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Data Communications
Transmission System: Structure and Function
Nathaniel Kinsey
Hamilton College
The purpose of this discussion is to outline the major components and theories that comprise any data transmission system. Digital signaling and analog signaling are discussed as are the differences between digital and analog signals. One specific example of a data transmission system is discussed. This study is not a complete survey of data/computer networking and areas of further study are suggested. A problem set is given to illustrate the material and test the reader’s understanding of the concepts of this paper.
1. Introduction
It is the purpose of this paper to provide an overview of some of the problems and techniques associated with data communications. We will cover most of the physics and theory which explain the transmission of data between points on some form of network. The general communications model consists of a source, transmitter, transmission system, receiver, and destination. Source : A device that generates data to be transmitted; examples are telephones and computers. We will assume that we wish to transmit digital data (consisting of 0s and 1s) for the majority of this paper.
Transmitter : A device that encodes the data to be transmitted in such a way as to create electromagnetic signals that can be transmitted across some kind of transmission system.
Transmission System : The physical medium that carries the signals produced by the transmitter. This can be a single wire connecting two telephones or a vast network connecting thousands of computers.
Receiver : A device that accepts a signal from the transmission system and converts it into a usable form for the destination device.
Destination : Accepts the incoming data from the receiver. The destination device can be a telephone, a computer, a network switch, etc. The device usually processes the data in some way so that it is usable by a human user or a program running on the device.
The communications model defines the transmission system as the data carrier between source and destination. We will examine the structure and function of the transmission system in this paper. There are two physical ways to carry data: guided transmission media or unguided transmission media. Guided transmission occurs over solid wave carrying materials (wire or fiber optic cable). Unguided transmission (TV/radio, space communication) broadcasts signals into air or space and allows them to propagate to the receiver. Each of these will be discussed in greater depth later. We first examine the terminology of electromagnetic waves and then two specific cases of data transmission. After a general discussion of the transmission system we will discuss a specific example of how transmitter and receiver work in a system used in modern computer networks.
2. Electromagnetic Waves
For now we will concern ourselves with the vocabulary and theory of electromagnetic waves. Regardless of transmission media type and data type, all data is transmitted using an electromagnetic signal. Note that an electromagnetic signal is composed of one or more electromagnetic waves. For the sake of this discussion we will examine a simple signal as opposed to a complex wave consisting of several simple waves.
2.1 Time Domain
Discrete Figure 4 Continuous Analog
3. Frequency Domain
We now shift our discussion from a time domain discussion to a more useful analysis: Frequency Domain. Analyzing signals with respect to the frequencies they contain is valuable because it provides a background for understanding how we measure the capacities of a transmission medium.
3.1 Complex Signal Construction The individual sine waves that we discussed in the previous section are not used in real world applications because a periodic signal is not useful in real-world data carrying applications because it can not carry any data. In order to make a signal carry data we need to be able to alter it in some observable way. This section discusses the theory of constructing a non-periodic wave from periodic component waves. For example, Figure 5 shows the graphs of two separate frequencies and the effect of adding the two frequencies together. In this case the second frequency (b) is a multiple of the first. The first frequency in this case is called the fundamental frequency. Note that the period of the signal in (c) is the same as the period of the fundamental frequency. Fourier analysis can be used to show that any signal can be constructed using sinusoidal component frequencies. Thus we can construct any given signal from an array of sine waves. If we wish to construct a periodic square wave we would proceed as shown in Figure 6. The period is defined by the first wave (the fundamental frequency ) and is refined by the addition of higher and higher frequencies. With each higher frequency we note that the wave moves closer and closer to a representation of the signal that we wish to build. Note that a perfect square wave is not possible because Fourier analysis tells us we need an infinite number of component frequencies. Each step makes the wave a little “squarer” but we cannot create a perfect square wave.
