EC2353 -Antenna and wave propagation

Introduction

An antenna is an electrical conductor or system of conductors

Transmission - radiates electromagnetic energy into space Reception - collects electromagnetic energy from space

In two-way communication, the same antenna can be used for transmission and reception An antenna is a circuit element that provides a transition form a guided wave on a transmission line to a free space wave and it provides for the collection of electromagnetic energy. In transmit systems the RF signal is generated, amplified, modulated and applied to the antenna In receive systems the antenna collects electromagnetic waves that are ―cutting‖ through the antenna and induce alternating currents that are used by the receiver

CONCEPT OF VECTOR POTENTIA

UNIT I ELECTROMAGNETIC RADIATION AND

ANTENNA FUNDAMENTALS

Hertzian dipole

A simple practical antenna is a doublet or Hertzian dipole (see a figure below). It is very short length of wire over which the current distribution can be assumed uniform. Maxwell’s equations show that such an antenna when energized by a high frequency current is associated with an induction field which decreases inversely as square of the distance and a radiation field which decreases inversely as distance only. The later is still

measurable at large distances from the doublet and is well-known radiation field used in radio communications

DEFINITIONS

Radiation Intensity:In a given direction, the power radiated form an antenna perunit solid angle.

Directive Gain: In a given direction, 4ð times the ratio of theradiation intensity inthat direction to the total power radiated by the antenna.

Directivity: The value of the directive gain in the direction of its maximum value. Power Gain:In a given direction, 4ð times the ratio of the radiationintensity in

that direction to the net power accepted by the antenna from the connected transmitter. NOTES: (1) When thedirection is not stated, the power gain is usually taken to be thepower gain in the direction of its maximum value. (2) Power gain does not include reflection losses arising from mismatchof impedance.

Beamwidth is the angular separation of the half-power points of the radiatedpattern

Bandwidth is the difference between the upper and lowercutoff frequenciesof,for example, a filter, a communication channel, or a signal spectrum, and is typically measured in hertz. In case of a baseband channel or signal andwidth is equal to its upper cutoff frequency. Bandwidth in hertz is a centralconcept in many fields, including electronics, information theory, radio communications, signal processing, and spectroscopy

GAIN Gain is an antenna property dealing with an antenna's ability to direct its radiated

power in a desired direction, or to receive energy preferentially from a desired

direction. However, gain is not a quantity which can be defined in terms of physical

quantities such as the Watt, ohm or joule, but is a dimensionless ratio.

As a consequence, antenna gain results from the interaction of all other antenna

characteristics.Antenna characteristics of gain,

beamwidth, and efficiency areindependent of the antenna's use for either transmitting

or receiving. Generally these characteristics are more easilydescribed for the

transmitting case, however, the properties apply as well to receiving applications.

Radiation resistance An important property of a transmitting antenna is its radiation resistance which is

associated with power radiated by the antenna. If I is the r.m.s (root mean square)

antenna current and Rr is its radiation resistance, then the power radiated is I2Rr watts

where Rr is a fictitious resistance which accounts for the radiated power somewhat like

a circuit resistance which dissipates heat. The larger the radiation resistance the larger

the power radiated by the antenna. In contrast, for receiving antenna its input

impedance is important. The input impedance is defined as the ratio of voltage to

current at its input and it must be generally matched to the connecting line or cable.

The input impedance may or may not be equal to radiation resistance, though very

often it does. In most case Rr may be calculated or it can be determined

experimentally. Half-wavelength dipole

This type of antenna is a special case where each wire is exactly one-quarter of the wavelength, for a total of a half wavelength. The radiation resistance is about 73 ohms if wire diameter is ignored, making it easily matched to a coaxial transmission line. The directivity is a constant 1.64, or 2.15 dB. Actual gain will be a little less due to ohmic losses. Folded dipole

A folded dipole is a dipole where an additional wire (λ/2) links the two ends of the (λ/2) half wave dipole. The folded dipole works in the same way as a normal dipole, but the radiation resistance is about 300 ohms rather than the 75 ohms which is expected for a normal dipole. The increase in radiation resistance allows the antenna to be driven from a 300 ohm balanced line.

