DREXEL ECES 490 - Lectures 6-8 Point-to-Point Communication over Metallic Cables (43 pages)

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Lectures 6-8 Point-to-Point Communication over Metallic Cables



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Lectures 6-8 Point-to-Point Communication over Metallic Cables

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Pages:
43
School:
Drexel University
Course:
Eces 490 - ST:Cell and Tissue Image Anal
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Telecommunications Networking I Lectures 6 8 Point to Point Communication over Metallic Cables Copyright 1998 S D Personick All Rights Reserved Metallic Cables Insulated Copper Wires Insulator Shield Coaxial Cable Center Conductor Copyright 1998 S D Personick All Rights Reserved Metallic Cables Copper wire wire pair cable is a very important medium because essentially all homes and small businesses in the United States and in most other parts of the world currently access the worldwide telecommunications infrastructure using a pair of wires wire pairs are very commonly used for local area networks in offices and homes Copyright 1998 S D Personick All Rights Reserved Metallic Cables cont d Coaxial cable is a very important medium because more than 80 of residences in the U S and a large fraction of residences in many other parts of the world can access the telecommunications infrastructure using coaxial cable many local area networks utilize coaxial cable Copyright 1998 S D Personick All Rights Reserved Metallic Cables cont d While optical fibers and wireless carry a growing share of telecommunications traffic metallic cables will continue to carry the majority of local area network and access network traffic for many years to come The cost of replacing all of the metallic access cable in the U S with fiber would be around 1000 home x 100 million homes Copyright 1998 S D Personick All Rights Reserved Metallic Cable System Information s t Transmitter Cable Signal e g 1 volt peak Cable continued r t Receiver Information Copyright 1998 S D Personick All Rights Reserved What can we say about r t r t s t h t n t i t where s t is the signal that enters the cable h t is the impulse response of the cable n t is noise associated with the finite temperature of the cable i t is interference from other signals and a b means the convolution of a t and b t Copyright 1998 S D Personick All Rights Reserved What can we say about h t h t is the cable s impulse response and is equal to the Fourier transform of the cable s frequency response H f H f the cable s frequency response approximately takes the form 20 log H f aL f 1 2 where L is the cable length km and a is a constant dB km Hz 1 2 Copyright 1998 S D Personick All Rights Reserved Typical Coaxial Cable Losses 12 10 8 RG 174 RG 58 RG 8 dB 100 feet 6 4 2 0 1 MHz 10 MHz 100 1 GHz MHz Copyright 1998 S D Personick All Rights Reserved What can we say about h t cont d The frequency response H f rolls off as 10 square root of the frequency f due to the skin effect in a metallic cable either wire pair cable or coaxial cable This rolloff by definition attenuates higher frequencies more than lower frequencies and causes dispersion of the signal s t Copyright 1998 S D Personick All Rights Reserved Dispersion Input pulse volts vs time microseconds Output pulse millivolts vs time microseconds Copyright 1998 S D Personick All Rights Reserved What can we say about n t Noise as we define it here is an unwanted signal or the sum of several unwanted signals each of which is caused by a natural phenomenon Examples of sources of noise are thermally induced random fluctuations of the properties of materials thermal noise lightning Copyright 1998 S D Personick All Rights Reserved What can we say about n t In cables n t is usually well modeled as white Gaussian noise This additive noise is called thermal noise and results from the combination of the finite temperature of the cable e g 293K and the finite loss of the cable Copyright 1998 S D Personick All Rights Reserved What can we say about i t i t is a man made interference signal that adds to the desired signal at the receiver Interference can be caused by signals on other pairs of wire in the same wire pair cable called crosstalk signals generated outside of the cable that leak into the cable e g nearby strong radio signals Copyright 1998 S D Personick All Rights Reserved Our challenge Figure out how to do the best job we can of estimating the underlying information being communicated given the received signal r t Understand what the basic limitations of cable systems are e g how far can we transmit and still recover the underlying information with adequate fidelity Copyright 1998 S D Personick All Rights Reserved Example Dispersion Limited Operation 6dB maximum rolloff s t r t cable s t is a 1 volt pulse 100 ns wide The cable is RG8X with a loss of 1 8 dB 100ft 20MHz Suppose that the maximum allowable loss at 1 100ns 10 MHz is 6dB What is the maximum allowable cable length Copyright 1998 S D Personick All Rights Reserved Example Dispersion Limited Operation cont d If the cable loss at 20 MHz is 1 8 dB 100ft then the loss at 10 MHz is 1 8 x 10 20 0 5 1 8 707 1 3dB 100ft If the maximum allowable rolloff at 10MHz between the transmitter and the receiver is 6dB then the maximum allowable cable length is 6 1 3 100ft 460 feet Copyright 1998 S D Personick All Rights Reserved Example Noise Limited Operation s t cable H f Noise 4kTB H f Receiver includes equalizer G f Equalizer G f Copyright 1998 S D Personick All Rights Reserved Noise Limited Operation cont d The equalizer in the receiver amplifies higher frequencies more than lower frequencies to compensate for the rolloff in the cable The equalizer also amplifies the higher frequency noise at its input kT Boltzman s constant x temperature K approximately 4 x 10 21 J 293K Copyright 1998 S D Personick All Rights Reserved Example Noise Limited Operation Suppose the receiver has input noise within band B whose variance is 4kTB watts where B 1 100ns Suppose the signal to noise ratio SNR at the receiver input must be 100 1 20dB where SNR s max 2 R 10 aL 10 4kTB Suppose s max 1 volt a 5dB 100ft T 293K and R 50 ohms What is the maximum allowable cable length L Copyright 1998 S D Personick All Rights Reserved Example Noise Limited Operation cont d s max 2 R 1 2 50 0 02 watts 4kTB 4 4 x10 21 10 7 1 6x10 13 watts SNR 02 1 6x10 13 10 aL 10 1 25x10 11 10 aL 10 If the SNR must be greater than 100 I e 20dB then 10 aL 10 must be greater than 1 25x10 9 I e aL 89dB Copyright 1998 S D Personick All Rights Reserved Example Noise Limited Operation cont d If aL must be less than 89 dB and a equals 5 dB 100ft then the maximum cable length is 89 5 100 ft 1800 ft Copyright 1998 S D Personick All Rights Reserved Line Amplifiers We can extend the distance of transmission in …


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