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Chapter 3: DATA TRANSMISSION 3. DATA TRANSMISSION • • • • 3.1 Concepts and Terminology 3.2 Analog and Digital Data Transmission 3.3 Transmission Impairments 3.4 Channel Capacity 3.1 Transmission Terminology • Data transmission occurs over some transmission medium. • Transmission media may be guided or unguided. • A direct link between two devices is a point-topoint link. • More than two devices communicate over a multipoint link. • Transmission may be simplex, half-duplex, or full-duplex. 3.1 Time-Domain Concepts • A signal is continuous (in time) if its limit exists for all time. (Fig. 3.1) • An analog signal is a continuous. • A signal is discrete if it takes on only finite number of values. • A signal is periodic if s(t+T) = s(t) for all t, where T is a constant. (Fig. 3.2) 3.1 Time-Domain Concepts (cont.) • The amplitude is the instantaneous value of the signal at any time. • The frequency is the number of repetitions of the period per second; f=1/T Hz. • Phase is a measure of the relative position in time within a single period of a signal. (Fig. 3.3) 3.1 Time-Domain Concepts (cont.) • The wavelength of a signal is the distance occupied by a single cycle. • If n is the velocity of the signal then the wavelength l = nT = n (1/f). • Note: the velocity or propagation speed is often represented as some fraction of the speed of light, c = 3 x 108 meters/second. 3.1 Frequency Domain Concepts • Fourier Analysis--any signal is made up of components at various frequencies, where each component is a sinusoid. • Periodic signals can be represented as Fourier series. • Aperiodic signals can be represented as Fourier transforms. • Appendix A discusses Fourier Analysis. 3.1 Freq. Domain Concepts (cont.) • The spectrum of a signal is the range of frequencies that it contains. • The absolute bandwidth of a signal is the width of the spectrum. • The effective bandwidth (or just bandwidth) of a signal is the width of the spectrum that contains a large percentage of all the energy of the signal. • A DC voltage represents a constant offset from 0 volts and is considered the f=0Hz component in Fourier analysis. • Fig. 3.3--3.8 Appendix 3A: Signal Strength • Attenuation--the loss of signal strength as it propagates along a transmission medium. • Amplifiers can be used to provide a gain in signal strength. • The decibel is a measure of the difference in two power levels. – Let Pout and Pin be the input ant output power values of a system. – GdB= 10 x log10 (Pout/Pin) is the system gain. App. 3A: Signal Strength (cont.) • Gain is usually thought of as a positive value, and if the result is negative it is considered as a negative gain or (positive) loss. • To reduce confusion define loss as – LdB = -10 log10 (Pout/Pin) – = 10 log10 (Pin/Pout) App. 3A: Signal Strength (cont.) • The decibel can measure voltage differences. – Assume P is the power dissipated across a resistance R, and V is the voltage across R. – I=V/R, where I is the electrical current. – P = I x V = V/R x V = V2/R – Pout/Pin = (Vout/Vin)2 – Now log (X2)= 2 log (X). – Thus, GdB= 20 x log10 (Vout/Vin). App. 3A: Signal Strength (cont.) • The decibel can also be used to refer to absolute power and voltage . – Power (dBW) = 10 log10 (PowerW/1W ) – Voltage(dBmV) =20 log10(VoltagemV/1mV) App.3A: Signal Strength (cont.) • Example 3.9 Transmission Line – Let Pin = 10 mW – Let Pout= 5 mW – LdB = 10 log10(10mW/5mW) =10 (.301) = 3.01dB. App. 3A: Signal Strength (cont.) • Example 3.10 The overall gain for a pointto-point system can be calculated by adding component dB values. – System Gain= link 1 + amplfier+ link 2= (-12 dB) +(35 dB) + (-10 dB) = 13 dB. – How to find output power? • • • • GdB=13dB= 10 log10(Pout/Pin)=10 log10 (Pout/4mW) 1.3 = log10 (Pout/4mW) 10 1.3 = Pout/4mW Pout= 79.8 mW App.3A: Signal Strength (cont.) • Example 3.11 Absolute Power Levels – 1 W is equivalent to 0dBW. – 1000 W is equivalent to 30 dBW. – 1 mW is equivalent to -30dBW. 3.2 Analog and Digital Transmission • Analog--continuous time signals. • Digital--discrete time signals. • Three Contexts – Data--entities that convey meaning; signals are electric or electromagnetic encoding of data. – Signaling--the physical propagation of the signal along a suitable medium. – Transmission--the communication of data by the propagation and processing of signals. 