# Is Bandwidth Relative to Carrier Frequency?

Discussion in 'Wireless & RF Design' started by johnyradio, Sep 14, 2014.

Oct 26, 2012
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Is bandwidth determined by the absolute deviation occupied (eg "±75 kHz" or "±3 kHz")?

Or, is bandwidth determined by deviation RELATIVE to the frequency of the carrier?

In other words, does a ±75 kHz deviation on a 90 Mhz carrier contain the same amount of information as a ±75 kHz deviation on a 900 Mhz carrier?

thx!

2. ### MrChips Moderator

Oct 2, 2009
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Your first assumption is the correct one.

Oct 26, 2012
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Thx!

Followup question-- how can i calculate the effective dynamic range in db of an analog FM link?

For example, 16-bit audio contains ~65,000 steps, or ~15 ppm, or ~90db. But that's digital.

How can we calculate db range from analog FM Hz bandwidth?

In other words, how large hz deviation is required in an analog FM radio link to obtain 90db of dynamic range?

Oct 26, 2012
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5. ### vk6zgo Active Member

Jul 21, 2012
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Normally
The answer is fairly obvious from the deviation being quoted in kHz,not %.

Normally,Exciters in FM Transmitters generate the required deviation at an IF frequency.
The signal is then up-converted to the radiated frequency using Superheterodyne principles.
The deviation remains the same.

Older Transmitters generated a narrower deviation signal at a lower frequency,which was then
frequency multiplied (a non-linear process) up to the radiated frequency.
In that case,the deviation increased with the frequency multiplication.

6. ### vk6zgo Active Member

Jul 21, 2012
677
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Generally speaking,the greater the deviation,the more dynamic range.
That said,FM Broadcasting,is limited in dynamic range by several factors:-
(1)Lack of dynamic range in sound reproduction devices which may be used at the receiving end.
(2)Noise.

In the case of (1),it is fairly obvious that a home Sound system will not provide the dynamic range available in a live performance of an Orchestra.
Even movie soundtracks run into this problem,where in the theatre,two conspirators may hold a whispered conversation,followed by a large explosion.
The dynamic range of a theatre Sound system is great enough to handle such a range,but the little speaker in your analog TV set will not,so even with the limitations on dynamic range inherent in the TV sound system (which is FM),you are still stuck with the choice of---- -don't hear the whispers or be deafened by the explosion.

As for (2) I have carried out tests on FM BC Transmitters more times than I care to remember.
You are battling to get -70dB w.r.t full deviation---more commonly,it is in the range of -57 to -65 dBm.

Oct 26, 2012
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Thanks, i am aware of the potentially limited dynamic range of home stereo equipment. But i think it's not quite accurate to call that a limiting factor in FM transmissions, and anyway it's a separate issue. i'm only asking about the wireless link, and not factors external to the RF system.

Cool! Forgive my ignorance, but what's "BC"?

It would be super awesome if you could share the parameters of that battle. You mean reducing noise? If so, what are the main sources of the noise?

Btw, what do you mean by "full" deviation.

Last edited: Sep 15, 2014

Oct 26, 2012
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Quoted where? The article i linked? I read a bit deeper, and i realized they're not talking about dynamic range. In the article, DR is Deviation Ratio.

They define Deviation Ratio as:

the maximum deviation of the FM signal to the maximum modulating frequency:
DR= δ/fmax
I believe that's a relative, not absolute value. But again they're not talking about dynamic range.

ok thanks, this is interesting. Not sure yet how to apply it to my question about calculating dynamic range from frequency deviation, but it suggests to me that those two stages, audio-to-IF and IF-to-RF, might together reduce overall dynamic range. so maybe i need to think about both stages when trying to estimate dynamic range.

re older transmitters, i would expect that the larger deviation in the RF stage would have no effect on dynamic range, since the audio-to-IF stage would be the limiting factor. How will thinking about older transmitters help me out with my question?

thx

Last edited: Sep 15, 2014
9. ### vk6zgo Active Member

Jul 21, 2012
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FM Broadcasting is designed to meet Standards set by the appropriate Licencing Authorities.

The dynamic range of home equipment was an important part of defining these Standards.
Other things were: the finite amount of bandwidth available,the state of the Broadcasting art back in the late 1940s,& the state of the art of recording equipment which would provide most of the program material.

An FM Broadcasting system set up with no limitations would no doubt perform better,but in the real world these issues are important,as there is not much reason to go to extremes to outperform the associated sources & reproduction equipment by huge margins.

