Talk:Frequency modulation

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why the radio based on frequency modulation has very small transmission area?

It's nothing to do with the FM modulation, it's to do with the higher frequency used for FM radio broadcasts, compared with AM radio broadcasts. AM radio is on a lower frequency, so it travels further. The lower longer-range AM radio channels were handed out first, so they use the older (and more frequency-efficient, but less interference-tolerant) modulation. -- The Anome 11:04 18 Jul 2003 (UTC)

Actually, FM is more frequency efficent than AM, except that commercial FM uses wide FM to get more audio bandwidth into the signal. If FM used the same audio bandwidth as AM, it would use the same or less RF bandwidth than AM. Commercial frequencies (i.e., public safety) and amateur frequencies that use FM use narrow FM. --ssd 03:59, 23 Jun 2004 (UTC)

Note: we should have a radio propagation to explain why the lower frequency radio waves travel further. -- The Anome

I've started one, but there may be lots of factual inaccuracies, I'm not sure, I haven't done radio stuff in ages :) Dysprosia 11:26 18 Jul 2003 (UTC)

I started Category:Radio frequency propagation with the intent of writing an article including as many of those terms as sane. Feel free to use it as a seed. --ssd 03:59, 23 Jun 2004 (UTC)

Could we please stop moving the disambiguation page and setting to FM. FM does stand for more than one thing. Thank you. --Numerousfalx 23:51, 15 Dec 2004 (UTC)

1 Example
2 Too focused on radio
3 english lesson
4 font
5 Formula Error
6 FM recording
7 Wave Images
- 7.1 AM and FM compared
- 7.2 FM
8 Theory
9 How to demodulate FM ?
10 Assignments
11 Math confusing - statements about circuit design would be complimentary
12 Bessel Function table
13 FM capture and hearing 2 stations at once
14 Merge FM and PM?

[edit] Example

Can someone give an example for frequency modulation? let's say there is a test signal low tone, high tone, and a sweep. this composed audio signal is supposed to be put on FM radio - how would the modulated tone look like? how much bandwidth does FM radio need? When I detune my favorite radio station "92.2 MHz Rock" by, let's say +0.2 MHz, will the music and all transmitted acoustics be pitched to higher frequencies (so that radio moderators talk like Mickey Mouse) - or is FM resistant against those mistunings.

It would be great if someone could work my (answered) questions into the article. Thanks, --Abdull 21:41, 17 Jan 2005 (UTC)

I agree this sort of information should be covered by the article, preferably with diagrams. Answering these questions (for FM) is somewhat tricky, though, and involves a lot of math.

I can answer your last question here: no, tuning away from an FM station does not shift the frequency components of the output, so you won't hear "Mickey Mouse" voices like you would with SSB. The capture effect inherent to analog FM receivers means that slight mistunings are "automatically" compensated for. Tune far enough away and you hear static-y, distorted sound; tune further away and you hear only static.

Simon 18:20, 23 Jan 2005 (UTC)

Simon is correct about detuning an FM receiver that has no AFC (Automatic Frequency Control) or has AFC switched off. However most FM receivers do have AFC (because it is quite easy to implement) which truly compensates for mistuning. Try to tune away and the sound remains good, until you reach the limit of the AFC and suddenly lose the signal completely. Then the sound changes to the hiss heard between stations. Some receivers have an additional "squelch" function that mutes the hiss noise. Note: all the above observations are for home VHF FM radios, which the frequency Abdull mentions indicates.Cuddlyable3 18:50, 12 February 2007 (UTC)

[edit] Too focused on radio

The article reads as "FM as used in radio" with a little theory thrown in at the last minute. Shouldn't an article titled "Frequency Modulation" primarily cover the theory and link to separate articles on radio/data transmission/encoding (and FM synthesis)? The FM synth article has almost no theory at all.

That might be because the authors of the FM Synth article are unaware
of that FM-synthesis á la Yamaha is based on phase-modulation. /ja

The first sentence "...represents information as variations in the instantaneous frequency of a carrier wave" makes sense if you're reading about radio, but is hard to "get" if you're coming at this from the FM synth perspective.

Please have a look at the discussion page under "phase modulation" where I
present a few C like oneliners to make the point. /ja

I suppose it makes sense to add a bit more on the theory, whether the article should have its current focus or not; I'd do it myself, except for the fact that I don't really understand FM all that well yet.

magetoo 14:16, 27 Apr 2005 (UTC)

[edit] english lesson

"The phrase frequency-modulated, an adjective, should have a hyphen when used attributively."

