How Computer Work
- 1. How Computer Work Lecture 10 Introduction to the Physics of Communication
- 2. The Digital Abstraction Part 1: The Static Discipline Noise Tx Rx V ol V oh V ih V il
- 3. What is Information? Information Resolves ______________ Uncertainty
- 4. How do we measure information? Error-Free data resolving 1 of 2 equally likely possibilities = ________________ of information. 1 bit
- 5. How much information now? 3 independent coins yield ___________ of information # of possibilities = ___________ 3 bits 8
- 6. How about N coins ? N independent coins yield # bits = ___________________________ # of possibilities = ___________ N 2 N
- 7. What about Crooked Coins? P head = .75 P tail = .25 # Bits = - p i log 2 p i (about .81 bits for this example)
- 8. How Much Information ? None (on average)
- 9. How Much Information Now ? Predictor None (on average)
- 10. How About English? 6.JQ4 ij a vondurfhl co8rse wibh sjart sthdenjs. If every English letter had maximum uncertainty, average information / letter would be _________ Actually, English has only ______ bits of information per letter if last 8 characters are used as a predictor. English actually has _______ bit / character if even more info is used for prediction. log 2 (26) 2 1
- 11. Data Compression Lot’s O’ Redundant Bits Encoder Decoder Fewer Redundant Bits Lot’s O’ Redundant Bits
- 12. An Interesting Consequence: A Data Stream containing the most possible information possible (i.e. the least redundancy) has the statistics of ___________________ !!!!! Random Noise
- 13. Digital Error Correction Encoder Corrector Original Message + Redundant Bits Original Message Original Message
- 14. 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 ...
- 15. The Effect of “Analog” Noise
- 16. Max. Channel Capacity for Uniform, Bounded Amplitude Noise P N Noise Tx Rx Max # Error-Free Symbols = ________________ Max # Bits / Symbol = _____________________ P/N log 2 (P/N)
- 17. 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 = ____________________________ Note: This formula is slightly different for Gaussian noise. W log 2 (P/N)
- 18. 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.
- 19. The mythical equipotential wire
- 20. But every wire has parasitics: - + + -
- 21. 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
- 22. Fundamental Equations of Lossless Transmission Lines ... ... + -
- 23. Transmission Line Math Lets try a sinusoidal solution for V and I:
- 24. Transmission Line Algebra Propagation Velocity Characteristic Impedence
- 27. 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
- 28. When is a wire a transmission line? Rule of Thumb: Transmission Line Equipotential Line
- 29. Making Transmission Lines On Circuit Boards h w t Voltage Plane Insulating Dielectric Copper Trace r w/h h/w h / (w sqrt( r ) ) 1/sqrt( r )
- 30. Actual Formulas
- 31. A Typical Circuit Board G-10 Fiberglass-Epoxy 1 Ounce Copper