CHAPTER 3

INTRODUCTION TOTRANSMISSION LINES AND WAVEGUIDES

A TRANSMISSION LINE is a device designedto guide electrical energy from one point to another.It is used, for example, to transfer the output rf energyof a transmitter to an antenna. This energy will nottravel through normal electrical wire without greatlosses. Although the antenna can be connecteddirectly to the transmitter, the antenna is usuallylocated some distance away from the transmitter. Onboard ship, the transmitter is located inside a radioroom, and its associated antenna is mounted on a mast.A transmission line is used to connect the transmitterand the antenna.

The transmission line has a single purpose for boththe transmitter and the antenna. This purpose is totransfer the energy output of the transmitter to theantenna with the least possible power loss. How wellthis is done depends on the special physical andelectrical characteristics (impedance and resistance)of the transmission line.

TRANSMISSION LINE THEORY

The electrical characteristics of a two-wiretransmission line depend primarily on the constructionof the line. The two-wire line acts like a longcapacitor. The change of its capacitive reactance isnoticeable as the frequency applied to it is changed.Since the long conductors have a magnetic field aboutthem when electrical energy is being passed throughthem, they also exhibit the properties of inductance.The values of inductance and capacitance presenteddepend on the various physical factors that wediscussed earlier. For example, the type of line used,the dielectric in the line, and the length of the linemust be considered. The effects of the inductive andcapacitive reactance of the line depend on thefrequency applied. Since no dielectric is perfect,electrons manage to move from one conductor to theother through the dielectric. Each type of two-wiretransmission line also has a conductance value. Thisconductance 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 unitlength), then one small section of the line mayrepresent several feet. This illustration of a two-wiretransmission line will be used throughout the discussionof transmission lines; but, keep in mind that theprinciples presented apply to all transmission lines.We will explain the theories using LUMPED CON-STANTS and DISTRIBUTED CONSTANTS to furthersimplify these principles.

LUMPED CONSTANTS

A transmission line has the properties of induc-tance, capacitance, and resistance just as the moreconventional circuits have. Usually, however, theconstants in conventional circuits are lumped into asingle device or component. For example, a coil ofwire has the property of inductance. When a certainamount of inductance is needed in a circuit, a coil ofthe proper dimensions is inserted. The inductanceof the circuit is lumped into the one component. Twometal plates separated by a small space, can be usedto supply the required capacitance for a circuit. Insuch a case, most of the capacitance of the circuit islumped into this one component. Similarly, a fixedresistor can be used to supply a certain value of circuitresistance as a lumped sum. Ideally, a transmissionline would also have its constants of inductance,capacitance, and resistance lumped together, as shownin figure 3-1. Unfortunately, this is not the case.Transmission line constants are as described in thefollowing paragraphs.

DISTRIBUTED CONSTANTS

Transmission line constants, called distributedconstants, are spread along the entire length of thetransmission line and cannot be distinguished sepa-rately. The amount of inductance, capacitance, andresistance depends on the length of the line, the sizeof the conducting wires, the spacing between the

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Figure 3-1.—Two-wire transmission line.

wires, and the dielectric (air or insulating medium)between the wires. The following paragraphs willbe useful to you as you study distributed constantson a transmission line.

Inductance of a Transmission Line

When current flows through a wire, magnetic linesof force are set up around the wire. As the currentincreases and decreases in amplitude, the field aroundthe wire expands and collapses accordingly. Theenergy produced by the magnetic lines of forcecollapsing back into the wire tends to keep the currentflowing in the same direction. This represents a certainamount of inductance, which is expressed inmicrohenrys per unit length. Figure 3-2 illustratesthe inductance and magnetic fields of a transmissionline.

Capacitance of a Transmission Line

Capacitance also exists between the transmissionline wires, as illustrated in figure 3-3. Notice thatthe two parallel wires act as plates of a capacitor andthat the air between them acts as a dielectric. Thecapacitance between the wires is usually expressedin picofarads per unit length. This electric fieldbetween the wires is similar to the field that existsbetween the two plates of a capacitor.

Figure 3-2.—Distributed inductance.

Figure 3-3.—Distributed capacitance.

Resistance of a Transmission Line

The transmission line shown in figure 3-4 haselectrical resistance along its length. This resistanceis usually expressed in ohms per unit length and isshown as existing continuously from one end of theline to the other.

Figure 3-4.—Distributed resistance.

Leakage Current

Since any dielectric, even air, is not a perfectinsulator, a small current known as LEAKAGECURRENT flows between the two wires. In effect,the insulator acts as a resistor, permitting current topass between the two wires. Figure 3-5 shows thisleakage path as resistors in parallel connected betweenthe two lines. This property is called CONDUC-TANCE (G) and is the opposite of resistance.Conductance in transmission lines is expressed as thereciprocal of resistance and is usually given inmicromhos per unit length.

Figure 3-5.—Leakage in a transmission line.

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ELECTROMAGNETIC FIELDS CHARACTERISTIC IMPEDANCE

The distributed constants of resistance, inductance,and capacitance are basic properties common to alltransmission lines and exist whether or not any currentflow exists. As soon as current flow and voltage existin a transmission line, another property becomes quiteevident. This is the presence of an electromagneticfield, or lines of force, about the wires of thetransmission line. The lines of force themselves arenot visible; however, understanding the force that anelectron experiences while in the field of these linesis very important to your understanding of energytransmission.

There are two kinds of fields; one is associatedwith voltage and the other with current. The fieldassociated with voltage is called the ELECTRIC (E)FIELD. It exerts a force on any electric charge placedin it. The field associated with current is called aMAGNETIC (H) FIELD, because it tends to exerta force on any magnetic pole placed in it. Figure 3-6illustrates the way in which the E fields and H fieldstend to orient themselves between conductors of atypical two-wire transmission line. The illustrationshows a cross section of the transmission lines. TheE field is represented by solid lines and the H fieldby dotted lines. The arrows indicate the direction ofthe lines of force. Both fields normally exist togetherand are spoken of collectively as the electromagneticfield.

Figure 3-6.—Fields between conductors.

You can describe a transmission line in terms ofits 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 transmit-ter 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 thetransmission line and its source. If an infinitely longtransmission line could be used, the ratio of voltageto current at any point on that transmission line wouldbe some particular value of impedance. This imped-ance is known as the CHARACTERISTIC IMPED-ANCE.

The maximum (and most efficient) transfer ofelectrical energy takes place when the source imped-ance is matched to the load impedance. This fact isvery important in the study of transmission lines andantennas. If the characteristic impedance of thetransmission line and the load impedance are equal,energy from the transmitter will travel down thetransmission line to the antenna with no power losscaused by reflection.

LINE LOSSES

The discussion of transmission lines so far has notdirectly addressed LINE LOSSES; actually some lossesoccur in all lines. Line losses may be any of threetypes—COPPER, DIELECTRIC, and RADIATIONor INDUCTION LOSSES.

NOTE: Transmission lines are sometimes referredto as rf lines. In this text the terms are used inter-changeably.

Copper Losses

One type of copper loss is I2R LOSS. In rf linesthe resistance of the conductors is never equal to zero.Whenever current flows through one of these conduc-tors, 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, thispower loss is higher.

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Another type of copper loss is due to SKINEFFECT. When dc flows through a conductor, themovement of electrons through the conductor’s crosssection is uniform, The situation is somewhat differentwhen ac is applied. The expanding and collapsingfields about each electron encircle other electrons.This phenomenon, called SELF INDUCTION, retardsthe movement of the encircled electrons. The fluxdensity at the center is so great that electron movementat this point is reduced. As frequency is increased,the opposition to the flow of current in the center ofthe wire increases. Current in the center of the wirebecomes smaller and most of the electron flow is onthe wire surface. When the frequency applied is 100megahertz or higher, the electron movement in thecenter is so small that the center of the wire couldbe 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 thecross-sectional area, the resistance will increase as thefrequency is increased. Also, since power lossincreases as resistance increases, power losses increasewith an increase in frequency because of skin effect.

Copper losses can be minimized and conductivityincreased in an rf line by plating the line with silver.Since silver is a better conductor than copper, mostof the current will flow through the silver layer. Thetubing then serves primarily as a mechanical support.