Is this significant to FM for some reason? - Omegatron 21:39, May 25, 2005 (UTC)

[edit] font

Could the author consider changing the font on the maths? I found it very difficult to see on a computer screen whether I was reading "t" for time or "f" for frequency. Otherwise found the article well balanced.

I agree that the font used makes the formulae very hard to read, but the author correctly used TeX to create them; there is nothing to fix on this page.

In my opinion there is a problem with the HTML generation of formulae (it was just as unreadable in IE as Firefox). I will look around and see if there is somewhere I can raise this issue. In the meantime, I recommend changing your wikipedia math preferences to use png for all formulae (the default is to use HTML for 'simple' formulae and png for everything else). Happyharris 18:40, 18 August 2005 (UTC)

After reading some more doc, it seems that individual formula can be forced to PNG. That seems appropriate here so I did it (although I still think the default use of HTML is a wikepedia-wide fault) Happyharris 18:44, 30 August 2005 (UTC)

Happyharris, i really agree and have had some of my PNG converted to HTML like in Plank units at the bottom. but i think that consistency in notation and appearance is important. ironically, i was recently editing and was putting in in-line HTML math instead of the usual PNG. so maybe i got infected with WP orthodoxy. r b-j 05:15, 20 October 2005 (UTC)

[edit] Formula Error

The main theory discussion has a very common mistake in deriving frequency modulation. I picked up on it because I make the same mistake every time I start to review FM, and have to fix it. The formula x(t) = A*cos(2*pi*f(t)*t) is incorrect. It arises because A*cos(2*pi*f*t) is correct when f is a constant - f is the frequency. However, frequency is the rate of change of the cos() argument. If f(t) is time varying, then the rate of change of f(t)*t is not f(t), it is some complex derivative that is no fun at all.

A better derivation is to start with x(t) = A*cos(phi(t)). Frequency is defined as the rate of change of phi(t). To get sinusoidal FM, we need some phi(t) such that the derivative of phi(t) is 2*pi*deviation*cos(2*pi*rate*t). That isn't so hard - we know the derivative of sin(kt) is k*cos(kt), so we postulate phi(t) = deviation/rate *sin(2*pi*rate*t). It is inconvenient to carry the ratio of deviation/rate, so it is often called Beta. The final formula, then, is x(t)=A*cos(Beta * sin(2*pi*rate*t)) where Beta is deviation/rate, and both deviation and rate are in Hz.

This leads nicely to the Bessel functions, which are a formalized way of working out equations like cos(m sin(x)).

References: "Analog and Digital Communications" by Hwei Hsu (Schaum's Outline) and "Fundamentals of Electronics" by Aldo Vieira da Rosa.

[edit] FM recording

"FM is also used at intermediate frequencies by most analog VCR systems, including VHS, to record the luminance (black and white) portion of the video signal."

Has this method ever been tried for audio recording, aside from the HiFi modes on some analog VCR systems such as VHS and Betamax?144.139.87.8

On magnetic tape, the common method of adding a supersonic frequency to the audio signal reduces distortion very effectively, and exploits the dynamic range of the tape to the full. An FM signal with its sidebands would demand a faster tape speed, hence allow less recording time.

FM of an audio-frequency carrier has been useful as a means of recording low-rate digital data on audio tape (cassette) recorders. Such audio equipment could not handle long strings of repeated 0's or 1's directly because of limited low-frequency response.Cuddlyable3 19:01, 12 February 2007 (UTC)

"FM is the only feasible method of recording video to and retrieving video from magnetic tape without extreme distortion, as video signals have a very large range of frequency components — from a few hertz to several megahertz, too wide for equalisers to work with due to electronic noise below -60 dB. This sentence tries to say too many things and needs attention. The megahertz-wide frequency range of video does not force any particular choice of modulation method, nor is it difficult to "equalise" over the video frequency range. I think the subject of FM in video recording belongs in a new section, where the significant issues treated are linearity, pre- and post-emphasis, tape speed, head gaps and noise distribution.Cuddlyable3 18:53, 9 February 2007 (UTC)

[edit] Wave Images

[edit] AM and FM compared

The animation is nice. However the AM example is jerky, gives an impression that carrier cycles are individually modulated, and they don't look sinusoidal. There is also redundant text "modulatie", not even in English (the M's stand for modulation already). I think we have to look extra critically at animated drawings because of the relatively high data overhead they represent.Cuddlyable3 15:19, 15 February 2007 (UTC)

I have fixed the above with a new animation. Besides being accurate and non-language specific, it is a much smaller file, and we all like pages to load quickly, don't we?Cuddlyable3 01:04, 18 February 2007 (UTC)