RECIPROCITY: An antenna ability to transfer energy form the atmosphere to its receiver with the same efficiency with which it transfers energy from the transmitter into the atmosphere Antenna characteristics are essentially the same regardless of whether an antenna is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered as having a shorter effective length Le over which the current is assumed to be uniform and equal to its peak. The relationship between Le and L is given by:

Effective aperture The power received by an antenna can be associated with collecting area. Every

antenna may be considered to have such a collecting area which is called its effective aperture A. If Pd is a power density at the antenna and Pr is received power, then:

Polarization is the direction of the electric field and is the same as the physical attitude of the antenna

A vertical antenna will transmit a vertically polarized wave The receive and transmit antennas need to possess the same polarization

Antenna Gain Relationship between antenna gain and effective area

G = antenna gain Ae= effective area f = carrier frequency c = speed of light (» 3 ´ 108 m/s) λ = carrier wavelength

Radiation Pattern Radiation pattern is an indication of radiated field strength around the antenna. Power radiated from a λ/2 dipole occurs at right angles to the antenna with no power emitting from the ends of the antenna. Optimum signal strength occurs at right angles or 180° from opposite the antenna

Radiation pattern

Graphical representation of radiation properties of an antenna Depicted as two-dimensional cross section

Beam width (or half-power beam width) Measure of directivity of antenna

Receiving antenna’s equivalent to radiation pattern Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment. This temperature is not the physical temperature of the antenna. Moreover,

an antenna does not have an intrinsic "antenna temperature" associated with it; rather the

temperature depends on its gain pattern and the thermal environment that it is placed in.

To define the environment, we'll introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates. For

instance, the night sky is roughly 4 Kelvin; the value of the temperature pattern in the

direction of the Earth's ground is the physical temperature of the Earth's ground.

Thistemperature distribution will be written as . Hence, an antenna's

temperature will vary depending on whether it is directional and pointed into space or

staring into the sun.

For an antenna with a radiation pattern given by , the noise temperature is

mathematically defined as: This states that the temperature surrounding the antenna is integrated over the entire sphere, and weighted by the antenna's radiation pattern. Hence, an isotropic antenna would have a noise temperature that is the average of all temperatures around the antenna; for a perfectly directional antenna (with a pencil beam), the antenna temperature will only depend on the temperature in which the antenna is "looking".

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over: In the above, K is Boltzmann's constant (1.38 * 10^-23 [Joules/Kelvin = J/K]). The

receiver also has a temperature associated with it ( ), and the total system temperature

(antenna plus receiver) has a combined temperature given by . This

temperature can be used in the above equation to find the total noise power of the system.

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics, because the resulting systems very much depend on each other.

A parameter often encountered in specification sheets for antennas that operate in certain environments is the ratio of gain of the antenna divided by the antenna temperature (or system temperature if a receiver is specified). This parameter is written as G/T, and has units of dB/Kelvin [dB/K].

Half wave antenna

UNIT-2

WIRE ANTENNAS AND ANTENNA ARRAYS

Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end, that behaves as a dipole antenna. It is formed by a conductor in length. It is fed in the lower end, which is near a conductive surface which works as a reflector (see Effect of ground). The current in the reflected image has the same direction and phase that the current in the real antenna. The set quarter-wave plus image forms a half-wave dipole that radiates only in the upper half of space.

Antenna array is a group of antennas or antenna elements arranged to provide thedesired directional characteristics. Generally any combination of elements can form an array. However, equal elements in a regular geometry are usually used. PATTERN MULTIPLICATION The pattern multiplication principle states that the radiation patterns of an array of N identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of the antennas) and the array pattern Fa( ), where Fa( ) is the pattern obtained upon replacing all of the actual antennas with isotropic sources.

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1. These antennas have low radiation resistance and high reactance, so that their impedance is difficult to match to a transmitter. As a result, these antennas are most often used as receive antennas, where impedance mismatch loss can be tolerated.

The radius is a, and is assumed to be much smaller than a wavelength (a<< ).

The loop lies in the x-y plane.

Figure 1. Small loop antenna

.

Since the loop is electrically small, the current within the loop can be

approximated as being constant along the loop, so that I= .

The fields from a small circular loop are given by:

The variation of the pattern with direction is given by , so that the

radiation pattern of a small loop antenna has the same power pattern as that of a

short dipole. However, the fields of a small dipole have the E- and H-

fieldsswitched relative to that of a short dipole; the E-field is horizontally

polarized in the x-y plane.

