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-to-point 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 point-to-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.