# Bandwidth and datarate

#### jaygatsby

Joined Nov 23, 2011
182
Will someone please explain to me why higher data rates require greater bandwidth, if the modulation remains the same? I understand nyquist theorem and whatnot is involved, but I've been unable to wrap my head around it. To me if you are using a digital modulation scheme, then you use a single, discreet frequency, and key it (on/off) with your data, at a speed determined by your desired data rate. But the bandwidth actually broadens with the data rate.

Thank you

#### crutschow

Joined Mar 14, 2008
26,013
It depends somewhat on the modulation type, but in general the transmitted data appears as sideband frequencies to the center RF frequency. Then the higher the data rate frequency, the higher sideband frequency and the greater the required bandwidth.

#### w2aew

Joined Jan 3, 2012
219
Will someone please explain to me why higher data rates require greater bandwidth, if the modulation remains the same? I understand nyquist theorem and whatnot is involved, but I've been unable to wrap my head around it. To me if you are using a digital modulation scheme, then you use a single, discreet frequency, and key it (on/off) with your data, at a speed determined by your desired data rate. But the bandwidth actually broadens with the data rate.
In your example - ON/OFF keying is used. This is a form of Amplitude Modulation. AM, just like any other modulation, has modulation sidebands that are a function of the baseband signal that is modulating the carrier. Let's use simple audio modulation as an example. If you modulate a carrier with a 100Hz sinewave, you wind up with energy at the carrier frequency, as well as energy at the carrier +/- 100Hz. If you use 1KHz to modulate the carrier, you get the carrier plus energy at +/-1KHz. The "faster" the modulating signal, the more bandwidth is used.

For digitally modulated on/off keying as you described, you will get upper and lower sidebands that are composed of the spectral content of the data. Square-wave type signals have energy at the fundamental datarate, as well as energy at harmonic frequencies. The faster the data and rise/fall times, the more high frequency content exists - therefore the more modulation BW is required.

There are techniques with filtering, etc, and other modulation types to help restrict the BW, but there is no free lunch. Higher datarates require more bandwidth, whether you are doing simply ASK or something more complex like 16QAM modulation.

#### mik3

Joined Feb 4, 2008
4,843
Higher data rates require shorter pulses which in turn require faster rise/fall times to achieve a square wave pulse. Thus, the shorter the pulse duration the higher the required bandwidth in order to keep the shape of the pulse squared.

For example, for a 1000us pulse if the rise/fall time is 1us is not a big problem. However, for a 2us pulse if the rise/fall time is 1us the pulse shape will not be square (not enough time for the voltage to rise/fall). If the rise/fall time is reduced to 1ns the 1us pulse will have a square shape. This requires more bandwidth.

Consider the fourier analysis of a square wave, the faster the rise/fall time is or the sharper the square pulse is, the higher the energy contained in the high frequency components.

#### K7GUH

Joined Jan 28, 2011
190
Consider the lowly funnel. With a one gallon capacity. A 1/4 inch diameter spout will pass the gallon in x units of time, using only the force of gravity to drive the "data". A larger outlet, say 1 inch diameter, will pass the gallon more quickly, to be precise, in x / n units of time. The value of n is related to the diameter of the outlet, the precise relationship is left as an exercise to the reader. I call upon your intuition to realize that if you want to pass a gallon of liquid quickly it takes a spout capable of delivering a stream rather than a dribble.

And FWIW, the simple on-off method is likely to be called ICW, for interrupted continuous wave, for those new to the age of Marconi.

#### jaygatsby

Joined Nov 23, 2011
182
In your example - ON/OFF keying is used. This is a form of Amplitude Modulation. AM, just like any other modulation, has modulation sidebands that are a function of the baseband signal that is modulating the carrier. Let's use simple audio modulation as an example. If you modulate a carrier with a 100Hz sinewave, you wind up with energy at the carrier frequency, as well as energy at the carrier +/- 100Hz. If you use 1KHz to modulate the carrier, you get the carrier plus energy at +/-1KHz. The "faster" the modulating signal, the more bandwidth is used.

