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Navy Electricity and Electronics Training Series (NEETS)
Module 10—Introduction to Wave Propagation, Transmission Lines,
and Antennas
Chapter 3:  Pages 3-1 through 3-10

Module 10—Introduction to Wave Propagation, Transmission Lines, and Antennas
Pages i - ix, 1-1 to 1-10, 1-11 to 1-20, 1-21 to 1-30, 1-31 to 1-40,
1-41 to 1-47, 2-1 to 2-10, 2-11 to 2-20, 2-21 to 2-30, 2-31 to 2-40,
2-40 to 2-47, 3-1 to 3-10, 3-11 to 3-20, 3-21 to 3-30, 3-31 to 3-40,
3-41 to 3-50, 3-51 to 3-58, 4-1 to 4-10, 4-11 to 4-20, 4-21 to 4-30,
4-31 to 4-40, 4-41 to 4-50, 4-51 to 4-60, Index

 

CHAPTER 3


 

PRINCIPLES OF TRANSMISSION LINES


 

LEARNING OBJECTIVES


 
Upon completion of this chapter, you will be able to:
 
1.   State what a transmission line is and how transmission lines are used.
 
2.   Explain the operating principles of transmission lines.
 
3.   Describe the five types of transmission lines.
 
4.   State the length of a transmission line.
 
5.   Explain the theory of the transmission line.
 
6.   Define the term LUMPED CONSTANTS in relation to a transmission line.
 
7.   Define the term DISTRIBUTED CONSTANTS in relation to a transmission line.
 
8.   Define LEAKAGE CURRENT.
 
9.   Describe how the electromagnetic lines of force around a transmission line are affected by the distributed constants.
 
10.   Define the term CHARACTERISTIC IMPEDANCE and explain how it affects the transfer of energy along a transmission line.
 
11.   State how the energy transfer along a transmission line is affected by characteristic impedance and the infinite line.
 
12.   Identify the cause of and describe the characteristics of reflections on a transmission line.
 
13.   Define the term STANDING WAVES as applied to a transmission line.
 
14.   Describe how standing waves are produced on a transmission line and identify the types of terminations.
 
15.   Describe the types of standing-wave ratios.
 

INTRODUCTION TO 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,
 
 

3-1




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.
 
TERMINOLOGY
 
All transmission lines have two ends (see figure 3-1). 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.
 

Basic transmission line - RF Cafe

Figure 3-1.—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.
 
Q1.   What connecting link is used to transfer energy from a radio transmitter to its antenna located on the mast of a ship?
 
Q2.   What term is used for the end of the transmission line that is connected to a transmitter?
 
Q3.   What term is used for the end of the transmission line that is connected to an antenna?

TYPES OF TRANSMISSION MEDIUMS
 
The Navy uses many different types of TRANSMISSION MEDIUMS in its electronic applications. Each medium (line or wave guide) has a certain characteristic impedance value, current-carrying capacity, and physical shape and is designed to meet a particular requirement.
 
 

3-2




The five types of transmission mediums that we will discuss in this chapter include PARALLEL-LINE, TWISTED PAIR, SHIELDED PAIR, COAXIAL LINE, and WAVEGUIDES. The use of a particular line depends, among other things, on the applied frequency, the power-handling capabilities, and the type of installation.
 
NOTE: In the following paragraphs, we will mention LOSSES several times. We will discuss these losses more thoroughly under "LOSSES IN TRANSMISSION LINES."
 
Two-Wire Open Line
 
One type of parallel line is the TWO-WIRE OPEN LINE illustrated in figure 3-2. This line consists of two wires that are generally spaced from 2 to 6 inches apart by insulating spacers. This type of line is most often used for power lines, rural telephone lines, and telegraph lines. It is sometimes used as a transmission line between a transmitter and an antenna or between an antenna and a receiver. An advantage of this type of line is its simple construction. The principal disadvantages of this type of line are the high radiation losses and electrical noise pickup because of the lack of shielding. Radiation losses are produced by the changing fields created by the changing current in each conductor.
 

Parallel two-wire line - RF Cafe

Figure 3-2.—Parallel two-wire line.


 
Another type of parallel line is the TWO-WIRE RIBBON (TWIN LEAD) illustrated in figure 3-3. This type of transmission line is commonly used to connect a television receiving antenna to a home television set. This line is essentially the same as the two-wire open line except that uniform spacing is assured by embedding the two wires in a low-loss dielectric, usually polyethylene. Since the wires are embedded in the thin ribbon of polyethylene, the dielectric space is partly air and partly polyethylene.
 

Two-wire ribbon type line - RF Cafe

Figure 3-3.—Two-wire ribbon type line.



