NationMaster - Encyclopedia: Frequency mixer

In telecommunication, a mixer is a nonlinear circuit or device that accepts as its input two different frequencies and presents at its output (a) a signal equal in frequency to the sum of the frequencies of the input signals, (b) a signal equal in frequency to the difference between the frequencies of the input signals, and, if they are not filtered out, (c) the original input frequencies. BlackBerry 7100t Telecommunication refers to communication over long distances. ... In telecommunications a mixer is a frequency mixer. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... An electrical network or electrical circuit is an interconnection of electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... The term input has a variety of uses in different fields. ... // Information processing In information processing, output is the process of transmitting information by an object (verb usage). ... Signaling or signal may mean: Look up signal and signaling in Wiktionary, the free dictionary. ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...

Source: from Federal Standard 1037C Federal Standard 1037C entitled Telecommunications: Glossary of Telecommunication Terms is a U.S. Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended. ...

Mixers have three ports. The LO (local oscillator) port, RF (radio frequency) port and IF (intermediate frequency) port. To achieve the sum of two frequencies, input one signal into the LO port and the other signal into the IF port. The RF port will be the output. To achieve the difference of two frequencies, input one signal into the LO port and the other signal into the RF port. The IF port will be the output. LO or Lo or lo may stand for: Lo or LÃ¶ is often used as a greeting to replace hello in internet chat rooms and IRC. LO, Local Oscillator in a superheterodyne receiver. ... Rf or RF may stand for: Radio frequency, a term in broadcasting Right field(er), a defensive position in baseball Rutherfordium (Rf), symbol for the chemical element RF, rheumatoid factor RF, a Mazda piston engine The Russian Federation This is a disambiguation page — a navigational aid which lists other pages... The Super Heterodyne receiver (or to give it its full name, The Supersonic Heterodyne Receiver) was invented by Edwin Armstrong in 1918. ...

1 Mathematical mechanism
- 1.1 Mathematics of the practicalities
2 Spurious signals
3 See also

Mathematical mechanism

The two frequencies that are to be mixed are, in reality, sinusoidal voltage waves. They can be represented as: In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ...

$v_1 = A_1sin (2pi f_1 t),$

$v_2 = A_2sin (2pi f_2 t),$

where

$v_1, v_2,$ represent the two varying voltages
$A_1, A_2,$ represent the respective maximum voltages (amplitudes)
$f_1, f_2,$ represent the two frequencies in hertz
$t,$ represents time

If we can find a way to multiply these two signals by each other at each instant in time, we could apply the following trigonometric identity: The hertz (symbol: Hz) is the SI unit of frequency. ... Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent. ...

$sin(A) cdot sin(B) equiv frac{1}{2}left[cos(A-B)-cos(A+B)right],$

We get:

$v_1 cdot v_2 = frac{A_1 A_2}{2}left[cos(2pi[f_1-f_2]t)-cos(2pi[f_1+f_2]t)right],$

So, you can see the sum ( $f_1 + f_2,$ ) and difference ( $f_1 - f_2,$ ) frequencies as required.

Mathematics of the practicalities

The next question is, how are we going to achieve this multiplication? There are complex circuits that tackle this question with increasing accuracy, but the simplest answer is so simple that it is also worth some analysis. It is to use a forward-biased semiconductor diode. ...

A diode is a non-linear device. Almost any device whose output changes non-linearly with respect to changes in its input could form the basis of a mixer. Many other semiconductor devices can also fulfill this criterion in different ways.

From the diode page we find that the I-V equation for an ideal diode is: ...

$I=I_mathrm{S} left( {e^{qV_mathrm{D} over nkT}-1} right),$

From the Taylor series page, we see that we can expand the exponential function as below: As the degree of the Taylor series rises, it approaches the correct function. ...

$e^{x} = sum^{infin}_{n=0} frac{x^n}{n!},$ or

$e^{x} = 1 + x + frac{x^2}{2!} + frac{x^3}{3!} + frac{x^4}{4!} + dots,$

Now, we are going to start simplifying things (without forgetting that we have done so!)