Dielectric Losses

DIELECTRIC LOSSES result from the heatingeffect on the dielectric material between the conductors.Power from the source is used in heating the dielectric.The heat produced is dissipated into the surroundingmedium. When there is no potential differencebetween two conductors, the atoms in the dielectricmaterial between them are normal and the orbits ofthe electrons are circular. When there is a potentialdifference between two conductors, the orbits of theelectrons change. The excessive negative charge onone conductor repels electrons on the dielectric towardthe positive conductor and thus distorts the orbits ofthe electrons. A change in the path of electronsrequires more energy, introducing a power loss.

The atomic structure of rubber is more difficultto distort than the structure of some other dielectricmaterials. The atoms of materials, such as polyethyl-ene, distort easily. Therefore, polyethylene is oftenused as a dielectric because less power is consumedwhen its electron orbits are distorted.

Radiation and Induction Losses

RADIAION and INDUCTION LOSSES aresimilar in that both are caused by the fields surround-ing the conductors. Induction losses occur when theelectromagnetic field about a conductor cuts throughany nearby metallic object and a current is inducedin that object. As a result, power is dissipated in theobject and is lost.

Radiation losses occur because some magnetic linesof force about a conductor do not return to theconductor when the cycle alternates. These lines offorce are projected into space as radiation, and thisresults in power losses. That is, power is suppliedby the source, but is not available to the load.

VOLTAGE CHANGE

In an electric circuit, energy is stored in electricand magnetic fields. These fields must be broughtto the load to transmit that energy. At the load, energycontained in the fields is converted to the desired formof energy.

Transmission of Energy

When the load is connected directly to the sourceof energy, or when the transmission line is short,problems concerning current and voltage can be solvedby applying Ohm’s law. When the transmission linebecomes long enough so the time difference betweena change occurring at the generator and a changeappearing at the load becomes appreciable, analysisof the transmission line becomes important.

Dc Applied to a Transmission Line

In figure 3-7, a battery is connected through arelatively long two-wire transmission line to a loadat the far end of the line. At the instant the switch

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is closed, neither current nor voltage exists on the line.When the switch is closed, point A becomes a positivepotential, and point B becomes negative. These pointsof difference in potential move down the line.However, as the initial points of potential leave pointsA and B, they are followed by new points of differencein potential, which the battery adds at A and B. Thisis merely saying that the battery maintains a constantpotential difference between points A and B. A shorttime after the switch is closed, the initial points ofdifference in potential have reached points A’ and B’;the wire sections from points A to A’ and points Bto B’ are at the same potential as A and B, respec-tively. The points of charge are represented by plus(+) and minus (-) signs along the wires, The directions

of the currents in the wires are represented by thearrowheads on the line, and the direction of travel isindicated by an arrow below the line. Conventionallines of force represent the electric field that existsbetween the opposite kinds of charge on the wiresections from A to A’ and B to B’. Crosses (tails ofarrows) indicate the magnetic field created by theelectric field moving down the line. The movingelectric field and the accompanying magnetic fieldconstitute an electromagnetic wave that is moving fromthe generator (battery) toward the load. This wavetravels at approximately the speed of light in freespace. The energy reaching the load is equal to thatdeveloped at the battery (assuming there are no lossesin the transmission line). If the load absorbs all ofthe energy, the current and voltage will be evenlydistributed along the line.

Ac Applied to a Transmission Line

When the battery of figure 3-7 is replaced by anac generator (fig. 3-8), each successive instantaneousvalue of the generator voltage is propagated down the

Figure 3-7.—Dc voltage applied to a line.

Figure 3-8.—Ac voltage applied to a line.

line at the speed of light. The action is similar to thewave created by the battery, except the applied voltageis sinusoidal instead of constant. Assume that theswitch is closed at the moment the generator voltageis passing through zero and that the next half cyclemakes point A positive. At the end of one cycle ofgenerator voltage, the current and voltage distributionwill be as shown in figure 3-8.

In this illustration the conventional lines of forcerepresent the electric fields. For simplicity, themagnetic fields are not shown. Points of charge areindicated by plus (+) and minus (-) signs, the largersigns indicating points of higher amplitude of bothvoltage and current. Short arrows indicate directionof current (electron flow). The waveform drawn belowthe transmission line represents the voltage (E) andcurrent (I) waves. The line is assumed to be infinitein length so there is no reflection. Thus, travelingsinusoidal voltage and current waves continually travelin phase from the generator toward the load, or farend of the line. Waves traveling from the generatorto the load are called INCIDENT WAVES. Wavestraveling from the load back to the generator are calledREFLECTED WAVES and will be explained in laterparagraphs.

STANDING-WAVE RATIO

The measurement of standing waves on a transmis-sion line yields information about equipment operating

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conditions. Maximum power is absorbed by the loadwhen ZL = Z0. If a line has no standing waves, thetermination for that line is correct and maximum powertransfer takes place.

You have probably noticed that the variation ofstanding waves shows how near the rf line is to beingterminated in Z0. A wide variation in voltage alongthe length means a termination far from Z0. A smallvariation means termination near Z0. Therefore, theratio of the maximum to the minimum is a measureof the perfection of the termination of a line. Thisratio is called the STANDING-WAVE RATIO (swr)and is always expressed in whole numbers. Forexample, a ratio of 1:1 describes a line terminated inits characteristic impedance (Z0).

Voltage Standing-Wave Ratio

The ratio of maximum voltage to minimum voltageon a line is called the VOLTAGE STANDING-WAVERATIO (vswr). Therefore:

The vertical lines in the formula indicate that theenclosed quantities are absolute and that the two valuesare taken without regard to polarity, Depending onthe nature of the standing waves, the numerical valueof vswr ranges from a value of 1 (ZL = Z0, no standingwaves) to an infinite value for theoretically completereflection. Since there is always a small loss on aline, the minimum voltage is never zero and the vswris always some finite value. However, if the vswris to be a useful quantity. the power losses along theline must be small in comparison to the transmittedpower.

voltage. Since power is proportional to the squareof the voltage, the ratio of the square of the maximumand minimum voltages is called the power stand-ing-wave ratio. In a sense, the name is misleadingbecause the power along a transmission line does notvary.

Current Standing-Wave Ratio

The ratio of maximum to minimum current alonga transmission line is called CURRENT STAND-ING- WAVE RATIO (iswr). Therefore:

This ratio is the same as that for voltages. It can beused where measurements are made with loops thatsample the magnetic field along a line. It gives thesame results as vswr measurements.

TRANSMISSION MEDIUMS

The Navy uses many different types of TRANS-MISSION MEDIUMS in its electronic applications.Each medium (line or waveguide) has a certaincharacteristic impedance value, current-carryingcapacity, and physical shape and is designed to meeta particular requirement.

The five types of transmission mediums that wewill discuss in this topic include PARALLEL-LINE,TWISTED PAIR, SHIELDED PAIR, COAXIALLINE, and WAVEGUIDES. The use of a particularline depends, among other things, on the appliedfrequency, the power-handling capabilities, and thetype of installation.

Power Standing-Wave Ratio Parallel Line

The square of the vswr is called the POWER One type of parallel line is the TWO-WIRE OPEN

STANDING-WAVE RATIO (pswr). Therefore: LINE, illustrated in figure 3-9. This line consists oftwo wires that are generally spaced from 2 to 6 inchesapart by insulating spacers. This type of line is mostoften used for power lines, rural telephone lines, andtelegraph lines. It is sometimes used as a transmission

This ratio is useful because the instruments used to line between a transmitter and an antenna or between

detect standing waves react to the square of the an antenna and a receiver. An advantage of this type

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Figure 3-9.—Two-wire open

of line is its simple construction.

line.

The principaldisadvantages of this type of line are the high radiationlosses and electrical noise pickup because of the lackof shielding. Radiation losses are produced by thechanging fields created by the changing current in eachconductor.

Another type of parallel line is the TWO-WIRERIBBON (TWIN LEAD) LINE, illustrated in figure3-10. This type of transmission line is commonly usedto connect a television receiving antenna to a hometelevision set. This line is essentially the same as thetwo-wire open line except that uniform spacing isassured by embedding the two wires in a low-lossdielectric, usually polyethylene. Since the wires areembedded in the thin ribbon of polyethylene, thedielectric space is partly air and partly polyethylene.

