Antenna and Wave Propagation

antennas and wave propagation





lectures notes
written by
dr. saad saffah










contains

1-1 introduction and definitions:
1-1-1 the electromagnetic spectrum
1-1-2 the radio transmitter
1-1-3 the radio receiver
1-1-4 wireless communication systems
1.2 maxwell’s equations and the fundamental of radiation:
1-2-1 uniform plane wave (upw) solution
1-2-2 propagation in lossless, charge-free region
1-2-3 poynting vector
2-1 radiated field of a hertzian dipole
2-1 basic antenna parameters:
2-1-1 directivity and gain:
2-1-2 radiation resistance:
2-1-3 effective area of an antenna:
2-1-4 effective length/height of the antenna:
2-1-5 antenna equivalent circuit:
3-1 half wave dipole antenna:
3-2 quarter wave monopole antenna:
4-1 small loop antennas:
5-1 introduction to antenna arrays:
5-2 array of identical elements:
5-3 two-element array:
5-3-1 case-1:
5-3-2 case 2:
5-4 uniform one-dimensional array
5-4-1 broad side case:
5-4-2 end fire case:
5-5 array pattern synthesis:

































1-1 introduction and definitions:
there are more “radios” being built than ever before!
1. telephony
cellular
public cabinets system (pcs)
global satellite systems
microwave links
2. broadcasting
am radio, fm radio, vhf/uhf tv
satellite links
direct broadcasting
3. networking
lan
wifi
wimax
lifi
4. radar and navigation
global positioning system (gps)
radar detection, tracking and imaging
radio frequency identification (rfid)
q: just what is a radio?
a: a device that transfers information to a distant site, by means of unbounded electromagnetic propagation.
a radio system has three sections, with antennas serving as couplers between each section:


1-1-1 the electromagnetic spectrum
we can propagate energy anywhere within the electromagnetic spectrum, but we typically use frequencies less than, say, 40 ghz.
q: why don’t we use frequencies greater than 40 ghz ?
a: two reasons:
the difficulty in making electronic components.
the earth’s atmosphere rapidly attenuates the propagating wave!
1-1-2 the radio transmitter


there are five main components of a transmitter:
1) the signal a(t) – this is the information we are trying to transmit. it may be in either digital or analog form. it also may have been encoded to remove redundancy, in a process known as source coding.
2) rf source – generates electromagnetic energy at rf/microwave frequencies that are suitable for electromagnetic propagation (subject to fcc restrictions !).
3) modulator – places signal a(t) (i.e., the information) onto the rf signal, known as the carrier. accomplished by modulating some parameter of the carrier signal – e.g., magnitude, phase, frequency, or some combination thereof. in general, this process is called channel coding. its goal is to maximize the rate at which information is sent, while minimizing the effect of unknown channel parameters.
4) power amplifier – increases the power (i.e., energy flow) of the modulated carrier signal, without (hopefully) distorting it.
5) antenna – acts as the coupling mechanism between the bounded e.m. wave of a transmission line and the unbounded propagating wave in space. often, an antenna is required to launch the unbounded wave in a specific direction.
1-1-3 the radio receiver
there are eight basic components in a radio receiver:
1) antenna – couples the incoming em propagating wave into the receiver.
2) low-noise amplifier – boosts the power of the initial signal above the receiver noise.
3) pre-selector filter – allows only the frequency band of interest to pass into the receiver (e.g., for fm radio 88-108 mhz).
4) local oscillator/mixer – translates the signal from its propagation frequency to a lower, fixed intermediate frequency (if).
5) if amplifier – a high-gain amplifier that greatly increases signal power (i.e., to a detectable level).
6) if filter - allows only the signal of interest to pass. bandwidth is typically that of the desired signal. (e.g., 200 khz for fm radio, 20 khz for am radio).
7) detector/demodulator – extracts the signal information from the if signal.
8) the recovered signal a ?(t)- the receiver’s at what the original signal was.

1-1-4 wireless communication systems
in wireless communication systems, signals are radiated in space as an electromagnetic wave by using a transmitting antenna and a fraction of this radiated power is intercepted by using a receiving antenna. thus, an antenna is a device used for radiating or receiver radio waves.

an antenna can also be thought of as a transitional structure between free space and a guiding device (such as transmission line or waveguide). usually antennas are metallic structures, but dielectric antennas (lens antennas) are also used now a day. in our discussion, we shall consider only metallic antennas. here we shall restrict our discussion to some very commonly used antenna structures. some of the most commonly used antenna structures are shown.