First we apply a small voltage to a diode that represents our two sine waves added together: $v_1 + v_2,$ , then we generate a second voltage proportional to the current that flows through the diode (a simple resistor will do this, according to ohm's law). Ohms law, named after its discoverer Georg Ohm [1], states that the potential difference or voltage drop (U or V) between the ends of a conductor and the current (I) flowing through the conductor are proportional at a given temperature: The equation contains the proportionality constant R, which is...

According to the Taylor series expansion, the second, output voltage from our diode mixer will be related to the following:

$v_mathrm{o} = 1+(v_1+v_2)+frac{(v_1+v_2)^2}{2!}+frac{(v_1+v_2)^3}{3!} + dots,$

The terms represent

1, a DC shift, which we shall ignore
The original two signals, which we expected and shall ignore
a square-law signal: the square of the sum
signals equivalent to the cube and higher powers.

We said this was going to be a small signal, compared to the other voltages around – like the 0.6 V forward bias that the diode expects, etc. With that in mind, we are going to ignore all cube and higher power terms too for now. Although related to the more mathematical concepts of infinitesimal , the idea of something being negligible is particularly useful in practical disciplines like physics, chemistry, mechanical and electronic engineering, computer programming and in everyday decision-making. ...

Also ignoring the constant divisor, the square of the sum term expands out to:

$(v_1+v_2)^2 = v_1^2 + 2 v_1 v_2 + v_2^2,$

So, among other things, we have achieved our goal to multiply the two signals: we have $2 v_1 v_2,$ in there.

Spurious signals

Main article: Spurious emission

Now, recalling what we found in the previous section, every multiplication produces sum and difference frequencies. From the first two terms alone we can expect signal at the following frequencies: $f_1, f_2, 2f_1, 2f_2, f_1+f_2,$ and $f_1-f_2,$ . A spurious emission is any radio frequency not deliberately created or transmitted, especially in a device which normally does create other frequencies. ...

If $f_1,$ and $f_2,$ are both large and relatively close in value, then by far the smallest of these will be the last, the frequency difference signal. This is the one that is almost exclusively selected in modern, low cost radio receivers that use this simple mixer technology.

Don't forget also that we ignored the cube and all higher order terms earlier. These will produce a plethora of other high frequencies, and a few not so high. Any of these could slip into or break into the passband of the low-cost filters that would follow this diode mixer and it is these that set the main performance limitations of this approach.

Signal-amplification frequency-conversion apparatus having a common active component - Patent 4313223 (4374 words)
	The mixer circuit 37 is comprised of a band-rejection filter (BRF) 33, having a rejection center frequency set at the frequency of the local-oscillation output, a circulator 34, a mixer diode 35, and a BPF 36, having a pass center frequency equal to the intermediate frequency.
	In this apparatus, the frequency mixer section 203 thereof is fed at a terminal 204 with the intermediate-frequency signal and at another terminal 205 with the local-oscillation signal and the signal frequency-converted at a mixer diode 201 to the transmission-signal frequency appears at a terminal 207, passing through a circulator 202.
	As seen from the input-output characteristic A or B of the mixer diode 201 in relation to the local-oscillation signal, the local-oscillation signal is totally reflected by the mixer diode 201 to appear at the terminal 207 unchanged as long as the level of the local-oscillation signal applied is low.

Introduction to Mixers (2755 words)
	A fundamental reason for frequency conversion is to allow amplification of the received signal at a frequency other than the RF, or the audio, frequency.
	Conversion compression for high level mixers is specified since it sometimes provides an indication of the mixer's two tone performance and it is likely to be important in high level operation.
	ZL is the input impedance of the mixer, and

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Mathematical mechanism GA_googleFillSlot("encyclopedia_square");

Mathematics of the practicalities

Spurious signals

See also

Mathematical mechanism