It means the same as "Broadcast".

Detection of FM signals is not an inherently noise free process.
The signal power of a program signal at the higher audio frequencies is very much lower than at lower ones,so the total deviation at those higher frequencies is lower,hence there is a worse sugnal to noise ratio.

Broadcasting uses a technique of "Pre-emphasis",where the higher frequencies are caused to deviate the
carrier to a greater extent than the lower frequencies.
I am a Transmitter Tech,not a Modulation Guru,so you may be able to find something which goes a bit deeper by Googling.

Again, this is,for FM Broadcasting-------75kHz deviation,a Standard.
You modulate the Transmitter to 75kHz with a 400Hz audio signal,calibrate the Noise measuring device,then terminate the audio input.
You can then read the system noise.
That is + & -75kHz as referred to in your initial post.

10. ### MrChips Moderator

Oct 2, 2009
14,514
4,278
Quoted where? What vk6zgo is referring to is the units (or dimensions) used.
If the units are kHz then those are absolute numbers where as % is a dimension-less number and hence is a ratio.

Note that dB is a ratio. Also note that dynamic range refers to the ratio of modulating amplitude not frequency.

You may want to look up FM and FM broadcasting.

11. ### vk6zgo Active Member

Jul 21, 2012
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You refer to a deviation of +- 75kHz in your first post.-----that is what I was referring to.
"Deviation Ratio" is a useful concept,but it is not commonly used in practical work.
I'm not sure if you can define a precise relationship between deviation & dynamic range which is always
applicable.

I mentioned the older Transmitters just to point out the fact that it can be done in that matter.
In fact they don't have IFs.

In both Superheterodyne & Frequency Multiplier Transmitters,the later stages can affect Distortion,Noise
and Dynamic range.

FM is as messy as hell,& the simple picture of a carrier jazzing back & fault doesn't quite hack it.
All types of modulation add sidebands---but this again needs Googling for!

Oct 26, 2012
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Of course. But I'm not inquiring about Commercial Broadcasting, nor the history of same. Altho i appreciate the historical perspective, I seek electronic knowledge not restricted to commercial FM regulations or behaviors. Sorry if i did not clarify that in my OP.

That said, i'm very interested in methods used in commercial FM broadcasting to improve audio quality.

that is super-helpful and relevant. Thx for that.

ah, thx. That is very useful!

Last edited: Sep 15, 2014

Oct 26, 2012
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i thought "dynamic range" refers to the difference between the loudest reproducible audio and the quietest reproducible audio. Eg full orchestra playing at loudest volume vs a whisper.

Or the distance between the noise-floor and the loudest reproducible sound (maybe that's "headroom"?)

either way, i was using the term "dynamic range" to refer to the volume range of the audio output, not to modulation of any kind.

Last edited: Sep 15, 2014
14. ### alfacliff Well-Known Member

Dec 13, 2013
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defviation affects the dynamic range of the recieved signal, how fast the signal is deviated determines the bandwidth of the recieved signal, if you are refering to bandwidth of recieved signal, not bandwidth used in transmitting.

Oct 26, 2012
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yes, exactly why i'm inquiring about it. That's the topic of this thread.

hrm, i thought the "speed" of deviation is determined by the slope of the modulating source audio waveform, and is related to accuracy of the reproduced waveform, not bandwidth or dynamic range. Bandwidth means the size of frequency deviation of the FM carrier, and not how "fast" it deviates. No?

16. ### alfacliff Well-Known Member

Dec 13, 2013
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how fast the frequency changes (deviates) is deterfmined by the frequency of the modulating signal. simploy put, it wiggles back and forth at 1000 times a second for a 1000 hz tone modulation. how far it wiggles determines the volume.

Oct 26, 2012
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I mainly agree, but i think how fast it deviates is determined by the instantaneous slope, or transition time of the audio waveform. Even a low frequency audio signal may have a fast slope on some parts of the waveshape. And, a high frequency can have a slow slope on some parts of the waveform.

For example, a square wave at 1 Hz has a VERY fast transition-time. How fast the frequency changes (deviates) is very high (a straight, vertical line. Basically, as fast as your electronics can go).

But, the frequency of the modulating signal, 1 Hz, is very low.