3.2 Analog and Digital Transmission--Data • Analog data--continuous values on some interval. – Ex.: audio, video, temperature and pressure sensors. • Digital data--discrete values. – Ex.: text, integers. – Encoding using binary patterns: Ex: ASCII. • • • • • 3.2 Analog and Digital Transmission--Signals Analog signal--a continuously varying electromagnetic wave that may be propagated over a variety of media, depending on bandwidth. Digital signal--a sequence of voltage pulses that may be transmitted over a wire medium. Fig. 3.11--Attenuation of digital signals. Fig. 3.12--Speech and analog signals. Fig. 3.13--Text input and digital signals. 3.2 Analog and Digital Transmission--Signals • Analog data can also be represented by digital signals and digital data can be represented by analog signals. • Digital Data can be represented by analog signals: modem. • Analog Data can be represented by digital signals: codec. • Fig. 3.14 Signaling of Data (4 Examples) 3.2 Analog and Digital Transmission-Transmission • Analog transmission--transmission of analog signals without regard to content. – For long distances, amplifiers are used . – Amplifiers boost noise, and are "imperfect". – Analog voice is tolerant of the distortion, but for digital data errors will be introduced. 3.2 Analog and Digital Transmission-Transmission • Digital transmission-- transmission of digital data (using either analog or digital signals). – For long distances, repeaters are used. – If spaced properly, the errors are eliminated. – Preferred because of: digital technology, data integrity(error coding), capacity utilization, security, integration (of voice, data and more.) 3.3 Transmission Impairments • Attenuation--a decrease in magnitude of current, voltage, or power of a signal in transmission between points. (Fig. 3.15a) – If signal is too weak, it cannot be detected or errors may be introduced. – Attenuation tends to be an increasing function of frequency as well as distance. 3.3 Transmission Impairments (cont.) • Delay Distortion--distortion of a signal occurring when the propagation delay for the transmission medium is not constant over the frequency range of the signal. – Can cause intersymbol interference, i.e., the energy of one signal interval carriers over into the next--the result for digital transmission is a possible bit error. – Can be compensated for by using equalization circuits (or line conditioning). 3.3 Transmission Impairments (cont.) • Noise (Figure 3.16) – Thermal noise--caused by thermal agitation of electrons in a conductor (No = k Temp is the noise power density--the amount of noise in 1 Hz). – Intermodulation noise--due to the nonlinear combination of signals of different frequencies. – Crosstalk--phenomenon in which a signal transmitted on one circuit or channel of a transmission system creates an undesired effect in another circuit or channel. – Impulse noise--a high-amplitude, short- duration noise pulse. 3.3 Transmission Impairments (cont.) • Example 3.3--Thermal noise density at room temperature. – No = kT (W/Hz) where k is Boltzmann’s constant (1.38 x 10-23 J/K). – Let T =290 Kelvins (17 degrees C) – No= -204 dBW/Hz. 3.3 Transmission Impairments (cont.) • Example 3.4 Thermal noise in B Hz bandwidth. – – – – – N = kTB NdBW = 10 log10k + 10 log10T + 10 log10 B NdBW = -228.6dBW + 10 log10T + 10 log10 B Let T = 294 degrees K and B = 10 M Hz. NdBW = -133.9 dBW 3.4 Channel Capacity • Channel Capacity--the rate at which data can be communicated over a given communication path. • Nyquist: C = 2 B log2 (M) (bits/sec) – – – – B is the bandwidth M is the number of discrete signal levels Noise is not considered. Example: C = 2 x 3100 x log2 ( 8) = 18,600 bps 3.4 Channel Capacity (cont.) • Shannon: C = B log2 (1 + SNR) (bits/sec) – B is the bandwidth. – SNR is the signal to noise ratio (NOT in dB) • Example3.3:B=1M Hz; SNR=251 (or 24dB) – Shannon: C = 106 x log2 (1+251)= 8 M bps. – Nyquist: For the same C, M=16 signal levels. 3.4 Channel Capacity (cont.) • The Expression Eb/No – Signal energy per bit divided by the noise power density (per Hz). – Recall that energy=power x time (1 watt = 1 Joule/sec and 1 Joule= 1 watt x 1 sec.) – Eb=STb where S is the signal power and Tb is the time required to send one bit. – Tb = 1/R where R is the bit rate. – Eb/No = STb/(k x Temp)=S/ (k x Temp x R) – The bit error rate is a decreasing function of Eb/No.