The small loop is often referred to as the dual of the dipole antenna, because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole), the fields would resemble that of a small loop.

While the short dipole has a capacitive impedance (imaginary part of impedance is negative), the impedance of a small loop is inductive (positive imaginary part). The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop. If there are N turns of a small loop antenna, each with a surface area S (we don't require the loop to be circular at this point), the radiation resistance for small loops can be approximated (in Ohms) by: For a small loop, the reactive component of the impedance can be determined by finding the inductance of the loop, which depends on its shape (then X=2*pi*f*L). For a circular loop with radius a and wire radius p, the reactive component of the impedance is given by:

Small loops often have a low radiation resistance and a highly inductive component to their reactance. Hence, they are most often used as receive antennas. Exaples of their use include in pagers, and as field strength probes used in wireless measurements.

Loop antenna

A loop antenna has a continuous conducting path leading from one conductor of a two-wire transmission line to the other conductor. All planar loops are directional antennas with a sharp null, and have a radiation pattern similar to the dipoleantenna. However, the large and small loops have different orientations with respect totheir radiation pattern.

Small loops A loop is considered a small loop if it is less than 1/4 of a

wavelength in circumference. Most directional receiving loops are about 1/10 of a wavelength. The small loop is also called the magnetic loop because it is more sensitivie to the magnetic component of the electromagnetic wave. As such, it is less sensitive to near field electric noise when properly shielded. The received voltage of a small loop can be greatly increased by bringing the loop into resonance with a tuning capacitor.

Since the small loop is small with respect to a wavelength, the current around the antenna is nearly completely in phase. Therefore, waves approaching in the plane of the loop will cancel, and waves in the axis perpendicular to the plane of the loop will be strongest. This is the opposite mechanism as the large loop.

Large loops The (large) loop antenna is similar to a dipole, except that the

ends of the dipole are connected to form a circle, triangle () or square. Typically a loop is a multiple of a half or full wavelength in circumference. A circular loop gets higher gain (about 10%) than the other forms of large loop antenna, as gain of this antenna is directly

proportional to the area enclosed by the loop, but circles can be hard to support in a flexible wire, making squares and triangles much more popular. Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane. The large loop has its strongest signal in the plane of the loop, and nulls in the axis perpendicular to the plane of the loop. This is the opposite orientation to the small loop.

AM loops AM loops are loops tuned for the AM broadcasting band.

Because of the extremely long wavelength, an AM loop may have multiple turns of wire and still be less than 1/10 of a wavelength. Typically these loops are tuned with a capacitor, and may also be wound around a ferrite rod to increase aperture.

Direction finding with loops Loops are somewhat directional along the axis of highest gain, but have a sharp null in the axis perpendicular to their highest gain. Therefore, when using a loop for direction finding, the plane of the antenna is rotated until the signal disappears. As planar loops have a 180 degree symmetry, other methods must be used to determine if the signal is in front or behind the loop.

Frequently, a dipole and a loop are used together, to obtain a combined cardioid radiation pattern with a sharp null on only one side.

Uniform linear array

SLOT ANTENNAS: Slot antennasare used typically at frequencies between 300 MHz and24 GHz. These antennas are popular because they can be cut out of whatever surface they are to be mounted on, and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna, as we'll see). The polarization is linear. The slot size, shape and what is behind it (the cavity) offer design variables that can be used to tune performance. Consider an infinite conducting sheet, with a rectangular slot cut out of dimensions a andb, as shown in Figure 1. If we can excite some reasonable fields in the slot (often called the aperture), we have an antenna.

UNIT III

APERTURE ANTENNAS

Figure 1. Rectangular Slot antenna with dimensions a andb.

To gain an intuition about slot antennas, first we'll learn Babinet's principle (put into antenna terms by H. G. Booker in 1946). This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna. The dual of a slot antenna would be if the conductive material and air were interchanged - that is, the slot antenna became a metal slab in space. An example of dual antennas is shown in Figure 2:

Figure 2.Dual antennas.

Note that a voltage source is applied across the short end of the slot. This induces an E-field distribution within the slot, and currents that travel around the slot perimeter, both contributed to radiation. The dual antenna is similar to a dipole antenna. The voltage source is applied at the center of the dipole, so thatthe voltage source is rotated.

