Channel Spacing and Channel Bandwidth

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gatekeep

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This is sort of a more technical question (I think)...heres my question:

Lets say we have a frequency of 460.4125 and the license specifies that the emissions of: 11K0F3E ... or 11.0khz bandwidth analog FM voice.

Is the spacing of the channel based specifically on the .4125 portion of the frequency (in that it is set in 12.5khz steps)? And what part does the bandwidth actually play?

I know this sounds like a new guy'ish question, don't get me wrong, I'm very familar with radios ... but I've always had a problem wrapping my head around if there was an actual connection between channel spacing and channel bandwidth.
 

jon_k

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The bandwidth is a measure of how much splatter you're going to get above and below the specific frequency you're transmitting on. What that means is although you're transmitting on say 110.5mhz your bandwidth is the range of frequencies your modulated carrier will occupy. You'll leak your modulated carrier on a radiant scale above and below 110.5mhz.

On VFO's that allow fine tuning and let you ignore the spacing, you can witness this by tuning into a signal and slowly rotate the dial away from the center broadcast frequency. You will hear the modulated transmission, albeit less and less as you get further away.

This is the way I've understood it.

When you use terms like 11K0F3E it's over my head. I don't know what OF3E means. I do know all this is covered in the General amateur radio test. I've done some light studying however and I'm not fully educated on the subject yet.
 
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Raccon

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Channel spacing - the difference between two adjacent channels. E.g. if Channel 1 is on 500MHz and the next channel on 501MHZ, then the channel spacing is 1MHz. (500 and 501MHz are also called the center frequencies)

Channel bandwidth - the "width" of the signal on one particular channel, i.e. if the bandwith is 500kHz then the frequency range on aforementioned Channel 1 would occupy 500MHz +/-250kHz (measured at 3dB from the peak).

In many systems the channel spacing is equal to the bandwidth though as it's the most efficient way of using the frequency band available.
 
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zz0468

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And what part does the bandwidth actually play?
It makes more sense to answer your questions in reverse order...

The bandwidth designator defines what's called the "occupied bandwidth" of a transmitted signal. If your carrier on 460.4125 had absolutely no modulation on it, it's bandwidth would be zero. Applying voice or data increases the bandwidth, the limit of which is specified on the station license, in your stated example, 11 KHz. That means that the bandwidth occupies the space 6.5 KHz above, and 6.5 KHz below the center frequency.

Is the spacing of the channel based specifically on the .4125 portion of the frequency (in that it is set in 12.5khz steps)?
Ok. Now you know that your 11K0F3E modulated signal takes up space, and how much. If channels are spaced too close, the adjacent channels would interfere with each other. If spaced too far apart, spectrum gets wasted. So, the channel spacing you see assigned takes the occupied bandwidth into account as it tries to strike a happy balance between acceptable adjacent channel performance, and efficient spectrum usage.

p.s. I like your tag line.
 

WayneH

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Here's a link to the FCC page describing FCC designators. F=Frequency modulated, 3=analog, single channel, and E=telephony.

The full designator in this instance means you have a frequency falling on 12.5kHz spacing, utilizing 2.5kHz deviation (aka "narrowband" operation) and running FM analog voice. Even though 2.5k(x2) doesn't add up to the full bandwidth it's what it really equates to in simplistic terms. There's a bit of math involved in determining the bandwidth and it isn't the deviation times two. Maybe someone else can explain the calculations.

zz0468, 6.5 + 6.5 equals 13, not 11. Did you mean 5.5?
 
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AK9R

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Actually, the math for determining bandwidth of an FM signal can be simplified to some pretty simple algebra.

Bandwidth = 2 x ( Modulation frequency + Peak deviation )

Modulation frequency is the highest frequency of the sound you want to pass through the system. For voice communications, modulation frequency is generally accepted to be 3000 Hz. In other words, the range of audio frequencies that will pass through the system tops out at 3000 Hz. This goes back to studies done at the Bell Labs when they were trying to figure out how much bandwidth a telephone system needed in order to be intelligible and sound natural to the listener.