For digitally modulated on/off keying as you described, you will get upper and lower sidebands that are composed of the spectral content of the data. Square-wave type signals have energy at the fundamental datarate, as well as energy at harmonic frequencies. The faster the data and rise/fall times, the more high frequency content exists - therefore the more modulation BW is required.

There are techniques with filtering, etc, and other modulation types to help restrict the BW, but there is no free lunch. Higher datarates require more bandwidth, whether you are doing simply ASK or something more complex like 16QAM modulation.
I don't get it. If I wanted to 'key' something to you using a flashlight, i'd just turn it off and on at my datarate. There would be no sidebands. I don't understand...

#### thatoneguy

Joined Feb 19, 2009
6,359
I don't get it. If I wanted to 'key' something to you using a flashlight, i'd just turn it off and on at my datarate. There would be no sidebands. I don't understand...
Then you are using the maximum bandwidth for the lowest signal rate. Worse case scenario, basically.

For an analog line, learning about QAM will help you understand why ICW (flashlight on/off, morse code, etc) is a waste of bandwidth. You can get 6bits/Hz instead of 1 bit every hundred cycles in the morse code scenario.

#### crutschow

Joined Mar 14, 2008
26,013
I don't get it. If I wanted to 'key' something to you using a flashlight, i'd just turn it off and on at my datarate. There would be no sidebands. I don't understand...
But you will have sidebands. Switching the light off and on will add sideband sum and difference frequencies to the fundamental frequency of the electromagnetic light wave as determined by the Fourier frequencies of the risetime, falltime, and period of the light pulse. Granted it will be so small that you likely can't measure it with a practical instrument, but never-the-less it is still there.

#### w2aew

Joined Jan 3, 2012
219
I don't get it. If I wanted to 'key' something to you using a flashlight, i'd just turn it off and on at my datarate. There would be no sidebands. I don't understand...
I think you will agree that simple Amplitude Modulation contains modulation sidebands - upper and lower sidebands that mirror the spectrum of the baseband signal that is modulating the carrier.

On-Off keying, or OOK modulation, is simply an extreme case of AM. Thus, it will have modulation sidebands that mirror the spectral content of the digital (on-off) signal that is modulating it. The spectrum of this digital signal is a function of the signalling rate (datarate) and the rise/fall time.

#### gojirasan

Joined Dec 17, 2011
22
But you will have sidebands. Switching the light off and on will add sideband sum and difference frequencies to the fundamental frequency of the electromagnetic light wave as determined by the Fourier frequencies of the risetime, falltime, and period of the light pulse. Granted it will be so small that you likely can't measure it with a practical instrument, but never-the-less it is still there.
So the size of those sidebands are proportional to the rise and fall times of the pulse? Let's say you had a pulsed green laser with very short pulse times. Maybe only a few attoseconds. That would correspond to a bandwidth of 3 x 10^18 Hz. Would your green laser become a white laser?

One thing that I'm not clear on when it comes to this bandwidth stuff is why amplitude modulation results in a change in frequency. I get that mixing 2 signals gives you the sum and difference of the baseband signal in the carrier, but I don't quite get why. Something to do with the nature of multiplying two sine waves together? It would be nice if there were some way of changing the amplitude of an EM wave without changing its frequency.

#### crutschow

Joined Mar 14, 2008
26,013
So the size of those sidebands are proportional to the rise and fall times of the pulse? Let's say you had a pulsed green laser with very short pulse times. Maybe only a few attoseconds. That would correspond to a bandwidth of 3 x 10^18 Hz. Would your green laser become a white laser?

One thing that I'm not clear on when it comes to this bandwidth stuff is why amplitude modulation results in a change in frequency. I get that mixing 2 signals gives you the sum and difference of the baseband signal in the carrier, but I don't quite get why. Something to do with the nature of multiplying two sine waves together? It would be nice if there were some way of changing the amplitude of an EM wave without changing its frequency.
You would get a shift in color but only for a few attoseconds.