Babinet's principle relates these two antennas. The first result states that the

impedanceof the slot ( ) is related to the impedance of its dual antenna ( )

by the relation:

In the above, is the intrinsic impedance of free space. The second major

result of Babinet's/Booker's principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged,

and called "duals"). That is, the fields of the slot antenna (given with a

subscript S) are related to the fields of it's complement (given with a subscript

C) by:

Hence, if we know the fields from one antenna we know the fields of the other antenna. Hence, since it is easy to visualize the fields from a dipole antenna, the fields and impedance from a slot antenna can become intuitive if Babinet's principle is understood.

Note that the polarization of the two antennas are reversed. That is, since the dipole antenna on the right in Figure 2 is vertically polarized, the slot antenna on the left will be horizontally polarized.

Duality Example

As an example, consider a dipole similar to the one shown on the right in Figure 2. Suppose the length of the dipole is 14.4 centimeters and the width is 2 centimeters, and that the impedance at 1 GHz is 65+j15 Ohms. The fields from the dipole antenna are given by: What are the fields from a slot at 1 GHz, with the same dimensions as the dipole?

Using Babinet's principle, the impedance can be easily found:

The impedance of the slot for this case is much larger, and while the dipole's impedance is inductive (positive imaginary part), the slot's impedance is capacitive (negative imaginary part). The E-fields for the slot can be easily found:

We see that the E-fields only contain a phi (azimuth) component; the antenna is therefore horizontally polarized.

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (I've heard of horns operating as high as 140 GHz). They often have a directional radiation pattern with a high gain , which can range up to 25 dB in some cases, with 10-20 dB being typical. Horns have a wide impedance

bandwidth, implying that theinput impedanceis slowly varying over a widefrequency range (which also implies low values for S11 or VSWR). The bandwidth for practical horn antennas can be on the order of 20:1 (for instance, operating from 1 GHz-20 GHz), with a 10:1 bandwidth not being uncommon.

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased. Horns have very little loss, so the directivity of a horn is roughly equal to its gain.

Horn antennas are somewhat intuitive and not relatively simple to manufacture. In addition, acoustic horns also used in transmitting sound waves (for example, with a megaphone). Horn antennas are also often used to feed a dish antenna, or as a "standard gain" antenna in measurements.

Popular versions of the horn antenna include the E-plane horn, shown in Figure 1. This horn is flared in the E-plane, giving the name. The horizontal dimension is constant at w.

Figure 1.E-plane horn.

Another example of a horn is the H-plane horn, shown in Figure 2. This horn is flared in the H-plane, with a constant height for the waveguide and horn of h.

Figure 2.H-Plane horn.

The most popular horn is flared in both planes as shown in Figure 3. This is a pyramidal horn, and has width B and height A at the end of the horn.

Figure 3.Pyramidal horn.

Horns are typically fed by a section of a waveguide, as shown in Figure 4. The waveguide itself is often fed with a short dipole, which is shown in red in Figure 4. A waveguide is simply a hollow, metal cavity. Waveguides are used to guide electromagnetic energy from one place to another. The waveguide in Figure 4 is a rectangular waveguide of width b and height a, with b>a. The E-field distribution for the dominant mode is shown in the lower part of Figure 1.

Figure 4. Waveguide used as a feed to horn antennas.

Reflector Antenna To increase the directivity of an antenna, a fairly intuitive solution is to use a reflector. For example, if we start with a wire antenna (lets say a half-wavedipoleantenna), we could place a conductive sheet behind it to direct radiationin the forward direction. To further increase the directivity, a corner reflector may be used, as shown in Figure 1. The angle between the plates will be 90 degrees.

Figure 1.Geometry of Corner Reflector.

The radiation pattern of this antenna can be understood by using image theory, and then calculating the result via array theory. For ease of analysis, we'll assume the reflecting plates are infinite in extent. Figure 2 below shows the equivalent source distribution, valid for the region in front of the plates.

Figure 2.Equivalent sources in free space.

The dotted circles indicate antennas that are in-phase with the actual antenna; the x'd out antennas are 180 degrees out of phase to the actual antenna.

Assume that the original antenna has an omnidirectional pattern given by .

