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6.2 Wireline channels

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The analysis and transfer characteristics of wireline channels.

Wireline channels were the first used for electrical communications in the mid-nineteenth century for the telegraph.Here, the channel is one of several wires connecting transmitter to receiver. The transmitter simply creates a voltage relatedto the message signal and applies it to the wire(s). We must have a circuit—a closed path—that supports current flow. In thecase of single-wire communications, the earth is used as the current's return path. In fact, the term ground for the reference node in circuits originated in single-wire telegraphs. You can imagine that the earth's electricalcharacteristics are highly variable, and they are. Single-wire metallic channels cannot support high-quality signaltransmission having a bandwidth beyond a few hundred Hertz over any appreciable distance.

Coaxial cable cross-section

Coaxial cable consists of one conductor wrapped around the central conductor. This type of cable supports broaderbandwidth signals than twisted pair, and finds use in cable television and Ethernet.

Consequently, most wireline channels today essentially consist of pairs of conducting wires ( [link] ), and the transmitter applies a message-related voltage across the pair. How these pairs of wires arephysically configured greatly affects their transmission characteristics. One example is twisted pair , wherein the wires are wrapped about each other. Telephonecables are one example of a twisted pair channel. Another is coaxial cable , where a concentric conductor surrounds a central wire with a dielectric material in between.Coaxial cable, fondly called "co-ax" by engineers, is what Ethernet uses as its channel. In either case, wireline channelsform a dedicated circuit between transmitter and receiver. As we shall find subsequently, several transmissions can share thecircuit by amplitude modulation techniques; commercial cable TV is an example. These information-carrying circuits are designedso that interference from nearby electromagnetic sources is minimized. Thus, by the time signals arrive at the receiver,they are relatively interference- and noise-free.

Both twisted pair and co-ax are examples of transmission lines , which all have the circuit model shown in [link] for an infinitesimally small length. This circuit model arisesfrom solving Maxwell's equations for the particular transmission line geometry.

Circuit model for a transmission line

The so-called distributed parameter model for two-wire cables has the depicted circuit model structure. Element valuesdepend on geometry and the properties of materials used to construct the transmission line.
The series resistance comes from the conductor used in the wires and from the conductor's geometry.The inductance and the capacitance derive from transmission line geometry, and the parallel conductance from the medium betweenthe wire pair. Note that all the circuit elements have values expressed by the product of a constant times a length; thisnotation represents that element values here have per-unit-length units. For example, the series resistance R ∼ has units of ohms/meter. For coaxial cable, the element values depend on the inner conductor's radius r i , the outer radius of the dielectric r d , the conductivity of the conductors σ , and the conductivity σ d , dielectric constant ε d , and magnetic permittivity μ d of the dielectric as
R ∼ 1 2 δ σ 1 r d 1 r i
C ∼ 2 ε d r d r i G ∼ 2 σ d r d r i L ∼ μ d 2 r d r i For twisted pair, having a separation d between the conductors that have conductivity σ and common radius r and that are immersed in a medium having dielectric and magnetic properties, the elementvalues are then
R ∼ 1 r δ σ
C ∼ ε d 2 r G ∼ σ d 2 r L ∼ μ δ 2 r d 2 r

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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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