3.2 Bandwidth The spectrum of a signal is the range of frequencies that it contains. Many signals will contain an arbitrary range of frequencies due to the process described in the previous section. If a signal has many sharp peaks and hard edges, we will need many high frequencies to approximate those peaks and edges. Remember that we can create an arbitrarily large sequence of signal approximations, each better than the previous one. In creating that sequence we use a corresponding sequence of higher and higher frequencies. Most of the signal strength is contained in a range of frequencies in the middle of the signal. High frequencies used to construct signals cannot be of higher amplitude than the fundamental frequency. The sum of a set of increasing amplitude signals does not yield a square wave. So, as the frequency goes up, the amplitude goes down and thus each higher frequency is weaker than the previous frequency. Receivers are limited in the range of signal strengths they can detect so most of the detectable energy in the signal is
in a narrow band of frequencies. Though theoretically a signal uses a near infinite range of frequencies, equipment can detect only a small portion of it. The bandwidth of any signal used in communications is very wide in theory, but since the transmission medium limits us to a narrower band we define this usable area of the signal to be the bandwidth of the signal. Similarly, any transmission medium has a range of frequencies in which it is effective. Copper wire can carry waves varying in frequency from 0 Hz to about 3 MHz. The upper end is not a hard edge but the majority of the power is contained in the given range. Of course, copper wire cannot transmit light waves, so there is an upper bound on the range of frequencies that a medium can transmit. The range of frequencies a medium can transmit effectively is defined as the bandwidth of that medium.
4. Frequency Addition
Just as we can add two simple sine waves together, we can add two (or more) complex analog signals together. A complex signal is one that is constructed from several constituent frequencies and may or may not carry data. The result is an even more complex signal that does not appear to preserve any of its constituent frequencies. Look back at Figure 6 and note that it is not immediately obvious that (d) contains a high frequency, let alone what they are. When we add two complex signals together the result is similar to Figure 6 but much more complicated. If we add two complex signals that each use the entire 10-100Hz range of frequencies, the result will be unusable (provided our task is to separate the signals) because we have no way of knowing which signal each component belongs to. If we were to use entirely separate bands of frequencies to construct the two signals, we could add them and have a usable product. The reason that one sum is worthless while the other is usable is explained by how receivers work. A receiver is tuned to listen for a specific band of frequencies. Thus if a receiver is tuned to a range from 50Hz to 100Hz it will ignore frequencies in the 0-49 Hz range. If two signals are summed (one in 50-100Hz, the other in 0-49Hz) and transmitted we can extract both signals by using two differently tuned receivers.
4.1 Frequency Division Multiplexing The important part of Frequency Addition is that more than one signal can be transmitted at once on a single transmission medium as in radio or TV. We define Frequency Division Multiplexing (FDM) as the process where signals are distributed into separate ranges of frequencies in the carrier bandwidth. For example, a voice grade line can carry frequencies in the 300 Hz to 3400 Hz range. Suppose we split this bandwidth at 1700 Hz and center the two carrier frequencies one at 1170 Hz and one at 2125 Hz. Then each carrier frequency can be modulated by 100 Hz on either side of the carrier frequency with no overlap in the middle. Modulation is the process of varying the characteristics of a signal in such a way as to represent some set of data. FDM allows many signals to be transmitted at once, greatly improving channel utilization. We can also transmit signals in two directions at once in a guided medium (in separate ranges of the bandwidth). Computer networks rarely use FDM (except for ISDN) but it is valuable for phone companies and unguided computer communications.
5. Data Transmission
Up to now we have limited our discussion to the theory of analog signaling. We will now focus our discussion on communication between two connected points on a
bandwidth as the data rate. Thus, since a twisted pair connection can support frequencies from 0 to about 3 MHz, the data rate will be about 3 Mbps.
5.1.2 Baseband We define the above method of transmitting data as baseband. Digital signals are dropped on the wire as voltage pulses and consume the entire bandwidth of the medium. Remember that if we want to create a close approximation of a square wave we need to use lots of high frequencies to approximate the square edges in the wave. A digital signal’s voltage pulses are essentially a square wave and Fourier theory tells us that we have to use the whole spectrum of the medium to create the square wave. Since the entire spectrum of the transmission medium is used, FDM is not possible. In order to send data from several sources at once we employ Time Division Multiplexing , as discussed in the next section.
5.1.3 Time Division Multiplexing Unlike analog signaling and transmission, digital signals cannot be combined and transmitted at once. If several data sources are present and all wish to send at once, digital systems must string the data together into one continuous stream. This method of communication is called Time-Division Multiplexing (TDM). As the name suggests, the transmission system divides up time into slots and reserves one of the slots for each source. Thus a source can only have its data transmitted during its time slots. A prioritizing system can be implemented so heavily loaded sources have more time slots dedicated to them than to less important sources. Note that if a source has no data to transmit during its time slot that time slot is wasted since the system does not check to see which sources actually have data to send. Due to the nature of digital signaling, multiplexing of signals must occur in the preparation of data before it is sent. Reconstruction of the separate data sets requires advance communication. At the receiving end there are a number of receivers, one for each source. Once the data stream is broken apart into the separate data streams each receiver accepts the data at the same rate it was transmitted.