3-3




Twisted Pair
 
The TWISTED PAIR transmission line is illustrated in figure 3-4. As the name implies, the line consists of two insulated wires twisted together to form a flexible line without the use of spacers. It is not used for transmitting high frequency because of the high dielectric losses that occur in the rubber insulation. When the line is wet, the losses increase greatly.

 


 

Twisted pair - RF Cafe

Figure 3-4.—Twisted pair.


 
Shielded Pair
 
The SHIELDED PAIR, shown in figure 3-5, consists of parallel conductors separated from each other and surrounded by a solid dielectric. The conductors are contained within a braided copper tubing that acts as an electrical shield. The assembly is covered with a rubber or flexible composition coating that protects the line from moisture and mechanical damage. Outwardly, it looks much like the power cord of a washing machine or refrigerator.
 

Shielded pair - RF Cafe

Figure 3-5.—Shielded pair.


 
The principal advantage of the shielded pair is that the conductors are balanced to ground; that is, the capacitance between the wires is uniform throughout the length of the line. This balance is due to the uniform spacing of the grounded shield that surrounds the wires along their entire length. The braided copper shield isolates the conductors from stray magnetic fields.
 
Coaxial Lines
 
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.
 
 

3-4




The rigid coaxial line consists of a central, insulated wire (inner conductor) mounted inside a tubular outer conductor. This line is shown in figure 3-6. 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 3-6.—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 3-7) 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 insulators between the two conductors. However, the rubber insulators caused excessive losses at high frequencies.
 
 

3-5



 

Flexible coaxial line - RF Cafe

Figure 3-7.—Flexible coaxial line.


 
Because of the high-frequency losses associated with rubber insulators, polyethylene plastic was developed to replace rubber and eliminate these losses. Polyethylene plastic is a solid substance that remains flexible over a wide range of temperatures. It is unaffected by seawater, gasoline, oil, and most other liquids that may be found aboard ship. The use of polyethylene as an insulator results in greater high-frequency losses than the use of air as an insulator. However, these losses are still lower than the losses associated with most other solid dielectric materials.
 
Waveguides
 
The WAVEGUIDE is classified as a transmission line. However, the method by which it transmits energy down its length differs from the conventional methods. Waveguides are cylindrical, elliptical, or rectangular (cylindrical and rectangular shapes are shown in figure 3-8). The rectangular waveguide is used more frequently than the cylindrical waveguide.
 

Waveguides - RF Cafe

Figure 3-8.—Waveguides.


 
The term waveguide can be applied to all types of transmission lines in the sense that they are all used to guide energy from one point to another. However, usage has generally limited the term to mean a hollow metal tube or a dielectric transmission line. In this chapter, we use the term waveguide only to mean "hollow metal tube." It is interesting to note that the transmission of electromagnetic energy along a waveguide travels at a velocity somewhat slower than electromagnetic energy traveling through free space.
 
A waveguide may be classified according to its cross section (rectangular, elliptical, or circular), or according to the material used in its construction (metallic or dielectric). Dielectric waveguides are
 
 

3-6




seldom used because the dielectric losses for all known dielectric materials are too great to transfer the electric and magnetic fields efficiently.
 
The installation of a complete waveguide transmission system is somewhat more difficult than the installation of other types of transmission lines. The radius of bends in the waveguide must measure greater than two wavelengths at the operating frequency of the equipment to avoid excessive attenuation. The cross section must remain uniform around the bend. These requirements hamper installation in confined spaces. If the waveguide is dented, or if solder is permitted to run inside the joints, the attenuation of the line is greatly increased. Dents and obstructions in the waveguide also reduce its breakdown voltage, thus limiting the waveguide’s power-handling capability because of possible arc over. Great care must be exercised during installation; one or two carelessly made joints can seriously inhibit the advantage of using the waveguide.
 
We will not consider the waveguide operation in this module, since waveguide theory is discussed in NEETS, Module 11, Microwave Principles.
 
Q4.   List the five types of transmission lines in use today.
 
Q5.   Name two of the three described uses of a two-wire open line.
 
Q6.   What are the two primary disadvantages of a two-wire open line?
 
Q7.   What type of transmission line is often used to connect a television set to its antenna?
 
Q8.   What is the primary advantage of the shielded pair?
 
Q9.   What are the two types of coaxial lines in use today?
 
Q10.   What is the chief advantage of the air coaxial line?
 
Q11.   List the three disadvantages of the air coaxial line.
 
Q12.   List the two common types of waveguides in use today.
 
LOSSES IN TRANSMISSION LINES
 
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.
 
NOTE: Transmission lines are sometimes referred to as rf lines. In this text the terms are used interchangeably.
 
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.


3-7




The flux density at the center is so great that electron movement at this point is reduced. As frequency is increased, the opposition to the flow of current in the center of the wire increases. Current in the center 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 center is so small that the center 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 results in power losses. That is, power is supplied by the source, but is not available to the load.
 
