Physical Layer Part 1 Lecture -3

TCP/IP or Internet Model

Position of the Physical Layer

Position of the Physical Layer

Services at Physical Layer

Things to be Covered Data and Signals – Chapter 3 Digital Transmission –Chapter 4 Analogy Transmission –Chapter 5 Multiplexing – Chapter 6 Transmission Media – Chapter 7 Circuit Switching and Telephone Network – Chapter 8

Signals Note: Analog and Digital Data Periodic and Aperiodic Signals To be transmitted, data must be transformed to electromagnetic signals

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

Analog Signals: Things to be covered Sine Wave Phase Examples of Sine Waves Time and Frequency Domains Composite Signals Bandwidth

Sine wave Attributes of a sine wave: Amplitude Frequency (Period) Phase

1. Amplitude Amplitude: Amplitude is define as a value of signal at any point on the wave on a time domain plot graph. Or Amplitude is the strength of a signal, measured in volts

Periodic Signal and Aperiodic Signal In essence, signal analysis is the mathematical analysis of amplitude, frequency, and phase of a signal Electrical signals are voltage –time or current –time variations Mathematically, a single-frequency voltage waveform is: Where: v(t)time varying voltage sine wave V peak amplitude (volts) f frequency t time   phase (degree or radians)

This waveform is called a periodic wave because it repeat at uniform rate (i.e., each successive cycle of the signal takes exactly the same length of time and has exactly the same amplitude variations of every other cycle) Periodic wave form can be analyzed in either the time domain or frequency domain If the signal isn’t periodic, it’s aperiodic Aperiodic signal is a signal that does not exhibit a pattern or repeating cycle.

Example of Aperiodic Signals

2. Frequency and Period Frequency is defined as the number of cycles per second Period is defined as the time it takes to complete one cycle

Period and Frequency

Frequency and period are inverses of each other. Relationship between Frequency and Period Note: Frequency and period are inverses of each other.

Units of Periods and Frequencies Equivalent Seconds (s) 1 s hertz (Hz) 1 Hz Milliseconds (ms) 10–3 s kilohertz (KHz) 103 Hz Microseconds (µs) 10–6 s megahertz (MHz) 106 Hz Nanoseconds (ns) 10–9 s gigahertz (GHz) 109 Hz Picoseconds (ps) 10–12 s terahertz (THz) 1012 Hz

Example 1 Express a period of 100 ms in microseconds, and express the corresponding frequency in kilohertz. Solution From Table above we find the equivalent of 1 ms (1 ms is 10-3 s) 1s is 106 ms . We make the following substitutions: 100 ms = 100  10-3 s = 100  10-3  106 ms = 105 ms Now we use the inverse relationship to find the frequency, changing hertz to kilohertz 100 ms = 100  10-3 s = 10-1 s f = 1/10-1 Hz = 10  10-3 KHz = 10-2 KHz

Note: 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.

More on Low Frequency and High Frequency

Note: If a signal does not change at all, its frequency is zero. If a signal changes instantaneously, its frequency is infinite.

Sine wave examples

Sine wave examples (continued)

Sine wave examples (continued)

Time and Frequency Domain Time domain: it’s amplitude –versus –time representation of the signal and is commonly called signal waveform Frequency domain: It ‘s amplitude versus frequency plot , and is commonly called frequency spectrum

Time and frequency domains

Time and frequency domains (continued)

Time and frequency domains (continued)

Note: An analog signal is best represented in the frequency domain.

Composite Signal A single-frequency sine wave is not useful in data communications; we need to change one or more of its characteristics to make it useful. When we change one or more characteristics of a single-frequency signal, it becomes a composite signal made of many frequencies.

Note: According to Fourier analysis, any composite signal can be represented as a combination of simple sine waves with different frequencies, phases, and amplitudes.

Composite Periodic Signal

Components in a composite periodic signal If the composite signal is periodic, the decomposition gives a series of signals with discrete frequencies

Decomposition of composite periodic signal

Decomposition of composite periodic signal

Non-Periodic Composite signal It can be a signal created by microphone or a telephone set when a word or two is pronounced. The composite signal can not be periodic, because that implies that we are repeating the same word or words with exactly the same tone If the composite signal is non-periodic, the decomposition gives a combination of sine waves with continuous frequencies

In time-domain representation of composite non-periodic signal (from previous slide), there are an infinite number of sine frequencies. Although the number of frequencies in a human voice is infinite, the range is limited. A normal human being can create a continuous range of frequencies between 0 – 4kHz

Bandwidth The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal Bandwidth is expressed in Hz For Example, if a composite periodic signal contains frequencies between 1000 and 5000, its bandwidth is BW = 5000 – 1000 = 4000Hz See the figure in the next slide

Bandwidth

The bandwidth of a periodic and non-periodic composite signals

Example 3 If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is the bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V. Solution B = fh - fl = 900 - 100 = 800 Hz The spectrum has only five spikes, at 100, 300, 500, 700, and 900 (see Figure in next slide)

For Example 3

Example 4 A 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 integral frequencies of the same amplitude. Solution B = fh - fl 20 = 60 - fl fl = 60 - 20 = 40 Hz

For Example 4 The spectrum contains all integer frequencies. This can be shown by series of spikes

Example 5 A signal has a spectrum with frequencies between 1000 and 2000 Hz (bandwidth of 1000 Hz). A medium can pass frequencies from 3000 to 4000 Hz (a bandwidth of 1000 Hz). Can this signal faithfully pass through this medium? Solution The answer is definitely no. Although the signal can have the same bandwidth (1000 Hz), the range does not overlap. The medium can only pass the frequencies between 3000 and 4000 Hz; the signal is totally lost.

Next Digital Signals