# Talk:Frequency mixer

## Question

Another form of mixer operates by switching, with the smaller input signal being passed inverted or uninverted according to the phase of the local oscillator (LO). This would be typical of the normal operating mode of a packaged double balanced mixer, with the local oscillator drive considerably higher than the signal amplitude.

I wish this sentence could be explained more fully. 89.217.6.135 (talk) 19:00, 24 March 2014 (UTC)

## Untitled

JC wept! As an engineer who uses mixers daily, I wouldn't recognize the article as being related to either a simple, or a pedantic, treatment of mixers. While most of the words written are true, they are irrelevant and uninformative, one would need to be an expert to understand in what sense they are true, a beginner would be hopelessly lost.

As I mostly was, except for the math. 89.217.6.135 (talk) 22:34, 24 March 2014 (UTC)

What is the purpose of the wiki? Is it to record some words vaguely related to the subject at hand, or is it to inform or educate? It might be easier to dig up any one of a dozen better written tutorials in the back pages of mixer manufacturers' catalogues, many available on the web and just point to them, than to write a new text which doesn't overtly plagiarise any of them.

For instance this link http://www.hobbyprojects.com/general_theory/mixer.html is very short, a bit confused (talking about fans beating) BUT the neophyte will come away from it understanding a damned sight more about mixers than from this article, and the expert will recognise it for what it is, a slightly flawed over simplificiation rather than the pile of dingoes kidneys that make up this article.

A mixer does not deal with sine waves, a simplified model of them does. A mixer is a component, not a mathematical equation. Exponential signal expansions convey nothing to somebody who wants to find out what a mixer does.

calms down, thinks, comes back

Perhaps I should be a bit more positive about this, but I'm not up to writing the article at the moment. I will present some definitions and ideas here in talk, and hope that others might consider whether the different approach has merit, and if so whether to modify, replace, rewrite or leave alone the main article. First some comments

The maths in the present article, the diode, exponential stuff etc. This should really be in a separate article entitled "How a non-linear system creates mixing products". It is all correct, just not really applicable to understanding what a "frequency mixer" is, how it's built, why it's used etc.

Proto-article

A frequency mixer is a component, that accepts two electrical signals, and is intended to produce as an output a signal, which has two frequency components, one at the sum of the two input signal frequencies and and one at the difference. Any mixer, whether practical or theoretical, will also produce other unwanted outputs. It is the reduction of these unwanted outputs that consumes most of the engineering time developing better mixers.

A mixer is used where frequencies must be changed for practical processing reasons. In a cell-phone for example, an input radio signal at 2GHz is mixed down to an intermediate frequency (or IF) of 70MHz using a local oscillator (or LO) of 1.93GHz. This is referred to as down-mixing. A transmitter will often use a frequency mixer to up-mix a low IF up to a high RF frequency for transmission.

The practice of mixers frequently uses jargon, so RF = radio frequency, usually the highest signal frequency, IF = Intermediate frequency, usually the lowest signal frequency, both relatively low level signals and often modulated, so not a single sine-wave. LO = local oscillator, a high level signal, always a single frequency, but may be sine or square.

There are two principal ways of performing the conversion. The first and mathematically simplest uses a multiplying mixer, usually abbreviated to multiplier, which is linear to the signal at each mixer port and performs the operation z(t) = y(t) * x(t), where x, y and z are the time varying voltages at each port. Multipliers tend to use semiconductor ICs, (496, what manufacturer, AD834 Analog Devices) but they are very noisy so have limited dynamic range. The second, and more commonly used, is a switching mixer, which performs the operation z(t) = y(t) * sign(x(t)), where again x, y and z are the voltages at each port. In the switching mixer, x is the LO.

This is a lot clearer than the present article, where one of the signals is inverted depending (how?) on the phase of the other. 89.217.6.135 (talk) 22:34, 24 March 2014 (UTC)

A switching mixer usually works with diodes, the high level LO serves to switch the diodes rapidly from conducting to non-conducting, producing a switching action for the lower level signals. Recently, MOSFETs have begun to be used as the switching element in switching mixers, offering the advantage of lower power on the LO port.

The type of mixer is determined by the topology of diodes and balancing transformers are involved (a few diagrams here would not go amiss). A single diode mixer is unbalanced, has no isolation between ports, but is very simple and is the mixer of choice when frequencies are so ridiculously high that the only component that can be fabricated and got to work is a single diode (optical, teraHertz etc). Much better is a balanced mixer, which uses transformers and diodes to provide isolation between the ports. A double balanced mixer uses two transformers and four diodes, and provides isolation between all pairs of ports. The single balanced topolgy is sometimes used (one transformer, two diodes) at fairly high frequencies. A triple balanced topology (three transformers, 4 or more usually 8 diodes) is gaining popularity with its very good rejection of distortion products.