5.1.4 Full/Half Duplex Transmitting data in both directions at once is called Full-Duplex transmission. Full-duplex transmission can be achieved either by using two separate transmission channels or, in some cases, a single channel. Half-duplex systems allow data to flow in both directions but only one station can transmit data at one time. Half-duplex systems can use one or two channels, depending on transmitter/receiver arrangements. Digital signals cannot be sent in a full-duplex system with a single channel. If two signals are sent at once, the result will be unreadable because the voltages will add or cancel, resulting in a garbled string of bits. Full-duplex transmission of digital signals can be accomplished with two channels, one for each direction. Each station has its receiving apparatus listening on one channel, and its sending capability on the other. One channel can support half-duplex with the understanding that only one station can send at one time. In order to support half-duplex each station must possess both receiving and transmitting equipment. Thus each station can transmit and receive. Note that collisions and corrupted data occur if both stations attempt to transmit at once. We leave the theory of detecting and preventing simultaneous transmission in half-duplex to discussions of data flow control.
5.1.5 Signal Regeneration As mentioned before, no transmission medium is capable of carrying a signal for arbitrary distances. Electrical resistance and outside interference degrade signals and if the transmission distance is great enough the signal will be reduced to a worthless stream of errors. In order to protect the data stream, some method of regenerating the signal is needed. A device called a repeater is used to maintain the signal. A repeater receives the incoming signals and recovers the digital data and then retransmits a brand new clean signal. Using this technique, noise and interference caused by the medium are eliminated at each repeater. Thus, using a series of repeaters, a signal can be transmitted an arbitrary distance with little concern for data loss.
5.2 Digital Data, Analog Signals
In the previous section, we discussed the concepts of digital signaling and digital signal transmission. This section will discuss the problem of transmitting digital data using analog signals. Computer users are most familiar with this problem when communicating over the public telephone system. The telephone system is designed to switch and transmit analog signals in a range of frequencies that are suitable for voice communication. Digital switching and transmitting hardware is not currently installed, so end users must use a device to translate digital data into some analog signal. Such a device is called a modem (from Modulator-Demodulator).
5.2.1 Encoding Since an analog signal is a continuous wave, we must change that signal in some way to encode digital data. When we explored sine waves, we discussed three characteristics of a signal: Amplitude, Frequency, and Phase. We can modulate (change) a signal with respect to one of those characteristics to encode digital data. We will discuss modulating the amplitude and frequency of a signal. Each of these cases follows the general rule for analog signals: occupation of a given bandwidth centered at a given frequency (carrier frequency).
Amplitude Shift (AS) In AS, the binary values are represented by two different amplitudes of the carrier frequency. A common method of AS looks a lot like a digital signal because it uses pulses of the carrier frequency to denote 1, and absence of a signal for 0. As one might imagine, this system is very prone to error. Any outside interference is certain to affect the amplitude of the signal so that almost every data point can be in error in a poor transmission environment. AS is used very successfully to transmit data over optical fiber. A pulse of light is really just an analog signal for a short time. Since light waves have such a high frequency, the pulses can be very short (remember: T = 1/ f ). Thus for very large f , the period, T , is very small. Any pulse of a signal in AS must be at least T long otherwise it doesn’t appear as a signal at all! Optical fiber signals are transmitted in pulses, a pulse corresponding to a 1, no signal or a very low background signal corresponding to 0.
Frequency Shift (FS)
6.1 Guided Transmission Media
6.1.1 Twisted Pair A twisted pair is two insulated copper wires twisted together. One twisted pair acts as a single communication path. Sets of twisted pairs are bundled together in a larger line for runs of longer distances. The large bundles are shielded to reduce interference from outside electrical sources and from neighboring bundles of twisted pair. The most common application of twisted pairs is the telephone service to homes and businesses. Each house is connected to a phone company office by a twisted pair as discussed earlier. The system was originally designed for analog voice communications but there are ways to create an analog signal that carries digital data. Twisted pairs can and are used to send digital information in the form of digital signals. However, telephone companies require analog signals since phone company switching offices are equipped to handle analog signals, not digital signals (the switching and retransmission requirements are different). The capacity of twisted pair is fairly low. The medium was designed for only a few voice channels and its 250 kHz bandwidth is sufficient for that purpose. Because the bandwidth is fairly low, digital data rates of only a few Mbps are possible for long distances. However, 100 Mbps is possible with high quality transmitters and receivers and short distances. Twisted pair cable comes in several flavors. The simplest is unshielded twisted pair (UTP): regular telephone wire. Most office buildings are pre-wired with lots of UTP. Since it is readily available, cheap, and easy to work with, UTP is frequently used for local area networks. UTP can be improved by adding braided wire shielding. Shielded twisted pair (STP) is more expensive and harder to work with. A new standard was created in 1995 to specify several types of both UTP and STP. There are three categories of UTP and we will discuss the two most important and widely used.