Twisted Pair

The TWISTED PAIR transmission line is illustratedin figure 3-11. As the name implies, the line consistsof two insulated wires twisted together to form aflexible line without the use of spacers. It is not usedfor transmitting high frequency because of the highdielectric losses that occur in the rubber insulation.When the line is wet, the losses increase greatly.

Figure 3-10.—Two-wire ribbon line.

Figure 3-11.—Twisted pair.

Shielded Pair

The SHIELDED PAIR, shown in figure 3-12,consists of parallel conductors separated from eachother and surrounded by a solid dielectric. Theconductors are contained within a braided coppertubing that acts as an electrical shield. The assemblyis covered with a rubber or flexible compositioncoating that protects the line from moisture andmechanical damage. Outwardly, it looks much likethe power cord of a washing machine or refrigerator.

Figure 3-12.—Shielded pair.

The principal advantage of the shielded pair is thatthe conductors are balanced to ground; that is, thecapacitance between the wires is uniform throughoutthe length of the line. This balance is due to theuniform spacing of the grounded shield that surroundsthe wires along their entire length. The braided coppershield isolates the conductors from stray magneticfields.

Coaxial Lines

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

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The rigid coaxial line consists of a central, insulatedwire (inner conductor) mounted inside a tubular outerconductor. This line is shown in figure 3-13. In someapplications, the inner conductor is also tubular. Theinner conductor is insulated from the outer conductorby insulating spacers or beads at regular intervals.The spacers are made of Pyrex, polystyrene, or someother material that has good insulating characteristicsand low dielectric losses at high frequencies.

Figure 3-13.—Air coaxial line.

The chief advantage of the rigid line is its abilityto minimize radiation losses. The electric and magneticfields in a two-wire parallel line extend into space forrelatively great distances and radiation losses occur.However, in a coaxial line no electric or magneticfields extend outside of the outer conductor. The fieldsare confined to the space between the two conductors,resulting in a perfectly shielded coaxial line. Anotheradvantage is that interference from other lines isreduced.

The rigid line has the following disadvantages:(1) it is expensive to construct; (2) it must be keptdry to prevent excessive leakage between the twoconductors; and (3) although high-frequency lossesare somewhat less than in previously mentioned lines,they are still excessive enough to limit the practicallength of the line.

Leakage caused by the condensation of moistureis prevented in some rigid line applications by the useof an inert gas, such as nitrogen, helium, or argon.It is pumped into the dielectric space of the line ata pressure that can vary from 3 to 35 pounds persquare inch. The inert gas is used to dry the line whenit is first installed and pressure is maintained to ensurethat no moisture enters the line.

Flexible coaxial lines (fig. 3-14) are made withan inner conductor that consists of flexible wireinsulated from the outer conductor by a solid,continuous insulating material. The outer conductoris made of metal braid, which gives the line flexibility.Early attempts at gaining flexibility involved usingrubber insulators between the two conductors.However, the rubber insulators caused excessive lossesat high frequencies.

Figure 3-14.—Flexible coaxial line.

Because of the high-frequency losses associatedwith rubber insulators, polyethylene plastic wasdeveloped to replace rubber and eliminate these losses.Polyethylene plastic is a solid substance that remainsflexible over a wide range of temperatures. It isunaffected by seawater, gasoline, oil, and most otherliquids that may be found aboard ship. The use ofpolyethylene as an insulator results in greaterhigh-frequency losses than the use of air as aninsulator. However, these losses are still lower thanthe losses associated with most other solid dielectricmaterials.

This concludes our study of transmission lines.The rest of this chapter will be an introduction intothe study of waveguides.

WAVEGUIDE THEORY

The two-wire transmission line used in conventionalcircuits is inefficient for transferring electromagneticenergy at microwave frequencies. At these frequencies,energy escapes by radiation because the fields are notconfined in all directions, as illustrated in figure 3-15.Coaxial lines are more efficient than two-wire linesfor transferring electromagnetic energy because thefields are completely confined by the conductors, asillustrated in figure 3-16. Waveguides are the most

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efficient way to transfer electromagnetic energy.WAVEGUIDES are essentially coaxial lines withoutcenter conductors. They are constructed fromconductive material and may be rectangular, circular,or elliptical in shape, as shown in figure 3-17.

Figure 3-15.—Fields confined in two directions only.

Figure 3-16.—Fields confined in all directions.

WAVEGUIDE ADVANTAGES

Waveguides have several advantages over two-wireand coaxial transmission lines. For example, the largesurface area of waveguides greatly reduces COPPER(12R) LOSSES. Two-wire transmission lines have largecopper losses because they have a relatively smallsurface area. The surface area of the outer conductor

Figure 3-17.—Waveguide shapes.

of a coaxial cable is large, but the surface area of theinner conductor is relatively small. At microwavefrequencies, the current-carrying area of the inner con-ductor is restricted to a very small layer at thesurface of the conductor by an action called SKINEFFECT.

Skin effect tends to increase the effective resistanceof the conductor. Although energy transfer in coaxialcable is caused by electromagnetic field motion, themagnitude of the field is limited by the size of thecurrent-carrying area of the inner conductor. The smallsize of the center conductor is even further reducedby skin effect, and energy transmission by coaxialcable becomes less efficient than by waveguides.DIELECTRIC LOSSES are also lower in waveguidesthan in two-wire and coaxial transmission lines.Dielectric losses in two-wire and coaxial lines arecaused by the heating of the insulation between theconductors. The insulation behaves as the dielectricof a capacitor formed by the two wires of thetransmission line. A voltage potential across the twowires causes heating of the dielectric and results ina power loss. In practical applications, the actualbreakdown of the insulation between the conductorsof a transmission line is more frequently a problemthan is the dielectric loss.

This breakdown is usually caused by stationaryvoltage spikes or “nodes,” which are caused bystanding waves. Standing waves are stationary andoccur when part of the energy traveling down the line

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is reflected by an impedance mismatch with the load.The voltage potential of the standing waves at thepoints of greatest magnitude can become large enoughto break down the insulation between transmissionline conductors.

The dielectric in waveguides is air, which has amuch lower dielectric loss than conventional insulatingmaterials. However, waveguides are also subject todielectric breakdown caused by standing waves.Standing waves in waveguides cause arcing, whichdecreases the efficiency of energy transfer and canseverely damage the waveguide. Also since theelectromagnetic fields are completely contained withinthe waveguide, radiation losses are kept very low.

Power-handling capability is another advantageof waveguides. Waveguides can handle more powerthan coaxial lines of the same size becausepower-handling capability is directly related to thedistance between conductors. Figure 3-18 illustratesthe greater distance between conductors in awaveguide.

Figure 3-18.—Comparisonand a circular waveguide.

of spacing in coaxial cable

In view of the advantages of waveguides, youwould think that waveguides should be the only typeof transmission lines used. However, waveguides havecertain disadvantages that make them practical for useonly at microwave frequencies.

WAVEGUIDE DISADVANTAGES

Physical size is the primary lower-frequencylimitation of waveguides. The width of a waveguidemust be approximately a half wavelength at thefrequency of the wave to be transported. For example,a waveguide for use at 1 megahertz would be about700 feet wide. This makes the use of waveguides atfrequencies below 1000 megahertz increasinglyimpractical. The lower frequency range of any systemusing waveguides is limited by the physical dimensionsof the waveguides.

Waveguides are difficult to install because of theirrigid, hollow-pipe shape. Special couplings at thejoints are required to assure proper operation. Also,the inside surfaces of waveguides are often plated withsilver or gold to reduce skin effect losses. Theserequirements increase the costs and decrease thepracticality of waveguide systems at any other thanmicrowave frequencies.

DEVELOPING THE WAVEGUIDEFROM PARALLEL LINES

You may better understand the transition fromordinary transmission line concepts to waveguidetheories by considering the development of awaveguide from a two-wire transmission line. Figure3-19 shows a section of a two-wire transmission linesupported on two insulators. At the junction with theline, the insulators must present a very high impedanceto ground for proper operation of the line. A lowimpedance insulator would obviously short-circuit theline to ground, and this is what happens at very highfrequencies. Ordinary insulators display the character-istics of the dielectric of a capacitor formed by thewire and ground. As the frequency increases, the

overall impedance decreases. A better high-frequencyinsulator is a quarter-wave section of transmissionline shorted at one end. Such an insulator is shownin figure 3-20. The impedance of a shorted quar-ter-wave section is very high at the open-end junctionwith the two-wire transmission line. This type ofinsulator is known as a METALLIC INSULATORand may be placed anywhere along a two-wire line.

