{x^n}{n!} and can be approximated for small x (that is, small voltages) by the first few terms of that series: e^x-1\approx x + \frac{x^2}{2}

Suppose that the sum of the two input signals v_1+v_2 is applied to a diode, and that an output voltage is generated that is proportional to the current through the diode (perhaps by providing the voltage that is present across a resistor in series with the diode). Then, disregarding the constants in the diode equation, the output voltage will have the form v_\mathrm{o} = (v_1+v_2)+\frac12 (v_1+v_2)^2 + \dots The first term on the right is the original two signals, as expected, followed by the square of the sum, which can be rewritten as (v_1+v_2)^2 = v_1^2 + 2 v_1 v_2 + v_2^2, where the multiplied signal is obvious. The ellipsis represents all the higher powers of the sum which we assume to be negligible for small signals.

Output As every multiplication produces sum and difference frequencies, from the quadratic polynomial term of the series we expect to find signals at frequencies 2f_1 and 2f_2 from v_1^2 and v_2^2, and f_1+f_2 and f_1-f_2 from the v_1v_2 term. Often f_1,f_2\gg|f_1-f_2|, so the difference signal has a much lower frequency than the others; extracting this distinct signal is often the principal purpose of using a mixer in such devices as radio receivers.

The other terms of the series give rise to a number of other, weaker signals at various frequencies which act as noise for the desired signal; they may be filtered out downstream to an extent, but sensitive applications will require cleaner output and thus a more complicated design.

See also

External links

Frequency mixer - Wikipedia, the free encyclopedia
In telecommunication, a mixer is a nonlinear or time-varying circuit or device that accepts as its input two different frequencies and presents at its output a mixture of signals ...

Mixer - Wikipedia, the free encyclopedia
Mixer may refer to: An electronics device: Electronic mixer, a device for mixing signals; Frequency mixer, a telecommunications device used to alter the carrier frequency of a ...

Frequency Mixer
PlayStation" and the "PS" Family logo are registered trademarks of Sony Computer Entertainment Inc. The Sony Computer Entertainment logo is a registered trademark of Sony ...

QIFM
Acronym Finder: QIFM stands for Quadrature Intermediate Frequency Mixer ... Suggest new definition. This definition appears very rarely and is found in the following Acronym Finder ...

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Frequency mixer – Wikibooks tiếng Việt
In telecommunication, a mixer is a nonlinear circuit or device that accepts as its input two different frequencies and presents at its output a mixture of signals at several ...

get_mixer_frequency
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Balanced Mixer/Frequency Converters
The units described here are either standard Spacek Labs products or they are a small sample of many special designs produced to specific customer requirements.