NeilUK 19:43, 5 June 2006 (UTC)

Thanks NeilUK for writing something practical. --NA 03:03, 10 October 2007 (UTC)
NeilUK, please add your description of a frequency mixer to the wiki and then we'll have an understandable description (for non eng types) and we'll still have the "math" geek description too.64.50.249.202 (talk) 13:21, 1 June 2008 (UTC)
As a reader I would love to see this written into the wiki! Your explanation includes information I have not seen in any other article. 89.217.6.135 (talk) 19:00, 24 March 2014 (UTC)

## Wrong output??

Isn't the output of the mixer a) a signal equal to the sum of the input frequencies (usually filterd) b) the difference of the frequencies (usually the IF) and c)TWICE the original input frequency? See for example heterodyne detection.

## Remove 'tone' tag from article

I'm removing the {{tone}} template from the top of this article. It has been there for some time with no explanation, and with no discussion here. I assume it was added because someone saw the word we in the text. Looking at WP:Manual of Style#Avoid first-person pronouns and one, mathematical discussions such as where we may be found here are clearly made an exception to the normal rule: "It is also acceptable to use “we” in mathematical derivations; for example: “To normalize the wavefunction, we need to find the value of the arbitrary constant A.”" --Nigelj 00:30, 11 November 2006 (UTC)

Well, I see the {{tone}} template has been re-added, but still no discusssion or comment regarding my quote above from the Manual of Style. I think the problem is either lack of familiarity with mathematical texts, or the same with the Manual of Style. I can't be bothered to keep trying to help here without constructive discussion. --Nigelj 18:57, 11 November 2006 (UTC)
I don't think the "we" has anything to do with it directly; I get the feeling it was re-added because of the conversational nature of the prose, as a dialog with questions and suggestions rather than as a simple narrative. I've rewritten the entire article to say the same thing more clinically, and removed the {{tone}}; I hope it will be easier to improve it further now (perhaps with NeilUK's suggestions at the top of this page). --Tardis 22:57, 5 December 2006 (UTC)

## Regarding merger with Electronic mixer

• Agree As they are on the same subject, but taking two different approaches: one based on the principles, the other based on the implementation and uses. IMHO the should be merged - Figarema 22:10, 29 August 2007 (UTC)
• Disagree As I explain in the talk page of that article, it needs a very serious edit, but definitely not merging into this. --Nigelj 19:24, 1 September 2007 (UTC)
• Disagree Although the two functions are represented by similar mathematics, a frequency mixer is not the same as an electronic mixer. The articles should be linked and one or the other article should explain the differences. An electronic mixer typically responds symmetrically to the two input ports, while a well-designed frequency mixer has very different response at its local oscillator port than at a signal port. Also, the uses and performance criteria for frequency mixers are very different than for electronic signal mixers. Muennemann (talk) 23:56, 20 February 2008 (UTC)
comment: Muennemann, you seem to be talking about the difference between a Gilbert cell and a ring modulation circuit. Remind me again -- which one is not electronic, and which one is not a frequency mixer? --68.0.124.33 (talk) 14:55, 13 January 2009 (UTC)
• Agree The Electronic mixer article covers two totally different devices: a summing amplifier such as used in audio mixing boards, and a frequency mixer. The summing amplifier content should be merged into that article, and the frequency mixer content merged here. I think in engineering usage an electronic mixer almost always means a frequency mixer, so Electronic mixer should redirect here. --ChetvornoTALK 09:34, 28 November 2010 (UTC)
• Disagree The terminology at the intersection of RF and audio disciplines is a bit of a mess. Mixer or Electronic mixer can imply multiplication or addition depending on context. Frequency mixer implies a multiplier. Sum implies addition. Merging is not the way to start sorting this out. --Kvng (talk) 18:10, 29 November 2010 (UTC)

## Merge from Heterodyne

These either need to be properly refactored or merged. The same maths is shown under two different titles.Either we put all the maths under 'heterodyne' and use this article to talk about devices (such as the fabled and much edited Pentagrid converter) or else put it all in one place. REferences would be handy, too. --Wtshymanski (talk) 06:24, 28 November 2010 (UTC)