[edit] FM

I may be wrong, since I'm still studying elementary physics, but does the first graph show a frequency over time (signal) superimposed on an amplitude over time (carrier)? To remain consistent, I would think that the two graphs should have the same two variables. --Pyg 01:09, 11 March 2006 (UTC)

Your question confuses me but the graphs do not. They all have the variables voltage (vertical) and time (horizontal).Cuddlyable3 18:18, 9 February 2007 (UTC)

The red curve shows the signal as advertised, which is a varying voltage input to the modulator. Only after the modulation does the carrier frequency over time take on the same curve (or it could be inverted since there is no fixed convention about the direction of frequency deviation).Cuddlyable3 21:22, 11 March 2007 (UTC)

I think the first image (AM, green waveform) is incorrect - it should be showing a varying signal amplitude (vertical scale) at a fixed frequency. Nogami 00:47, 12 August 2006 (UTC)

It is correct. The carrier drawn in green has neither AM nor FM.Cuddlyable3 18:18, 9 February 2007 (UTC)

[edit] Theory

There seems to be something wrong with the formula. It is different from the one shown in one of the external links (http://www.fas.org/man/dod-101/navy/docs/es310/FM.htm). In this page the formula does not involve an integral at all. It seems to me that the formula as it is now requires the time integral of the signal Xm(t) from 0 to t to be restricted to [-1,1] for all t. This is not necessarily true even if |Xm(t)| < 1. Also it would be interesting to know how to recover the transmitted signal from the modulated carrier wave.

The integral is correct - it comes from the fact that FM is actually a special case of PM (phase modulation), and phase is the integral of frequency w.r.t. time. Also, I don't see why the time integral must be restricted to [-1,+1]. The only reason that the restriction

| X m (t) | < 1

exists is so that the frequency is restricted to $f_c \pm f_\Delta$ . Oli Filth 09:58, 22 January 2007 (UTC)

Could someone expand the theory section significantly? I think it could use more math/physics background and a sub-section on the engineering of actually accomplishing frequency modulation. Ryanluck 15:55, 6 November 2006 (UTC)

I disagree that the theory section needs more math/physics background. FM and radio is essentially the product of engineering and the mathematics behind it is nice to understand - but not fundamental. The explanation of FM given here is equivalent to asking someone the time and getting and answer on how his watch was built with a precise explanation of the location of every cog in the structure. It may in fact include the information being sought, however more than likely the questioner still won't know what time it is. A far more practical explanation of the theory of frequency modulation is given in the reference http://www.fas.org/man/dod-101/navy/docs/es310/FM.htm:

Frequency modulation uses the information signal, Vm(t) to vary the carrier frequency within some small range about its original value. Here are the three signals in mathematical form:

   * Information: Vm(t)
   * Carrier: Vc(t) = Vco sin ( 2 p fc t + f )
   * FM: VFM (t) = Vco sin (2 p [fc + (Df/Vmo) Vm (t) ] t + f)

Df is the peak frequency deviation. In this form, you should be able to see that the carrier frequency term: fc + (Df/Vmo) Vm (t) now varies between the extremes of fc - Df and fc + Df. The interpretation of Df becomes clear: it is the farthest away from the original frequency that the FM signal can be. Sometimes it is referred to as the "swing" in the frequency.

We can also define a modulation index for FM, analogous to AM:

b = Df/fm , where fm is the maximum modulating frequency used.

The simplest interpretation of the modulation index, b, is as a measure of the peak frequency deviation, Df. In other words, b represents a way to express the peak deviation frequency as a multiple of the maximum modulating frequency, fm, i.e. Df = b fm.

Example: suppose in FM radio that the audio signal to be transmitted ranges from 20 to 15,000 Hz (it does). If the FM system used a maximum modulating index, b, of 5.0, then the frequency would "swing" by a maximum of 5 x 15 kHz = 75 kHz above and below the carrier frequency.

Here is a simple FM signal:

Here, the carrier is at 30 Hz, and the modulating frequency is 5 Hz. The modulation index is about 3, making the peak frequency deviation about 15 Hz. That means the frequency will vary somewhere between 15 and 45 Hz. How fast the cycle is completed is a function of the modulating frequency. —Preceding unsigned comment added by 67.142.130.42 (talk) 18:26, 5 October 2007 (UTC)

[edit] How to demodulate FM ?

There is no explanation given of how the transmitted signal is recovered. That is cheating the reader after promising "The rest of this article...concentrates on the FM modulation [sic] and demodulation process." A solution could be instead to link to descriptions of the established FM detectors (Ratio, Foster-Seeley, Slope and PLL) in the article on Detector (radio).Cuddlyable3 17:54, 9 February 2007 (UTC)

Common methods used in FM receiver are slope detection and phase-locked loops.

