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How Computer Work Lecture 10 Introduction to the Physics of Communication
The Digital Abstraction Part 1: The Static Discipline Noise Tx Rx V ol V oh V ih V il
What is Information? Information Resolves ______________ Uncertainty
How do we measure information? Error-Free data resolving 1 of 2 equally likely possibilities = ________________  of information. 1 bit
How much information now? 3 independent coins yield ___________ of information # of possibilities = ___________ 3 bits 8
How about N coins ? N independent coins yield # bits = ___________________________ # of possibilities = ___________  N 2 N
What about Crooked Coins? P head  = .75 P tail  = .25 # Bits = -   p i  log 2  p i (about .81 bits for this example)
How Much Information ?  None (on average)
How Much Information Now ?   Predictor None (on average)
How About English? ,[object Object],[object Object],[object Object],[object Object],log 2 (26) 2 1
Data Compression Lot’s O’ Redundant Bits Encoder Decoder Fewer Redundant Bits Lot’s O’ Redundant Bits
An Interesting Consequence: ,[object Object],Random Noise
Digital Error Correction Encoder Corrector Original Message + Redundant Bits Original Message Original Message
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 ...
The Effect of “Analog” Noise  
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)
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)
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.
The mythical equipotential wire
But every wire has parasitics: - + + -
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
Fundamental Equations of Lossless Transmission Lines ... ... + -
Transmission Line Math Lets try a sinusoidal solution for V and I:
Transmission Line Algebra Propagation Velocity Characteristic Impedence
Parallel Termination
Series Termination
Series or Parallel ? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
When is a wire a transmission line? Rule of Thumb: Transmission Line Equipotential Line
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  )
Actual Formulas
A Typical Circuit Board G-10 Fiberglass-Epoxy 1 Ounce Copper

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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.
  • 11. Data Compression Lot’s O’ Redundant Bits Encoder Decoder Fewer Redundant Bits Lot’s O’ Redundant Bits
  • 12.
  • 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.
  • 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.
  • 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 )
  • 31. A Typical Circuit Board G-10 Fiberglass-Epoxy 1 Ounce Copper