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Losses in Transmission Lines

In: Science

Submitted By benazeerali121
Words 3394
Pages 14
ABSTRACT: -
The transmission lines are considered to be impedance matching circuits designed to deliver rf power from the transmitter to the antenna, and maximum signal from the antenna to the receiver. During this signal transfer certain types of losses occurs e.g.-conductor losses, dielectric heating losses, radiation losses, insertion losses, power losses, and losses due to corona. The objective of this paper is to discuss all these losses.

INTRODUCTION:-
Before discussing about losses in transmission lines we have to know about transmission lines, their history, their theory, their properties and different types of transmission lines. A TRANSMISSION LINE is a device designed to guide electrical energy from one point to another. It is used, for example, to transfer the output rf energy of a transmitter to an antenna. This energy will not travel through normal electrical wire without great losses. Although the antenna can be connected directly to the transmitter, the antenna is usually located some distance away from the transmitter. On board ship, the transmitter is located inside a radio room and its associated antenna is mounted on a mast. A transmission line is used to connect the transmitter and the antenna. The transmission line has a single purpose for both the transmitter and the antenna. This purpose is to transfer the energy output of the transmitter to the antenna with the least possible power loss. How well this is done depends on the special physical and electrical characteristics (impedance and resistance) of the transmission line. In an electronic system, the delivery of power requires the connection of two wires between the source and the load. At low frequencies, power is considered to be delivered to the load through the wire. In the microwave frequency region, power is considered to be in electric and magnetic fields that are guided from place to place by some physical structure. Any physical structure that will guide an electromagnetic wave place to place is called a Transmission Line. Components of transmission lines include wires, coaxial cables, dielectric slabs, optical fibers, electric power lines, and waveguides.

HISTORY:- Mathematical analysis of the behavior of electrical transmission lines grew out of the work of James Clerk Maxwell, Lord Kelvin and Oliver Heaviside. In 1855 Lord Kelvin formulated a diffusion model of the current in a submarine cable. The model correctly predicted the poor performance of the 1858 trans-Atlantic submarine telegraph cable. In 1885 Heaviside published the first papers that described his analysis of propagation in cables and the modern form of the telegrapher’s equations.

TERMINOLOGY:-

All transmission lines have two ends (see figure1.) The end of a two-wire transmission line connected to a source is ordinarily called the INPUT END or the GENERATOR END. Other names given to this end are TRANSMITTER END, SENDING END, and SOURCE. The other end of the line is called the OUTPUT END or RECEIVING END. Other names given to the output end are LOAD END and SINK.

Figure 1.—Basic transmission line.

You can describe a transmission line in terms of its impedance. The ratio of voltage to current (Ein/Iin) at the input end is known as the INPUT IMPEDANCE (Zin). This is the impedance presented to the transmitter by the transmission line and its load, the antenna.

The ratio of voltage to current at the output (Eout/Iout) end is known as the OUTPUT IMPEDANCE (Zout). This is the impedance presented to the load by the transmission line and its source. If an infinitely long transmission line could be used, the ratio of voltage to current at any point on that transmission line would be some particular value of impedance. This impedance is known as the CHARACTERISTIC IMPEDANCE. Z0=√ (L/C)

Now certain properties of transmission lines are discussed in brief as given below:-

LUMPED CONSTANTS are theoretical properties (inductance, resistance, and capacitance) of a transmission line that are lumped into a single component.

DISTRIBUTED CONSTANTS:-

Transmission line constants, called distributed constants, are spread along the entire length of the transmission line and cannot be distinguished separately. The amount of inductance, capacitance, and resistance depends on the length of the line, the size of the conducting wires, the spacing between the wires and the dielectric (air or insulating medium) between the wires.

Inductance of a Transmission Line:-

When current flows through a wire, magnetic lines of force are set up around the wire. As the current increases and decreases in amplitude, the field around the wire expands and collapses accordingly. The energy produced by the magnetic lines of force collapsing back into the wire tends to keep the current flowing in the same direction. This represents a certain amount of inductance, which is expressed in micro henrys per unit length. Figure2. Illustrate the inductance and magnetic fields of transmission lines.¬ Figure2. –Distributed inductance

Capacitance of a Transmission Line: -

Capacitance also exists between the transmission line wires, as illustrated in figure 3. Notice that the two parallel wires act as plates of a capacitor and that the air between them acts as a dielectric. The capacitance between the wires is usually expressed in Pico farads per unit length. This electric field between the wires is similar to the field that exists between the two plates of a capacitor. Figure 3.—Distributed capacitance

Resistance of a Transmission Line: -

The transmission line shown in figure ( 4.) has electrical resistance along its length. This resistance is usually expressed in ohms per unit length and is shown as existing continuously from one end of the line to the other. Figure 4.—Distributed resistance.