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Figure 3-19.—Two-wire transmission line.

Figure 3-20.—Quarter-wave section of transmissionline shorted at one end.

Note that quarter-wave sections are insulators at onlyone frequency. This severely limits the bandwidth,efficiency, and application of this type of two-wireline.

Figure 3-21 shows several metallic insulators oneach side of a two-wire transmission line. As moreinsulators are added, each section makes contact withthe next, and a rectangular waveguide is formed. Thelines become part of the walls of the waveguide, asillustrated in figure 3-22. The energy is thenconducted within the hollow waveguide instead ofalong the two-wire transmission line.

The comparison of the way electromagnetic fieldswork on a transmission line and in a waveguide isnot exact. During the change from a two-wire lineto a waveguide, the electromagnetic field configurationsalso undergochanges, the

many changes. As a result of thesewaveguide does not actually operate

Figure 3-21.—Metallic insulator on each sidetwo-wire line.

Figure 3-22.—Forming a waveguide by addingquarter-wave sections.

like a two-wire line that is completely shuntedquarter-wave sections. If it did, the use of a wave-guide would be limited to a single-frequency wavelength that was four times the length of the quarter-wave sections. In fact, waves of this length cannotpass efficiently through waveguides. Only a smallrange of frequencies of somewhat shorter wavelength(higher frequency) can pass efficiently.

of a

by

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As shown in figure 3-23, the widest dimensionof a waveguide is called the “a” dimension anddetermines the range of operating frequencies. Thenarrowest dimension determines the power-handlingcapability of the waveguide and is called the “b”dimension.

Figure 3-23.—Labeling waveguide dimensions,

NOTE: This method of labeling waveguides isnot standard in all texts, Different methods may beused in other texts on microwave principles, but thismethod is in accordance with Navy Military Standards(MIL-STDS).

In theory, a waveguide could function at an infinitenumber of frequencies higher than the designedfrequency; however, in practice, an upper frequencylimit is caused by modes of operation, which will bediscussed later.

If the frequency of a signal is decreased so muchthat two quarter-wavelengths are longer than the widedimension of a waveguide, energy will no longer passthrough the waveguide. This is the lower frequencylimit, or CUTOFF FREQUENCY of a givenwaveguide. In practical applications, the widedimension of a waveguide is usually 0.7 wavelengthat the operating frequency. This allows the waveguideto handle a small range of frequencies both above andbelow the operating frequency. The “b” dimensionis governed by the breakdown potential of thedielectric, which is usually air. Dimensions rangingfrom 0.2 to 0.5 wavelength are common for the “b”sides of a waveguide.

ENERGY PROPAGATION INWAVEGUIDES

Since energy is transferred through waveguidesby electromagnetic fields, you need a basic understand-ing of field theory. Both electric (E FIELD) andmagnetic fields (H FIELD) are present in waveguides,and the interaction of these fields causes energy totravel through the waveguide. This action is bestunderstood by first looking at the properties of thetwo individual fields.

E Field

An electric field exists when a difference ofpotential causes a stress in the dielectric between twopoints. The simplest electric field is one that formsbetween the plates of a capacitor when one plate ismade positive compared to the other, as shown in viewA of figure 3-24. The stress created in the dielectricis an electric field.

Electric fields are represented by arrows that pointfrom the positive toward the negative potential. Thenumber of arrows shows the relative strength of thefield. In view B, for example, evenly spaced arrowsindicate the field is evenly distributed. For ease ofexplanation, the electric field is abbreviated E field,and the lines of stress are called E lines.

H Field

The magnetic field in a waveguide is made up ofmagnetic lines of force that are caused by current flowthrough the conductive material of the waveguide.Magnetic lines of force, called H lines, are continuousclosed loops, as shown in figure 3-25. All of the Hlines associated with current are collectively calleda magnetic field or H field. The strength of the Hfield, indicated by the number of H lines in a givenarea, varies directly with the amount of current.

Although H lines encircle a single, straight wire,they behave differently when the wire is formed intoa coil, as shown in figure 3-26. In a coil the individualH lines tend to form around each turn of wire. Since

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Figure 3-24.—Simple electric fields.

Figure 3-25.—Magnetic field on a single wire.

the H lines take opposite directions between adjacentturns, the field between the turns is canceled. Insideand outside the coil, where the direction of each Hfield is the same, the fields join and form continuousH lines around the entire coil. A similar action takesplace in a waveguide.

Figure 3-26.—Magnetic field on a coil.

BOUNDARY CONDITIONS INA WAVEGUIDE

The travel of energy down a waveguide is similar,but not identical, to the travel of electromagnetic wavesin free space. The difference is that the energy in a

waveguide is confined to the physical limits of theguide. Two conditions, known as BOUNDARYCONDITIONS, must be satisfied for energy to travelthrough a waveguide.

The first boundary condition (illustrated in fig.3-27, view A can be stated as follows:

For an electric field to exist at the surfaceof a conductor, it must be perpendicularto the conductor.

Thein view

Figure 3-27.—E field boundary condition.

opposite of this boundary condition, shownB, is also true. An electric field CANNOT

exist parallel to a perfect conductor.

The second boundary condition, which is illustratedin figure 3-28, can be stated as follows:

For a varying magnetic field to exist, it mustform closed loops in parallel with theconductors and be perpendicular to theelectric field.

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Figure 3-28.—H field boundary condition.

Since an E field causes a current flow that in turnproduces an H field, both fields always exist at thesame time in a waveguide. If a system satisfies oneof these boundary conditions, it must also satisfy theother since neither field can exist alone.

WAVEFRONTS WITHIN AWAVEGUIDE

Electromagnetic energy transmitted into spaceconsists of electric and magnetic fields that are at rightangles (90 degrees) to each other and at right anglesto the direction of propagation. A simple analogy toestablish this relationship is by use of the right-handrule for electromagnetic energy, based on thePOYNTING VECTOR. It indicates that a screw(right-hand thread) with its axis perpendicular to theelectric and magnetic fields will advance in thedirection of propagation if the E field is rotated tothe right (toward the H field). This rule is illustratedin figure 3-29.

Figure 3-29.—The Poynting vector.

The combined electric and magnetic fields forma wavefront that can be represented by alternatenegative and positive peaks at half-wavelength

intervals, as illustrated in figure 3-30. Angle isthe direction of travel of the wave with respect to somereference axis.

Figure 3-30.—Wavefronts in space.

The reflection of a single wavefront off the “b”wall of a waveguide is shown in figure 3-31. Thewavefront is shown in view A as small particles, Inviews B and C particle 1 strikes the wall and isbounced back from the wall without losing velocity.If the wall is perfectly flat, the angle at which it thewall, known as the angle of incidence is the sameas the angle of reflection An instant after particle1 strikes the wall, particle 2 strikes the wall, as shown

Figure 3-31.—Reflection of a single wavefront.

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in view C, and reflects in the same manner. Becauseall the particles are traveling at the same velocity,particles 1 and 2 do not change their relative positionwith respect to each other. Therefore, the reflectedwave has the same shape as the original. Theremaining particles as shown in views D, E, and Freflect in the same manner. This process results ina reflected wavefront identical in shape, but oppositein polarity, to the incident wave.

Figure 3-32, views A and B, each illustrate thedirection of propagation of two different electromag-netic wavefronts of different frequencies being radiatedinto a waveguide by a probe. Note that only thedirection of propagation is indicated by the lines andarrowheads. The wavefronts are at right angles tothe direction of propagation. The angle of incidence

and the angle of reflection of the wavefrontsvary in size with the frequency of the input energy,but the angles of reflection are equal to each otherin a waveguide. The CUTOFF FREQUENCY in awaveguide is a frequency that would cause angles ofincidence and reflection to be perpendicular to thewalls of the guide. At any frequency below the cutofffrequency, the wavefronts will be reflected back andforth across the guide (setting up standing waves) andno energy will be conducted down the waveguide.

Figure 3-32.—Different frequencies in a waveguide.

