Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!uunet!seismo!sundc!pitstop!sun!decwrl!labrea!jade!ucbvax!SIMTEL20.ARPA!W8SDZ From: W8SDZ@SIMTEL20.ARPA (Keith Petersen) Newsgroups: comp.dcom.modems Subject: What is Max speed possible on phone lines? Message-ID: Date: Tue, 3-Nov-87 01:51:00 EST Article-I.D.: SIMTEL20.KPETERSEN.12347581516.BABYL Posted: Tue Nov 3 01:51:00 1987 Date-Received: Fri, 6-Nov-87 22:45:46 EST Sender: daemon@ucbvax.BERKELEY.EDU Organization: The ARPA Internet Lines: 270 [From SIMTEL20 file PD:WHATBAUD.DOC] What is Baud? Anyone reading technical echomail may have noticed a large number of messages about baud rates, bit rates, band widths, and modulation techniques involved with modems. There is a fair amount of confusion relating to baud rate verses bit rate and how they are limited by the telephone line band width. This is nothing new, texts on the subject generally avoid the term "baud" except within the narrow context where it is germane. This article will define some of the various terms used in data communications, and discuss limitations of phone lines to communication speed. Serial transmission of data is the most common method of moving data over distance, and the most common way of interfacing serial devices to each other is RS232. The essence of RS232 is signal levels which represent ON or SPACE levels, and OFF or MARK levels. ON is any voltage between +3 volts and +15 volts while OFF is -3 to -15 volts. The signal shape is really a square wave centered at zero volts and is a baseband signal. A baseband signal is one whose spectrum extends down to zero hertz, or near zero. The signal is polled at regular intervals to determine its voltage, and therefore the data it contains. RS232 has only the two voltage levels defined so it is a binary coded signal. Besides signal shape and levels, RS232 defines a number of parallel signals such as "clear to send" and "data terminal ready". Some of these signals are status flags such as "carrier detect", while others are meant as flow control, such as "data terminal ready" or "request to send". Since a typical modem provides only the transmit and receive functions, the flow control must be done within the data stream. Some modems however send data as packets with error control (akin to XMODEM) that can recreate all of the hardware signals so as to make a distant terminal appear to be hard wired. Regular phone lines were designed for voice communications, but due to their wide use and therefore low cost, they have been widely used for data communications. A baseband signal such as is found in RS232 doesn't lend itself to phone lines since they don't have frequency response down to D.C. or zero hertz. When voice grade phone lines were designed the band of frequencies they had to pass was determined by the nature of human speech. Very low frequencies (below 300 hz) and higher ones (above 3000hz) were found to be unnecessary for voice recognition at the receiving end, as a result the total "BAND WIDTH" available to a phone user is only around 2700 hz. BAND WIDTH when used to describe frequency response is the difference in hertz between the high and low, half power frequencies. In electrical systems, power dissipated across a load (or resistance) in terms of voltage is: V * V / R. Where "V" in this case will be the amplitude of the sign wave being applied to the circuit. In between the high and low half power frequencies there will be a frequency where the amplitude of the response wave will be maximized, call that voltage Vm. The half power points will be reached when V=Vm/sqrt(2). The output power at that point would be Vm * Vm / (2 * R) which is one half the mid band power. The cause for the fall off of power at different frequencies is due to capacitive and/or inductive elements in the circuit. In phone lines capacitance comes naturally in parallel, that is it tend to shunt the signal to ground. In this configuration the higher the frequency the lower the "resistance" will be. Inductance is added on purpose by the phone companies in the form of loading coils which are added to decrease signal attenuation in the mid frequencies. In any case the band width of a voice grade line is strictly limited so that many calls can be stacked on top of each other, in order to use transmission lines more effectively. Data equipment must strive to make the best use of this narrow band width. There is a hard limit to the amount of data that can be sent through a telephone line as will be seen later. The signal type of choice to carry data through phone lines is the sine wave. A sine wave has but one frequency associated with it. This means that if its frequency is within th band width of the line carrying it, then the received sine wave will not have its shape altered due to clipping of the high frequency components. This can't be said for the square or triangular waves which requires an infinite band width to fully describe them. The sine wave is simply defined: v= A * sin( w*t + p) A is the amplitude (in units of volts for this exercise) w is the frequency which must be in radians per second t is time in seconds p is the phase angle in radians Information can be encoded by the sine wave in three different ways. By altering "A" which is amplitude modulation (AM), by altering "w" which is frequency modulation (FM), or by altering "p" which is phase modulation (PM). There are mixed modes which come into use in the more exotic modem schemes, used to get the really high bit rates. FSK or frequency shift keying was the most widely used method for data transfer through modems. This is a FM process whereby a RS232 MARK would be represented by the presence of one frequency while a SPACE would be indicated by another frequency. Now is the time to introduce the term BAUD. A "BAUD" is the time interval in which data is carried, that is the minimum time in which a signal holds a single state which the receiver is to recognize and convert into data. The baud rate is how many BAUD times occur in a second. The baud rate is NOT the same as the bit rate as will be seen later in multiple state modulation. In FSK type modems (Bell 103) the baud time happens to be the same as the bit rate since each signal state encodes a single bit. Many would think that the baud rate is limited to highest frequency available to be transmitted (3000 hz) but this is not necessarily so. Nyquist showed in 1928 that the maximum signal change rate (baud rate) for a band width "W" would be 2*W baud. This is called the Nyquist rate and is an upper limit that assumes no inter-symbol interference. This could be visualized by considering a sine wave. Each cycle has a positive and negative part. The amplitude in each part could be independently altered while still having a sine wave, therefore a 1200 hz signal