# Electromagnetic Signal. Transmission Fundamentals. Time-Domain Concepts. Time-Domain Concepts. Time-Domain Concepts. Sine Wave Parameters

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1 Electromagnetic Signal Transmission Fundamentals Chapter 2 Function of time Can also be expressed as a function of frequency Signal consists of components of different frequencies Time-Domain Concepts Analog signal - signal intensity varies in a smooth fashion over time No breaks or discontinuities in the signal Digital signal - signal intensity maintains a constant level for some period of time and then changes to another constant level Periodic signal - analog or digital signal pattern that repeats over time s(t +T ) = s(t ) - < t < + where T is the period of the signal Time-Domain Concepts Aperiodic signal - analog or digital signal pattern that doesn't repeat over time Peak amplitude (A) - maximum value or strength of the signal over time; typically measured in volts Frequency (f ) Rate, in cycles per second, or Hertz (Hz) at which the signal repeats Time-Domain Concepts Period (T ) - amount of time it takes for one repetition of the signal T = 1/f Phase (φ) - measure of the relative position in time within a single period of a signal Wavelength (λ) - distance occupied by a single cycle of the signal Or, the distance between two points of corresponding phase of two consecutive cycles Sine Wave Parameters General sine wave s(t ) = A sin(2πft + φ) Figure 2.3 shows the effect of varying each of the three parameters (a) A = 1, f = 1 Hz, φ = 0; thus T = 1s (b) Reduced peak amplitude; A=0.5 (c) Increased frequency; f = 2, thus T = ½ (d) Phase shift; φ = π/4 radians (45 degrees) note: 2π radians = 30 = 1 period

2 Sine Wave Parameters Time vs. Distance When the horizontal axis is time, as in Figure 2.3, graphs display the value of a signal at a given point in space as a function of time With the horizontal axis in space, graphs display the value of a signal at a given point in time as a function of distance At a particular instant of time, the intensity of the signal varies as a function of distance from the source Frequency-Domain Concepts Fundamental frequency - when all frequency components of a signal are integer multiples of one frequency, it s referred to as the fundamental frequency Spectrum - range of frequencies that a signal contains Absolute bandwidth - width of the spectrum of a signal Effective bandwidth (or just bandwidth) - narrow band of frequencies that most of the signal s energy is contained in Frequency-Domain Concepts Any electromagnetic signal can be shown to consist of a collection of periodic analog signals (sine waves) at different amplitudes, frequencies, and phases The period of the total signal is equal to the period of the fundamental frequency Relationship between Data Rate and Bandwidth The greater the bandwidth, the higher the information-carrying capacity Conclusions Any digital waveform will have infinite bandwidth BUT the transmission system will limit the bandwidth that can be transmitted AND, for any given medium, the greater the bandwidth transmitted, the greater the cost HOWEVER, limiting the bandwidth creates distortions Data Communication Terms Data - entities that convey meaning, or information Signals - electric or electromagnetic representations of data Transmission - communication of data by the propagation and processing of signals

3 Examples of Analog and Digital Data Analog Video Audio Digital Text Integers Analog Signals A continuously varying electromagnetic wave that may be propagated over a variety of media, depending on frequency Examples of media: Copper wire media (twisted pair and coaxial cable) Fiber optic cable Atmosphere or space propagation Analog signals can propagate analog and digital data Digital Signals Analog Signaling A sequence of voltage pulses that may be transmitted over a copper wire medium Generally cheaper than analog signaling Less susceptible to noise interference Suffer more from attenuation Digital signals can propagate analog and digital data Digital Signaling Reasons for Choosing Data and Signal Combinations Digital data, digital signal Equipment for encoding is less expensive than digitalto-analog equipment Analog data, digital signal Conversion permits use of modern digital transmission and switching equipment Digital data, analog signal Some transmission media will only propagate analog signals Examples include optical fiber and satellite Analog data, analog signal Analog data easily converted to analog signal

4 Analog Transmission Transmit analog signals without regard to content Attenuation limits length of transmission link Cascaded amplifiers boost signal s energy for longer distances but cause distortion Analog data can tolerate distortion Introduces errors in digital data Digital Transmission Concerned with the content of the signal Attenuation endangers integrity of data Digital Signal Repeaters achieve greater distance Repeaters recover the signal and retransmit Analog signal carrying digital data Retransmission device recovers the digital data from analog signal Generates new, clean analog signal About Channel Capacity Impairments, such as noise, limit data rate that can be achieved For digital data, to what extent do impairments limit data rate? Channel Capacity the maximum rate at which data can be transmitted over a given communication path, or channel, under given conditions Concepts Related to Channel Capacity Data rate - rate at which data can be communicated (bps) Bandwidth - the bandwidth of the transmitted signal as constrained by the transmitter and the nature of the transmission medium (Hertz) Noise - average level of noise over the communications path Error rate - rate at which errors occur Error = transmit 1 and receive 0; transmit 0 and receive 1 Nyquist Bandwidth For binary signals (two voltage levels) C = 2B With multilevel signaling C = 2B log 2 M M = number of discrete signal or voltage levels Signal-to-Noise Ratio Ratio of the power in a signal to the power contained in the noise that s present at a particular point in the transmission Typically measured at a receiver Signal-to-noise ratio (SNR, or S/N) signal power ( SNR) db = 10log10 noise power A high SNR means a high-quality signal, low number of required intermediate repeaters SNR sets upper bound on achievable data rate

5 Shannon Capacity Formula Equation: C = B log 2 ( 1+ SNR) Represents theoretical maximum that can be achieved In practice, only much lower rates achieved Formula assumes white noise (thermal noise) Impulse noise is not accounted for Attenuation distortion or delay distortion not accounted for Example of Nyquist and Shannon Formulations Spectrum of a channel between 3 MHz and 4 MHz ; SNR db = 24 db B = 4 MHz 3 MHz = 1MHz SNR db = 24 db = 10log10 SNR = 251 Using Shannon s formula C = 10 log 2 ( SNR) ( ) 10 8 = 8Mbps Example of Nyquist and Shannon Formulations How many signaling levels are required? C = 2B log2m 8 10 = 2 4 = log2 M M = 1 ( 10 ) log M 2 Classifications of Transmission Media Transmission Medium Physical path between transmitter and receiver Guided Media Waves are guided along a solid medium E.g., copper twisted pair, copper coaxial cable, optical fiber Unguided Media Provides means of transmission but does not guide electromagnetic signals Usually referred to as wireless transmission E.g., atmosphere, outer space Unguided Media Transmission and reception are achieved by means of an antenna Configurations for wireless transmission Directional Omnidirectional General Frequency Ranges Microwave frequency range 1 GHz to 40 GHz Directional beams possible Suitable for point-to-point transmission Used for satellite communications Radio frequency range 30 MHz to 1 GHz Suitable for omnidirectional applications Infrared frequency range Roughly, 3x10 11 to 2x10 14 Hz Useful in local point-to-point multipoint applications within confined areas

7 Multiplexing Techniques Frequency-division Multiplexing Frequency-division multiplexing (FDM) Takes advantage of the fact that the useful bandwidth of the medium exceeds the required bandwidth of a given signal Time-division multiplexing (TDM) Takes advantage of the fact that the achievable bit rate of the medium exceeds the required data rate of a digital signal Time-division Multiplexing

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