a radio antenna: may be defined as the structure associated with the region of transition between a guided wave and a free-space wave, or vice versa.
to be more explicit, the region of transition between the guided wave and the free-space wave may be defined as an antenna.
electromagnetic wave: an electromagnetic wave, as the name implies, consists of a combination of the properties of both electric and magnetic fields.
it is conceptually easy to generate an electromagnetic wave. all you need to do is to cause a changing current in a conductor and a wave will propagate outward to the end of the universe.
a transmission line: is a device for transmitting or guiding radio-frequency energy from one point to another. usually it is desirable to transmit the energy with a minimum of attenuation, heat and radiation losses being as small as possible.
the term transmission line (or transmission system) include not only coaxial and 2-wire transmission lines but also hollow pipes, or waveguides.
the wave transmitted along the line: is 1-dimensional in that it does not spread out into space but follows along the line.
a generator connected to an infinite, lossless transmission line produces a uniform traveling wave along the line. if the line is short-circuited, the outgoing traveling wave is reflected, producing a standing wave on the line due to the interference between the outgoing and reflected waves.
a guided wave traveling along a transmission line which opens out, as in fig. 2-1, will radiate as a free-space wave. the guided wave is a plane wave while the free-space wave is a spherically expanding wave.
resonant circuit: the energy concentrations in such a wave oscillate from entirely electric to entirely magnetic and back twice per cycle. such energy behavior is characteristic of a resonant circuit, or resonator.




1.2 maxwell’s equations and the fundamental of radiation:
radiation is the process of emitting energy from a source. electromagnetic radiation can be at all frequencies except zero (dc), but radiation at various frequencies may take different forms. the energy associated with the radiation depends on the frequency.
time varying currents radiate electromagnetic waves. a time varying current generates time varying electric and magnetic fields. when such fields exist, power is generated and propagated.
in regions of free space (i.e. the vacuum), where no electric charges, no electric currents and no matter of any kind are present, maxwell’s equations (in differential form) are:

we can de-couple maxwell’s equations e.g. by applying the curl operator to equations (3) and (4):

these are three-dimensional de-coupled wave equations for e ? and b ?
note that they have exactly the same structure – both are linear, homogeneous, 2nd order differential equations.
remember that each of the above equations is explicitly dependent on space and time, i.e. e ?=e ?(r ?,t) and b ?=b ?(r ?,t)

thus, maxwell’s equations implies that empty space (the vacuum: which is not empty, at the microscopic scale) supports the propagation of {macroscopic} electromagnetic waves, which propagate at the speed of light:
c=1/?(?_o ?_o )=3×?10?^8 m/s .
em waves have associated with them a frequency f and wavelength ?, related to each other via =f? .

1-2-1 uniform plane wave (upw) solution
now, let’s try to solve the wave equation. we suppose that we have
a). electrical filed only have one components (say ex component)
b). this components is constant in two directions (say x-y plane), only change along z-axis (propagation direction).
so the proposed solution is

how do we know this is a solution?
just plug in the wave equation, if we can find an ex(z) which satisfies the wave equation, we have a solution.

the solution is


if we translate this solution back into instantaneous solution, it is:

the first term characterizes the forward-propagating upw, the second term characterizes the backward-propagating one.
by the help of the maxwell equations, we can also figure out other field such d, b. and h.

therefore, the h field can be calculated as




having e and h solution available, the ratio between the e and h field can be taken. let’s take a forward-propagation upw as examples:



since e and h fields have unit (v/m) and (a/m). the ratio yields a unit of (?). this ratio is referred as intrinsic impedance (?) of the materials.

now, we can see, the propagation characteristics for upw is ultimately determined by .

1-2-2 propagation in lossless, charge-free region
in a charge free region with zero loss, the propagation constant

?=0, so

a special example will be vacuum, where ? = ?o , ? = ?o.



1-2-3 poynting vector


the cross product in the left-hand side can be written as following and known as instantaneous poynting vector.


upw power transmission, apply poynting theorem to upw. we can easily show that the time-averaged power density in a plane wave is

the power through a surface is then
.
if we have a plane wave traveling in lossy media, the spatial part of wave is

the intrinsic impedance can be complex and can be written in the form of

the magnetic field is then

the poynting vector can be expressed as:




















1-3 polarization
the polarization of a upw describes the shape and locus of the tip of e-vector at a given point in space as function of time. if we have a upw traveling along +z direction, the e-field could have two components along x-axis and y-axis. mathematically, it can be written as:

if we observe the e-field at a fix point, say… z = 0 , we have:

in an x-y plane, the above equation represent parametric equations describing various shape of circle, ellipse, or straight line. these all depends on the phase in two axis and amplitudes. if we choose a proper reference point for the time, we can set ?x = 0, and ? = ?y - ?x , so


1-3-1 linear polarization
if the phases ?x and ?y are in phase or completely out of phase


if we observe the e-field at a fix point, say… z = 0 , we have:

the ? is defined as inclination angle shown below. since ? is independent of both z and t, e(z,t) maintains a direction along the line making an angle ? with the x-axis.


1-3-2 circular polarization
if exo = eyo ? a, and the phase different between two e-field components are

here we have two situations:
left-handed circular (lhc) polarization
right-handed circular (rhc) polarization
for lhc polarization, at z=0 (observation point)

from above equations, we see that the amplitude of the total e-field is a constant, however, the inclination angle linearly decreases. if you face the incoming em field, you find that e-field is left-hand-circulated.

for rhc polarization, at z=0 (observation point)

from above equations, we see that the amplitude of the total e-field is a constant, however, the inclination angle linearly increases. if you face the incoming em field, you find that e-field is right-hand-circulated.


