Lecture 2 Most basic facts from Electricity needed for understanding telecommunications Local transmission lines in the telephone system Decibels Signals and Noise Mathematical facts

Resistors are components that oppose the flow of current Resistors transform electrical energy into heat and dissipate it to the environment Resistance is measured in units called Ohm, e.g. R =1  Ohm’s Law says that: The voltage across an ideal resistor is proportional to the current through it., V = I R, where V is Voltage in Volts and I is the current in Amps The larger the resistance, the weaker the current that flows through the resistor (assuming same voltage).

A capacitor is essentially a sandwich of two layers of metal separated by an insulating material, or dielectric. Its primary function is to store electrical energy. Its capacitance depends on the size, geometry and on materials. Capacitors of various capacitances are used in circuits to create dynamic effects Capacitance is measured in units called “farads”. 1F 1 Farad is very large, practically we use microfarads or even smaller capacitances

Inductors are elements that transform the electric energy of the current into a magnetic energy of the field in the environment Inductors are “obstacles” for high frequency electric currents, but an ideal inductor has zero resistance and is not an obstacle to constant (DC) current inductance L is measured in units of henrys H.

On-line resources for basic concepts of Electricity Electric circuits Animation of Ohm's law Animation of an RLC circuit with AC currents Animation of a clipping circuit Animation of Fourier synthesis of oscillatory signals Propagation of Electromagnetic Wave

Transmission lines Copper wire is still the most widely used transmission medium Impairments: losses due to resistance R, attenuation at higher frequencies due to inductance L and capacitance C, electromagnetic coupling between parallel lines, echoes, and noise. Telephone lines are often called “twisted pair” – these are insulated copper wires twisted together; neighboring pairs are twisted with different twist lengths; the pairs are stranded into units of up to 100 pairs and cables into plastic-sheathed cores. The primary constants R, L, C depend on the gauge of the wire, temperature, materials, and operating frequency. = characteristic impedance of the line - must be matched by source impedance and load impedance

Transmission lines, part 2 American Wire Gauge, AWG standard GaugeDiameter, mmDiameter, in

Transmission lines, pt 3 To ensure sufficient current level in the loop (20 mA) the resistance of the wire should not exceed certain limit. This limits the length of the twisted pair line from central office to the subscriber Ohms is a typical value. AWGOhms/1000 ft Thus for the 26-gauge loop the maximum length limit is 1700/83.5 = 20,359 feet. A different limit, called loss limit is 15, 680 ft (to ensure no more than 8 dB loss of voice)

Decibels Decibel, dB, is a measure of a relative amplitude (or power) of a signal, be it acoustic or electric The term “relative” means that we are measuring the ratio of the given amplitude to another amplitude, for example the ratio of the amplitude (Volts) at the end of the phone line to the amplitude (Volts) at the beginning of the phone line In acoustics, the decibel is a measure of the relative level of sound or noise compared to some standardized level of sound or noise. One decibel (0.1 bel) equals 10 times the logarithm of the power ratio of the given sound to the power of the sound barely perceptible by human ear. The minimum audible pressure amplitude, at the threshold of hearing, is about 10-5 pascal, or about standard atmosphere, corresponding to a minimum intensity of about10-12 watt per square meter. Doubling the intensity of a sound means an increase of a little more than three dB.

dB value = 10 log (Output power/Input Power) dB value = 20 log (Output voltage/ Input Voltage) e.g. power gain = 2 implies dB value = 10 log 2 = dB e.g. voltage gain = 100 implies dB value 20 log 100 = 40 dB e.g. voltage loss 50% implies 20 log (0.5) = dB e.g. AWG 24 produces loss of dB/km or 2.16 dB/mile Decibels, part 2

Transmission Impairments Signal transmitted gets distorted Causes: –Attenuation and attenuation distortion –Delay distortion –Noise Effects: either the analog signal distortion or the binary signal errors

Attenuation Signal strength weakens with distance Received signal strength: –must be enough to be detected (e.g. 20 mA) –must be sufficiently higher than noise to be received without error (8 dB power loss) Attenuation is a function of frequency

Noise sources Thermal –Due to thermal agitation of electrons –Uniformly distributed, white noise From other signals –Signals that are combinations of original frequencies sharing a medium

Noise sources continued Cross-talk –A signal from one line is picked up by another Impulse disturbance –Irregular pulses or spikes of short duration and high amplitude –electromagnetic interference

Characterizations of Channel Capacity Data rate –Bps, In bits per second –Sps - In bauds: symbols per second Bandwidth –In cycles per second or Hertz –Bandwidth is limited by electronics and medium