Incidentally amplitude modulation doesn't change the carrier frequency, it adds sum and difference sideband frequencies next to the carrier frequency. A spectrum analyzer will show the carrier frequency and the sideband frequencies.

It's a fundamental information transmission law that the transmission of information requires bandwidth proportion to the amount of information transmitted. Thus your wish has to be put in the same realm as over-unity power devices.

#### gojirasan

Joined Dec 17, 2011
22
You would get a shift in color but only for a few attoseconds.
Well in my example the pulse itself is only a few attoseconds.

crutschow said:
Incidentally amplitude modulation doesn't change the carrier frequency, it adds sum and difference sideband frequencies next to the carrier frequency. A spectrum analyzer will show the carrier frequency and the sideband frequencies.
So you end up with 3 distinct monochromatic waves at 3 different frequencies? The frequencies in between the sideband frequencies are not used? In the pulsed laser example you would just end up with 3 distinct colors? If you examined the pulse with a spectrometer you would end up with 3 distinct lines? One monochromatic green and one at each sideband frequency? This leaves me confused as to how AM uses up bandwidth. In that example you could use an ultra narrowband receiver with 3 channels. One for each sideband frequency and one for the carrier frequency. Unless the sideband frequencies dynamically change in frequency along with the change in amplitude. If you were watching the laser pulse with a spectrometer would the sideband lines seem to change color with time?

crutschow said:
It's a fundamental information transmission law that the transmission of information requires bandwidth proportion to the amount of information transmitted. Thus your wish has to be put in the same realm as over-unity power devices.
But you seem to be saying that my wish is actually the truth. Amplitude modulation doesn't affect the frequency of the carrier wave. I am still shocked by this. It is potentially really good news for me even though it does seem to violate the TAINSTAFL law.

I have no wish to violate Shannon-Hartley. In the example I am thinking of no information is being sent intentionally. The only difference between my example and an unmodulated CW carrier is the length of the on time which would be short, but would not vary in duration or spacing.

#### thatoneguy

Joined Feb 19, 2009
6,359
This leaves me confused as to how AM uses up bandwidth. In that example you could use an ultra narrowband receiver with 3 channels. One for each sideband frequency and one for the carrier frequency.
A conversation on SCSSB upper band can occur at the same time as a different conversation on SCSSB lower band.

Now, since two data streams are used in the same bandwidth as a full modulated AM broadcast, that would imply the AM broadcast is at least 50% inefficient, wouldn't it?

Look up a few posts to my link on how QAM works. It will make a lot more sense. (post #7)

#### xylon89del

Joined Dec 28, 2011
17
Well in my example the pulse itself is only a few attoseconds.

So you end up with 3 distinct monochromatic waves at 3 different frequencies? The frequencies in between the sideband frequencies are not used? In the pulsed laser example you would just end up with 3 distinct colors? If you examined the pulse with a spectrometer you would end up with 3 distinct lines? One monochromatic green and one at each sideband frequency? This leaves me confused as to how AM uses up bandwidth. In that example you could use an ultra narrowband receiver with 3 channels. One for each sideband frequency and one for the carrier frequency. Unless the sideband frequencies dynamically change in frequency along with the change in amplitude. If you were watching the laser pulse with a spectrometer would the sideband lines seem to change color with time?

But you seem to be saying that my wish is actually the truth. Amplitude modulation doesn't affect the frequency of the carrier wave. I am still shocked by this. It is potentially really good news for me even though it does seem to violate the TAINSTAFL law.

I have no wish to violate Shannon-Hartley. In the example I am thinking of no information is being sent intentionally. The only difference between my example and an unmodulated CW carrier is the length of the on time which would be short, but would not vary in duration or spacing.
May be some mathematics will show you:
Take carrier angular frequency=wc; modulating angular frequency=wm

Carrier signal, C(t)=A*cos(wc*t)
Modulating signal, M(t)=A*cos(wm*t)

The amplitude modulated output,
O(t)=(A+M(t))*cos(wc*t)
O(t)=(A+A*cos(wm*t))*cos(wc*t)
O(t)=A*cos(wc*t)+A*cos(wm*t)*cos(wc*t)
O(t)=A*cos(wc*t)+A/2*cos((wc+wm)*t)+A/2*cos((wc-wm)*t)

So, in the result, you can see there is frequency component, wc, wc+wm and wc-wm

The same concept can be applied to all similar cases.