1-3-3 elliptical polarization
in most general cases, we have ex0 ? ey0, and ? ? 0, ?, or ? ?/2. the wave is said to be elliptically polarized. the shape and handedness (rh or lh) are determined by the values of the ratio (ey0 / ex0).
illustrated by the figure below, the major and minor axes of the ellipse do not necessarily overlap with the x and y-axis. we then define the rotation angle ? that is between the major axis ? and the x-axis. if we define an auxiliary angel ?0:

we can prove that the rotation angle is:



also, we have
if ? > 0, then sin? > 0, this leads to left-handed rotation
if ? < 0, then sin? < 0, this leads to right-handed rotation

example: determine the polarization state of a plane wave with e-field.



chapter 2: radio wave propagation
2.1- electromagnetic fields
there are two basic fields associated with every antenna an induction field and a radiation field.
2.1.1- induction field
figure 2-1, a low-frequency generator connected to an antenna, will help you understand how the induction field is produced. let us follow the generator through one cycle of operation.
initially, you can consider that the generator output is zero and that no fields exist about the antenna, as shown in view (a).
now assume that the generator produces a slight potential and has the instantaneous polarity shown in view (b). because of this slight potential, the antenna capacitance acts as a short, allowing a large flow of current (i) through the antenna in the direction shown. this current flow, in turn, produces a large magnetic field about the antenna. since the flow of current at each end of the antenna is minimum, the corresponding magnetic fields at each end of the antenna are also minimum.
as time passes, charges, which oppose antenna current and produce an electrostatic field (e field), collect at each end of the antenna. eventually, the antenna capacitance becomes fully charged and stops current flow through the antenna. under this condition, the electrostatic field is maximum, and the magnetic field (h field) is fully collapsed, as shown in view (c).
as the generator potential decreases back to zero, the potential of the antenna begins to discharge. during the discharging process, the electrostatic field collapses and the direction of current flow reverses, as shown in view (d).
when the current again begins to flow, an associated magnetic field is generated. eventually, the electrostatic field completely collapses, the generator potential reverses, and current is maximum, as shown in view (e).
as charges collect at each end of the antenna, an electrostatic field is produced and current flow decreases. this causes the magnetic field to begin collapsing. the collapsing magnetic field produces more current flow, a greater accumulation of charge, and a greater electrostatic field. the antenna gradually reaches the condition shown in view (f), where current is zero and the collected charges are maximum.
as the generator potential again decreases toward zero, the antenna begins to discharge and the electrostatic field begins to collapse. when the generator potential reaches zero, discharge current is maximum and the associated magnetic field is maximum. a brief time later, generator potential reverses, and the condition shown in view b recurs.
note: the electric field (e field) and the electrostatic field (e field) are the same. they will be used interchangeably throughout this text.
the graph shown in figure 2-2 shows the relationship between the magnetic field (h-field) and the electric field (e-field) plotted against time. note that the two fields are 90 degrees out of phase with each other.
if you compare the graph in figure 2-2 with figure 2-1, you will notice that the two fields around the antenna are displaced 90 degrees from each other in space. (the h field exists in a plane perpendicular to the antenna. the e field exists in a plane parallel with the antenna, as shown in figure 2-1

figure 2-1.—induction field about an antenna.


figure 2-2.—phase relationship of induction field components.
all the energy supplied to the induction field is returned to the antenna by the collapsing e and h fields. no energy from the induction field is radiated from the antenna. therefore, the induction field is considered a local field and plays no part in the transmission of electromagnetic energy. the induction field represents only the stored energy in the antenna and is responsible only for the resonant effects that the antenna reflects to the generator.
2.1.2- radiation fields
the e and h fields that are set up in the transfer of energy through space are known collectively as the radiation field. the radiation field decreases as the distance from the antenna is increased. because the decrease is linear, the radiation field reaches great distances from the antenna.
let us look at a half-wave antenna to illustrate how this radiation actually takes place. simply stated, a half-wave antenna is one that has an electrical length equal to half the wavelength of the signal being transmitted. assume, for example, that a transmitter is operating at 30 megahertz. if a half-wave antenna is used with the transmitter, the antenna s electrical length would have to be at least 16 feet long. (the formula used to compute the electrical length of an antenna would be explained later).

figure 2-3 is a simple picture of an e field detaching itself from an antenna. (the h field will not be considered, although it is present.)
in view (a), the voltage is maximum and the electric field has maximum intensity. the lines of force begin at the end of the antenna that is positively charged and extend to the end of the antenna that is negatively charged. note that the outer e lines are stretched away from the inner lines. this is because of the repelling force that takes place between lines of force in the same direction.
as the voltage dropings view (b), the separated charges come together, and the ends of the lines move toward the center of the antenna. but, since lines of force in the same direction repel each other, the centers of the lines are still being held out.
as the voltage approaches zero view (b), some of the lines collapse back into the antenna. at the same time, the ends of other lines begin to come together to form a complete loop. notice the direction of these lines of force next to the antenna in view (c). at this point, the voltage on the antenna is zero.
as the charge starts to build up in the opposite direction, view (d), electric lines of force again begin at the positive end of the antenna and stretch to the negative end of the antenna. these lines of force, being in the same direction as the sides of the closed loops next to the antenna, repel the closed loops and force them out into space at the speed of light. as these loops travel through space, they generate a magnetic field in phase with them.

figure 2-3.—radiation from an antenna.

figure 2-4 shows a comparison between the induction field and the radiation field.


figure 2-4.—e and h components of induction and radiation fields.
q1. which two composite fields (composed of e and h fields) are associated with every antenna?
q2. what composite field (composed of e and h fields) is found stored in the antenna?
q3. what composite field (composed of e and h fields) is propagated into free space?