So, if you have a radio system where the peak deviation is 2.5 kHz, the formula works out like this:

Bandwidth = 2 ( 3000 + 2500 ) = 2 ( 5500 ) = 11000 Hz = 11 kHz

This bandwidth number is the first part of the FCC emission designator, hence "11K0".

Older "wideband" FM systems have more bandwidth because they are using 5 kHz peak deviation.

Bandwidth = 2 ( 3000 + 5000 ) = 2 ( 8000 ) = 16000 Hz = 16 kHz

That's why the emission designator for the older systems starts out with "16K0".
 

gatekeep

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p.s. I like your tag line.
So do I ;). I actually like that line you have, its pretty humorous.

Bandwidth = 2 x ( Modulation frequency + Peak deviation )
After doing some rudimentary research, and guess work, you say that its commonly accepted to use 3khz as the modulation frequency ... but for systems with a 20khz channel bandwidth the math doesn't work out right?

For instance, we'll solve for peak deviation:
20khz = 2 * ( 3khz + Δf )
10khz = ( 3khz + Δf )

After we subtract off the 3khz from both sides we end up with: Δf = 7khz ...

On a side note, I've found channel spacing seems to be relative to the peak deviation ... hence, 2.5khz peak deviation * 5 = 12.5khz ... this math seems to work for ALL the channel spacing's and peak deviations ...

1.25khz * 5 = 6.25khz
2.5khz * 5 = 12.5khz
5khz * 5 = 25khz

Back to the topic at hand, with that said a peak deviation of 7khz doesn't make sense as the relative channel spacing would be ... 7khz * 5 = 35khz ?

Unless I'm missing something ...
 
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WayneH

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What I have in my notes:

16k0 = 5kHz on 25kHz chan
11k0 = 2.5kHz on 12.5kHz chan
8k10 = 3.6kHz on 12.5kHz (C4FM)

That was based on licensed information. I've also seen 20K0 for all bands using 25kHz spacing, 10K0 for digital on 12.5, 13K6 for all bands using telemetry (F1D), 8K60 for F1D telemetry on 12.5 spacing, 14K0 for analog and 8K70 for Motorola "LSM" IMBE format. I haven't attempted to figure the math on these..
 

zz0468

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Back to the topic at hand, with that said a peak deviation of 7khz doesn't make sense as the relative channel spacing would be ... 7khz * 5 = 35khz ?

Unless I'm missing something ...
Be careful about reading too much into it, as well as missing things. First, Carson's rule is merely an approximation of occupied bandwidth based on a complex waveform, as opposed to a single tone. It estimates the bandwidth for approximately 98% of the energy contained in the FM sidebands. Since theoretically an FM signal has sidebands out to infinity, you have to stop somewhere when it comes time to calculate. With a single voice circuit, Carsons is close enough.

More complex modulation requires more precision in calculating the occupied bandwidth. So, there are other formulas for calculating FM bandwidth. Using Carson's rule to calculate the occupied bandwidth of a stereo FM broadcast transmitter, for example, will lead you far astray. Even further astray if your interest is in an analog point to point circuit with lots of multiplexed channels.

One thing we haven't factored into current channel spacings is history. Many of the bands have been split, then split again. The 15 KHz and then the 7.5 KHz channel spacing on VHF is more rooted in history than anything else. On the UHF bands, the channel spacing went from 25 KHz, to 12.5 KHz, and now to 6.25 KHz.

Going back to your comment quoted above, bear in mind that not all radios will specify 3 KHz as the maximum modulating frequency, nor will voice be the only modulation applied to the transmitter. Many licenses will show several bandwidths and modulation formats to account for voice, data, and various signaling schemes, all from the same radio.

The existing and future channel spacings take ALL of the above into account.
 
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