1. Physical Layer
Part 1
Lecture -3

2. TCP/IP or Internet Model

3. Position of the Physical Layer

4. Position of the Physical Layer

5. Services at Physical Layer

6. 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

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

8. 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

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

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

11. 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

12. 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)

13. 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.

14. Example of Aperiodic Signals

15. 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

16. Period and Frequency

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

18. 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

19. 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

20. 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.

21. More on Low Frequency and High Frequency

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

23. Sine wave examples

24. Sine wave examples (continued)

25. Sine wave examples (continued)

26. 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

27. Time and frequency domains

28. Time and frequency domains (continued)

29. Time and frequency domains (continued)

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

31. 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.

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

33. Composite Periodic Signal

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

35. Decomposition of composite periodic signal

36. Decomposition of composite periodic signal

37. 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

38. 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

39. 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

40. Bandwidth

41. The bandwidth of a periodic and non-periodic composite signals

42. 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 = = 800 Hz
The spectrum has only five spikes, at 100, 300, 500, 700, and 900 (see Figure in next slide)

43. For Example 3

44. 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 = = 40 Hz

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

46. 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.

47. Next Digital Signals