2.2- radio waves
an energy wave generated by a transmitter is called a radio wave. the radio wave radiated into space by the transmitting antenna is a very complex form of energy containing both electric and magnetic fields. because of this combination of fields, radio waves are also referred to as electromagnetic radiation.
note: the term radio wave is not limited to communications equipment alone. the term applies to all equipment that generate signals in the form of electromagnetic energy.
2.2.1- components of radio waves
the basic shape of the wave generated by a transmitter is that of a sine wave. the wave radiated out into space, however, may or may not retain the characteristics of the sine wave.
the frequencies falling between 3000 hertz (3 khz) and 300,000,000,000 hertz (300 ghz) are called radio frequencies (abbreviated rf) since they are commonly used in radio communications. this part of the radio frequency spectrum is divided into bands, each band being 10 times higher in frequency than the one immediately below it. this arrangement serves as a convenient way to remember the range of each band. the rf bands are shown in table 2-1. the usable radio-frequency range is roughly 10 kilohertz to 100 gigahertz.
table 2-1.—radio frequency bands
description abbreviation frequency
very low vlf 3 to 30 khz
low lf 30 to 300 khz
medium mf 300 to 3000 khz
high hf 3 to 30 mhz
very high vhf 30 to 300 mhz
ultrahigh uhf 300 to 3000 mhz
super high shf 3 to 30 ghz
extremely high ehf 30 to 300 ghz

any frequency that is a whole number multiple of a smaller basic frequency is known as a harmonic of that basic frequency. the basic frequency itself is called the first harmonic or, more commonly, the fundamental frequency. a frequency that is twice as great as the fundamental frequency is called the second harmonic a frequency three times as great is the third harmonic and so on. for example:
first harmonic (fundamental frequency) 3000 khz
second harmonic 6000 khz
third harmonic 9000 khz
the period of a radio wave is simply the amount of time required for the completion of one full cycle. if a sine wave has a frequency of 2 hertz, each cycle has a duration, or period, of one-half second. if the frequency is 10 hertz, the period of each cycle is one-tenth of a second. since the frequency of a radio wave is the number of cycles that are completed in one second, you should be able to see that as the frequency of a radio wave increases, its period decreases.
q4. what is the term used to describe the basic frequency of a radio wave?
q5. what is the term used to describe a whole number multiple of the basic frequency of a radio wave?

2.3- wavelength-to-frequency conversions
as discussed earlier, a radio wave travels 300,000,000 meters a second (speed of light) therefore, a radio wave of 1 hertz would have traveled a distance (or wavelength) of 300,000,000 meters. obviously then, if the frequency of the wave is increased to 2 hertz, the wavelength will be cut in half to 150,000,000 meters. this illustrates the principle that the higher the frequency, the shorter the wavelength.
wavelength-to-frequency conversions of radio waves are really quite simple because wavelength and frequency are reciprocals: either one divided into the velocity of a radio wave yields the other. remember, the formula for wavelength is:


q6. it is known that wwv operates on a frequency of 10 megahertz. what is the wavelength of wwv?
q7. a station is known to operate at 60-meters. what is the frequency of the unknown station?

2.4- polarization
for maximum absorption of energy from the electromagnetic fields, the receiving antenna must be located in the plane of polarization. this places the conductor of the antenna at right angles to the magnetic lines of force moving through the antenna and parallel to the electric lines, causing maximum induction.
normally, the plane of polarization of a radio wave is the plane in which the e field propagates with respect to the earth. if the e field component of the radiated wave travels in a plane perpendicular to the earth s surface (vertical), the radiation is said to be vertically polarized, as shown in figure 2-5, view a. if the e field propagates in a plane parallel to the earth s surface (horizontal), the radiation is said to be horizontally polarized, as shown in view b.

figure 2-5.—vertical and horizontal polarization.
the position of the antenna in space is important because it affects the polarization of the electromagnetic wave. when the transmitting antenna is close to the ground, vertically polarized waves cause a greater signal strength along the earth s surface. on the other hand, antennas high above the ground should be horizontally polarized to get the greatest possible signal strength to the earth s surface.
if you know the directions of the e and h components, you can use the "right-hand rule" (see figure 2-6) to determine the direction of wave propagation. this rule states that if the thumb, forefinger, and middle finger of the right hand are extended so they are mutually perpendicular, the middle finger will point in the direction of wave propagation if the thumb points in the direction of the e field and the forefinger points in the direction of the h field. since both the e and h fields reverse directions simultaneously, propagation of a particular wavefront is always in the same direction (away from the antenna).

figure 2-6.—right-hand rule for propagation.
q8. if a transmitting antenna is placed close to the ground, how should the antenna be polarized to give the greatest signal strength?
q9. in the right-hand rule for propagation, the thumb points in the direction of the e field and the forefinger points in the direction of the h field. in what direction does the middle finger point?