I agree there is a good deal of redundancy in the maths in the two articles which should be eliminated, but I don't think all the math can be confined to one article. I'd like to see the main math derivations in the Heterodyne article stay, but I's also like to see a description of square-law mixers in this article, which would require some maths. I enthusiastically agree about the references. --ChetvornoTALK 09:54, 28 November 2010 (UTC)
I feel something odd in title of article to merge with, "Frequency mixer", probably because hierarchy of related articles is not well defined.
1. The term Frequency mixer seems to imply only a circuit or equipment used on Heterodyne (or Frequency mixing), for example. Also the term Frequency mixing seems to not imply the explict concept of Frequency translation.
2. On the other hand, the term Heterodyne may imply a concrete method to put Frequency translation into practice.
3. Also, generic article on Frequency translation is not found on Wikipedia, except for disambiguation page and power electronics specific article. To clarify the relations between a bunch of related technologies (ex. Ring modulation, Frequency shifter), a generalized article about Frequency translation may be needed.
4. Main phenomena laying under these articles may be Interference of waves, also known as Beating, but not well mentioned on two articles.
Anyway, on merging these two articles, we may need to rename the article and extend the coverage of article. --Clusternote (talk) 04:06, 26 January 2011 (UTC)
Here is my take on that:
I've redirected Frequency translation and Frequency shifting to Heterodyne. --Kvng (talk) 02:12, 14 February 2011 (UTC)
I've done work on both articles. I tried to follow suggestions provided. I'm still not fully convinced there needs to be two articles. Have a look at the current state of things and let me know what you think. --Kvng (talk) 03:27, 14 February 2011 (UTC)
I'd hoped that "Heterodyne" could discuss the maths and the general principles of frequency conversion, where "frequency mixer" could get more into the grubby details of circuits and their non-ideal properties (noise, power consumption, non-isolation, and so on). And we have to be careful to explain that "frequency mixers" multiply but an audio mixer just adds - non-linearity is the key. A book that I'll have to find again with Google discusses the unfortunate name "mixer", and Ithink if I can find it again I'll paraphrase the discussion of the inappropriate name. A couple of resistors and an op-amp make a find audio mixer, but is useless as a modulator, for example - we need to explain why. --Wtshymanski (talk) 04:40, 14 February 2011 (UTC)
You seem to be suggesting that we have two articles as an organizational aid. If you're shooting for WP:SUMMARY style, I don't think we're dealing with a large enough topic to warrant this. As to merge criteria, have a look at WP:MERGE. Primary justifications for separate articles are a/ Single article would be too large or b/ We're dealing with two different subjects. The former is clearly not the case. Can you make an arguement there is a fundamental difference between heterodyning and frequency mixing? --Kvng (talk) 22:33, 14 February 2011 (UTC)
"Frequency mixing" and "heterodyning", no. Frequency mixer and heterodyning, yes - one's a device, the other is a process. The heterodyning article talks about optical applications (about which I know nothing), whereas I can retype things out of "Art of Electronics" and the "ARRL" and "RSGB" books on radio mixers here. Yes, it could all be one well-written tightly organized thoroughly cited work of scholarship, but getting that done in the Wikipedia will happen shortly after peace in the Mid East. --Wtshymanski (talk) 01:39, 15 February 2011 (UTC)
I don't see anything here that argues against doing the merge. It's really not that hard to change things. If it doesn't work out, it can always be changed back. Don't let perfection defeat good. --Kvng (talk) 22:48, 15 February 2011 (UTC)

The current lead sentence says: "In electronics a mixer is a nonlinear electrical circuit which produces an output signal that is the product of two input signals." This gives the erroneous impression that a mixer is identical to an analog multiplier. I think the essential points in the definition of a mixer are that (1) its purpose is to generate new frequencies from the input frequencies, and (2) it does this by the heterodyning process. I think the lead should include these two points. --ChetvornoTALK 09:09, 28 November 2010 (UTC)

