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

6.02 Spring 2010 Lecture 2 , Slide #6

Sending 0101110, 2.5 microseconds/bit

Received Voltage has not “settled”

10 samples/bit, 400,000 bits/sec

6.02 Spring 2010 Lecture 2 , Slide #7

Sending 0101110, 5 microseconds/bit

Received Voltage is more “settled”.

20 samples/bit, 200,000 bits/sec

6.02 Spring 2010 Lecture 2 , Slide #8

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

6.02 Spring 2010 Lecture 2 , Slide #10

The 6.02 IR Tranceiver – Bounce off ceiling

40 Samples/bit

Dark Room Lights On

100 Samples/bit

6.02 Spring 2010 Lecture 2 , Slide #11

Intersymbol InterferenceLong Bit Period (slow rate)

Short Bit Period (Fast Rate)

6.02 Spring 2010 Lecture 2 , Slide #12

Received Data – Noisy Channel, 24 sample/bit

DigitizingThreshold

Any Bit Errors?

6.02 Spring 2010 Lecture 2 , Slide #13

Eye Diagram-Overlay 3 Period Sections

6.02 Spring 2010 Lecture 2 , Slide #14

Eyes for Ringing versus Slow System

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

Ring

Slow

6.02 Spring 2010 Lecture 2 , Slide #15

Eye Diagram for IR Detector

Eye Diagram 40 Samples per bit, dark room

Eye Diagram 40 Samples per bit, lights on!

6.02 Spring 2010 Lecture 2 , Slide #16

Superposition

6.02 Spring 2010 Lecture 2 , Slide #17

Edge

Superposition

Step Response and results from superposition

6.02 Spring 2010 Lecture 2 , Slide #18

Step Response For Another Example Channel

6.02 Spring 2010 Lecture 2 , Slide #19

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

6.02 Spring 2010 Lecture 2 , Slide #20

Sending 0101110, 1.25 microseconds/bit

5 samples/bit, 800,000 bits/sec

6.02 Spring 2010 Lecture 2 , Slide #21

Eye Diagram for 1.25 microsecond bit period

6.02 Spring 2010 Lecture 2 , Slide #22

Sending 0101110, 2.25 microseconds/bit

6.02 Spring 2010 Lecture 2 , Slide #23

Eye Diagram for 2.25 microsecond bit period

6.02 Spring 2010 Lecture 2 , Slide #24

Sending 0101110, 3.25 microseconds/bit

6.02 Spring 2010 Lecture 2 , Slide #25

Eye Diagram for 3.25 microsecond bit period

6.02 Spring 2010 Lecture 2 , Slide #26

Step Response for Slow Channel

6.02 Spring 2010 Lecture 2 , Slide #27

Slow Channel Response

6.02 Spring 2010 Lecture 2 , Slide #28

Slow Channel Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #29

Slow Channel Response

6.02 Spring 2010 Lecture 2 , Slide #30

Slow Channel Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #31

Slow Channel Response

6.02 Spring 2010 Lecture 2 , Slide #32

Slow Channel Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #33

Slow Channel Response

6.02 Spring 2010 Lecture 2 , Slide #34

Slow Channel Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #35

Slow Channel Response

6.02 Spring 2010 Lecture 2 , Slide #36

Slow Channel Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #37

Step Response for Ringing Channel

6.02 Spring 2010 Lecture 2 , Slide #38

Ringing Channel Response

6.02 Spring 2010 Lecture 2 , Slide #39

Ringing Channel Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #40

Ringing Channel Response

6.02 Spring 2010 Lecture 2 , Slide #41

Ringing Channel Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #42

Ringing Channel Response

6.02 Spring 2010 Lecture 2 , Slide #43

Ringing Channel Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #44

Ringing Channel Response

6.02 Spring 2010 Lecture 2 , Slide #45

Ringing Channel Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #46

Straight Rise Step Response

6.02 Spring 2010 Lecture 2 , Slide #47

Straight Rise Response

6.02 Spring 2010 Lecture 2 , Slide #48

Striaght Rise Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #49

Straight Rise Response

6.02 Spring 2010 Lecture 2 , Slide #50

Striaght Rise Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #51

Straight Rise Response

6.02 Spring 2010 Lecture 2 , Slide #52

Striaght Rise Eye Diagram

6.02 Spring 2010 Lecture 2 , Slide #53

Straight Rise Response

6.02 Spring 2010 Lecture 2 , Slide #54

Striaght Rise Eye Diagram