Category 3 Category 3 wire and hardware are rated up to about 16 MHz. This corresponds to a newer voice grade cable and connection system. A data network using Category 3 wire is capable of data rates of close to 16 Mbps. Modern office buildings are wired with Category 3 cable and hardware is readily available for local area networks.
Category 5 Category 5 cable is designed for data transmission and can support much higher frequencies (up to 100 MHz). The physical design is different; the wire is twisted much more tightly. Category 5 cable is more expensive to produce, but the increased data rates it can support are worth the expense for high traffic/high speed networks.
6.1.2 Coaxial Cable Coaxial cable can be used to transmit analog or digital signals. Coaxial cable consists of 2 conductors like twisted pair, but is constructed with a hollow outer cylindrical conductor separated from a solid inner conductor by insulating material. Think of a pipe with a wire suspended in the middle of it. Due to its construction, coaxial cable is less susceptible to interference than twisted pair. Coaxial cable is capable of supporting a much higher frequency range than twisted pair. Its design limits
interference so that repeater/amplifier spacing can be much greater. Coaxial cable supports an analog bandwidth of about 400 MHz. For example, a single voice channel requires about 4 kHz and if we divide the full bandwidth of 400 MHz into 4 kHz blocks we end up with 100,000 voice channels! The volume is not quite that high due to multiplexing techniques and frequency band spacing but this illustrates the capacity of coaxial cable. Such a high capacity makes it an important part of telephone company’s long distance networks. Another commonly seen application of coaxial cable is for cable television. Its high bandwidth can carry dozens or close to hundreds of TV channels for distances up 10 miles. The higher bandwidth also allows for data rates to approach 500 Mbps (remember the rule of thumb concerning the relationship between maximum frequency and data rate). Coaxial cable is quite useful in a local area network for applications that experience high load or a high number of network devices or both.
6.1.3 Optical Fiber Optical fiber is the highest capacity guided medium available for any application. The maximum data rate for coaxial cable is in the hundreds of Mbps over a few kilometers. Optical fiber operates with near infrared light sources and so has a much higher bandwidth. In fact, the maximum data rate is only limited by our ability to modulate the light source and detect the modulation. The frequency of light is
approximately 1015 Hz. If we take a bandwidth of 1% of that total frequency we have 1013 Hz but one GHz is just 10 9 Hz which is just 1/10000 of the available bandwidth. So the upper limit of 2-3 Ghz is imposed by our ability to modulate the light and detect the changes. The practical bandwidth translates to 2-3 Gbps over tens of kilometers. Since the transmission properties of fiber are very good, repeaters can be spread out dramatically (compared to coaxial or twisted pair). Optical fiber is used exclusively for extremely high load applications. It is also present in local area networks serving as a main backbone between switches or areas of a network. Cross country telephone trunk lines use optical fiber as do large data communication routes. An optical fiber is constructed from a very thin stand of glass or ultra pure plastic that is incased in a cladding of glass or plastic with optical properties different from those of the inner core. An outer jacket encases the cladding and core and guards them against moisture and damage. Data is transmitted by sending pulses of light in the infrared or visible spectrums down the core of the fiber. As light enters the core it hits the edges of the core at a variety of angles. The core material is designed to reflect light that hits at a relatively low angle. Light that hits the edge at a steep angle goes though and is absorbed by the jacket. We refer to optical signaling as multi-mode if more than one angle can reflect. If the core radius is reduced, fewer angles will be reflected. Reduction to the width of about a wavelength allows rays at only a single angle to reflect. If only one angle can reflect we refer to the signaling as single-mode. Single-mode transmission is preferable because multi-mode transmission creates several propagation paths so signal elements spread out in time. This spreading out limits the rate at which the data can be received. Single- mode transmission has only a single propagation path so the data elements do not spread out. Two different light sources are used for optical signaling. The Light Emitting Diode (LED) and the injection laser diode (ILD) are both semiconductor devices that emit light when supplied with a voltage. The LED is cheaper and operates in less forgiving environments and lasts longer. In contrast, the ILD is more expensive and but
communicate and that in some situations that communication can break down in the form of signal collisions. We will now discuss a specific medium access control technique. A medium access control technique is a set of rules guiding how multiple stations may access the communication medium they use and how they deal with errors. One such technique is Carrier Sense Multiple Access with Collision Detection (CSMA/CD).