I don't disagree that the lead could use some work but have a look at heterodyning. Where do you get the idea that a frequency mixer is anything but an analog multiplier? --Kvng (talk) 18:10, 29 November 2010 (UTC)
The Heterodyning introduction is a little misleading, look at the "Output of a mixer" section. Heterodyning works by the multiplication of frequency components, not necessarily signals. It doesn't require an analog multiplier circuit, it occurs in most nonlinear devices, when two frequencies are applied. Mixers usually operate at radio frequencies far above the range that analog multipliers can handle. Most mixers consist of a transistor operated in its nonlinear region, or (at microwave frequencies) a diode. The nonlinearity creates sum and difference frequencies, but also a lot of harmonics; the desired frequency is filtered out of this mess. The output of a mixer is usually nowhere near the "...product of the two input signals"; it's a misleading description. --ChetvornoTALK 20:51, 29 November 2010 (UTC)
Thanks, I've learned something. The useful bit of the nonlinear element is the inner product (multiplication) term. I'm not clear on whether mixer or hetrodyne refers to the messy process involving nonlinearity or the idealized process of multiplication. Do you have a citation? --Kvng (talk) 02:57, 30 November 2010 (UTC)
"It is not necessary to form an accurate analog product to mix two signals. In fact, any nonlinear combination of the two signals will produce sum and difference frequencies." "Among the methods used to make mixers are the following: (a)simple nonlinear transistor and diode circuits... (b)dual-gate FETs... (c)multiplier chips... (d)balanced mixers constructed from transformers and arrays of diodes..." Paul Horowitz (1999) The Art of Electronics, p.886
"Historically, many devices (e.g. electrolytic cell, magnetic ribbons, brain tissue, rusty scissors ...in addition to...tubes and transistors) ...have been used, demonstrating that virtually any nonlinear device can be used as a mixer." Thomas Lee (2004) The design of CMOS radio frequency integrated circuits, p.405
"[Mixing] can be accomplished with either diodes or amplifiers, as any device with a nonlinear transfer function will work." Robert Dixon (1998) Radio receiver design, p. 147
"However, mixers are not simple multipliers." Toumazou, Moschytz, Gilbert (2001) Tradeoffs in analog circuit design, p. 789
"With the ideal analog multiplication process...no harmonics or spurious signals are produced. But in reality, mixers always produce many spurious outputs that consist of harmonics of ω1 and ω2 and additional mixing products..." Mishra, Singh (2007) Semiconductor device physics, p. 190
--ChetvornoTALK 07:55, 30 November 2010 (UTC)

The ideal mixer is indeed a four-quadrant multiplier, and that is not a nonlinear device. The basic identity establishing the sum/difference frequency behaviour is the prosthaphaeresis formula sin (ω1t)⋅sin (ω2t) = cos(ω1t − ω2t) − cos(ω1t + ω2t)/2. There is a huge tradeoff between DC accuracy and bandwidth among analog multipliers; balanced RF mixers such as the Gilbert cell and its vacuum tube complement, the beam deflection tube, are designs optimized for bandwidth.

Nonlinear devices are a faster and/or cheaper substitute that merely emulate a 1-quadrant multiplier by having the oscillator move the input signal up and down their nonlinear gain curve. The best results can be obtained with a quadratic curve, since ab = (a+b)2 − (ab)2/4 where one of the quadratic terms can be omitted in the circuit if the mixer output is fed into an IF bandpass anyway, as with triode mixers in historic VHF/UHF receivers. Today's bipolar semiconductors behave exponentially, distorting the IF bandpass input signal some more. --Mkratz (talk) 22:43, 26 June 2013 (UTC)