The velocity of propagation of a wave along awaveguide is less than its velocity through free space(speed of light). This lower velocity is caused by thezigzag path taken by the wavefront. Theforward-progress velocity of the wavefront in awaveguide is called GROUP VELOCITY and issomewhat slower than the speed of light.

The group velocity of energy in a waveguide isdetermined by the reflection angle of the wavefrontsoff the “b” walls. The reflection angle is determinedby the frequency of the input energy. This basicprinciple is illustrated in figure 3-33. As frequencyis decreased. the reflection angle increases, causingthe group velocity to decrease. The opposite is alsotrue; increasing frequency increases the group velocity.

Figure 3-33.—Reflection angle at various frequencies.

WAVEGUIDE MODES OFOPERATION

The waveguide analyzed in the previous paragraphsyields an electric field configuration known as thehalf-sine electric distribution. This configuration,called a MODE OF OPERATION, is shown in figure3-34. Recall that the strength of the field is indicatedby the spacing of the lines; that is, the closer the lines,the stronger the field. The regions of maximumvoltage in this field move continuously down thewaveguide in a sine-wave pattern. To meet boundaryconditions. the field must always be zero at the “b”walls.

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Figure 3-34.—Half-sine E field distribution.

The half-sine field is only one of many fieldconfigurations, or modes, that can exist in a rectangularwaveguide. A full-sine field can also exist in arectangular waveguide because, as shown in figure3-35, the field is zero at the “b” walls.

Figure 3-35.—Full-sine E field distribution.

The magnetic field in a rectangular waveguide isin the form of closed loops parallel to the surface ofthe conductors. The strength of the magnetic fieldis proportional to the electric field. Figure 3-36illustrates the magnetic field pattern associated witha half-sine electric field distribution. The magnitudeof the magnetic field varies in a sine-wave patterndown the center of the waveguide in “time phase” withthe electric field. TIME PHASE means that the peakH lines and peak E lines occur at the same instant intime, although not necessarily at the same point alongthe length of the waveguide.

The dominant mode is the most efficient mode.Waveguides are normally designed so that only thedominant mode will be used. To operate in thedominant mode, a waveguide must have an “a” (wide)dimension of at least one half-wavelength of thefrequency to be propagated. The “a” dimension ofthe waveguide must be kept near the minimumallowable value to ensure that only the dominant modewill exist. In practice, this dimension is usually 0.7wavelength.

Figure 3-36.—Magnetic field caused by a half-sineE field.

Of the possible modes of operation available fora given waveguide, the dominant mode has the lowestcutoff frequency. The high-frequency limit of arectangular waveguide is a frequency at which its “a”dimension becomes large enough to allow operationin a mode higher than that for which the waveguidehas been designed.

Circular waveguides are used in specific areas ofradar and communications systems, such as rotatingjoints used at the mechanical point where the antennasrotate. Figure 3-37 illustrates the dominant mode ofa circular waveguide. The cutoff wavelength of acircular guide is 1.71 times the diameter of thewaveguide. Since the “a” dimension of a rectangularwaveguide is approximately one half-wavelength atthe cutoff frequency, the diameter of an equivalentcircular waveguide must be 2/1.71, or approximately

Figure 3-37.—Dominant mode in a circularwaveguide.

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1.17 times the “a” dimension of a rectangularwaveguide.

MODE NUMBERING SYSTEMS

So far, only the most basic types of E and H fieldarrangements have been shown. More complicatedarrangements are often necessary to make possiblecoupling, isolation, or other types of operation. Thefield arrangements of the various modes of operationare divided into two categories: TRANSVERSEELECTRIC (TE) and TRANSVERSE MAGNETIC(TM).

In the transverse electric (TE) mode, the entireelectric field is in the transverse plane, which isperpendicular to the waveguide, (direction of energytravel). Part of the magnetic field is parallel tothe length axis.

In the transverse magnetic (TM) mode, theentire magnetic field is in the transverse plane andhas no portion parallel to the length axis.

Since there are several TE and TM modes,subscripts are used to complete the description of thefield pattern. In rectangular waveguides, the first

subscript indicates the number of half-wave patternsin the “a” dimension, and the second subscript indicatesthe number of half-wave patterns in the “b” dimension.

The dominant mode for rectangular waveguidesis shown in figure 3-38. It is designated as the TEmode because the E fields are perpendicular to the“a” walls. The first subscript is 1, since there is onlyone half-wave pattern across the “a” dimension. There

Figure 3-38.—Dominant mode in a rectangular

are no E-field patterns across the “b” dimension, sothe second subscript is 0. The complete modedescription of the dominant mode in rectangularwaveguides is TE1,0. Subsequent description ofwaveguide operation in this text will assume thedominant (TE1,0) mode unless otherwise noted.

A similar system is used to identify the modes ofcircular waveguides. The general classification of TEand TM is true for both circular and rectangularwaveguides. In circular waveguides the subscriptshave a different meaning. The first subscript indicatesthe number of fill-wave patterns around the circumfer-ence of the waveguide. The second subscript indicatesthe number of half-wave patterns across the diameter.

In the circular waveguide in figure 3-39, the Efield is perpendicular to the length of the waveguidewith no E lines parallel to the direction of propagation.Thus, it must be classified as operating in the TEmode. If you follow the E line pattern in a counter-clockwise direction starting at the top, the E linesgo from zero, through maximum positive (tail ofarrows), back to zero, through maximum negative(head of arrows), and then back to zero again. Thisis one full wave, so the first subscript is 1. Alongthe diameter, the E lines go from zero throughmaximum and back to zero, making a half-wavevariation. The second subscript, therefore, is also 1.TE1,1 is the complete mode description of the dominantmode in circular waveguides. Several modes arepossible in both circular and rectangular waveguides.Figure 3-40 illustrates several different modes thatcan be used to verify the mode numbering system.

Figure 3-39.—Counting wavelengths in a circularwaveguide.

waveguide.

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Figure 3-40.—Various modes of operation for rectangular and circular waveguides.

WAVEGUIDE INPUT/OUTPUTMETHODS

A waveguide, as explained earlier in this topic,operates differently from an ordinary transmission line.Therefore, special devices must be used to put energyinto a waveguide at one end and remove it from theother end.

The three devices used to injector remove energyfrom waveguides are PROBES, LOOPS, and SLOTS.Slots may also be called APERTURES or WINDOWS.

When a small probe is inserted into a waveguideand supplied with microwave energy, it acts as aquarter-wave antenna. Current flows in the probe andsets up an E field such as the one shown in figure3-41, view A. The E lines detach themselves fromthe probe. When the probe is located at the point ofhighest efficiency, the E lines set up an E field ofconsiderable intensity.

The most efficient place to locate the probe is inthe center of the “a” wall, parallel to the “b” wall, andone quarter-wavelength from the shorted end of thewaveguide, as shown in figure 3-41, views B and

C. This is the point at which the E field is maximumin the dominant mode. Therefore, energy transfer(coupling) is maximum at this point. Note that thequarter-wavelength spacing is at the frequency requiredto propagate the dominant mode.

In many applications a lesser degree of energytransfer, called loose coupling, is desirable. Theamount of energy transfer can be reduced by decreasingthe length of the probe, by moving it out of the centerof the E field, or by shielding it. Where the degreeof coupling must be varied frequently, the probe ismade retractable so the length can be easily changed.

The size and shape of the probe determines itsfrequency, bandwidth, and power-handling capability.As the diameter of a probe increases, the bandwidthincreases. A probe similar in shape to a door knobis capable of handling much higher power and a largerbandwidth than a conventional probe. The greaterpower-handling capability is directly related to theincreased surface area. Two examples o fbroad-bandwidth probes are illustrated in figure 3-41,view D. Removal of energy from a waveguide is

simply a reversal of the injection process using thesame type of probe.

Another way of injecting energy into a waveguideis by setting up an H field in the waveguide. Thiscan be accomplished by inserting a small loop thatcarries a high current into the waveguide, as shownin figure 3-42, view A. A magnetic field builds uparound the loop and expands to fit the waveguide, asshown in view B. If the frequency of the current inthe loop is within the bandwidth of the waveguide,energy will be transferred to the waveguide.

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Figure 3-41.—Probe coupling in a rectangular waveguide.

Figure 3-42.—Loop coupling in a rectangularwaveguide.

