Is there a relationship between information data rate and carrier frequency?

[Qacer]

Just doing some reading and it got me wondering. Looking at Shannon-Hartley theorem, http://en.wikipedia.org/wiki/Shannon–Hartley_theorem, it seems that channel capacity is only dependent on channel bandwidth. Assuming that all the variables in the equation are the same, will a 1 Hz bandwidth signal centered at 500 MHz and a signal centered at 20 kHz have the same channel capacity?

My next question, about amplitude modulation especially amplitude-shift keying, if my carrier signal is at 1 MHz, will I be able to modulate it with a digital signal rated at 20 Mbits/sec?

Thanks!

 

[William Gaatjes]

Just doing some reading and it got me wondering. Looking at Shannon-Hartley theorem, http://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem, it seems that channel capacity is only dependent on channel bandwidth. Assuming that all the variables in the equation are the same, will a 1 Hz bandwidth signal centered at 500 MHz and a signal centered at 20 kHz have the same channel capacity?

Hello, i am a bit out of my field (as always ) but you have a few things messed up. What you could do is do some background reading on FM : frequency modulation. On AM : Amplitude modulation in the analog field first. This will give you some understanding about limitations.

http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/RadCom/part9/page1.html

My next question, about amplitude modulation especially amplitude-shift keying, if my carrier signal is at 1 MHz, will I be able to modulate it with a digital signal rated at 20 Mbits/sec?
Thanks!

No.

It is a matter of bandwidth and interference and mixing.
On the math side, when you do that ,(i maybe mistaken thus you have to check this) If you modulate a signal that changes a 1000 000 times with a signal that changes 20 000 000 times you created a mixer.

http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/RadCom/intro.html

http://en.wikipedia.org/wiki/Phase-shift_keying

The reason why high frequencies are used :
The main issue is not the transmitter but the receiver. Your transmitter wil not be the only one. Then there is interference, harmonics, not ideal function filters.

 

[Colt45]

Yep, centre freq is of almost no concern, however it is a lot easier to make oscillators run 100 - 200MHz, than it is to have an LO run from 1 - 20MHz. (one is one octave, where the other is uh.. 4 and a bit? But the single octave one is 5 times the BW! Before PLL's you couldn't get much more than one octave out of most oscs, and even PLL's have their limits) There are a bunch of other caveats, but I'm half asleep...

two.. ain't gonna work. I think you'd want the carrier to be at least twice as fast as your signal. ( I guess ~40MHz+ in this case) [~nyquist-ish]?

If you think back, when you do AM, and you have a 1MHz carrier, and modulate it with a 10kHz signal, it will create a sideband, 10k from the carrier, on either side - So the bandwidth for AM is (modfreq * 2), 20kHz in this case.

Now if You modulate a 100MHz signal with a 20MHz - you'll get sidebands 20MHz in either direction (we'd just call these separate carriers, and the "AM modulator" would be called a mixer...). Now, since you won't be sending 0xAA all day, the effective freq will sometimes be 20MHz, sometimes 10, 5, etc, so you'd have sidebands showing up all over, between +/-20MHz - The thing would suck 40MHz of bandwidth!
That's assuming pure sinewaves too, and you'd have square wave... so there would be harmonics all over the place too. Kind of a barf situation.

Can't say I've ever heard of anyone slapping the key faster than the carrier though, which is about all ASK is used for, afaik...?

If you use something like QAM-256, you can push a byte per symbol, so... slower frequency, so less BW... right?

Someone correct me if I'm wrong, which I could be... I'm just a hobby electronics guy, not an engineer.

 

[William Gaatjes]

Someone correct me if I'm wrong, which I could be... I'm just a hobby electronics guy, not an engineer.

I am an engineer but not in the field of rf. For the most part i acquired what i know just like you from the hobby. Autodidact rules. ^_^

Everybody should have a hobby to withdraw into after a busy day. It gives piece of mind...
Must be a hobby that gives you good karma though... :\

 

[bobsmith1492]

This topic has been somewhat discussed here: http://forums.anandtech.com/showthread.php?t=326236&highlight=shannon

But yes, theoretically it is only the bandwidth that is important, not the actual frequency. There are usually practical limitations, though. For example you'd need a crazy and large antenna for wide bandwidth at extremely-low frequencies.

20mb/sec is a very large throughput. Wi-fi uses about 22MHz bandwidth (http://en.wikipedia.org/wiki/File:2.4_GHz_Wi-Fi_channels_%28802.11b,g_WLAN).svg) to support 54mbps, so you can expect to use a similarly large bandwidth depending on your coding scheme of course. As such you would not be able to center such a signal around 1MHz.

Second, you say "carrier signal at 1MHz." Wi-fi is spread-spectrum, so there is no set carrier frequency. Why would you not use spread spectrum? It provides many benefits... Otherwise, you might be able to tighten up your bandwidth use with a higher-power CW signal as opposed to a spread signal.

 

[esun]

So others have covered the issue of bandwidth vs. carrier frequency pretty well. I just wanted to add another practical consideration for choosing a carrier frequency: some frequencies are absorbed more or less by certain gases (e.g., water vapor, oxygen, etc. absorb certain frequencies quite selectively), so we tend not to avoid strongly absorbed frequencies for terrestrial communications.

Regarding your question of whether you could push 20 Mbps at a carrier of 1 MHz, sure you could. You'd just have to use a very high order modulation. ASK isn't limited to using two levels (binary ASK). You could use 4 billion levels (that is, take every sequence of 32 bits and encode it as a different amplitude in the carrier). It's just that your SNR would have to be so ridiculously high to receive the signal that it wouldn't work in practice.

 

[bobsmith1492]

I asked my mentor/boss at work today about this; he's pretty much the RF expert, having designed anti-radar systems for the military at Northrop and worked at Motorola in the boom of the cell phone era.

He had a couple of things to say. Naturally, you can encode lots of information into an arbitrarily narrow bandwidth assuming you have a good enough signal-to-noise ratio, up to the Shannon limit. For the kind of data rate you're talking about you'd need some kind of cable - over-the-air would probably be out of the question.

The next issue is the transmission medium's coherence bandwidth. Signals at different frequencies propagate differently through the air. So, information that relies basically on the phase relationship between different frequencies is lost unless you use special techniques to recover it. But the practicality of the coding scheme diminishes. Apparently that was a major problem for the original cell phones at 800Mhz; the coherence bandwidth was only about 20KHz. I'd imagine that down at 1MHz, you'd get barely any available bandwidth.