On the other hand, the waveshape below (TR-808 Roland drum machine) at 10 Ghz has a transition time that slows to a dead stop. Every cycle. So, during some parts of the wave, how fast the frequency changes (deviates) is very low, but the frequency of the modulating signal is very high.

http://everystockphoto.s3.amazonaws.com/tr808_waveform_grid_1023309_o.jpg

Basically, how fast the source audio voltage deviates changes constantly over the course of the wave cycle.

How fast the signal is deviated does not determine the "bandwidth" of the recieved signal.

Bandwidth means, how BIG is the deviation. When the source audio voltage travels up and down (in irregular, unpredictable motions), it pushes the frequency of your carrier oscillation up and down. How big is the distance between it's fastest and slowest oscillation? That's bandwidth.

If it oscillates from 1,000 Hz to 1,100 Hz, it's bandwidth is 100 Hz (= 1,100 - 1,000).

If it oscillates between 100,000 Hz and 100,100 Hz, it's bandwidth is still 100 Hz (=100,100 - 100,000).

yes.
I agree, tho I would say, how far it wiggles is determined by the amplitude of your source audio, multiplied by the sensitivity of your VCO.

Glad we're getting clear on basic concepts and terms.

Would really appreciate if you can shed any light on how to estimate dynamic range in an FM system.

Last edited: Sep 15, 2014

Oct 26, 2012
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yeah, i've been learning about sidebands too. As i understand, wideband FM has more of them, and requires more filtering to get rid of them. But for the moment, i just want to figure out the dynamic range issue.

thx!

19. ### vk6zgo Active Member

Jul 21, 2012
677
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You don't want to 'get rid" of too many sidebands,or your FM system will not work!
Theoretically,FM has an infinite series of sidebands,but in the real world many of the sidebands at a long way out from the carrier carry little essential information,& can be filtered out.

If you pass the FM signal through too narrow a filter,you not only lose essential information,but also create
a problem called "AM Noise" due to the same mechanism which allows you to "slope tune" an AM receiver
to listen to FM signals.

AM Noise is not a great problem with PLL detectors,but with Ratio Detectors & the like which convert FM to AM so as to detect it,this can be a major source of received noise.
The loss of information still affects all types of detectors,though,appearing as distortion.

2x Deviation is a fair "rough guide" to deviation for narrowband FM,but is not the whole story in the wideband case.

The dynamic range of any radio system is the ratio between the maximum modulating signal level & the minimum modulating signal level which it can reproduce at the receiver end of the system.
Signal to Noise ratio is inextricably tied up with this,as you cannot reproduce a signal which is lower in level than the system noise floor.

Analysis of FM modulation is not something which you can do on the basis of a few paragraphs in this forum.
You need to do your own research---hopefully your local University library will have some books which go more deeply into this subject than your current textbooks,if any.
Even if you aren't a student at that Uni,they usually won't mind.

I haven't done any serious study in this field for about 30 years,so you have pretty much "wrung me dry".

Oct 26, 2012
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yes, i've just learned that too. the sidebands are actually needed to reconstruct the original audio accurately. They extend infinitely in both directions, but in the real world you're limited by your available bandwidth. So, FCC "allotted bandwidth" includes not only your deviation range, but also the sidebands! That's a new insight for me. Therefor, the receiver must be demodulating the whole complex waveform containing the sidebands, not just the sinewave at transmission freq. Wow.

"mechanism which allows you to "slope tune" an AM receiver to listen to FM signals."

what!? ok, i'm going to have to research that.

"AM Noise is not a great problem with PLL detectors,but with Ratio Detectors & the like which convert FM to AM so as to detect it,this can be a major source of received noise."

ok, thx, i'm thinking PLL.

"The loss of information still affects all types of detectors,though,appearing as distortion."

"2x Deviation is a fair "rough guide" to deviation for narrowband FM,but is not the whole story in the wideband case."

2x what? the highest freq in your source audio?

commercial broadcast FM is considered wideband, right?

http://www.silabs.com/Marcom Documents/Resources/FMTutorial.pdf

"The dynamic range of any radio system is the ratio between the maximum modulating signal level & the minimum modulating signal level which it can reproduce at the receiver end of the system."

Yes. Ie, difference between the loudest sound and quietest reproducible sound.

"Analysis of FM modulation is not something which you can do on the basis of a few paragraphs in this forum. You need to do your own research"

I'm continuing to read everything i can get my hands on, but there's a lot i don't understand. I come to forums to get help where i don't understand the research.

"I haven't done any serious study in this field for about 30 years,so you have pretty much "wrung me dry".

i highly doubt that, you're a great resource.

thx

Last edited: Sep 16, 2014