For the most efficient coupling to the waveguide,the loop is inserted at one of several points where themagnetic field will be of greatest strength. Four ofthose points are shown in figure 3-42, view C.

When less efficient coupling is desired, you canrotate or move the loop until it encircles a smallernumber of H lines. When the diameter of the loopis increased, its power-handling capability alsoincreases. The bandwidth can be increased byincreasing the size of the wire used to make the loop.

When a loop is introduced into a waveguide inwhich an H field is present, a current is induced inthe loop. When this condition exists, energy isremoved from the waveguide.

Slots or apertures are sometimes used when veryloose (inefficient) coupling is desired, as shown infigure 3-43. In this method energy enters througha small slot in the waveguide and the E field expandsinto the waveguide. The E lines expand first acrossthe slot and then across the interior of the waveguide.

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Figure 3-43.—Slot coupling in a waveguide.

Minimum reflections occur when energy is injectedor removed if the size of the slot is properly propor-tioned to the frequency of the energy.

After learning how energy is coupled into and outof a waveguide with slots, you might think that leavingthe end open is the most simple way of injecting orremoving energy in a waveguide. This is not the case,however, because when energy leaves a waveguide,fields form around the end of the waveguide. Thesefields cause an impedance mismatch which, in turn,causes the development of standing waves and a drasticloss in efficiency. Various methods of impedancematching and terminating waveguides will be coveredin the next section.

WAVEGUIDE IMPEDANCEMATCHING

Waveguide transmission systems are not alwaysperfectly impedance matched to their load devices.The standing waves that result from a mismatch causea power loss, a reduction in power-handling capability,and an increase in frequency sensitivity. Imped-ance-changing devices are therefore placed in thewaveguide to match the waveguide to the load. Thesedevices are placed near the source of the standingwaves.

Figure 3-44 illustrates three devices, called irises,that are used to introduce inductance or capacitanceinto a waveguide. An iris is nothing more than a metalplate that contains an opening through which the wavesmay pass. The iris is located in the transverse planeof either the magnetic or electric field.

An inductive iris and its equivalent circuit areillustrated in figure 3-44, view A. The iris places ashunt inductive reactance across the waveguide thatis directly proportional to the size of the opening.Notice that the inductive iris is in the magnetic plane.The shunt capacitive reactance, illustrated in viewB, basically acts the same way. Again, the reactanceis directly proportional to the size of the opening, butthe iris is placed in the electric plane. The iris,illustrated in view C, has portions in both the magnetic

Figure 3-44.—Waveguide irises.

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and electric transverse planes and forms an equivalentparallel-LC circuit across the waveguide. At theresonant frequency, the iris acts as a high shuntresistance. Above or below resonance, the iris actsas a capacitive or inductive reactance.

POSTS and SCREWS made from conductivematerial can be used for impedance-changing devicesin waveguides. Views A and B of figure 3-45,illustrate two basic methods of using posts and screws.A post or screw that only partially penetrates into thewaveguide acts as a shunt capacitive reactance. Whenthe post or screw extends completely through thewaveguide, making contact with the top and bottomwalls, it acts as an inductive reactance. Note that whenscrews are used, the amount of reactance can be varied.

Figure 3-45.—Conducting posts and screws.

WAVEGUIDE TERMINATIONS

Electromagnetic energy is often passed througha waveguide to transfer the energy from a source intospace. As previously mentioned, the impedance ofa waveguide does not match the impedance of space,and without proper impedance matching standing wavescause a large decrease in the efficiency of thewaveguide.

Any abrupt change in impedance causes standingwaves, but when the change in impedance at the endof a waveguide is gradual, almost no standing wavesare formed. Gradual changes in impedance can beobtained by terminating the waveguide with afunnel-shaped HORN, such as the three types illustratedin figure 3-46. The type of horn used depends uponthe frequency and the desired radiation pattern.

Figure 3-46.—Waveguide horns.

As you may have noticed, horns are really simpleantennas. They have several advantages over otherimpedance-matching devices, such as their largebandwidth and simple construction.

A waveguide may also be terminated in a resistiveload that is matched to the characteristic impedanceof the waveguide. The resistive load is most oftencalled a DUMMY LOAD, because its only purposeis to absorb all the energy in a waveguide withoutcausing standing waves.

There is no place on a waveguide to connect afixed termination resistor; therefore, several specialarrangements are used to terminate waveguides. Onemethod is to fill the end of the waveguide with agraphite and sand mixture, as illustrated in figure 3-47,view A. When the fields enter the mixture, theyinduce a current flow in the mixture that dissipatesthe energy as heat. Another method (view B) is touse a high-resistance rod placed at the center of theE field. The E field causes current to flow in the rod,and the high resistance of the rod dissipates the energyas a power loss, again in the form of heat.

Still another method for terminating a waveguideis the use of a wedge of highly resistive material, asshown in view C of figure 3-47. The plane of thewedge is placed perpendicular to the magnetic lines

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Figure 3-47.—Terminating waveguides.

of force. When the H lines cut through the wedge,current flows in the wedge and causes a power loss.As with the other methods, this loss is in the formof heat. Since very little energy reaches the end ofthe waveguide, reflections are minimum.

All of the terminations discussed so far aredesigned to radiate or absorb the energy withoutreflections. In many instances, however, all of theenergy must be reflected from the end of thewaveguide. The best way to accomplish this is topermanently weld a metal plate at the end of thewaveguide, as shown in view D of figure 3-47.

WAVEGUIDE PLUMBING

Since waveguides are really only hollow metalpipes, the installation and the physical handling ofwaveguides have many similarities to ordinaryplumbing. In light of this fact, the bending, twisting,joining, and installation of waveguides is commonlycalled waveguide plumbing. Naturally, waveguidesare different in design from pipes that are designed

to carry liquids or other substances. The design ofa waveguide is determined by the frequency and powerlevel of the electromagnetic energy it will carry. Thefollowing paragraphs explain the physical factorsinvolved in the design of waveguides.

Waveguide Bends

The size, shape, and dielectric material of awaveguide must be constant throughout its length forenergy to move from one end to the other withoutreflections. Any abrupt change in its size or shapecan cause reflections and a loss in overall efficiency.When such a change is necessary, the bends, twists,and joints of the waveguides must meet certainconditions to prevent reflections.

Waveguides maybe bent in several ways that donot cause reflections. One way is the gradual bendshown in figure 3-48. This gradual bend is knownas an E bend because it distorts the E fields. The Ebend must have a radius greater than two wavelengthsto prevent reflections.

Figure 3-48.—Gradual E bend.

Another common bend is the gradual H bend (fig.3-49). It is called an H bend because the H fieldsare distorted when a waveguide is bent in this manner.Again, the radius of the bend must be greater thantwo wavelengths to prevent reflections. Neither theE bend in the “a” dimension nor the H bend in the“b” dimension changes the normal mode of operation.

Figure 3-49.—Gradual H bend.

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A sharp bend in either dimension may be usedif it meets certain requirements. Notice the two45-degree bends in figure 3-50; the bends are 1/4λapart. The reflections that occur at the 45-degree bendscancel each other, leaving the fields as though noreflections have occurred.

Figure 3-50.—Sharp bends.

Sometimes the electromagnetic fields must berotated so that they are in the proper phase to matchthe phase of the load. This may be accomplished bytwisting the waveguide as shown in figure 3-51. Thetwist must be gradual and greater than

Figure 3-51.—Waveguide twist.

The flexible waveguide (fig. 3-52) allows specialbends, which some equipment applications mightrequire. It consists of a specially wound ribbon ofconductive material, the most commonly used is brass,with the inner surface plated with chromium. Powerlosses are greater in the flexible waveguide becausethe inner surfaces are not perfectly smooth. Therefore,it is only used in short sections where no otherreasonable solution is available.

Waveguide Joints

beSince an entire waveguide system cannot possibly

molded into one piece, the waveguide must be

Figure 3-52.—Flexible waveguide.

constructed in sections and the sections connected withjoints. The three basic types of waveguide joints arethe PERMANENT, the SEMIPERMANENT, and theROTATING JOINTS. Since the permanent joint isa factory-welded joint that requires no maintenance,only the semipermanent and rotating joints will bediscussed.

Sections of waveguide must be taken apart formaintenance and repair. A semipermanent joint, calleda CHOKE JOINT, is most commonly used for thispurpose. The choke joint provides good electromag-netic continuity between the sections of the waveguidewith very little power loss.

