Data Transmision

Data Transmision

The successful transmission of data depends principally on two factors: the

quality of the signal being transmitted and the characteristics of the tranmission

medium. The objective of this lesson and the next is to provide the

reader with an intuitive feeling for the nature of these two factors.

The first section presents some concepts and terms from the field of electrical

engineering; this should provide sufficient background for the remainder of the

lesson. Section 2.2 clarifies the use of the terms analog and digital. Either analog

or digital data may be transmitted using either analog or digital signals. Furthermore,

it is common for intermediate processing to be performed between source

and destination, and this processing has either an analog or digital character.

Section 2.3 looks at the various impairments that may introduce errors into

the data during transmission. The chief impairments are attenuation, delay distortion,

and the various forms of noise.

2.1 CONCEPTS AND TERMINOLOGY

In this section we introduce some concepts and terms that will be referred to

throughout the rest of the lesson and, indeed, throughout Part I.

Transmission Terminology

Data transmission occurs between transmitter and receiver over some transmission

medium. Transmission media may be classified as guided or unguided. In both

cases, communication is in the form of electromagnetic waves. With guided media,

the waves are guided along a physical path; examples of guided media are twisted

pair, coaxial cable, and optical fiber. Unguided media provide a means for transmitting

electromagnetic waves but do not guide them; examples are propagation

through air, vacuum, and sea water.

The term direct link is used to refer to the transmission path between two

devices in which signals propagate directly from transmitter to receiver with no

intermediate devices, other than amplifiers or repeaters used to increase signal

strength. Both parts of Figure 2.1 depict a direct link. Note that this term can apply

to both guided and unguided media.

A guided transmission medium is point-to-point if, first, it provides a direct

link between two devices and, second, those are the only two devices sharing the

medium (Figure 2.la). In a multipoint guided configuration, more than two devices

share the same medium (Figure 2.lb).

A transmission may be simplex, half-duplex, or full-duplex. In simplex transmission,

signals are transmitted in only one direction; one station is the transmitter

and the other is the receiver. In half-duplex operation, both stations may transmit,

but only one at a time. In full-duplex operation, both stations may transmit simultaneously.

In the latter case, the medium is carrying signals in both directions at the

same time. How this can be is explained in due course.

We should note that the definitions just given are the ones in common use in

the United States (ANSI definitions). In Europe (ITU-T definitions), the term

"simplex" is used to correspond to half-duplex, as defined above, and "duplex" is

used to correspond to full-duplex, as also defined above.

Frequency, Spectrum, and Bandwidth

In this lesson, we are concerned with electromagnetic signals, used as a means to

transmit data. At point 3 in Figure 1.2, a signal is generated by the transmitter and

transmitted over a medium. The signal is a function of time, but it can also be

expressed as a function of frequency; that is, the signal consists of components of

different frequencies. It turns out that the frequency-domain view of a signal is far

more important to an understanding of data transmission than a time-domain view.

Both views are introduced here.

Time-Domain Concepts

Viewed as a function of time, an electromagnetic signal can be either continuous or

discrete. A continuous signal is one in which the signal intensity varies in a smooth

fashion over time. In other words, there are no breaks or discontinuities in the signal.'

A discrete signal is one in which the signal intensity maintains a constant level

for some period of time and then changes to another constant level. Figure 2.2

shows examples of both kinds of signals. The continuous signal might represent

speech, and the discrete signal might represent binary Is and 0s.

The simplest sort of signal is aperiodic signal, in which the same signal pattern

repeats over time. Figure 2.3 shows an example of a periodic analog signal (sine

' A mathematical definition: A signal s(t) is continuous if lim s(t) = s(a) for all a.

     f -0

wave) and a periodic digital signal (square wave). Mathematically, a signal s(t) is

defined to be periodic if and only if

where the constant T is the period of the signal. (T is the smallest value that satisfies

the equation.) Otherwise, a signal is aperiodic.

The sine wave is the fundamental continuous signal. A general sine wave can

be represented by three parameters: amplitude (A), frequency (f), and phase (4).

The amplitude is the peak value or strength of the signal over time; typically, this

value is measured in volts or watts. The frequency is the rate (in cycles per second,

or Hertz (Hz)) at which the signal repeats. An equivalent parameter is the period

(T) of a signal, which is the amount of time it takes for one repetition; therefore,

T = l/f. Phase is a measure of the relative position in time within a single period of

a signal, as illustrated below.

The general sine wave can be written

 

Figure 2.4 shows the effect of varying each of the three parameters. In part (a) of

the figure, the frequency is 1 Hz; thus, the period is T = 1 second. Part (b) has the

same frequency and phase but an amplitude of 112. In part (c), we have f = 2, which

is equivalent to T = 112. Finally, part (d) shows the effect of a phase shift of d 4 radians,

which is 45 degrees (257- radians = 360" = 1 period).

In Figure 2.4, the horizontal axis is time; the graphs display the value of a signal

at a given point in space as a function of time. These same graphs, with a change

of scale, can apply with horizontal axes in space. In this case, the graphs display the

value of a signal at a given point in time as a function of distance. For example, for

a sinusoidal transmission (say an electromagnetic radio wave some distance from a

radio antenna, or sound some distance from a loudspeaker), at a particular instant

of time, the intensity of the signal varies in a sinusoidal way as a function of distance

from the source.

Frequency Domain Concepts

In practice, an electromagnetic signal will be made up of many frequencies. For

example, the signal

is shown in Figure 2.5. The components of this signal are just sine waves of frequencies

fl and 3f1; parts a and b of the figure show these individual components.

