The Basic Parameters of a Data Channel
BANDWIDTH Frequency Defined
Electrical currents can be classified in two general categories-direct or alternating. Direct current (d c) travels in only one direction in a circuit, while alternating current (a c) travels first in one direction (+), then in the other (-).
Figure 1 shows graphically an alternating current starting at a zero value, going through its positive phase and returning to zero, then going through its negative phase and again returning to zero. This is one cycle of alternating current. Either half of the cycle is called a baud.
JUNE 1979 ~ 1979 DATAPRO RESEARCH CORPORATION, DELRAN, NJ 08075 USA
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The Basic Parameters of a Data Channel
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Figure 1. One (l'cle of alternating current
The number of cycles completed per second is the current's frequency, and is expressed in hertz. I
The Frequency Spectrum
Frequencies vary over an extremely wide range, beginning at zero and increasing progressively through acoustics, radio, infrared (heat), light, ultra-violet, X-rays, gamma rays, and cosmic rays. The acoustic range is from about 20 Hz to about 20,000 Hz and varies considerably from person to person.
The radio range extends from about 14 kHz to over 10 million kHz.
Figure 2 indicates the disparity between the fre-quencies that can be detected by the human ear and those that can be transmitted over a telephone channel. The human voice ( 100 to 1100Hz), however, falls mostly within the limits imposed by the telephone circuit.
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TELEPHONE CHANNEL (3,000 Hz) I·
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AUDIBLE RANGE (ABOUT 20,000 Hz)
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Figure 2. Frequency disparity between human ear and telephone channel
Frequency of a Data Signal
A data communication signal often consists of a range of frequencies. The frequency of a signal at any particular moment depends on the composition of the code being transmitted. For illustration, assume a character with the binary representation of 11110000 is transmitted. If binary 1 's are given a positive voltage and O's a negative voltage, only one cycle would have been transmitted during the time required to transmit the character: the line voltage would have gone from zero to a positive voltage (for the duration of the I bits) and then would have swung down through zero to a negative voltage while the O's were transmitted.
IThe term hertz, abbreviated Hz, has taken the place of cycles per second to promote internationai understanding.
On the other hand, if a character with the binary equivalent of 10101010 were transmitted, four cycles of current would have occurred during the same character-time. In fact, transmission of the second character would have resulted in the highest possible frequency for that particular signal, since it had caused the greatest number of transitions from one signal state (positive) to the other (negative). Thus the number of bits of transmission channel can carry per unit of time is directly related to the upper limit of its usable frequency range.
Bandwidth and Passband
Bandwidth is a measurement of the width of a range of frequencies. The telephone channel described in the above graph has a bandwidth of 3000 Hz (3 kHz).
A passband, on the other hand, is a slot at a certain place in the frequency spectrum that allows a particular range of frequencies (bandwidth) to pass.
The passband of the telephone channel was defined by its limits of 300 and 3300 Hz. Notice that passband defines a particular slot in the frequency spectrum, while bandwidth defines a range of frequencies.
A major difference between the grades of available channels (teletypewriter, voice television, etc.) is their bandwidth. Bandwidth has a great deal to do with the quality of a received signal as compared with the signal originally transmitted. Intelligibility of the human voice, for example, requires a bandwidth of about 400 Hz. Articulation-the pitch and tonal qualities of a voice-requires about 1200 Hz of band-width, three times that of intelligibility.
Cutoff Frequencies
Since communications media often have many simul-taneous conversations (or other information) imposed upon them, it is necessary to restrict each conversation to its own path. The electrical filters used for this purpose create a passband that allows frequencies within a certain range to pass through the circuit but will block all frequencies outside this range. The points at the upper and lower edges of the passband are called cutoff frequencies. (See Figure 3.) DISTORTION
If it were possible to transmit a signal over a channel that had no imperfections, the signal would arrive at its destination exactly as it had. been sent. Perfect channels, however, exist only in theory; thus signals become distorted during transmission.
Noise is an unpredictable phenomenon that is best described statistically. Distortion, however, has a fixed affect on a signal and is a function of each
© 1979 DATAPRO RESEARCH CORPORATION. DELRAN, NJ 08075 USA REPRODUCTION PROHIBITED
JUNE 1979
The Basic Parameters of a Data Channei
CUTOFF FREQUENCIES
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Figure 3. Passband created by using filters
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individual channel. There are three types of distortion that a channel may impart to a signal: delay distor-tion, attenuation distordistor-tion, and jitter.
Delay (Phase) Distortion
To have some degree of understanding about the effects a channel imparts on signals it carries, it is helpful to examine the char~cteristic~ of .a p~rfect
signal and to compare these wIth the dIstortIOn SIgnal that appears at the receiving end of a channel.
