dillon@overload.Berkeley.CA.US (Matthew Dillon) (05/12/91)
In article <1252@cnw01.storesys.coles.oz.au> iann@cnw01.storesys.coles.oz.au (Ian Nicholls) writes: >In <dillon.7375@overload.Berkeley.CA.US> dillon@overload.Berkeley.CA.US (Matthew Dillon) writes: > >> A normal phone line has a bandwidth of around 38KBaud. As any >> RF/electrical engineer will tell you, it's nearly impossible to utilize >> all the available bandwidth of a medium. It's hard enough to utilize >> half of it, which is what 9600bps (V.32) modems do now (9600bps full >> duplex = 19.2KB bandwidth). The best you will ever see on a phone line >> is probably around 19.2KB uncompressed. > >I thought that the higher speed modems used a different baud from bps. > >That is, a 2400 bps modem still sends at 1200 baud, it just sends two bits >at a time (by phase-shifting; each state uses a different quarter-phase ). > >The 9600 buad modems use some sort of trellis encoding, so that sixteen >states can exist, meaning four bits at a time get sent, but still at 2400 >baud (states per second). > >From this basis, higher speeds can be possible with a more sensitive >discriminator circuit, to detect more states. I don't know what the >ultimate speed would be, but it won't be cheap. > >My reference is the Byte magazine, sometime in the past three years. You'll >have to look up an index if you want the exact issue. >-- >"If it's OK to start by stealing pencils, where then do we draw the line?" >Ian Nicholls Phone : +61 3 829 6088 Fax: +61 3 829 6886 \_o_/ >Coles/Myer Ltd. E-mail: iann@cnw01.storesys.coles.oz.au \\| >L1 M11, PO Box 480, Glen Iris 3146, Australia \\ This is a common mistake many people make. Actually, it might be partially my fault, I have a tendancy to call the maximum theoretical 'bits per second' rate over a medium 'bandwidth', which has nothing to do with frequency bandwidth. Basically there are two factors that limit the amount of data you can get through any given medium: (1) frequency bandwidth of the medium .. on the order of 3KHz for a phone line, more if you equalize it. (2) noise on the medium There is a theoretical minimum noise governed by Boltzmann's noise equation, energy = 4KTdF (4 * Boltzmann's constant * temp. in kelvin * frequency bandwidth). At 3KHz and room temp. this is 50nV at 50ohms impedence. However, no circuit is ever this good. (now you know why the receiver for radio telescopes is generally submerged in liquid nitrogen or liquid helium). Generally noise is described in terms of the signal to noise ratio, or SNR... basically the amount of signal over the amount of noise in dB. A phone line has around a 30dB SNR == 1000:1 signal over noise. There is a formula, called Shannon's "capacity" formula which takes both bandwidth and S/N into account. C = W Log2(1 + S/N) C = capacity, bits per second W = bandwidth S/N = signal over noise. 30dB == 1000 S/N (dB = 10 log S/N) At W=3KHz, S/N=1000 you get around 30Kbps. This is a good approximation of the theoretical maximum possible over a line with the above characteristics. Note that as your signal-to-noise gets better, it is possible to get more out of the same frequency bandwidth, but you can never get better than Boltzmann's equation over a wire due to the inherent noise that exists at the atomic level. A typical CD player has an SNR of around 140dB. Humans cannot generally hear noise below 90db (p.s. theoretical nuts, I am not putting in minus signs for this tutorial). But, as I said, 30Kbps for 3KHz bandwidth and 30dB SNR is the theoretical maximum... it's nearly impossible to device a circuit that is actually able to UTILIZE a channel to that point. Typically, it is cost effective to get a little over half way there or on the order of 19.2Kbps. Now, there are several methods used to utilize more of your bandwidth without falling into the noise. The best one found so far is what is known as phase modulation. that is, you have a modem at some carrier frequency and instead of switching frequencies to pass information (FSK) you simply change the phase of the carrier (PSK). The rate at which you change the phase is called the BAUD, and the number of possible phase changes per baud determines the number of BITS PER BAUD. The BAUD is not necessarily related to the carrier