Then the radiation pattern (R) of the "equivalent set of radiators" of Figure 2

can be written as:

The above directly follows from Figure 2 and array theory (k is the wavenumber. The resulting pattern will have the same polarization as the originalvertically polarized antenna. The directivity will be increased by 9-12 dB. The above equation gives the radiated fields in the region in front of the plates. Since we assumed the plates were infinite, the fields behind the plates are zero.

The directivity will be the highest when d is a half-wavelength. Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by ,

the fields for this case are shown in Figure 3.

Figure 3.Polar and azimuth patterns of normalized radiation pattern.

The radiation pattern, impedance and gain of the antenna will be influenced by the distance d of Figure 1. The input impedance is increased by the reflector when the spacing is one half wavelength; it can be reduced by moving the antenna closer to the reflector. The length L of the reflectors in Figure 1 are typically 2*d. However, if tracing a ray travelling along the y-axis from the

antenna, this will be reflected if the length is at least . The height of the

plates should be taller than the radiating element; however since linear antennas

do not radiate well along the z-axis, this parameter is not critically important.

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna, commonly known as a satellite dish antenna. Examples of this dish antenna are shown in the following Figures.

Figure 1.The "big dish" of Stanford University.

Figure 2.A random "direcTV dish" on a roof.

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low crosspolarization. They also have a reasonable bandwidth, with thefractional bandwidthbeing at least 5% on commercially available models, and can be very wideband in the case of huge dishes (like the Stanford "big dish" above, which can operate from 150 MHz to 1.5 GHz).

The smaller dish antennas typically operate somewhere between 2 and 28 GHz. The large dishes can operate in the VHF region (30-300 MHz), but typically need to be extremely large at this operating band.

The basic structure of a parabolic dish antenna is shown in Figure 3. It consists of a feed antenna pointed towards a parabolic reflector. The feed antenna is often a horn antenna with a circular aperture.

Figure 3.Components of a dish antenna.

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation, the reflecting dish must be much larger than a wavelength in size. The dish is at least several wavelengths in diameter, but the diameter can be on the order of 100 wavelengths for very high gain dishes (>50 dB gain). The distance between the feed antenna and the reflector is typically several wavelenghts as well. This is in contrast to the corner reflector, where the antenna is roughly a half-wavelength from the reflector.

In the next section, we'll look at the parabolic dish geometry in detail and why a parabola is a desired shape.

To start, let the equation of a parabola with focal length F can be written in the (x,z) plane as:

This is plotted in Figure 1.

Figure 1.Illustration of parabola with defining parameters.

The parabola is completely described by two parameters, the diameter D and

the focal length F. We also define two auxilliary parameters, the vertical height

of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ). These parameters are related to each other by the following

equations: To analyze the reflector, we will use approximations from geometric optics. Since the reflector is large relative to a wavelength, this assumption is reasonable though not precisely accurate. We will analyze the structure via straight line rays from the focal point, with each ray acting as a plane wave. Consider two transmitted rays from the focal point, arriving from two distinct angles as shown in Figure 2. The reflector is assumed to be perfectly conducting, so that the rays are completely reflected.

Figure 2.Two rays leaving the focal point and reflected from the parabolic reflector.

There are two observations that can be made from Figure 2. The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal). . The rays are said to be collimated. The second important observation is that the path lengths ADE and ABC are equal. This can be proved with a little bit of geometry, which I won't reproduce here. These facts can be proved for any set of angles chosen. Hence, it follows that:

All rays emanating from the focal point (the source or feed antenna) will be reflected towards the same direction. The distance each ray travels from the focal point to the reflector and then to the focal plane is constant.

As a result of these observations, it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction. This gives rise to the parabolic dish antennas highly directional radiation pattern. This is why the shape of the dish is parabolic.

Finally, by revolving the parabola about the z-axis, a paraboloid is obtained, as shown below.

For design, the value of the diameter D should be increased to increase the gain

of the antenna. The focal length F is then the only free parameter; typical values

are commonly given as the ratio F/D, which usually range between 0.3 and 1.0.

Factors affecting the choice of this ratio will be given in the following sections.

In the next section, we'll look at gain calculations for a parabolic reflector antenna.

The fields across the aperture of the parabolic reflector is responsible for this antenna's radiation. The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture:

The actual gain is in terms of the effective aperture, which is related to the physical area by the efficiency term ( ). This efficiency term will often be on the order of 0.6-0.7 for a well designed dish antenna:

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector. The efficiency can be written as the product of a series of terms:

We'll walk through each of these terms.

Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses,

as discussed on the efficiency page. Since horn antennas are often used as

feeds, and these have very little loss, and because the parabolic reflector is

typically metallic with a very high conductivity, this efficiency is typically

close to 1 and can be neglected.

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antenna's aperture. In general, an antenna will have the maximum

gain if the E-field is uniform in amplitude and phase across the aperture (the

far-field is roughly the Fourier Transform of the aperture fields). However, the

aperture fields will tend to diminish away from the main axis of the reflector,

which leads to lower gain, and this loss is captured within this parameter.

This efficiency can be improved by increasing the F/D ratio, which also lowers the cross-polarization of the radiated fields. However, as with all things in engineering, there is a tradeoff: increasing the F/D ratio reduces the spillover efficiency, discussed next.

Spillover Efficiency

The spillover efficiency is simple to understand. This measures the amount

of radiation from the feed antenna that is reflected by the reflector. Due to the

finite size of the reflector, some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than , thus not being

reflected. This efficiency can be improved by moving the feed closer to the

reflector, or by increasing the size of the reflector.

Other Efficiencies

There are many other efficiencies that I've lumped into the parameter . This

is a major of all other "real-world effects" that degrades the antenna's gain and

consists of effects such as:

Surface Error - small deviations in the shape of the reflector degradesperformance, especially for high frequencies that have a small wavelength and become scattered by small surface anomalies Cross Polarization - The loss of gain due tocross-polarized(non-desirable)radiation

Aperture Blockage - The feed antenna (and the physical structure that holdsit up) blocks some of the radiation that would be transmitted by the reflector. Non-Ideal Feed Phase Center - The parabolic dish has desirable propertiesrelative to a single focal point. Since the feed antenna will not be a point source, there will be some loss due to a non-perfect phase center for a horn antenna.

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antenna's radiation pattern. Instead of introducing complex formulas for some of these terms, we'll make use of some results by S. Silver back in 1949. He calculated the aperture efficiency for a class of radiation patterns given as:

TYpically, the feed antenna (horn) will not have a pattern exactly like the

above, but can be approximated well using the function above for some value

of n. Using the above pattern, the aperture efficiency of a parabolic reflector

can be calculated. This is displayed in Figure 1 for varying values of and the

F/D ratio.

Figure 1. Aperture Efficiency of a Parabolic Reflector as a function of F/D or

the angle , for varying feed antenna radiation patterns.

Figure 1 gives a good idea on design of optimal parabolic reflectors. First, D is made as large as possible so that the physical aperture is maximized. Then the F/D ratio that maximizes the aperture efficiency can be found from the above

graph. Note that the equation that relates the ratio of F/D to the angle can be

found here.

In the next section, we'll look at the radiation pattern of a parabolic antenna.

In this section, the 3d radiation patterns are presented to give an idea of what they look like. This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths. The F/D ratio will be 0.5. A circular horn antenna will be used as the feed.

The maximum gain from the physical aperture is ; the

actual gain is 29.3 dB = 851, so we can conclude that the overall efficiency is

77%. The 3D patterns are shown in the following figures.

As can be seen, the pattern is highly directional. The HPBW is approximately 5 degrees, and the front-to-back ratio is approximately 33 dB. LENS ANTENNA.—Another antenna that can change spherical waves into flat plane waves is the lens antenna. This antenna uses a microwave lens, which is similar to an optical lens to straighten the sphericalwavefronts. Since this type of antenna uses a lens to straighten the wavefronts, its design is based on the laws of refraction, rather than reflection. Two types of lenses have been developed to provide a plane-wavefront narrow beam for tracking radars, while avoiding the problems

associated with the feedhorn shadow. These are the conducting (acceleration) type and

thedielectric (delay) type. The lens of an antenna is substantially transparent to microwave energy that passes through it. It will, however, cause the waves of energy to be either converged or diverged as they exit the lens. Consider the action of the two types of lenses. The conducting type of lens is illustrated in figure 1-10, view A. This type of lens consists of flat metal strips placed parallel to the electric field of the wave and spaced slightly in excess of one-half of a wavelength. To the wave these strips look like parallel waveguides. The velocity of phase propagation of a wave is greater in a waveguide than in air. Thus, since the lens is concave, the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion.