There are several interesting points that can be made about this figure:

The second frequency is an integer multiple of the first frequency. When all

of the frequency components of a signal are integer multiples of one fre

quency, the latter frequency is referred to as the fundamental frequency.

The period of the total signal is equal to the period of the fundamental frequency.

The period of the component sin (2njflt)is T = l/fl, and the period of

s(t) is also T, as can be seen from Figure 2.5~.

It can be shown, using a discipline known as Fourier analysis, that any signal

is made up of components at various frequencies, in which each component is a

sinusoid. This result is of tremendous importance, because the effects of various

transmission media on a signal can be expressed in terms of frequencies, as is dis

cussed later in this lesson. For the interested reader, the subject of Fourier analysis

is introduced in Lesson 2A at the end of this lesson.

So, we can say that for each signal, there is a time-domain function s(t) that

specifies the amplitude of the signal at each instant in time. Similarly, there is a frequency-

domain function S(f) that specifies the constituent frequencies of the signal.

Figure 2.6a shows the frequency-domain function for the signal in Figure 2.5~N. ote

that, in this case, S(f) is discrete. Figure 2.6b shows the frequency domain function

for a single square pulse that has the value 1 between -XI2 and Xl2, and is 0 elsewhere.

Note that in this case S(f) is continuous, and that it has nonzero values indefinitely,

although the magnitude of the frequency components becomes smaller for

larger f. These characteristics are common for real signals.

The spectrum of a signal is the range of frequencies that it contains. For the

signal in Figure 2.5c, the spectrum extends from fi to 3fi. The absolute bandwidth of

a signal is the width of the spectrum. In the case of Figure 2.5c, the bandwidth is 2fi.

Many signals, such as that of Figure 2.6b, have an infinite bandwidth. However,

most of the energy in the signal is contained in a relatively narrow band of frequencies.

This band is referred to as the effective bandwidth, or just bandwidth.

One final term to define is dc component. If a signal includes a component of

zero frequency, that component is a direct current (dc) or constant component. For

example, Figure 2.7 shows the result of adding a dc component to the signal of Figure

2.6. With no dc component, a signal has an average amplitude of zero, as seen

in the time domain. With a dc component, it has a frequency term at f = 0 and a

nonzero average amplitude.

Relationship Between Data Rate and Bandwidth

The concept of effective bandwidth is a somewhat fuzzy one. We have said that it is

the band within which most of the signal energy is confined. The term "most" in this

context is somewhat arbitrary. The important issue here is that, although a given

waveform may contain frequencies over a very broad range, as a practical matter

any transmission medium that is used will be able to accommodate only a limited

band of frequencies. This, in turn, limits the data rate that can be carried on the

transmission medium.

To try to explain these relationships, consider the square wave of Figure 2.3b.

Suppose that we let a positive pulse represent binary 1 and a negative pulse represent

binary 0. Then, the waveform represents the binary stream 1010. . . . The duration

of each pulse is 1/2fl; thus, the data rate is 2fl bits per second (bps). What are

the frequency components of this signal? To answer this question, consider again

Figure 2.5. By adding together sine waves at frequencies fl and 3f1, we get a waveform

that resembles the square wave. Let us continue this process by adding a sine

wave of frequency 5f1, as shown in Figure 2.8a, and then adding a sine wave of frequency

7f1, as shown in Figure 2.8b. As we add additional odd multiples of fl, suitably

scaled, the resulting waveform approaches more and more closely that of a

square wave.

Indeed, it can be shown that the frequency components of the square wave

can be expressed as follows:

Thus, this waveform has an infinite number of frequency components and, hence,

an infinite bandwidth. However, the amplitude of the kth frequency component,

kfl, is only llk, so most of the energy in this waveform is in the first few frequency

components. What happens if we limit the bandwidth to just the first three frequency

components? We have already seen the answer, in Figure 2.8a. As we can

see, the shape of the resulting waveform is reasonably close to that of the original

square wave.

 

 

We can draw the following general conclusions from the above observations.

In general, any digital waveform will have infinite bandwidth. If we attempt to

transmit this waveform as a signal over any medium, the nature of the medium will

limit the bandwidth that can be transmitted. Furthermore, for any given medium,

the greater the bandwidth transmitted, the greater the cost. Thus, on the one hand,

economic and practical reasons dictate that digital information be approximated by

a signal of limited bandwidth. On the other hand, limiting the bandwidth creates

distortions, which makes the task of interpreting the received signal more difficult.

The more limited the bandwidth, the greater the distortion, and the greater the

potential for error by the receiver.

One more illustration should serve to reinforce these concepts. Figure 2.9

shows a digital bit stream with a data rate of 2000 bits per second. With a bandwidth

of 1700 to 2500 Hz, the representation is quite good. Furthermore, we can generalize

these results. If the data rate of the digital signal is W bps, then a very good representation

can be achieved with a bandwidth of 2W Hz; however, unless noise is

very severe, the bit pattern can be recovered with less bandwidth than this.

Thus, there is a direct relationship between data rate and bandwidth: the

higher the data rate of a signal, the greater is its effective bandwidth. Looked at the

other way, the greater the bandwidth of a transmission system, the higher is the data

rate that can be transmitted over that system.

Another observation worth making is this: If we think of the bandwidth of a

signal as being centered about some frequency, referred to as the center frequency,

then the higher the center frequency, the higher the potential bandwidth and therefore

the higher the potential data rate. Consider that if a signal is centered at

2 MHz, its maximum bandwidth is 4 MHz.

We return to a discussion of the relationship between bandwidth and data rate

later in this lesson, after a consideration of transmission impairments.