2.5- atmospheric propagation
within the atmosphere, radio waves can be reflected, refracted, and diffracted like light and heat waves.
2.5.1- reflection
radio waves may be reflected from various substances or objects they meet during travel between the transmitting and receiving sites. the amount of reflection depends on the reflecting material. smooth metal surfaces of good electrical conductivity are efficient reflectors of radio waves. the surface of the earth itself is a fairly good reflector. the size of the area required for reflection to take place depends on the wavelength of the radio wave and the angle at which the wave strikes the reflecting substance.
figure 2-7 shows two radio waves being reflected from the earth s surface. notice that the positive and negative alternations of radio waves (a) and (b) are in phase with each other in their paths toward the earth s surface.

figure 2-7.—phase shift of reflected radio waves.
2.5.2- refraction
another phenomenon common to most radio waves is the bending of the waves as they move from one medium into another in which the velocity of propagation is different. this bending of the waves is called refraction.
as an example, the radio wave shown in figure 2-8 is traveling through the earth s atmosphere at a constant speed. as the wave enters the dense layer of electrically charged ions, the part of the wave that enters the new medium first travels faster than the parts of the wave that have not yet entered the new medium. this abrupt increase in velocity of the upper part of the wave causes the wave to bend back toward the earth. this bending, or change of direction, is always toward the medium that has the lower velocity of propagation.

figure 2-8.—radio wave refraction.
2.5.3- diffraction
a radio wave that meets an obstacle has a natural tendency to bend around the obstacle as illustrated in figure 2-9. the bending, called diffraction, results in a change of direction of part of the wave energy from the normal line-of-sight path. this change makes it possible to receive energy around the edges of an obstacle as shown in view a or at some distances below the highest point of an obstruction, as shown in view b. although diffracted rf energy usually is weak, it can still be detected by a suitable receiver.

figure 2-9.—diffraction around an object.
q10. what is one of the major reasons for the fading of radio waves that have been reflected from a surface?

2.6- the effect of the earth s atmosphere on radio waves
this discussion of electromagnetic wave propagation is concerned mainly with the properties and effects of the medium located between the transmitting antenna and the receiving antenna. while radio waves traveling in free space have little outside influence affecting them, radio waves traveling within the earth s atmosphere are affected by varying conditions. atmospheric conditions vary with changes in height, geographical location, and even with changes in time (day, night, season, and year). a knowledge of the composition of the earth s atmosphere is extremely important for understanding wave propagation.
the earth s atmosphere is divided into three separate regions, or layers. they are the troposphere, the stratosphere, and the ionosphere. the layers of the atmosphere are illustrated in figure 2-10.

figure 2-10.—layers of the earth s atmosphere.
2.6.1- troposphere
the troposphere is the portion of the earth s atmosphere that extends from the surface of the earth to a height of about 3.7 miles (6 km) at the north pole or the south pole and 11.2 miles (18 km) at the equator. virtually all weather phenomena take place in the troposphere. the temperature in this region decreases rapidly with altitude, clouds form, and there may be much turbulence because of variations in temperature, density, and pressure. these conditions have a great effect on the propagation of radio waves, which will be explained later in this chapter.
2.6.2- stratosphere
the stratosphere is located between the troposphere and the ionosphere. the temperature throughout this region is considered to be almost constant and there is little water vapor present. the stratosphere has relatively little effect on radio waves because it is a relatively calm region with little or no temperature changes.
2.6.3- ionosphere
the ionosphere extends upward from about 31.1 miles (50 km) to a height of about 250 miles (402 km). it contains four cloud-like layers of electrically charged ions, which enable radio waves to be propagated to great distances around the earth. this is the most important region of the atmosphere for long distance point-to-point communications. this region will be discussed in detail a little later in this chapter.
q11. what are the three layers of the atmosphere?
q12. which layer of the atmosphere has relatively little effect on radio waves?

2.7- radio wave transmission
electromagnetic (radio) energy travels from a transmitting antenna to a receiving antenna in two principal ways. one way is by ground waves and the other is by sky waves. ground waves are radio waves that travel near the surface of the earth (surface and space waves). sky waves are radio waves that are reflected back to earth from the ionosphere. (see figure 2-11.)

figure 2-11.—ground waves and sky waves.

