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**Chapter 3: DATA TRANSMISSION**

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**3. DATA TRANSMISSION 3.1 Concepts and Terminology**

3.2 Analog and Digital Data Transmission 3.3 Transmission Impairments 3.4 Channel Capacity

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**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.

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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)

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**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)

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**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.

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**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.

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**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

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**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.

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**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)

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**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).

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**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)

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**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.

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**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) = Pout/4mW Pout= 79.8 mW

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**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.

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**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.

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**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.

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**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 Attenuation of digital signals. Fig Speech and analog signals. Fig Text input and digital signals.

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**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 Signaling of Data (4 Examples)

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**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.

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**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.)

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**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.

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**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).

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**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.

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**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 J/K). Let T =290 Kelvins (17 degrees C) No= -204 dBW/Hz.

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**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 = dBW + 10 log10T + 10 log10 B Let T = 294 degrees K and B = 10 M Hz. NdBW = dBW

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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

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**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.

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**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.

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