7.1 CSMA
With CSMA, a station that wishes to send data first listens to the medium to see if any other station is transmitting. If the medium is in use (a signal is sensed) then the station must wait until no signal is present. When the line is idle, any station with data to send may do so. However, if two stations attempt to send data at once (they both sense the line idle at the same time) a collision will occur. Since we are using baseband signals both data streams will be garbled and unreadable. In CSMA, a station just listens a set length of time (which takes into account propagation delay, i.e. the time it takes a signal to travel between two points, and that the receiver must contend for the medium) for a return acknowledgement from the receiver. If the sending station does not receive an acknowledgement it assumes a collision occurred and attempts to retransmit. Propagation delay changes the effectiveness of this scheme. If the propagation delay is significantly shorter than the time it takes to transmit one chunk of data, then CSMA is effective. Collisions could only occur if two stations attempt to transmit within the length of the propagation delay. After that period of time the whole length of the medium is filled with the data stream and no other stations can transmit. We need an algorithm to decide what to do when a station senses the medium and finds it in use. The technique used in the Ethernet standard is called the 1-persistent technique. A station that wishes to transmit listens to the medium as above and obeys the following rules:
- If the medium is idle, transmit; otherwise, go to step 2.
- If the medium is busy, keep listening to it until the channel is sensed empty and then transmit immediately. If two stations wish to send while another is transmitting, of course a collision is guaranteed and the mess will get sorted out after the collision. When two data sets collide, the medium is unusable for the duration of transmission of both data sets. If the data sets are especially long, this delay can be substantial. We could eliminate this problem by having the stations listen to the medium as they transmit. If they detect garbled data while transmitting they should immediately stop transmission, as they are causing a collision.
7.2 CSMA/CD
CSMA/CD adds collision detection by refining the rule set as follows:
- If the medium is idle, transmit; otherwise, go to step 2
- If the medium is busy, keep listening to it until the channel is sensed empty and then transmit immediately.
- If a collision is detected while transmitting, transmit a signal to notify other stations of the collision and then cease transmission.
- After transmitting the collision signal, wait a random length of time and attempt to retransmit (step 1).
With collision detection, efficiency is significantly increased. In fact, the amount of wasted time is reduced to the length of time it takes to detect a collision. How long is that? Consider the worst possible case: Take two stations that are as far apart as possible and let the first start transmitting. Let the second station start to transmit just before the first stations signal reaches it. The second station will cause an immediate collision and will detect it stop transmitting very quickly. However, the garbled content must travel back to the first station before it realizes what has happened. Thus we can say that the time to detect a collision is less than or equal to twice the maximum propagation delay. One important rule to maintain efficiency in this system is that data sets must be long enough to ensure collision detection before the end of transmission. If the data sets are too short, CSMA/CD will have the same efficiency of CSMA.
8. Conclusion
The discussion of data communications does not stop here. We have shown how and why the transmission system functions. The study of computer networking includes many more issues and problems. Flow control and routing algorithms provide logic for sending data through a large network in some efficient manner. Error correction/detection allow for flawed data to be detected and corrected either by retransmission or through other means. Network security studies encryption, authentication, and, increasingly, ethics. And one can study and create network applications: computer address databases, Web browsers, and designing systems for cataloging and retrieving information. But don’t forget: All of the advanced topics mentioned here use a transmission system!
9. Problem Set
- Why does a full duplex analog signal transmission have to be broken up into separate frequencies for each station? What happens if the channel is not divided?
- Why is frequency shift encoding less prone to error than amplitude shift encoding?
- Some personal tape/radio players use the headphone wire as their antenna for receiving FM radio broadcasts. How is it possible for the wire to be used as an antenna when it is already carrying an amplified signal to the speakers?
- With CSMA, if two stations wish to transmit while another is transmitting, a collision is guaranteed. After the guaranteed collision why doesn’t the system get caught in an endless cycle of collisions caused by those two stations?
- How fast must a receiver be able to detect changes in a signal in order to receive an alternating (10101…) bit stream sent using a 10 MHz periodic signal? Generalize this result for any signaling rate. We call this result the sampling rate.
- Why are amplifiers not used for retransmission of digital signals?
f( x)=sin(x)
Figure 1
Amplitude
One Period
Figure 2
Figure
(a)
Fundamental Wave
(b)
Increased Frequency
Figure 5
(a)
(b)
(c)