LEAKAGE CURRENT flows between the wires of a transmission line through the dielectric. The dielectric act as a resistor.

An ELECTROMAGNETIC FIELD exists along transmission line when current flows through it.

CHARACTERISTIC IMPEDANCE, Z0, is the ratio of E to I at every point along the line. For maximum transfer of electrical power, the characteristic impedance and load impedance must be matched.

STANDING WAVE RATIO is the measurement of maximum voltage (current) to minimum voltage (current) on a transmission line and measures the perfection of the termination of the line. A ratio of 1:1 describes a line terminated in its characteristic impedance. SWR=Imax¬¬/Imin or Emax/Emin

TYPES OF TRANSMISSION LINES:-

There are two types of commonly used transmission lines.
• The balanced lines(parallel-wires)
• Unbalanced lines(co-axial cables)

THE BALANCED LINES

In telecommunication and professional audio, a balanced line or balanced signal pair is a transmission line consisting of two conductors of the same type, and equal impedance to ground and other circuits.

Transmission lines are generally unbalanced or balanced. Unbalanced are usually coaxial cables, rarely single-wire earth returns while balanced are twin-lead for radio frequency signals or twisted pair for lower frequencies. A balun may be used to connect the two kinds.

Balanced lines are often operated with differential signals. External interfering sources, when present, tend to induce a common mode signal on the line.

The balanced impedances to ground minimize differential pickup due to stray electric fields. The conductors are sometimes twisted together to ensure that each conductor is equally exposed to any external magnetic fields that would induce unwanted noise. The line is capable of being operated in such a way that when the impedances of the two conductors’ at all transverse planes are equal in magnitude and opposite in polarity with respect to ground, the currents in the two conductors are equal in magnitude and opposite in direction.

ADVANTAGES

Compared to single-wire earth return circuits, balanced lines reduce the amount of noise per distance, allowing a longer cable run to be practical. This is because electromagnetic interference will affect both signals the same way. Similarities between the two signals are automatically removed at the end of the transmission path when one signal is subtracted from the other.

TWO-WIRE OPEN LINES are parallel lines and have uses such as power lines, rural telephone lines, and telegraph lines. This type of line has high radiation losses and is subject to noise pickup.

TWIN LEAD has parallel lines and is most often used to connect televisions to their antennas.

A TWISTED PAIR consists of two insulated wires twisted together. This line has high insulation loss.

A SHIELDED PAIR has parallel conductors separated by a solid dielectric and surrounded by copper braided tubing. The conductors are balanced to ground.

UNBALANCED LINES (CO-AXIAL CABLES)

There are two types of COAXIAL LINES, RIGID (AIR) COAXIAL LINE and FLEXIBLE (SOLID) COAXIAL LINE. The physical construction of both types is basically the same; that is, each contains two concentric conductors.

The rigid coaxial line consists of a central, insulated wire (inner conductor) mounted inside a tubular outer conductor. This line is shown in figure 5. In some applications, the inner conductor is also tubular. The inner conductor is insulated from the outer conductor by insulating spacers or beads at regular intervals. The spacers are made of Pyrex, polystyrene, or some other material that has good insulating characteristics and low dielectric losses at high frequencies.