could be changed 2400 times a second which is 2400 baud. This type of change (AM) is not very useful in phone lines since it is the type of change most commonly caused by natural phenomena. In Bell 103 the baud rate is commonly 300 which is over 3.5 cycles at the lowest carrier frequency. The practical considerations of detecting frequency changes requires about 1.5 cycles so 300 baud is some what conservative. PSK or phase shift keying gets by the frequency barrier that keeps FSK from producing the higher bit rates. In PSK (a PM method) the only parameter in the sine wave changed each BAUD is the phase angle "p". The Bell 212A modem specification uses a four level phase modulation technique. The term four level means that four different phases are used and detected by the receiver during each BAUD. The number of bits an M level state can represent is n=log2(M) or log(M)/log(2). A four level state can represent two bits during each baud. In the 212A specification +90 degrees would be 00, 0 degrees 01, +270 degrees 11, and +180 degrees 10. The 212A baud rate is 600 which means the bit rate would be: bit rate=600 BAUD/second * 2 bits/BAUD= 1200 bits/second To increase the bit rate to the next state would require 3 bits/baud or 8 phases. To get 2400 bps using such a scheme would require 16 different phases (22.5 degrees apart). The problem here is that one class of noise present in phone lines called "phase jitter" can cause phase errors up to and sometimes over 30 degrees. To avoid the bulk of this type of noise the phase angle difference should be kept above this amount. The 2400 baud modems common today use a form of QAM (quadrature amplitude modulated). This method uses a combination of two waves with different amplitudes to get the required 16 levels. A QAM signal can be expressed in equation as follows: s(t)=a(t)cos(wt+p)+b(t)cos(wt+90+p) a(t) is the in-phase modulating wave form while b(t) is the quadrature modulating wave form. During each baud a(t) and b(t) are constants so the equation simplifies to: s(tn)=c*cos(wt+theta+p) {p is a single arbitrary phase angle tn stands for a specific baud time c=sqrt(a*a+b*b) theta=atan(b/a)} The new pure sine (cosine) wave has amplitude and phase differences which can multiply the number of states possible. If there are 4 values for amplitude and 8 values for phase then the signal could have 32 different states or five bits. The random variations in phase "p" has less effect the outcome since it effects both waves the same. The phase difference in the resultant wave is due to the interaction of the two wave forms. QAM is the method used to get up to 9600 baud out of a phone line. Other types of noise are present in a phone system, and are mostly due to switching and cross over with other wires. The error rate at the higher bit rates would be unacceptable if there weren't some error recovery used. This is now quite easy to do from a hardware standpoint, since the memory and processing power needed to do it takes a small amount of space and cost little enough to make the increase in bit rate worth it. The ability for high speed modems to run will increase due to another reason. More and more fiber optic phone line will replace conventional ones. These are immune from many of the noise sources that effect copper wires, sources such as RF and magnetic fields. The ultimate bit rate that could be "pumped" through a phone line is fixed by the band width AND the signal to noise ratio. Shannon's law relates random bit transmissions/second to band width and signal to noise ratio. It is derived from the concept of entropy. Entropy is a measure of randomness in a system. It is really a thermodynamic property but has applications in information theory. The maximum bit rate for a channel with signal power S and noise power N is given by: C=BW log2(1+S/N) where BW is the band width, S is the signal power and N is the noise power. With a typical band width 2600 hz and a typical signal to noise ratio of 30db (or 1000/1) the bit rate would be: bit rate=2600 * log2( 1001 ) or 25,914bps The noise factor is assumed white or Gaussian. This kind of noise is unavoidable in electrical systems. In fact "N" can be calculated by: N=kTW where k=1.37e-23 joule/degree T is absolute temperature (Kelvin) W is the band width in HZ This product gives "N" in terms of joules per second or watts. At room temperatures noise would be on the order of 1e-17 watts over a 2600 hz band width. If a phone signal were just 0.1 watts the signal to noise ratio could be as high as 160db. In practice it is about 30db so it can be expected that the signal to noise ratio will increase in the future so that the top bit rates will increase, and this increase will happen without an increase of the band width available. One last problem to consider with the high speed modems is compatibility. To get 9600 bps from a 600 baud signal would require 65,536 levels in a state. There is no obvious way in which to assign a level to a 16 bit pattern so the manufacturer must invent an "ALPHABET" for that conversion. Until an alphabet is standardized as well as error recovery techniques there is simply no way the modems will talk to each other. GLOSSARY: Alphabet: A table to convert signal states into characters they represent Amplitude modulation: Where information is encoded by changes in amplitude only. Band width: Range of frequencies within the half power limits. That is the difference between the two -3db frequencies. Baseband: The signal at its original frequency and shape. Baud: The minimum time where all signal parameters are held constant. Baud rate: The number of times the basic signal can be changed per second. Bit rate: The number if bits per second passing through a channel. In a modem it is the baud rate times the number if bits per baud. Decibel (db): 10 * log10(p2/p1) where p2 is referenced to p1. Both p1 and p2 represents power. For voltage db is calculated 20 * log10(v2/v1) Frequency modulation: Where information is encoded by changes in the carriers frequency. FSK: A way of represents data by a discrete change in frequency of the carrier. Hertz: Number of events per second. Modulation: The process of varying a signal according some aspect of another signal. Phase: The angular displacement of a cyclic signal In a sine wave Y=A sin(wt+p) p is the phase. Phase modulation: Technique of changing phase of signal to represent changes of the baseband signal. References: 1.*Clark, A.P., 'Principles if Digital Data Transmission' 2nd ed. (1983) 2. Martin, James, 'Telecommunications and the Computer', (1979) 3. 'IBM PC Technical Reference', (July 1982) 4. 'Hayes Smartmodem 1200 manual' *Reference (1) gives the most technical detail and over 500 other specific references. -----------------------------------------------------------------