Q13.   What are the three types of line losses associated with transmission lines?
 
Q14.   Losses caused by skin effect and the  I2R (power) loss are classified as what type of loss?
 
Q15.   What types of losses cause the dielectric material between the conductors to be heated?

 


 
LENGTH OF A TRANSMISSION LINE

A transmission line is considered to be electrically short when its physical length is short compared to a quarter-wavelength (1/4λ) of the energy it is to carry.
 
NOTE: In this module, for ease of reading, the value of the wavelength will be spelled out in some cases, and in other cases, the numerical value will be used.
 
 

3-8




A transmission line is electrically long when its physical length is long compared to a quarter- wavelength of the energy it is to carry. You must understand that the terms "short" and "long" are relative ones. For example, a line that has a physical length of 3 meters (approximately 10 feet) is considered quite short electrically if it transmits a radio frequency of 30 kilohertz. On the other hand, the same transmission line is considered electrically long if it transmits a frequency of 30,000 megahertz.
 
To show the difference in physical and electrical lengths of the lines mentioned above, compute the wavelength of the two frequencies, taking the 30-kilohertz example first:
 

Formula - RF Cafe


 
Now, computing the wavelength for the line carrying 30,000 megahertz:

 


 

Formula - RF Cafe


 
Thus, you can see that a 3-meter line is electrically very short for a frequency of 30 kilohertz. Also, the 3-meter line is electrically very long for a frequency of 30,000 megahertz.
 
When power is applied to a very short transmission line, practically all of it reaches the load at the output end of the line. This very short transmission line is usually considered to have practically no electrical properties of its own, except for a small amount of resistance.
 
 

3-9




However, the picture changes considerably when a long line is used. Since most transmission lines are electrically long (because of the distance from transmitter to antenna), the properties of such lines must be considered. Frequently, the voltage necessary to drive a current through a long line is considerably greater than the amount that can be accounted for by the impedance of the load in series with the resistance of the line.
 

TRANSMISSION LINE THEORY


 
The electrical characteristics of a two-wire transmission line depend primarily on the construction of the line. The two-wire line acts like a long capacitor. The change of its capacitive reactance is noticeable as the frequency applied to it is changed. Since the long conductors have a magnetic field about them when electrical energy is being passed through them, they also exhibit the properties of inductance. The values of inductance and capacitance presented depend on the various physical factors that we discussed earlier. For example, the type of line used, the dielectric in the line, and the length of the line must be considered. The effects of the inductive and capacitive reactances of the line depend on the frequency applied. Since no dielectric is perfect, electrons manage to move from one conductor to the other through the dielectric. Each type of two-wire transmission line also has a conductance value. This conductance value represents the value of the current flow that may be expected through the insulation. If the line is uniform (all values equal at each unit length), then one small section of the line may represent several feet. This illustration of a two-wire transmission line will be used throughout the discussion of transmission lines; but, keep in mind that the principles presented apply to all transmission lines. We will explain the theories using LUMPED CONSTANTS and DISTRIBUTED CONSTANTS to further simplify these principles.
 
LUMPED CONSTANTS
 
A transmission line has the properties of inductance, capacitance, and resistance just as the more conventional circuits have. Usually, however, the constants in conventional circuits are lumped into a single device or component. For example, a coil of wire has the property of inductance. When a certain amount of inductance is needed in a circuit, a coil of the proper dimensions is inserted. The inductance of the circuit is lumped into the one component. Two metal plates separated by a small space, can be used to supply the required capacitance for a circuit. In such a case, most of the capacitance of the circuit is lumped into this one component. Similarly, a fixed resistor can be used to supply a certain value of circuit resistance as a lumped sum. Ideally, a transmission line would also have its constants of inductance, capacitance, and resistance lumped together, as shown in figure 3-9. Unfortunately, this is not the case. Transmission line constants are distributed, as described below.
 
 

3-10



Introduction to Matter, Energy, and Direct Current, Introduction to Alternating Current and Transformers, Introduction to Circuit Protection, Control, and Measurement, Introduction to Electrical Conductors, Wiring Techniques, and Schematic Reading, Introduction to Generators and Motors, Introduction to Electronic Emission, Tubes, and Power Supplies, Introduction to Solid-State Devices and Power Supplies, Introduction to Amplifiers, Introduction to Wave-Generation and Wave-Shaping Circuits, Introduction to Wave Propagation, Transmission Lines, and Antennas, Microwave Principles, Modulation Principles, Introduction to Number Systems and Logic Circuits, Introduction to Microelectronics, Principles of Synchros, Servos, and Gyros, Introduction to Test Equipment, Radio-Frequency Communications Principles, Radar Principles, The Technician's Handbook, Master Glossary, Test Methods and Practices, Introduction to Digital Computers, Magnetic Recording, Introduction to Fiber Optics

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