2.7.1- ground waves
the ground wave is actually composed of two separate component waves. these are known as the surface wave and the space wave (fig. 2-11). the determining factor in whether a ground wave component is classified as a space wave or a surface wave is simple. a surface wave travels along the surface of the earth. a space wave travels over the surface.
2.7.1.1- surface wave.—the surface wave reaches the receiving site by traveling along the surface of the ground as shown in figure 2-12. a surface wave can follow the contours of the earth because of the process of diffraction. when a surface wave meets an object and the dimensions of the object do not exceed its wavelength, the wave tends to curve or bend around the object. the smaller the object, the more pronounced the diffractive action will be.

figure 2-12.—surface wave propagation.
as a surface wave passes over the ground, the wave induces a voltage in the earth. the induced voltage takes energy away from the surface wave, thereby weakening, or attenuating, the wave as it moves away from the transmitting antenna. to reduce the attenuation, the amount of induced voltage must be reduced. this is done by using vertically polarized waves that minimize the extent to which the electric field of the wave is in contact with the earth. when a surface wave is horizontally polarized, the electric field of the wave is parallel with the surface of the earth and, therefore, is constantly in contact with it.
another major factor in the attenuation of surface waves is frequency. recall from earlier discussions on wavelength that the higher the frequency of a radio wave, the shorter its wavelength will be. these high frequencies, with their shorter wavelengths, are not normally diffracted but are absorbed by the earth at points relatively close to the transmitting site. you can assume, therefore, that as the frequency of a surface wave is increased, the more rapidly the surface wave will be absorbed, or attenuated, by the earth.
2.7.1.2- space wave.—the space wave follows two distinct paths from the transmitting antenna to the receiving antenna—one through the air directly to the receiving antenna, the other reflected from the ground to the receiving antenna. this is illustrated in figure 2-13. the primary path of the space wave is directly from the transmitting antenna to the receiving antenna. therefore, the receiving antenna must be located within the radio horizon of the transmitting antenna.

figure 2-13.—space wave propagation.
space waves suffer little ground attenuation, they nevertheless are susceptible to fading. this is because space waves actually follow two paths of different lengths (direct path and ground reflected path) to the receiving site and, therefore, may arrive in or out of phase. if these two component waves are received in phase, the result is a reinforced or stronger signal. likewise, if they are received out of phase, they tend to cancel one another, which results in a weak or fading signal.
q13. what is the determining factor in classifying whether a radio wave is a ground wave or a space wave?
q14. what is the best type of surface or terrain to use for radio wave transmission?
q15. what is the primary difference between the radio horizon and the natural horizon?
q16. what three factors must be considered in the transmission of a surface wave to reduce attenuation?

2.7.2- sky wave
the sky wave, often called the ionospheric wave, is radiated in an upward direction and returned to earth at some distant location because of refraction from the ionosphere. this form of propagation is relatively unaffected by the earth s surface and can propagate signals over great distances. usually the high frequency (hf) band is used for sky wave propagation. the following in-depth study of the ionosphere and its effect on sky waves will help you to better understand the nature of sky wave propagation.
2.8- structure of the ionosphere
as we stated earlier, the ionosphere is the region of the atmosphere that extends from about 30 miles above the surface of the earth to about 250 miles. it is appropriately named the ionosphere because it consists of several layers of electrically charged gas atoms called ions. the ions are formed by a process called ionization.
2.8.1- four distinct layers
the ionosphere is composed of three layers designated d, e, and f, from lowest level to highest level as shown in figure 2-14. the f layer is further divided into two layers designated f1 (the lower layer) and f2 (the higher layer). the presence or absence of these layers in the ionosphere and their height above the earth varies with the position of the sun. at high noon, radiation in the ionosphere directly above a given point is greatest. at night, it is minimum. when the radiation is removed, many of the particles that were ionized recombine. the time interval between these conditions finds the position and number of the ionized layers within the ionosphere changing. since the position of the sun varies daily, monthly, and yearly, with respect to a specified point on earth, the exact position and number of layers present are extremely difficult to determine. however, the following general statements can be made:

figure 2-14.—layers of the ionosphere.
the d layer ranges from about 30 to 55 miles. ionization in the d layer is low because it is the lowest region of the ionosphere. this layer has the ability to refract signals of low frequencies. high frequencies pass right through it and are attenuated. after sunset, the d layer disappears because of the rapid recombination of ions.
the e layer limits are from about 55 to 90 miles. this layer is also known as the kennelly- heaviside layer, because these two men were the first to propose its existence. this layer has the ability to refract signals as high as 20 megahertz. for this reason, it is valuable for communications in ranges up to about 1500 miles.
the f layer exists from about 90 to 240 miles. during the daylight hours, the f layer separates into two layers, the f1 and f2 layers. the f layers are responsible for high frequency, long distance transmission.
q17. what causes ionization to occur in the ionosphere?
q18. how are the four distinct layers of the ionosphere designated?
q19. what is the height of the individual layers of the ionosphere?