The above is not true if by "common" we understand the majority of domestic radios.Cuddlyable3 19:06, 12 February 2007 (UTC)

That's what Carlson mentions. Please update the article if you have a more up-to-date reference. Alinja 21:16, 14 February 2007 (UTC)

Please help me by identifying what you mean by "Carlson". Until I check that, I like the solution I proposed i.e. a link to Detector (radio). BTW I have the impression that Slope detection of FM is too unwieldy for common use and is only kept mentioned in textbooks.Cuddlyable3 15:30, 15 February 2007 (UTC)

By Carlson I mean 'A. Bruce Carlson: "Communication systems, 2nd edition", McGraw-Hill, Inc, 1981'. A link to a more complete article about detectors is of course ok, but we want some kind of mention of how FM can be detected here anyway. Alinja 19:28, 15 February 2007 (UTC)

Thank you Alinja for that book reference. However FM signals having no amplitude variation are rather incompatible with AM detectors. The phenomenon called slope detection must have been an accidental discovery that AM radios nevertheless register some sound from FM transmissions. Slope detection is inferior in distortion, noise rejection and adjacent signal rejection compared to the established FM detectors and seems to be kept in textbooks only for its educational value.Cuddlyable3 00:48, 18 February 2007 (UTC)

I have tidied up the references to FM detection, relegating the explanation of actual detector circuits to Detector (radio).84.210.139.189 18:26, 9 March 2007 (UTC)

[edit] Assignments

Could this article include the assigned frequencies for the different uses? Such as 118.00 – 136.975 for Aviation, 108.000-117.975 Navigation, 151.5125- 158.400 BRS. I think a side bar would be best served for this purpose. —The preceding unsigned comment was added by 70.41.64.103 (talk) 00:50, 15 February 2007 (UTC).

There should be a linking with Radio frequency and Frequency allocation pages to avoid duplication. Probably Wikipedia should only link to the most detailed frequency allocations with their national variations, found on the web. I would like it kept clear that FM is a modulation type, and not intrinsically any frequency range.Cuddlyable3 15:42, 15 February 2007 (UTC)

...although FM broadcasting is better allocated to higher frequencies than those historically allocated to AM broadcasting, because of issues of coverage and bandwidth.Cuddlyable3 21:29, 11 March 2007 (UTC)

[edit] Math confusing - statements about circuit design would be complimentary

Specifically, $A \cos \left( 2 \pi \int_{0}^{t} \left[ f_c + f_\Delta x_m(\tau) \right] \, d \tau \right)$

makes it difficult to understand the underlying circuitry.

$\int_{0}^{t} \left[ f_c + f_\Delta x_m(\tau) \right] \, d \tau = t \times f_c + \int_{0}^{t} f_\Delta x_m(\tau) \, d \tau$

There's no electronic circuit that can indefinitely accumulate a non-zero average input as implied by this equation; while the equation may or may not be correct, it will inevitably be an indirect parallel to the physical model. Also, $f_\Delta x_m\left(\tau\right)$ is not clearly defined; the reader must infer it's nature from the integral, which may be incorrect.

$A \cos \left( 2 \pi \times f(t) \times t \right)$ would be a simpler, more direct mathematical model. It has a constant amplitude with a varying frequency.

$f(t) = \left( f_c + k \times input(t) \right)$ is a possible scenario; however, the article does not state (though it implies) that this the actual modulation.

The set of possible modulations is covered by $f_c + m\left(input(t)\right)$ where $input\left(t\right)$ is flat long-term.

note: I don't know how to get a proper multiplication dot; hence my multiplication looks like a cross-product; feel free to fix that if you know how.

It would be more helpful to state the exact modulation, or the exact circuit.

—Preceding unsigned comment added by 66.245.28.149 (talk • contribs) 09:06, 4 July 2007

The simpler mathematical model that you propose hides the continuous-phase nature of most frequency-modulation schemes. You're right that the existing model is not the easiest of equations to understand (in terms of intuition); however all the terms are clearly defined.

In most circumstances, it will be a direct representation of what's going on in the circuit. A VCO (or NCO) accumulates phase indefinitely; that's exactly what the equation shows. Oli Filth 11:33, 4 July 2007 (UTC)

Thank you for your help; I found one of the external links (www.fas.org) presented FM in a set of equations that cleared everything up for me personally. The confusion in the Wikipedia article is the result of the definition for $f Δ$ as "instantaneous maximum deviation": it's actually just a constant, but 'instantaneous implies that it is a variable in time.