frequency but is generally some integral multiple of it. Thus, a modem using a 2400 Hz carrier that changes the phase once per cycle runs at 2400 BAUD. If the modem is only able to change the phase 180 degrees (two possible phases), then only one bit per baud is transmitted. (p.s. these are contrived examples and do not reflect the actual algorithm used in 2400bps or greater modems) If, on the other hand, a modem is able to change the phase to an arbitrary 90 degree vector (0, 90, 180, 270), that's four possible symbols or 2 BITS PER BAUD, or 4800bps. So, you might ask, what prevents you from using 256 difference phases? The answer is that both FREQUENCY BANDWIDTH and NOISE limit how fast you can change phase. If you take a fourier series of two cycles with a phase change in the middle you will see what I mean. Changing phase basically glitches the output through, in the case of a phone line, a 3Khz low pass filter which will stretch some parts of the glitch, meaning that it takes more time to stabilize to the new phase even though it is at the same frequency. You can think of your frequency bandwidth (3KHz) as limiting the carrier frequency (2400Hz in my example). NOISE limits the number of phases you can have more directly. If you choose, say, 16 phases (4 bits per baud) and look at the zero crossing, you will note that they get pretty close together (take one cycle and mark it into 16 sections). ********* ** ** ** ... /-------* * * dV | * * * | * * * \----*--*--------------------------------- To be able to discriminate between the above two phases, the amount of noise cannot be greater than 1/2 dV, otherwise you can get a zero crossing due to noise and not be able to tell which phase is the right one. So there you have it. Frequency bandwidth limits the carrier frequency. A 3Khz bandwidth does NOT mean you can have a 3KHz carrier, by the way, you need enough slop so the high frequency elements created by the phase change will stabilize within one cycle of the carrier (or however many cycles you choose for your 'BAUD', it need not be one), and noise also limits the number of phases the receiver will be able to discern without error. In terms of bandwidth usage, phase modulation does a much better job than FSK which is why higher speed modems use it. This is simple to test... pick up the receiver of your phone connected to your modem while connected at 300 baud. What do you hear? A tone... obviously not much bandwidth is being used since a tone has a single term in a fourier series. FSK utilizes two frequencies and a few other elements due to switching between them. Now connect at 2400bps and pick up the receiver. What do you hear? Well, it sounds sort of like white noise. A 9600bps modem will sound even MORE like white noise. Why? What is the frequency spectrum of white noise? Yup, you got it... uniform energy over the entire bandwidth. In otherwords, more of the available bandwidth is being used to carry data. The ultimate goal of modem modulation techniques is to use as much of the available bandwidth as possible. V.32 uses half the theoretical bandwidth (19.2Kbps full duplex = 9600bps in each direction) and it isn't easy. -- This should also answer questions anybody has on leased lines and other dedicated lines. Generally you can get MUCH greater bandwidth and LESS noise out of these lines. Something like ethernet has a coaxial cable to play with -- easily 150MHz of frequency bandwidth though a coax (more, even), but due to ethernet being base band, barely 40Mhz of it is used for a 10MBit transmission rate. (base band == no carrier, but the sharpness of the edges you get putting square waves on the cable depends both on frequency bandwidth and on group propogation delay... different components of the fourier transform of the square wave will travel at different velocities down the wire). -- P.S. for all you RF engineers at there, keep in mind that I'm trying to make this a tutorial and am NOT bringing up problems associated with interference (like why trellis encoding is better than etc etc etc..), Gaussian noise distributions, etc, etc... group delay, intersymbol interference, ... -Matt -- Matthew Dillon dillon@Overload.Berkeley.CA.US 891 Regal Rd. uunet.uu.net!overload!dillon Berkeley, Ca. 94708 USA