Signals can be constructed in many ways. In the following discussion, signals composed of alternating currents of various frequencies will be discussed. First, a simple single-frequency wave is shown, then, a complex two-frequency wave, and finally, the effects of channel distortion will be examined.
Simple and Complex Waves
A simple (single-frequency) wave is shown in Figure 4. The simple wave (signal) shown here cal?- be repre-sented by a rotating vector. Vectors of thIS type are assumed to rotate counterclockwise, with the reference point, zero degrees, at the right. One com-plete rotation of the vector represents one comcom-plete cycle of the signal. Si~ce the waveform s~~ws that one cycle of the signal IS completed at 1 mIllIsecond, the signal frequency is 1000 Hz. Therefore, the vector will rotate 1000 times per second.
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Figure 4. Representation of a simple wave
Complex waves result from combining two or more simple waves. The instantaneous value of a complex wave is the sum of the instantaneous values of the simple waves it comprises. Figure 5 represents a complex wave (A + B) and its two components (A and B) as the signal was transmitted and as it would be received if sent through a perfect channel. Effects of channel imperfections on signals are discussed in following paragraphs.
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Figure 5. Plotting complex waves (A + B) Propagation Time
A signal's propagation time is a function of both the nature of the channel through which it is travelling and the frequency of the signal itself. A channel with no external influences and no resistance would move a signal at a maximum of 186,000 miles per second (the speed of light). A microwave carrier might move the signal at 100,000 miles per second (0.01 ms per mile), and a pair of wires in a cable would pass the signal at about 14,000 miles per second (0.0714 ms per mile). An additional 1.2 ms is used whenever the signal passes through terminals that convert from carrier to WIre (or vice versa), filters, and other equipment.
If the channel is distortionless, all frequencies will pass through it at the same speed. Under these cir-cumstances, the frequency and the phase of any given signal will have a con~tant (linear) r~lationship ~ith
respect to time (see FIgure 6). Themterval of tIme between the instant that a signal is transmitted and the instant it is received is called phase delay, absolute delay, or propagation time. All signals have s~me
phase delay, but the mere fact that a signal. arnves later than it was sent poses few problems In data transmission.
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Figure 6. Phase delay through a distortionless channel
JUNE 1979 © 1979 DATAPRO RESEARCH CORPORATION, DELRAN, NJ 08075 USA REPRODUCTION PROHIBITED
BasIc (;oncepts
The Basic Parameters of a Data Channel Envelope Delay (Phase Delay Distortion)
A cause of difficulty in data transmission is that the shift of phase with respect to frequency i~ not usually linear in most transmission media but has a curve similar to that of Figure 7. Under these circum-stances, some frequencies of a complex signal will be delayed more than others during transmission, result-ing in a distortion of the original signal. This phenomenon is called envelope delay, phase delay distortion, or merely phase distortion.
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Figure 7. Phase delay qj' normal voice channel
Mathematically, envelope delay is defined as the first derivative of phase delay. This means that the shape of the envelope delay curve reflects the degree of change in the slope of the phase vs frequency curve.
A linear phase shift vs frequency (dotted iine of Figure 7) results in no envelope delay (dotted line of Figure 8), while a nonlinear phase shift vs frequency results in a distortion of the transmitted signal.
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If we were to transmit a binary signal at 1000 bauds, each signal element (baud) would have a duration of
I ms. A relative envelope delay of only I ms between the mark and space frequencies, then, would cause the two frequencies to be superimposed at the receiver, obliterating the signal.
To understand the effects of envelope delay, compare the following three diagrams. The first, Figure 9, is the same as Figure 4 and shows the perfect complex waveform as it was transmitted at t
=
O. The 1000Hz and 3000Hz components are in phase at t = O.The second diagram, Figure 10, shows the complex wave as transmitted at t = 250 ms. Although the two
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Figure 9. Perfect complex waveform as it was transmitted at t = 0
vectors are not superimposed as they were at t = 0, they are still in phase, since one vector is rotating three times as fast as the other. As long as they maintain this 3-to-1 relationship, they will be in phase with each other.
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Figure 10. Complex waveform as it ~\'as transmitted at t = 250
The third diagram, Figure II, shows what happens to a complex waveform when its components fall out of phase. The transmitted signal was the same as above, but the channel has delayed the low-frequency component, thus changing the resulting waveform.
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Figure 11. Complex waveform ~n'th its components out (~lphase
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JUNE 1979
The Basic Parameters of a Data Channel Delay Equalizers
Although envelope delay will always be present in communications circuits, it is important to flatten this delay across the frequency bandwidth of the channel to minimize delay distortion. This is done by adding
"delay equalizer" networks to the channel circuits (see Figure 12). The equalizers introduce a delay inverse to that of the channel alone, and the cumulative result is a relatively flat delay across the channel's bandwidth.
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Figure 12. Flattening envelope delay by using delay equalizers (Courtesy of Rixon Electronics)