Figure 5.—Air coaxial line
The chief advantage of the rigid line is its ability to minimize radiation losses. The electric and magnetic fields in a two-wire parallel line extend into space for relatively great distances and radiation losses occur. However, in a coaxial line no electric or magnetic fields extend outside of the outer conductor. The fields are confined to the space between the two conductors, resulting in a perfectly shielded coaxial line. Another advantage is that interference from other lines is reduced.
The rigid line has the following disadvantages: (1) it is expensive to construct; (2) it must be kept dry to prevent excessive leakage between the two conductors; and (3) although high-frequency losses are somewhat less than in previously mentioned lines, they are still excessive enough to limit the practical length of the line.
Leakage caused by the condensation of moisture is prevented in some rigid line applications by the use of an inert gas, such as nitrogen, helium, or argon. It is pumped into the dielectric space of the line at a pressure that can vary from 3 to 35 pounds per square inch. The inert gas is used to dry the line when it is first installed and pressure is maintained to ensure that no moisture enters the line. Flexible coaxial lines (figure 6.) are made with an inner conductor that consists of flexible wire insulated from the outer conductor by a solid, continuous insulating material. The outer conductor is made of metal braid, which gives the line flexibility. Early attempts at gaining flexibility involved using rubber insulator between the two conductors. However, rubber insulators caused excessive losses at high frequencies.

Figure 6.—Flexible coaxial line.

WAVEGUIDES are hollow metal tubes used to transfer energy from one point to another. The energy travels slower in a waveguide than in free space.

LOSSES IN TRANSMISSION LINES:-

A real transmission line exhibits a certain amount of loss, caused by the resistance of the conductors used in the line and by dielectric losses in the line’s insulators.
The matched-line loss for a particular type and length of transmission line, operated at a particular frequency, is the loss when the line is terminated in a resistance equal to its characteristic impedance. The loss in a line is lowest when it is operated as a matched line. Line losses increase when SWR is greater than 1:1. Each time energy flows from the generator toward the load, or is reflected at the load and travels back toward the generator, a certain amount will be lost along the line. The net effect of standing waves on a transmission line is to increase the average value of current and voltage, compared to the matched-line case. An increase in current raises I¬¬2R (ohmic) losses in the conductors, and an increase in RF voltage increases E2/R losses in the dielectric. Line loss rises with frequency, since the conductor resistance is related to skin effect, and also because dielectric losses rise with frequency. Matched-line loss is stated in decibels per hundred feet at a particular frequency. These losses are discussed as follows:-

TRANSMISSION LOSS:-

The ratio of the power at one point in a transmission system to the power at a point farther along the line; usually expressed in decibels. The actual power that is lost in transmitting a signal from one point to another through a medium or along a line. Also known as loss.

The discussion of transmission lines so far has not directly addressed LINE LOSSES; actually some line losses occur in all lines. Line losses may be any of three types—COPPER, DIELECTRIC, and RADIATION or INDUCTION LOSSES. Instead of these losses certain other losses also exists. Losses are discussed as follows:-

Copper Losses

One type of copper loss is I2R LOSS. In rf lines the resistance of the conductors is never equal to zero. Whenever current flows through one of these conductors, some energy is dissipated in the form of heat. This heat loss is a POWER LOSS. With copper braid, which has a resistance higher than solid tubing, this power loss is higher.

Another type of copper loss is due to SKIN EFFECT. When dc flows through a conductor, the movement of electrons through the conductor's cross section is uniform. The situation is somewhat different when ac is applied. The expanding and collapsing fields about each electron encircle other electrons. This phenomenon, called SELF INDUCTION, retards the movement of the encircled electrons.

The flux density at the centre is so great that electron movement at this point is reduced. As frequency is increased, the opposition to the flow of current in the centre of the wire increases. Current in the centre of the wire becomes smaller and most of the electron flow is on the wire surface. When the frequency applied is 100 megahertz or higher, the electron movement in the centre is so small that the centre of the wire could be removed without any noticeable effect on current. You should be able to see that the effective cross-sectional area decreases as the frequency increases. Since resistance is inversely proportional to the cross-sectional area, the resistance will increase as the frequency is increased.
Also, since power loss increases as resistance increases, power losses increase with an increase in frequency because of skin effect. Copper losses can be minimized and conductivity increased in an rf line by plating the line with silver. Since silver is a better conductor than copper, most of the current will flow through the silver layer. The tubing then serves primarily as a mechanical support.

Dielectric Losses

DIELECTRIC LOSSES result from the heating effect on the dielectric material between the conductors. Power from the source is used in heating the dielectric. The heat produced is dissipated into the surrounding medium. When there is no potential difference between two conductors, the atoms in the dielectric material between them are normal and the orbits of the electrons are circular. When there is a potential difference between two conductors, the orbits of the electrons change. The excessive negative charge on one conductor repels electrons on the dielectric toward the positive conductor and thus distorts the orbits of the electrons. A change in the path of electrons requires more energy, introducing a power loss.