It's true as you say that a four-quadrant multiplier makes an ideal mixer because it doesn't produce product frequencies and your point that this is because it is a linear device is well taken. It was inaccurate of me to say that analog multipliers aren't used in RF mixers; modern mixers at intermediate frequencies are based on the multiplying Gilbert cell. But I think it is important for the article to emphasize that practical mixers at radio frequencies, even Gilbert cells, have significant nonlinearities and produce modulation products (mf1 + nf2). And of course at microwave frequencies and above, the fastest-expanding part of the radio spectrum and fastest-growing application of mixers, multiplying mixers can't be built and diode mixers are used, which are nowhere near linear. --ChetvornoTALK 14:46, 4 July 2013 (UTC)
I'm afraid that's not exactly what I meant. I meant that the prosthaphaeresis formula, and therefore multiplication, is the one and only way to obtain a sum or difference frequency, if you don't go all-digital. I was using "DC accuracy" as a synonyme for "linearity" in this context. The nonlinearity of the gilbert cell is the unwanted price to pay for its being optimized for bandwidth.
In the case of diode/triode/transistor mixers, the nonlinearity is the mechanism by which the device achieves multiplication (kind of, but good enough for the prosthaphaeresis formula to work as your IF filter gets rid of the factor frequencies anyway).
If you describe the nonlinear device as a two-port network with an input and an output, you can define the gain as g = Vout/Vin so Vout = gVin. Now if the gain itself is a function of Vin, then the output becomes a nonlinear function of the input. If, say, the gain were proportional to the input voltage (g = aVin), then the output becomes quadratic: Vout = (aVin)⋅Vin. The squaring involved here is the multiplying functionality which allows nonlinear devices to be used as mixers in the first place.
If the gain were some higher-order function of Vin, then that means only that a is no longer a constant and must be replaced by an appropriate polynomial. The multiplying functionality remains the working principle. So I think the article is misleading; it should say that mixing is always multiplying, and that is in most cases approximated by using nonlinear devices.--Mkratz (talk) 19:22, 7 July 2013 (UTC)
Actually the central role of the prosthaphaeresis formula in heterodyning is already acknowleged in WP, in the Heterodyne article "Mathematical principle" section (although I didn't know that trigonometric formula was called 'prosthaphaeresis' when I wrote it). I wouldn't mind having the math in this article too. But this thread was about how the introduction should describe mixers. A large part of the readers of this section will be nontechnical people. I think it will be misleading to them for the lead to say that a mixer is a device that multiplies signals. An example of the possible confusion appears at top of this thread: Kvng was led to believe that mixers were simply identical to analog multipliers. They aren't, necessarily, are they? --ChetvornoTALK 20:39, 7 July 2013 (UTC)
What I gathered from previous discussion and citations provided by User:Chetvorno above (thanks for that) is that the difference between a frequency mixer and analog multiplier is that a frequency mixer can be sloppy. It definitely must have a multiplication function but it can do other nasty stuff too. I think the lead would be improved if we added the word "multiplier" somewhere or even linked to analog multiplier. ~KvnG 00:38, 8 July 2013 (UTC)
That's pretty accurate. I think the multiplying function of mixers should be acknowledged, just not in the introduction. There is a big difference between having a multiplication function and being an analog multiplier. Some mixers like the Gilbert cell do multiply signals, but others, as Mkratz admitted, sum the two signals, then distort the sum in a nonlinear device and filter the 2nd order product terms out of the distorted output. Look at the detector circuits in 1, p. 383,384,393,394. They are not analog multipliers; their output is nowhere near the product of the input signals. Most WP:RSs don't define mixers as signal multipliers 2 3. --ChetvornoTALK 10:48, 8 July 2013 (UTC)
The two you cite do. The first states in chapter 13.2, 2nd paragraph: "At the core of all mixers presently in use is a multiplication of two signals in the time domain." The second states in the introduction, referring to the polynomial I mentioned earlier: "the higher-order terms in a system transfer characteristic are intentionally used to translate between one frequency and another." We are talking about non-harmonic distortion here. A nonlinear mixer performs two actions: First, it algebraically sums antenna and oscillator signal; second, it submits this sum to a nonlinear transfer function. The easiest case is the quadratic mixer: You get (a + b)2 = a2 + 2ab + b2. The first and last terms of the binomial are a job for your IF stage, the middle term is where prosthaphaeresis kicks in.-- Mkratz (talk) 15:01, 9 July 2013 (UTC)
Yes, but they don't in the introductory paragraph. Neither of the references mention multiplication in their introduction to mixers. That's all I'm arguing for. I absolutely agree that the role of multiplication and the prosthaphaeresis formula should be in the article, and the derivation of at least the quadratic mixer output you used as an example. Just not in the introduction. Describing a mixer to a nontechnical person as a circuit that multiplies signals would be inaccurate. Very few, if any, WP:RSs introduce mixers that way 1, p.477, 2, p.277, 3, p.778, 4, p.76 5, p.194 even engineering texts. --ChetvornoTALK 16:51, 9 July 2013 (UTC)
Well the questions then are: Is a 1-quadrant analog multiplier still an analog multiplier although it's sloppy with the signage because the user can live with that? Yes. Is a nonlinear mixer still an analog multiplier although it's sloppy with the polynomial terms because the user can live with that?- Mkratz (talk) 17:50, 9 July 2013 (UTC)

───────────────────────── If the two circuits are the same, why are they called by different names? Why are there separate chapters in engineering books on mixers and analog multipliers? --ChetvornoTALK 18:15, 9 July 2013 (UTC)

If all we're arguing about is whether to add the word "multiplier" to the lead, I say we stop arguing. The lead reads nicely enough as it stands. ~KvnG 22:28, 9 July 2013 (UTC)

I agree. --ChetvornoTALK 00:08, 10 July 2013 (UTC)
I expected you would :) ~KvnG 20:46, 11 July 2013 (UTC)