# Transmission Lines

**Topics:**Transmission line, Twisted pair, Impedance matching

**Pages:**13 (2952 words)

**Published:**March 13, 2013

Definition

A transmission line is the conductive connection between system elements that carry signal power This “conductor” may at first appear to be a short circuit, but in fact will react differently when high frequencies are propagated along the line.

Types of Transmission Lines

Two-wire open line Twisted pair Unshielded twisted pair (UTP) Shielded Pair Coaxial Lines Balanced/Unbalanced lines

Two Wire Open Line

Two Wire Open

Also called twin lead or two wire ribbon cable Usually spaced from ¼ to 6 inches apart Used as the transmission line from antenna to receiver or antenna to transmitter The end connected to the source is called the generator or input end The end connected to the load is the load or output end.

Electrical Characteristics

Depend on the construction Essentially a long capacitor where the capacitance is inversely proportional to the spacing between the wires and directly proportional to the length of the line Capacitive reactance is inversely proportional to the capacitance and frequency

Thus the line will have a total impedance resulting from:

• Pure resistance caused by the wire itself • Capacitive reactance • Conductance which passes through the dielectric medium • Inductive reactance caused by the magnetic fields which are produced by the passing of current through the wires

FIGURE 3

Equivalent circuit for a two-wire transmission line. two-

If the line is uniform along its length, the resistance and conductance are usually negligible which results in an LC network

FIGURE 4

Simplified circuit terminated with its characteristic impedance.

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Characteristic Impedance

Z0 symbolizes the characteristic impedance. This impedance can be determined by using Ohm’s Law: applied voltage divided by the current flowing through the wire.

If the inductance and capacitance is known, the impedance is given by taking the square root of (L/C) • A line with 4ηH/m and 1.5 pF/m will exhibit a characteristic impedance of 51.6 Ω

If the spacing between the wires and the diameter of one of the conductors and type of dielectric is known, the impedance can be found by: • Z0 =

276 2D log d ε

• A D/d ratio of 3 and air dielectric will result in an impedance of 215 Ω

Line Losses

When calculating impedance of lines, losses are often ignored, but in real life these losses cannot be ignored. Major losses • Copper • Dielectric • Radiation or induction

I2R losses

Resistance of any conductor is never zero. So when current is passed through the wire, energy is lost in the form of heat Since R = ρl/A These losses can be reduced by reducing the resistance of the wire by • Reducing the length • Increasing the cross sectional area of the wire • Using a wire with a lower resistivity

Skin Effect

At high frequencies, the I2R losses are generally due to skin effect. • When DC is applied the distribution of electron movement is fairly uniform • When AC is applied, the flux density at the center of the wire is greater than at the outer edge thus the the reactance is is also greater. The more reactance the lower the current. • If other words, when AC is applied the current will flow faster on the outer edge of the conductor than through the center

Skin Effect

Since inductive reactance is directly proportional to the frequency, the skin effect increases with frequency as well. Since the current is forced to the outside edge, the resistance cross section is also reduced thus increasing the resistance. At sufficiently high frequencies, current will cease to flow in two wire lines

Dielectric Losses

These losses are directly proportional to the voltage across the dielectric These losses also increase with frequency Losses are lowest in air dielectrics

Radiation or Induction Losses

These are caused by the electrostatic and electromagnetic fields...

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