#### gojirasan

Joined Dec 17, 2011
22
So for a 1000 Hz carrier wave amplitude modulated with a 20 hz sine wave you would end up with 3 distinct waves with frequencies of 980, 1 Khz, and 1020 Hz and that's it? This would seem to imply that you could transmit unmodulated carrier waves anywhere between 981 and 999 Hz and between 1001 and 1019 Hz without causing interference (assuming no carrier drift). Most of the 'bandwidth' for an AM signal seems to be unused and empty. I really have to look into receiver design and see why you couldn't just design one with 3 notch filters allowing for much better SNR than you could get with FM or PM. I'm sure there must be some reason why you can't do this. In general nature doesn't tend to like free lunches.

#### xylon89del

Joined Dec 28, 2011
17
So for a 1000 Hz carrier wave amplitude modulated with a 20 hz sine wave you would end up with 3 distinct waves with frequencies of 980, 1 Khz, and 1020 Hz and that's it? This would seem to imply that you could transmit unmodulated carrier waves anywhere between 981 and 999 Hz and between 1001 and 1019 Hz without causing interference (assuming no carrier drift). Most of the 'bandwidth' for an AM signal seems to be unused and empty. I really have to look into receiver design and see why you couldn't just design one with 3 notch filters allowing for much better SNR than you could get with FM or PM. I'm sure there must be some reason why you can't do this. In general nature doesn't tend to like free lunches.
notch filter is a band stop filter, i think you probably want to say bandpass filter.

Assume you can do it, but you are increasing the cost at receiver. If you just increase the transmitting power, the cost might be lower than implement 3 bandpass fitler at the receiver.

#### gojirasan

Joined Dec 17, 2011
22
xylon89del said:
notch filter is a band stop filter, i think you probably want to say bandpass filter.
Oops. Three narrow bandpass filters.

xylon89del said:
Assume you can do it, but you are increasing the cost at receiver. If you just increase the transmitting power, the cost might be lower than implement 3 bandpass fitler at the receiver.
Increasing the transmitter power is not an option for the application I'm thinking of. And the cost of the receiver is not a factor. I have been getting contradictory info on whether the sidebands themselves are monochromatic or wideband. The triple filtered AM receiver idea is only relevant if the sidebands are either monochromatic or very narrow band. If you have continuous RF energy between the sideband frequencies and the carrier frequency then of course it's not going to work.

#### crutschow

Joined Mar 14, 2008
26,013
So for a 1000 Hz carrier wave amplitude modulated with a 20 hz sine wave you would end up with 3 distinct waves with frequencies of 980, 1 Khz, and 1020 Hz and that's it? This would seem to imply that you could transmit unmodulated carrier waves anywhere between 981 and 999 Hz and between 1001 and 1019 Hz without causing interference (assuming no carrier drift). Most of the 'bandwidth' for an AM signal seems to be unused and empty. I really have to look into receiver design and see why you couldn't just design one with 3 notch filters allowing for much better SNR than you could get with FM or PM. I'm sure there must be some reason why you can't do this. In general nature doesn't tend to like free lunches.
Yes, much of the bandwidth is not used, but it is not necessarily all empty. Generally your are transmitting information with many frequencies and these generate a corresponding number of different sideband frequencies. For example, the spectrum of a pulse has a wide band of frequencies as per Fourier analysis, not a single frequency.

But your thought about wasted bandwidth is correct. Since the carrier carries no information, and the two sidebands carry duplicate information, single-sideband (SSB) modulation was invented. It suppresses the transmission of the carrier and one of the sidebands, leaving only one sideband. It's commonly used by HAMs to maximize their transmission range with the fixed amount of transmitted power they are allowed.