2.8.2- refraction in the ionosphere
when a radio wave is transmitted into an ionized layer, refraction, or bending of the wave, occurs. as we discussed earlier, refraction is caused by an abrupt change in the velocity of the upper part of a radio wave as it strikes or enters a new medium. the amount of refraction that occurs depends on three main factors:
(1) the density of ionization of the layer,
(2) the frequency of the radio wave,
(3) the angle at which the wave enters the layer.
2.8.2.1- density of layer
figure 2-15 illustrates the relationship between radio waves and ionization density. each ionized layer has a central region of relatively dense ionization, which tapers off in intensity both above and below the maximum region. as a radio wave enters a region of increasing ionization, the increase in velocity of the upper part of the wave causes it to be bent back toward the earth. while the wave is in the highly dense center portion of the layer, however, refraction occurs more slowly because the density of ionization is almost uniform. as the wave enters into the upper part of the layer of decreasing ionization, the velocity of the upper part of the wave decreases, and the wave is bent away from the earth.

figure 2-15.—effects of ionospheric density on radio waves.
if a wave strikes a thin, very highly ionized layer, the wave may be bent back so rapidly that it will appear to have been reflected instead of refracted back to earth. to reflect a radio wave, the highly ionized layer must be approximately no thicker than one wavelength of the radio wave. since the ionized layers are often several miles thick, ionospheric reflection is more likely to occur at long wavelengths (low frequencies).
2.8.2.2- frequency
for any given time, each ionospheric layer has a maximum frequency at which radio waves can be transmitted vertically and refracted back to earth. this frequency is known as the critical frequency. radio waves transmitted at frequencies higher than the critical frequency of a given layer will pass through the layer and be lost in space but if these same waves enter an upper layer with a higher critical frequency, they will be refracted back to earth. radio waves of frequencies lower than the critical frequency will also be refracted back to earth unless they are absorbed or have been refracted from a lower layer.
figure 2-16 shows three separate waves of different frequencies entering an ionospheric layer at the same angle. notice that the 5-megahertz wave is refracted quite sharply. the 20-megahertz wave is refracted less sharply and returned to earth at a greater distance. the 100-megahertz wave is obviously greater than the critical frequency for that ionized layer and, therefore, is not refracted but is passed into space.

figure 2-16.—frequency versus refraction and distance.
2.8.2.3- angle of incidence
the rate at which a wave of a given frequency is refracted by an ionized layer depends on the angle at which the wave enters the layer. figure 2-17 shows three radio waves of the same frequency entering a layer at different angles. the angle at which (wave a) strikes the layer is too nearly vertical for the wave to be refracted to earth. as the wave enters the layer, it is bent slightly but passes through the layer and is lost. when the wave is reduced to an angle that is less than vertical (wave b), it strikes the layer and is refracted back to earth. the angle made by (wave b) is called the critical angle for that particular frequency. any wave that leaves the antenna at an angle greater than the critical angle will penetrate the ionospheric layer for that frequency and then be lost in space. (wave c) strikes the ionosphere at the smallest angle at which the wave can be refracted and still return to earth. at any smaller angle, the wave will be refracted but will not return to earth.

figure 2-17.—different incident angles of radio waves.
q20. what factor determines whether a radio wave is reflected or refracted by the ionosphere?
q21. there is a maximum frequency at which vertically transmitted radio waves can be refracted back to earth. what is this maximum frequency called?
q22. what three main factors determine the amount of refraction in the ionosphere?

2.9- propagation paths
the path that a refracted wave follows to the receiver depends on the angle at which the wave strikes the ionosphere. you should remember, however, that the rf energy radiated by a transmitting antenna spreads out with distance. the energy therefore strikes the ionosphere at many different angles rather than a single angle.
after the rf energy of a given frequency enters an ionospheric region, the paths that this energy might follow are many. it may reach the receiving antenna via two or more paths through a single layer. it may also, reach the receiving antenna over a path involving more than one layer, by multiple hops between the ionosphere and earth, or by any combination of these paths.
figure 2-20 shows how radio waves may reach a receiver via several paths through one layer. the various angles at which rf energy strikes the layer are represented by dark lines and designated as rays 1 through 6.



figure 2-18.—ray paths for a fixed frequency with varying angles of incidence.
when the angle is relatively low with respect to the horizon (ray 1), there is only slight penetration of the layer and the propagation path is long. when the angle of incidence is increased (rays 2 and 3), the rays penetrate deeper into the layer but the range of these rays decreases. when a certain angle is reached (ray 3), the penetration of the layer and rate of refraction are such that the ray is first returned to earth at a minimal distance from the transmitter. notice, however, that ray 3 still manages to reach the receiving site on its second refraction (called a hop) from the ionospheric layer.
as the angle is increased still more (rays 4 and 5), the rf energy penetrates the central area of maximum ionization of the layer. these rays are refracted rather slowly and are eventually returned to earth at great distances. as the angle approaches vertical incidence (ray 6), the ray is not returned at all, but passes on through the layer.
2.9.1- absorption in the ionosphere
many factors affect a radio wave in its path between the transmitting and receiving sites. the factor that has the greatest adverse effect on radio waves is absorption. absorption results in the loss of energy of a radio wave and has a pronounced effect on both the strength of received signals and the ability to communicate over long distances.
2.9.2- fading
the most troublesome and frustrating problem in receiving radio signals is variations in signal strength, most commonly known as fading. there are several conditions that can produce fading.
fading also results from absorption of the rf energy in the ionosphere. absorption fading occurs for a longer period than other types of fading, since absorption takes place slowly.
usually, however, fading on ionospheric circuits is mainly a result of multipath propagation.
2.9.2.1- multipath fading
multipath is simply a term used to describe the multiple paths a radio wave may follow between transmitter and receiver. such propagation paths include the ground wave, ionospheric refraction, reradiating by the ionospheric layers, reflection from the earth s surface or from more than one ionospheric layer, etc. figure 2-19 shows a few of the paths that a signal can travel between two sites in a typical circuit. one path, xyz, is the basic ground wave. another path, xea, refracts the wave at the e layer and passes it on to the receiver at a. still another path, xfzfa, results from a greater angle of incidence and two refractions from the f layer. at point z, the received signal is a combination of the ground wave and the sky wave. these two signals having traveled different paths arrive at point z at different times. thus, the arriving waves may or may not be in phase with each other. radio waves that are received in phase reinforce each other and produce a stronger signal at the receiving site. conversely, those that are received out of phase produce a weak or fading signal. small alternations in the transmission path may change the phase relationship of the two signals, causing periodic fading. this condition occurs at point a. at this point, the double-hop f layer signal may be in or out of phase with the signal arriving from the e layer.


