Chapter 3
Introduction To
Physical Layer
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Chapter 3: Outline
3.1 DATA AND SIGNALS
3.2 PERIODIC ANALOG SIGNALS 3.3 DIGITAL SIGNALS
3.4 TRANSMISSION IMPAIRMENT 3.5 DATA RATE LIMITS
3.6 PERFORMANCE
Data can be analog or digital.
The term analog data refers to information that is continuous; Analog data takes on continuous values.
Digital data refers to information that has
discrete states. Digital data takes on discrete values.
Examples
•
Analog Signals: Human voice•
Digital Signals: Data stored in computer’s memory in the form of “0” and “1”3.3
3-1 ANALOG AND DIGITAL
Signals can be analog or digital.
Analog signals can have an infinite number of values in a range; digital
signals can have only a limited number of values.
Note
3.5
Figure 3.2: Comparison of analog and digital signals
Periodic and Non-periodic (aperiodic) signals
In data communications, we commonly use periodic analog signals and
nonperiodic digital signals.
Note
3.7
3-2 PERIODIC ANALOG SIGNALS
Periodic analog signals can be classified as simple or composite.
A simple periodic analog signal, a sine wave, cannot be decomposed into
simpler signals.
A composite periodic analog signal is composed of multiple sine waves.
Sine Wave
A sine wave is the most fundamental form of a periodic analog signal
It can be represented by three parameters:
Peak Amplitude
Frequency
Phase
3.9
Time Value
• • • Figure 3.3: A sine wave
Figure 3.4: Two signals with two different amplitudes
Peak amplitude
Peak amplitude
Peak amplitude
Peak amplitude
3.12
Table 3.1: Units of period and frequency
Period and frequency
Period or Time Period: Time required to complete one cycle. It is measured in seconds.
Frequency: Number of cycles
completed in one second. It is measured in Hz or cycles per second.
If “f” represents frequency and “T”
represents period then,
f = 1/T and T = 1/f
3.14
Frequency and period are the inverse of each other.
Note
3.16
Figure 3.5: Two signals with the same phase and amplitudes, but different frequencies
Frequency is the rate of change with respect to time.
Change in a short span of time means high frequency.
Change over a long span of time means low frequency.
Note
Examples to solve
Solve examples 3.3, 3.4 and 3.5 on pages 58 and 59
3.18
Two Extremes of Frequency
If a signal does not change at all, what is its frequency?
If a signal changes instantaneously (i.e., it changes in zero time), what is its
frequency?
The term phase, or phase shift, describes the position of the waveform relative to time 0.
If we think of the wave as something that can be shifted backward or forward along the time axis, phase describes the amount of that shift.
It indicates the status of the first cycle.
3.20
3.2.2 Phase
Figure 3.6: Three sine waves with different phases
3.22
A sine wave is offset 1/6 cycle with respect to time 0. What is its phase in degrees and radians?
Example 3.6
Solution
We know that 1 complete cycle is 360°. Therefore, 1/6 cycle is
Wavelength
Wavelength is the distance a signal can travel in a period
Wavelength can be calculated if one is given the propagation speed and the period of the signal
In data communication, wavelength is
usually used to describe the transmission of light in an optical fiber
3.24
Wavelength
Let λ be the wavelength, c be the speed of light and f be the frequency, then:
(Recall, distance = speed x time)
wavelength = propagation speed × period
= propagation speed × 1 𝑓 𝜆 = 𝑐
𝑓
Wavelength
Wavelength is measured in micrometers (i.e., microns)
Example:
We would like to calculate the wavelength of red light in air when
f = 4 x 1014:
𝜆 = 𝑐
𝑓 = 3×108
4×1014 = 0.75 × 10−6 m = 0.75𝜇m
3.26
Figure 3.7: Wavelength and period
Direction of propagation
3.28
Time and Frequency Domains
Time domain plot is an amplitude vs. time plot, i.e., it shows amplitude variations of a signal with respect to time
Frequency domain plot is an amplitude vs.
frequency plot, i.e., it shows which
frequencies and of what amplitude are present in the signal
3.30
Figure 3.8: The time-domain and frequency-domain plots of a sine wave
The frequency domain is more compact and useful when we are dealing with more than one sine wave. For example, Figure 3.9 shows three sine waves, each with different amplitude and frequency. All can be represented by three spikes in the frequency domain.
Example 3.7
3.32
Figure 3.9: The time domain and frequency domain of three sine waves
A single-frequency sine wave is not useful in data communications;
we need to send a composite signal, a signal made of many simple sine waves.
According to Fourier analysis, any composite signal is a combination of
simple sine waves with different frequencies, amplitudes, and phases.
Fourier analysis is discussed in Appendix E.
3.34
Figure 3.10: A composite periodic signal
Figure 3.11: Decomposition of a composite periodic signal
Time Amplitude
• • •
Amplitude
f 3f 9f
b. Frequency-domain decomposition of the composite signal
Frequency
3.36
Figure 3.12 shows a nonperiodic composite signal. It can be the signal created by a microphone or a telephone set when a word or two is pronounced. In this case, the composite signal cannot be periodic, because that implies that we are repeating the same word or words with exactly the
same tone.
Example 3.9
Figure 3.12: Time and frequency domain of a non-periodic signal
The range of frequencies contained in a composite signal is its bandwidth.
The bandwidth is normally a difference between two numbers. For example, if a composite signal contains frequencies
between 1000 and 5000, its bandwidth is 5000 − 1000, or 4000.
3.38
3.2.6 Bandwidth
Figure 3.13: The bandwidth of periodic and nonperiodic composite signals
3.40
If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is its bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V.
Example 3.10
Solution
Let fh be the highest frequency, fl the lowest frequency, and B the bandwidth. Then
Figure 3.14: The bandwidth for example 3.10
3.42
A periodic signal has a bandwidth of 20 Hz. The highest frequency is 60 Hz. What is the lowest frequency? Draw the spectrum if the signal contains all frequencies of the same amplitude.
Example 3.11
Solution
Let fh be the highest frequency, fl the lowest frequency, and B the bandwidth. Then
The spectrum contains all integer frequencies. We show this by a series of spikes (see Figure 3.15).
Figure 3.15: The bandwidth for example 3.11
3.44
A nonperiodic composite signal has a bandwidth of 200 kHz, with a middle frequency of 140 kHz and peak amplitude of 20 V. The two extreme frequencies have an amplitude of 0. Draw the frequency domain of the signal.
Example 3.12
Solution
The lowest frequency must be at 40 kHz and the highest at 240 kHz. Figure 3.16 shows the frequency domain and the bandwidth.
Figure 3.16: The bandwidth for example 3.12
