Telecommunications Networking IMetallic CablesSlide 3Metallic Cables (cont’d)Slide 5Metallic Cable SystemWhat can we say about r(t)?What can we say about h(t)?Typical Coaxial Cable LossesWhat can we say about h(t)? (cont’d)“Dispersion”What can we say about n(t)?Slide 13What can we say about i(t)?Our challenge:Example: Dispersion-Limited Operation; 6dB maximum rolloffExample: Dispersion Limited Operation (cont’d)Example: Noise Limited OperationNoise Limited Operation (cont’d)Slide 20Example:Noise Limited Operation (cont’d)Example: Noise Limited Operation (cont’d)Line AmplifiersLine Amplifiers (cont’d)Line Amplifiers (Con’t)Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Line Amplifiers (continued)Traditional Cable Television SystemFrequency Division Multiplexing (FDM): Typical Cable SystemFDM: Typical Cable SystemCable TV FDM: IssuesImpact of Distortion on FDMImpact of Distortion (cont’d)Impact of NoiseRadio Frequency InterferenceHome “Wiring” ConcernsCopyright 1998, S.D. Personick. All Rights Reserved.Telecommunications Networking ILectures 6-8Point-to-Point Communication over Metallic CablesCopyright 1998, S.D. Personick. All Rights Reserved.Metallic CablesInsulated Copper Wires Coaxial Cable Center ConductorShield InsulatorCopyright 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 homesCopyright 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 cableCopyright 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 homesCopyright 1998, S.D. Personick. All Rights Reserved.Metallic Cable SystemInformationTransmitterSignal (e.g., 1 volt peak)CableCable (continued)s(t)r(t)ReceiverInformationCopyright 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, anda*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 Losses024681012dB/100 feet1 MHz 10MHz100MHz1 GHzRG-174RG-58RG-8Copyright 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)-lightningCopyright 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 cableCopyright 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 rolloffs(t)r(t) cables(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 feetCopyright 1998, S.D. Personick. All Rights Reserved.Example: Noise Limited Operations(t) cable: H(f)Noise=4kTBReceiver, includes equalizer: G(f)H(f):Equalizer: G(f)Copyright 1998, S.D. Personick. All Rights Reserved.Noise Limited Operation (cont’d)•The