6.02 Spring 2010 Lecture #2 - Massachusetts Institute of...

6.02 Spring 2010 Lecture 2 , Slide #1

6.02 Spring 2010Lecture #2

• Samples and Bits• Real Wires• Models• Linearity and Superposition

6.02 Spring 2010 Lecture 2 , Slide #2

6.02 Lecture 2 – Wires and Models

• Wires, Samples, and Bits• Non-Ideal Transmission

– Example wires and signal impact– Intersymbol Interference and Eye Diagrams

• Modeling Wires– Causality– Time-invariance– Linearity

• SUPERPOSITION– Demonstrating why it is so super

6.02 Spring 2010 Lecture 2 , Slide #3

Types of Real “Wires”

http://materials.usask.ca/images/photos/SEMof3LevelCuInterconP98.GIF

IC Interconnect

http://www.gpv-pcb.com/Files/Billeder/fabrikker/chemitalic/Chem_pcb_hdi.jpg

Printed Circuit Board

http://www.satamerica.com/imagens/4a27897r1.jpg

Transatlantic Cable

Slow Response Ringing

May also have long delays (Receiver does NOT know)

6.02 Spring 2010 Lecture 2 , Slide #4

Transmission Setup and Notation

Xmit RcvrBits in

Bits out

Channel

Sample Rates:4 million Samples/Second (IR Transceiver)

Up to gigaSamples/Second (Fastest)

6.02 Spring 2010 Lecture 2 , Slide #5

Samples, Bit Period, Bit Rate• Our Hardware

– Updates transmitter output voltage every ¼ microsecond (4 million times a second).

– Remeasures receiver voltage every ¼ microsecond (4 million times a second).

• Bit Period and Bit Rate– BP = Samples/bit * ¼ microsecond– BR = Bits transmitted per second – BR = (4 million) / (Samples/bit)

• Slower Bit Rate = Longer Bit Period– More time to propagate through channel

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Sending 0101110, 2.5 microseconds/bit

Received Voltage has not “settled”

10 samples/bit, 400,000 bits/sec

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Sending 0101110, 5 microseconds/bit

Received Voltage is more “settled”.

20 samples/bit, 200,000 bits/sec

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Sending 0101110, 7.5 microseconds/bit

Received Voltage much more “settled”

30 samples/bit, 133,333 bits/sec

6.02 Spring 2010 Lecture 2 , Slide #9

The 6.02 Infrared Transceiver

400 Samples/bit

Xmit Rcvr Bits out

Loopback Setup

IR IR xmitter IR rcvr

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The 6.02 IR Tranceiver – Bounce off ceiling

40 Samples/bit

Dark Room Lights On

100 Samples/bit

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Intersymbol InterferenceLong Bit Period (slow rate)

Short Bit Period (Fast Rate)

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Received Data – Noisy Channel, 24 sample/bit

DigitizingThreshold

Any Bit Errors?

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Eye Diagram-Overlay 3 Period Sections

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Eyes for Ringing versus Slow System

Medium Bit Period(33 samples) Short Bit Period(20 samples)

Ring

Slow

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Eye Diagram for IR Detector

Eye Diagram 40 Samples per bit, dark room

Eye Diagram 40 Samples per bit, lights on!

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Superposition

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Edge

Superposition

Step Response and results from superposition

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Step Response For Another Example Channel

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0 01 1 1 0

Rising Edge add step response

Falling Edge, subtract step response

Rising Edge add step response

Falling Edge, subtract step response

XmitData

Time shifted and sign adjusted channel step reponses

Summed responses = Rcv’d data

Edge

Superposition

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Sending 0101110, 1.25 microseconds/bit

5 samples/bit, 800,000 bits/sec

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Eye Diagram for 1.25 microsecond bit period

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Sending 0101110, 2.25 microseconds/bit

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Eye Diagram for 2.25 microsecond bit period

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Sending 0101110, 3.25 microseconds/bit

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Eye Diagram for 3.25 microsecond bit period

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Step Response for Slow Channel

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Slow Channel Response

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Slow Channel Eye Diagram

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Slow Channel Response

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Slow Channel Eye Diagram

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Slow Channel Response

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Slow Channel Eye Diagram

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Slow Channel Response

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Slow Channel Eye Diagram

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Slow Channel Response

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Slow Channel Eye Diagram

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Step Response for Ringing Channel

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Ringing Channel Response

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Ringing Channel Eye Diagram

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Ringing Channel Response

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Ringing Channel Eye Diagram

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Ringing Channel Response

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Ringing Channel Eye Diagram

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Ringing Channel Response

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Ringing Channel Eye Diagram

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Straight Rise Step Response

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Straight Rise Response

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Striaght Rise Eye Diagram

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Straight Rise Response

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Striaght Rise Eye Diagram

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Straight Rise Response

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Striaght Rise Eye Diagram

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Straight Rise Response

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Striaght Rise Eye Diagram