A cross-sectional view of a choke joint is shownin figure 3-53. The pressure gasket shown betweenthe two metal surfaces forms an airtight seal. Noticein view B that the slot is exactly from the “a”wall of the waveguide. The slot is also deep,as shown in view A, and because it is shorted at point1, a high impedance results at point 2. Point 3 is from point 2. The high impedance at point 2 resultsin a low impedance, or short, at point 3. This effectcreates a good electrical connection between the twosections that permits energy to pass with very littlereflection or loss.

Whenever a stationary rectangular waveguide isto be connected to a rotating antenna, a rotating jointmust be used. A circular waveguide is normally usedin a rotating joint. Rotating a rectangular waveguidewould cause field pattern distortion. The rotatingsection of the joint, illustrated in figure 3-54, uses achoke joint to complete the electrical connection withthe stationary section. The circular waveguide isdesigned so that it will operate in the TM0,1 mode.

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The rectangular sections are attached as shown in theillustration to prevent the circular waveguide fromoperating in the wrong mode. Distance “O” is so that a high impedance will be presented to anyunwanted modes. This is the most common designused for rotating joints, but other types may be usedin specific applications.

WAVEGUIDE MAINTENANCE

The installation of a waveguide system presentsproblems that are not normally encountered whendealing with other types of transmission lines. Theseproblems often fall within the technician’s area ofresponsibility. A brief discussion of waveguidehandling, installation, and maintenance will helpprepare you for this maintenance responsibility,Detailed information concerning waveguide mainte-nance in a particular system may be found in thetechnical manuals for the system.

Figure 3-53.—Choke joint.

Figure 3-54.—Rotating joint.

Since a waveguide naturally has a low loss ratio,most losses in a waveguide system are caused by otherfactors. Improperly connected joints or damaged innersurfaces can decrease the efficiency of a system tothe point that it will not work at all. Therefore, youmust take great care when working with waveguidesto prevent physical damage. Since waveguides aremade from a soft, conductive material, such as copperor aluminum, they are very easy to dent or deform.Even the slightest damage to the inner surface of awaveguide will cause standing waves and, often,internal arcing. Internal arcing causes further damageto the waveguide in an action that is oftenself-sustaining until the waveguide is damaged beyonduse. Part of your job as a technician will be to inspectthe waveguide system for physical damage. Thepreviously mentioned dents are only one type ofphysical damage that can decrease the efficiency ofthe system. Another problem occurs becausewaveguides are made from a conductive material suchas copper while the structures of most ships are madefrom steel. When two dissimilar metals, such ascopper and steel, are in direct contact, an electricalaction called ELECTROLYSIS takes place that causesvery rapid corrosion of the metals. Waveguides canbe completely destroyed by electrolytic corrosion ina relatively short period of time if they are not isolatedfrom direct contact with other metals. Any inspection

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of a waveguide system should include a detailedinspection of all support points to ensure that electro-lytic corrosion is not taking place. Any waveguidethat is exposed to the weather should be painted andall joints sealed. Proper painting prevents naturalcorrosion, and sealing the joints prevents moisture fromentering the waveguide.

Moisture can be one of the worst enemies of awaveguide system. As previously discussed, thedielectric in waveguides is air, which is an excellentdielectric as long as it is free of moisture. Wet air,however, is a very poor dielectric and can cause seriousinternal arcing in a waveguide system. For this reason,care is taken to ensure that waveguide systems arepressurized with air that is dry. Checking the pressureand moisture content of the waveguide air may be oneof your daily system maintenance duties.

More detailed waveguide installation and mainte-nance information can be found in the technicalmanuals that apply to your particular system. Anothergood source is the Electronics Installation andMaintenance Handbooks (EIMB) published by NavalSea Systems Command. Installation Standards (EIMB)Handbook, NAVSEA 0967-LP-000-0110, is the volumethat deals with waveguide installation and maintenance.

WAVEGUIDE DEVICES

The discussion of waveguides, up to this point,has been concerned only with the transfer of energyfrom one point to another. Many waveguide deviceshave been developed, however, that modify the energyin some fashion during the transmission. Some devicesdo nothing more than change the direction of theenergy. Others have been designed to change the basiccharacteristics or power level of the electromagneticenergy.

This section will explain the basic operatingprinciples of some of the more common waveguidedevices, such as DIRECTIONAL COUPLERS,CAVITY RESONATORS, and HYBRID JUNCTIONS.

Directional Couplers

The directional coupler is a device that providesa method of sampling energy from within a waveguide

for measurement or use in another circuit. Mostcouplers sample energy traveling in one direction only.However, directional couplers can be constructed thatsample energy in both directions. These are calledBIDIRECTIONAL couplers and are widely used inradar and communications systems.

Directional couplers may be constructed in manyways. The coupler illustrated in figure 3-55 isconstructed from an enclosed waveguide section ofthe same dimensions as the waveguide in which theenergy is to be sampled. The “b” wall of this enclosedsection is mounted to the “b” wall of the waveguidefrom which the sample will be taken. There are twoholes in the “b” wall between the sections of thecoupler. These two holes are apart. The uppersection of the directional coupler has a wedge-o fenergy-absorbing material at one end and a pickupprobe connected to an output jack at the other end.The absorbent material absorbs the energy not directedat the probe and a portion of the overall energy thatenters the section.

Figure 3-55.—Directional coupler.

Figure 3-56 illustrates two portions of the incidentwavefront in a waveguide. The waves travel downthe waveguide in the direction indicated and enter thecoupler section through both holes. Since both portionsof the wave travel the same distance, they are in phasewhen they arrive at the pickup probe. Because thewaves are in phase, they add together and provide asample of the energy traveling down the waveguide.The sample taken is only a small portion of the energythat is traveling down the waveguide. The magnitudeof the sample, however, is proportional to themagnitude of the energy in the waveguide. Theabsorbent material is designed to ensure that the ratio

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between the sample energy and the energy in thewaveguide is constant. Otherwise, the sample wouldcontain no useful information. The ratio is usuallystamped on the coupler in the form of an attenuationfactor.

and the probe are in opposite positions from thedirectional coupler designed to sample the incidentenergy. This positioning causes the two portions ofthe reflected energy to arrive at the probe in phase,providing a sample of the reflected energy. Thetransmitted energy is absorbed by the absorbentmaterial.

Figure 3-56.—Incident wave in a directional couplerdesigned to sample incident waves.

The effect of a directional coupler on any reflectedenergy is illustrated in figure 3-57. Note that thesetwo waves do not travel the same distance to thepickup probe. The wave represented by the dottedline travels further and arrives at the probe 180degrees out of phase with the wave, represented bythe solid line. Because the waves are 180 degreesout of phase at the probe, they cancel each other andno energy is induced into the pickup probe. Whenthe reflected energy arrives at the absorbent material,it adds and is absorbed by the material.

Figure 3-57.—Reflected wave in a directionalcoupler.

A directional coupler designed to sample reflectedenergy is shown in figure 3-58. The absorbent material

Figure 3-58.—Directional coupler designed to sampleretlected energy.

A simple bidirectional coupler for sampling bothtransmitted and reflected energy can be constructedby mounting two directional couplers on opposite sidesof a waveguide, as shown in figure 3-59.

Figure 3-59.—Bidirectional coupler.

Resonators

definition, a resonant cavity is any space

Cavity

Bycompletely enclosed by conducting- walls that cancontain oscillating electromagnetic fields and possessresonant properties. The cavity has many advantages

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and uses at microwave frequencies. Resonant cavitieshave a very high Q and can be built to handlerelatively large amounts of power. Cavities with aQ value in excess of 30,000 are not uncommon. Thehigh Q gives these devices a narrow bandpass andallows very accurate tuning. Simple, rugged construc-tion is an additional advantage.

Although cavity resonators, built for differentfrequency ranges and applications, have a variety ofshapes, the basic principles of operation are the samefor all.

One example of a cavity resonator is the rectangularbox shown in figure 3-60, view A. It may be thoughtof as a section of rectangular waveguide closed at bothends by conducting plates. The frequency at whichthe resonant mode occurs is of the distancebetween the end plates. The magnetic field patternsin the rectangular cavity are shown in view B.