[edit] Bessel Function table

After Carson's rule, Bessel Functions and their role in calculating aspects of the sidebands created by FM needs to be added. I have added it, but it needs more explanation, and the table title needs repair as below.

Modulation Index	Carrier	Sideband Pairs

		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
0.00	1.00
0.25	0.98	0.12
0.5	0.94	0.24	0.03
1.0	0.77	0.44	0.11	0.02
1.5	0.51	0.56	0.23	0.06	0.01
2.0	0.22	0.58	0.35	0.13	0.03
2.41	0	0.52	0.43	0.20	0.06	0.02
2.5	−.05	0.50	0.45	0.22	0.07	0.02	0.01
3.0	−.26	0.34	0.49	0.31	0.13	0.04	0.01
4.0	−.40	−.07	0.36	0.43	0.28	0.13	0.05	0.02
5.0	−.18	−.33	0.05	0.36	0.39	0.26	0.13	0.05	0.02
5.53	0	−.34	−.13	0.25	0.40	0.32	0.19	0.09	0.03	0.01
6.0	0.15	−.28	−.24	0.11	0.36	0.36	0.25	0.13	0.06	0.02
7.0	0.30	0.00	−.30	−.17	0.16	0.35	0.34	0.23	0.13	0.06	0.02
8.0	0.17	0.23	−.11	−.29	−.10	0.19	0.34	0.32	0.22	0.13	0.06	0.03
8.65	0	0.27	0.06	−.24	−.23	0.03	0.26	0.34	0.28	0.18	0.10	0.05	0.02
9.0	−.09	0.25	0.14	−.18	−.27	−.06	0.20	0.33	0.31	0.21	0.12	0.06	0.03	0.01
10.0	−.25	0.04	0.25	0.06	−.22	−.23	−.01	0.22	0.32	0.29	0.21	0.12	0.06	0.03	0.01
12.0	0.05	−.22	−.08	0.20	0.18	−.07	−.24	−.17	0.05	0.23	0.30	0.27	0.20	0.12	0.07	0.03	0.01

Phillipbeynon 04:24, 1 August 2007 (UTC)

I don't think this table is a good (so-called) illustration. A graph would show better that:

Sidebands shown blank in the table are not non-existent, they are merely below an arbitrary quantising limit. The sidebands produced by sinusoidal FM are an infinite series.
A graph shows that particular sideband pairs are zero at particular modulation indices, which gives a common method of calibrating frequency modulators using a spectrum analyzer. Please sign your posts. Cuddlyable3 10:09, 30 July 2007 (UTC)
- Valid point about the undefined values. The harmonics produced by changing frequency continue ad infinitum; however, the arbitrary limit defining what are significant sidebands is 2% using Carson's rule and 1% for Bessel table values. I found it important to include the table for reference, as I myself was looking for it when I first read this page. A spectrograph would illustrate this infinite series better.--Phillipbeynon 04:24, 1 August 2007 (UTC)
  - I agree that a spectrograph would help explain the sideband behaviour. I notice that your table does identify the special values of modulation index where the carrier disappears, something which can surprise folks. I have another thought: since no FM radio channel can pass ALL the infinite sideband harmonics, every practical FM radio channel distorts a sine signal. I think Carson's rule is intended to be used to design the overall half-power bandwidth of a radio channel. Can we quote the maximum signal distortion that results? Cuddlyable3 13:49, 1 August 2007 (UTC)

[edit] FM capture and hearing 2 stations at once

Why is it that most sources claim that an FM receiver only demodulates the strongest signal available, and yet one will sometimes hear two stations simultaneously? Does this indicate something is wrong with the receiver or is this 'normal' if the signals' strengths are the same order of magnitude? I have a few times been able to enjoy a talk and music at the same time using my car radio (KXBL 99.5 FM and KAKS 99.5 FM).

-User: Nightvid

That is normal and does not indicate anything wrong with your receiver. Unlike AM signals, only a small increase in the received power from the stronger station is needed for it to "overpower" (make inaudible) the weaker station. Descriptions of this capture effect are sometimes exaggerated.Cuddlyable3 23:12, 7 October 2007 (UTC)

[edit] Merge FM and PM?

FM and PM are really the same thing, separated only by the mathematical viewpoint. Perhaps they should be merged into one article and then have FM treated as a special case? HatlessAtless (talk) 21:48, 23 April 2008 (UTC)

One might equally argue that PM is a special case of FM. The naming of the Wikipedia articles is influenced by the fact that AM and FM are worldwide broadcasting standards whereas PM outside narrow technical fields is relatively little known or used. Cuddlyable3 (talk) 06:01, 24 April 2008 (UTC)