Frequency mixer Totally Explained

Everything about Frequency Mixer totally explained

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 at several frequencies:

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 filtered out in subsequent filter stages.

This nonlinear effect can be created by using a nonlinear electrical component, such as a diode. The time-varying effect can be created using a multiplier circuit such as a Gilbert Cell or passive switches.
The manipulations of frequency performed by a mixer can be used to move signals between bands, 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 ť

v_i(t) = A_i sin 2pi 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 phases, but that doesn't enter here.) One common approach for adding and subtracting the frequencies is to multiply the two signals; using the trigonometric identity ť

sin(A) cdot sin(B) equiv frac = (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 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_2gg|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.

Further Information

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