There are two variables that determine the primaryfrequency of any resonant cavity. The first variableis PHYSICAL SIZE. In general, the smaller thecavity, the higher its resonant frequency. The secondcontrolling factor is the SHAPE of the cavity. Figure3-61 illustrates several cavity shapes that are commonlyused. Remember from the previously stated definitionof a resonant cavity that any completely enclosedconductive surface, regardless of its shape, can actas a cavity resonator.

Energy can be inserted or removed from a cavityby the same methods that are used to couple energyinto and out of waveguides. The operating principlesof probes, loops, and slots are the same whether usedin a cavity or a waveguide. Therefore, any of the threemethods can be used with cavities to inject or removeenergy.

The resonant frequency of a cavity can be variedby changing any of the three parameters: cavityvolume, cavity capacitance, or cavity inductance.Changing the frequencies of a cavity is known asTUNING. The mechanical methods of tuning a cavitymay vary with the application, but all methods usethe same electrical principles.

Figure 3-60.—Rectangular waveguide cavityresonator.

Waveguide Junctions

You may have assumed that when energy travelingdown a waveguide reaches a junction it simply dividesand follows the junction. This is not strictly true.

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Figure 3-61.—Types of cavities.

Different types of junctions affect the energy individed into two basic types, the E TYPE and the H

different ways. Since waveguide junctions are usedTYPE. HYBRID JUNCTIONS are more complicated

extensively in most systems, you need to understanddevelopments of the basic T junctions. The MAGIC-T

the basic operating principles of those most commonlyand the HYBRID RING are the two most commonly

used.used hybrid junctions.

The T JUNCTION is the most simple of theE-TYPE T JUNCTION.— An E-type T junction

commonly used waveguide junctions. T junctions areis illustrated in figure 3-62, view A.

Figure 3-62.—E fields in an E-type T junction.

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It is called an E-type T junction because the junctionarm extends from the main waveguide in the samedirection as the E field in the waveguide.

Figure 3-62, view B, illustrates cross-sectionalviews of the E-type T junction with inputs fed intothe various arms. For simplicity, the magnetic linesthat are always present with an electric field have beenomitted. In view K, the input is fed into arm b andthe outputs are taken from the a and c arms. Whenthe E field arrives between points 1 and 2, point 1becomes positive and point 2 becomes negative. Thepositive charge at point 1 then induces a negativecharge on the wall at point 3. The negative chargeat point 2 induces a positive charge at point 4. Thesecharges cause the fields to form 180 degrees out ofphase in the main waveguide; therefore, the outputswill be 180 degrees out of phase with each other.In view L, two in-phase inputs of equal amplitude arefed into the a and c arms. The signals at points 1 and

2 have the same phase and amplitude. No differenceof potential exists across the entrance to the b arm,and no energy will be coupled out. However, whenthe two signals fed into the a and c arms are 180degrees out of phase, as shown in view M, points1 and 2 have a difference of potential. This differenceof potential induces an E field from point 1 to point2 in the b arm, and energy is coupled out of this arm.Views N and P illustrate two methods of obtainingtwo outputs with only one input.

H-TYPE T JUNCTION.— An H-type T junctionis illustrated in figure 3-63, view A. It is called anH-type T junction because the long axis of the “b”arm is parallel to the plane of the magnetic lines offorce in the waveguide. Again, for simplicity, onlythe E lines are shown in this figure. Each X indicatesan E line moving away from the observer. Each dotindicates an E line moving toward the observer.

Figure 3-63.—E field in an H-type T junction.

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In view 1 of figure 3-63, view B, the signal is fedinto arm b and in-phase outputs are obtained fromthe a and c arms. In view 2, in-phase signals are fedinto arms a and c and the output signal is obtainedfrom the b arm because the fields add at the junctionand induce E lines into the b arm. If180-degree-out-of-phase signals are fed into arms aand c, as shown in view 3, no output is obtained fromthe b arm because the opposing fields cancel at thejunction. If a signal is fed into the a arm, as shownin view 4 , outputs will be obtained from the b andc arms. The reverse is also true. If a signal is fedinto the c arm, outputs will be obtained from the aand b arms.

MAGIC-T HYBRID JUNCTION.— A simpli-fied version of the magic-T hybrid junction is shownin figure 3-64. The magic-T is a combination of theH-type and E-type T junctions. The most commonapplication of this type of junction is as the mixersection for microwave radar receivers.

Figure 3-64.—Magic-T hybrid junction.

If a signal is fed into the b arm of the magic-T,it will divide into two out-of-phase components. Asshown in figure 3-65, view A, these two componentswill move into the a and c arms. The signal enteringthe b arm will not enter the d arm because of the zeropotential existing at the entrance of the d arm. Thepotential must be zero at this point to satisfy theboundary conditions of the b arm. This absence ofpotential is illustrated in views B and C where themagnitude of the E field in the b arm is indicated bythe length of the arrows. Since the E lines are atmaximum in the center of the b arm and minimumat the edge where the d arm entrance is located, nopotential difference exists across the mouth of the darm.

Figure 3-65.—Magic-T with input to arm b.

In summary, when an input is applied to arm bof the magic-T hybrid junction, the output signals fromarms a and c are 180 degrees out of phase with eachother, and no output occurs at the d arm.

The action that occurs when a signal is fed intothe d arm of the magic-T is illustrated in figure 3-66.As with the H-type T junction, the signal entering thed arm divides and moves down the a and c arms asoutputs that are in phase with each other and with theinput. The shape of the E fields in motion is shownby the numbered curved slices. As the E field movesdown the d arm, points 2 and 3 are at an equalpotential. The energy divides equally into arms a andc, and the E fields in both arms become identical inshape. Since the potentials on both sides of the b armare equal, no potential difference exists at the entranceto the b arm, resulting in no output.

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Figure 3-66.—Magic-T with input to arm d.

When an input signal is fed into the a arm asshown in figure 3-67, a portion of the energy iscoupled into the b arm as it would be in an E-typeT junction. An equal portion of the signal iscoupled through the d arm because of the action ofthe H-type junction. The c arm has two fieldsacross it that are out of phase with each other.Therefore, the fields cancel, resulting in no outputat the c arm. The reverse of this action takes placeif a signal is fed into the c arm, resulting inoutputs at the b and d arms and no output at the aarm.

Figure 3-67.—Magic-T with input to arm a.

Unfortunately, when a signal is applied to anyarm of a magic-T, the flow of energy in the outputarms is affected by reflections. Reflections arecaused by impedance mismatching at thejunctions. These reflections are the cause of thetwo major disadvantages of the magic-T. First, thereflections represent a power loss since all theenergy fed into the junction does not reach theload that the arms feed. Second, the reflectionsproduce standing waves that can result in internalarcing. Thus, the maximum power a magic-T canhandle is greatly reduced.

Reflections can be reduced by using somemeans of impedance matching that does not

destroy the shape of the junctions. One method isshown in figure 3-68. A post is used to match theH plane, and an iris is used to match the E plane.Even though this method reduces reflections, itlowers the power-handling capability even further.

Figure 3-68.—Magic-T impedance matching.

HYBRID RING.— A type of hybrid junctionthat overcomes the power limitation of the magic-T is the hybrid ring, also called a RAT RACE. Thehybrid ring, illustrated in figure 3-69, view A, isactually a modification of the magic-T. It isconstructed of rectangular waveguides moldedinto a circular pattern. The arms are joined to thecircular waveguide to form E-type T junctions.View B shows, in wavelengths, the dimensionsrequired for a hybrid ring to operate properly.

The hybrid ring is used primarily in high-powered radar and communications systems toperform two functions. During the transmitperiod, the hybrid ring couples microwave energyfrom the transmitter to the antenna and allows noenergy to reach the receiver. During the receivecycle, the hybrid ring couples energy from theantenna to the receiver and allows no energy toreach the transmitter. Any device that performsboth of these functions is called a DUPLEXER. Aduplexer permits a system to use the sameantenna for both transmitting and receiving.

SUMMARY

This concludes our discussion on transmissionlines and waveguides. In this volume you havebeen given a basic introduction on wavepropagation from the time it leaves thetransmitter to the point of reception. In volume 8you will be introduced to a variety of electronicsupport systems.

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Figure 3-69.—Hybrid ring with wavelengthmeasurements.

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