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How Computer Work Lecture 10 Introduction to the Physics of Communication How Computer Work Lecture 10 Page 1 The Digital Abstraction Part 1: The Static Discipline Vol Voh Tx Noise Rx Vil Vih How Computer Work Lecture 10 Page 2 What is Information? Information Resolves ______________ Uncertainty How Computer Work Lecture 10 Page 3 How do we measure information? Error-Free data resolving 1 of 2 equally likely possibilities = 1 bit ________________ of information. How Computer Work Lecture 10 Page 4 How much information now? 3 bits 3 independent coins yield ___________ of information 8 # of possibilities = ___________ How Computer Work Lecture 10 Page 5 How about N coins ? ........................ N independent coins yield # bits = ___________________________ N 2 N # of possibilities = ___________ How Computer Work Lecture 10 Page 6 What about Crooked Coins? Ptail = .25 Phead = .75 # Bits = - S pi log2 pi (about .81 bits for this example) How Computer Work Lecture 10 Page 7 How Much Information ? . . . 00000000000000000000000000000 . . . None (on average) How Computer Work Lecture 10 Page 8 How Much Information Now ? ...0101010 1010101010101... ...0101010 1010101010101... Predictor None (on average) How Computer Work Lecture 10 Page 9 How About English? • 6.JQ4 ij a vondurfhl co8rse wibh sjart sthdenjs. • If every English letter had maximum uncertainty, average information / letter would log (26) be _________ 2 • Actually, English has only ______ bits of 2 information per letter if last 8 characters are used as a predictor. • English actually has _______ bit / character if 1 even more info is used for prediction. How Computer Work Lecture 10 Page 10 Data Compression Lot’s O’ Redundant Bits Encoder Fewer Redundant Bits Decoder Lot’s O’ Redundant Bits How Computer Work Lecture 10 Page 11 An Interesting Consequence: • A Data Stream containing the most possible information possible (i.e. the least redundancy) has the statistics of ___________________ !!!!! Random Noise How Computer Work Lecture 10 Page 12 Digital Error Correction Original Message Encoder Original Message + Redundant Bits Corrector Original Message How Computer Work Lecture 10 Page 13 How do we encode digital information in an analog world? Once upon a time, there were these aliens interested in bringing back to their planet the entire library of congress ... How Computer Work Lecture 10 Page 14 The Effect of “Analog” Noise 01101110 01101110 How Computer Work Lecture 10 Page 15 Max. Channel Capacity for Uniform, Bounded Amplitude Noise P Tx Noise Rx N P/N Max # Error-Free Symbols = ________________ Max # Bits / Symbol = _____________________ log2(P/N) How Computer Work Lecture 10 Page 16 Max. Channel Capacity for Uniform, Bounded Amplitude Noise (cont) P = Range of Transmitter’s Signal Space N = Peak-Peak Width of Noise W = Bandwidth in # Symbols / Sec C = Channel Capacity = Max. # of Error-Free Bits/Sec C= W log2(P/N) ____________________________ Note: This formula is slightly different for Gaussian noise. How Computer Work Lecture 10 Page 17 Further Reading on Information Theory The Mathematical Theory of Communication, Claude E. Shannon and Warren Weaver, 1972, 1949. Coding and Information Theory, Richard Hamming, Second Edition, 1986, 1980. How Computer Work Lecture 10 Page 18 The mythical equipotential wire V1 V2 V3 How Computer Work Lecture 10 Page 19 But every wire has parasitics: dI V L - + dt dV IC + - dt How Computer Work Lecture 10 Page 20 Why do wires act like transmission lines? ... ... Signals take time to propagate Propagating Signals must have energy Inductance and Capacitance Stores Energy Without termination, energy reaching the end of a transmission line has nowhere to go - so it Echoes _________________________ How Computer Work Lecture 10 Page 21 Fundamental Equations of Lossless Transmission Lines V V ( x, t ) V I I ( x, t ) x - + x ... ... V I dC I x l t c l dL dx x I V c dx x t How Computer Work Lecture 10 Page 22 Transmission Line Math Lets try a sinusoidal solution for V and I: j ( t t x x ) j t t j x x V V0 e V0e e j ( t t x x ) j t t j x x I I0 e I0e e V I x l t jxV0 l jt I0 I c V jx I0 c jtV0 x t How Computer Work Lecture 10 Page 23 Transmission Line Algebra jxV0 l jt I0 x V0 l t I0 jx I0 c jtV0 x I0 c t V0 t 1 V0 l x lc I0 c Propagation Velocity Characteristic Impedence How Computer Work Lecture 10 Page 24 Parallel Termination How Computer Work Lecture 10 Page 25 Series Termination How Computer Work Lecture 10 Page 26 Series or Parallel ? • Series: – No Static Power Dissipation – Only One Output Point – Slower Slew Rate if Output is Capacitively Loaded • Parallel: – Static Power Dissipation – Many Output Points – Faster Slew Rate if Output is Capacitively Loaded • Fancier Parallel Methods: – AC Coupled - Parallel w/o static dissipation – Diode Termination - “Automatic” impedance matching How Computer Work Lecture 10 Page 27 When is a wire a transmission line? t fl l / v Rule of Thumb: tr 2.5 t fl tr 5 t fl Transmission Line Equipotential Line How Computer Work Lecture 10 Page 28 Making Transmission Lines On Circuit Boards Insulating Dielectric Copper Trace r w t h Voltage Plane Z0 h / (w sqrt( )) c r w/h r v 1/sqrt( ) l h/w r How Computer Work Lecture 10 Page 29 Actual Formulas How Computer Work Lecture 10 Page 30 A Typical Circuit Board 1 Ounce Copper G-10 Fiberglass-Epoxy w 015cm . t 0.0038cm h 0.038cm c 19 pF / cm . Z0 38 l 2.75 nH / cm v 1. 4 1010 cm / sec (14 cm / ns ) How Computer Work Lecture 10 Page 31

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posted: | 1/20/2011 |

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