figure 2-19.—multipath transmission.
multipath fading may be minimized by practices called space diversity and frequency diversity. in space diversity, two or more receiving antennas are spaced some distance apart. fading does not occur simultaneously at both antennas therefore, enough output is usually available from one of the antennas to provide a useful signal. in frequency diversity, two transmitters and two receivers are used, each pair tuned to a different frequency, with the same information being transmitted simultaneously over both frequencies. one of the two receivers will usually provide a useful signal.
2.9.2.2- selective fading
fading resulting from multipath propagation is variable with frequency since each frequency arrives at the receiving point via a different radio path. when a wide band of frequencies is transmitted simultaneously, each frequency will vary in the amount of fading. this variation is called selective fading. when selective fading occurs, all frequencies of the transmitted signal do not retain their original phases and relative amplitudes. this fading causes severe distortion of the signal and limits the total signal transmitted.
q23. what is the skip zone of a radio wave?
q24. where does the greatest amount of ionospheric absorption occur in the ionosphere?
q25. what is meant by the term "multipath"?
q26. when a wide band of frequencies is transmitted simultaneously, each frequency will vary in the amount of fading. what is this variable fading called?

2.10- weather versus propagation
weather is an additional factor that affects the propagation of radio waves. in this section, we will explain how and to what extent the various weather phenomena affect wave propagation.
wind, air temperature, and water content of the atmosphere can combine in many ways.
2.10.1- rain
attenuation because of raindropings is greater than attenuation because of other forms of precipitation. attenuation may be caused by absorption, in which the raindroping, acting as a poor dielectric, absorbs power from the radio wave and dissipates the power by heat loss or by scattering (fig. 2-24). raindropings cause greater attenuation by scattering than by absorption at frequencies above 100 megahertz. at frequencies above 6 gigahertz, attenuation by raindroping scatter is even greater.

figure 2-24.—rf energy losses from scattering.
2.10.2- fog
in the discussion of attenuation, fog may be considered as another form of rain. since fog remains suspended in the atmosphere, the attenuation is determined by the quantity of water per unit volume and by the size of the dropinglets. attenuation because of fog is of minor importance at frequencies lower than 2 gigahertz. however, fog can cause serious attenuation by absorption, at frequencies above 2 gigahertz.
2.10.3- snow
the scattering effect because of snow is difficult to compute because of irregular sizes and shapes of the flakes. while information on the attenuating effect of snow is limited, scientists assume that attenuation from snow is less than from rain falling at an equal rate. this assumption is borne out by the fact that the density of rain is eight times the density of snow. as a result, rain falling at 1 inch per hour would have more water per cubic inch than snow falling at the same rate.
q27. how do raindropings affect radio waves?
q28. how does fog affect radio waves at frequencies above 2 gigahertz?






answers to questions q1. through q28.
a1. induction field and radiation field.
a2. induction field.
a3. radiation field.
a4. fundamental frequency.
a5. harmonic frequency or harmonics.
a6. 30 meters.
a7. 5 megahertz.
a8. vertically polarized.
a9. direction of wave propagation.
a10. shifting in the phase relationships of the wave.
a11. troposphere, stratosphere, and ionosphere.
a12. stratosphere.
a13. whether the component of the wave is travelling along the surface or over the surface of the earth.
a14. radio horizon is about 1/3 farther.
a15. sea water.
a16. (a) electrical properties of the terrain (b) frequency (c) polarization of the antenna
a17. high-energy ultraviolet light waves from the sun.
a18. d, e, f1, and f2 layers.
a19. d layer is 30-55 miles, e layer 55-90 miles, and f layers are 90-240 miles.
a20. thickness of ionized layer.
a21. critical frequency.
a22. (a) density of ionization of the layer (b) frequency (c) angle at which it enters the layer
a23. a zone of silence between the ground wave and sky wave where there is no reception.

a24. where ionization density is greatest.
a25. a term used to describe the multiple pattern a radio wave may follow.
a26. selective fading.
a27. they can cause attenuation by scattering.
a28. it can cause attenuation by absorption.