The atomic structure of rubber is more difficult to distort than the structure of some other dielectric materials. The atoms of materials, such as polyethylene, distort easily. Therefore, polyethylene is often used as a dielectric because less power is consumed when its electron orbits are distorted.

Radiation and Induction Losses

RADIATION and INDUCTION LOSSES are similar in that both are caused by the fields surrounding the conductors. Induction losses occur when the electromagnetic field about a conductor cuts through any nearby metallic object and a current is induced in that object. As a result, power is dissipated in the object and is lost. Radiation losses occur because some magnetic lines of force about a conductor do not return to the conductor when the cycle alternates. These lines of force are projected into space as radiation and this result in power losses. That is, power is supplied by the source, but is not available to the load.

To REDUCE Radiation losses, (1) the transmission line height should be reduced, (2) the characteristic impedance be increased, (3) the propagation constant of the current be increased, and (4) the distance to the side plate be reduced.

Insertion Losses

In telecommunications, insertion loss is the loss of signal power resulting from the insertion of a device in a transmission line or optical fiber. Usually expressed as a ratio in dB relative to the transmitted signal power, it can also be referred to as attenuation.

If the power transmitted by the source is PT and the power received by the load is PR, then the insertion loss in dB is given by

In metallic conductor systems, radiation losses, resistive losses in the conductor as well as losses in the surrounding dielectric all reduce the power. Line terminations play an important part in insertion loss because they reflect some of the power. All of these effects can be conceptually modeled as various elements which make up the equivalent circuit of the line.

In an optical fiber system, insertion loss is introduced by things such as connectors, splices, and couplers.

These losses are also called coupling losses these occurs whenever there a connection is made to or from a transmission line or when two section of transmission line are connected together. Mechanical connections are discontinuities tend to heat up, radiate energy and dissipate power.

CORONA

CORONA is a luminous discharge that occurs between the two conductors of a transmission line, when the difference of potential between them exceeds the breakdown voltage of the dielectric insulator. Generally, when corona occurs transmission line is destroyed.

SUMMARY:-

Signal loss along transmission lines has become increasingly troublesome as frequencies increase to achieve higher bandwidth. A common measure of such loss is the attenuation per line length unit (e.g., dB [decibel]) per inch. As it turns out, minimizing loss comes at a cost. To understand this, we need to take a look at the sources of loss. There are losses due to the nature of the dielectric (dielectric loss) and due to conductor resistance (conductor loss). The resistance of a line is proportional to the bulk resistance of the conductor material and the line length and is inversely proportional to the line width and its thickness. So, in theory, we could reduce loss by using a more conductive material, but we are already using copper, whose conductivity is only second to silver, and silver is cost prohibitive for most applications. We could redesign the device for shorter lines (miniaturization) but the original design most likely did not have unnecessarily long transmission lines in the first place. We could increase the cross section of the conductor but at the expense of interconnect density, weight, and metal cost.

At higher frequencies, the signal does not travel through the bulk of the conductor but near its skin (skin effect). The skin depth at which the signal travels is inversely proportional to the square root of the frequency. So as the frequency goes up, the effective conductor cross section (skin depth) diminishes and resistance goes up. There are at least two more considerations to assess the impact of the skin effect. As the surface roughness of a conductor increases, the conductor loss increases, especially at higher frequencies. If we find a way to create extra smooth conductor surfaces, we may run into adhesion problems. If the surface of the copper that is in contact with the dielectric of the CCL is very smooth, the adhesion between the copper and the dielectric may be too low. If the surface of the copper foil that is in contact with the photo resist is too smooth, then the dry-film photo resist may have insufficient adhesion to survive etching or plating.

REFERENCES:-

 http://www.answers.com/topic/coaxial-cable

 http://en.wikipedia.org/wiki/Transmission_line
 http://www.tpub.com/content/neets/14182/css/14182_115.htm

 www3.interscience.wiley.com/journal/112456984/abstract?

 http://www.circuitree.com/CDA/Articles/Blog_Guest/BNP_GUID_9-5-2006_A_10000000000000451998

 http://yb1zdx.arc.itb.ac.id/data/OWP/arrl-books/arrl-handbook-2005/21.pdf…...

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