SPECIAL ANTENNAS

Helical Antenna

Antennas List Antenna Theory Home Helix antennas have a very distinctive shape, as can be seen in the following picture.

UNIT IV

SPECIAL ANTENNAS AND ANTENNA MEASUREMENTS

Photo courtesy of Dr. Lee Boyce.

The most popular helical antenna (often called a 'helix') is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix. These helixes are referred to as axial-mode helical antennas. The benefits of this antenna is it has a wide bandwidth, is easily constructed, has a real input impedance, and can produce circularly polarized fields. The basic geometry is shown in Figure 1.

Figure 1.Geometry of Helical Antenna.

The parameters are defined below. D - Diameter of a turn on the helix. C - Circumference of a turn on the helix (C=pi*D). S - Vertical separation between turns. - pitch angle, which controls how far the antenna grows in the z-direction per

turn, and is given by N - Number of turns on the helix. H - Total height of helix, H=NS.

The antenna in Figure 1 is a left handed helix, because if you curl your fingers on your left hand around the helix your thumb would point up (also, the waves emitted from the antenna are Left Hand Circularly Polarized). If the helix was

wound the other way, it would be a right handed helical antenna.

The pattern will be maximum in the +z direction (along the helical axis in Figure 1). The design of helical antennas is primarily based on empirical results, and the fundamental equations will be presented here.

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength: Once the circumference C is chosen, the inequalites above roughly determine the operating bandwidth of the helix. For instance, if C=19.68 inches (0.5 meters), then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation, or =0.75C=0.375 meters, which corresponds

to a frequency of 800 MHz. The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation, or =1.333C=0.667

meters, which corresponds to a frequency of 450 MHz. Hence, the fractional BW

is 56%, which is true of axial helices in general.

The helix is a travelling wave antenna, which means the current travels along the antenna and the phase varies continuously. In addition, the input impedance is primarly real and can be approximated in Ohms by:

The helix functions well for pitch angles ( ) between 12 and 14 degrees.

Typically, the pitch angle is taken as 13 degrees.

The normalized radiation pattern for the E-field components are given by:

For circular polarization, the orthogonal components of the E-field must be 90 degrees out of phase. This occurs in directions near the axis (z-axis in Figure 1) of the helix. The axial ratio for helix antennas decreases as the number of loops N is

added, and can be approximated by:

The gain of the helix can be approximated by:

In the above, c is the speed of light. Note that for a given helix geometry (specified in terms of C, S, N), the gain increases with frequency. For an N=10 turn helix, that has a 0.5 meter circumference as above, and an pitch angle of 13 degrees (giving S=0.13 meters), the gain is 8.3 (9.2 dB).

For the same example helix, the pattern is shown in Figure 2.

Figure 2.Normalized radiation pattern for helical antenna (dB).

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by:

Yagi-Uda Antenna

Antennas List Antenna Theory .com The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs. It is simple to construct and has a high gain, typically greater than 10 dB. These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz), although their bandwidth is typically small, on the order of a few percent of the center frequency. You are probably familiar with this antenna, as they sit on top of roofs everywhere. An example of a Yagi-Uda antenna is shown below.

The Yagi antenna was invented in Japan, with results first published in 1926. The work was originally done by ShintaroUda, but published in Japanese. The work was presented for the first time in English by Yagi (who was either Uda's professor or colleague, my sources are conflicting), who went to America and gave the first English talks on the antenna, which led to its widespread use. Hence, even though the antenna is often called a Yagi antenna, Uda probably invented it. A picture of Professor Yagi with a Yagi-Uda antenna is shown below.

In the next section, we'll explain the principles of the Yagi-Uda antenna. The basic geometry of a Yagi-Uda antenna is shown in Figure 1.

Figure 1. Geometry of Yagi-Uda antenna.</FONT< CENTER>

The antenna consists of a single 'feed' or 'driven' element, typically a dipole or a folded dipoleantenna. This is the only member of the above structure that isactually excited (a source voltage or current applied). The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction. The length of the feed element is given in Figure 1 as F. The feed antenna is almost always the second from the end, as shown in Figure 1. This feed antenna is often altered in size to make it resonant in the presence of the parasitic

elements (typically, 0.45-0.48 wavelengths long for a dipole antenna).

The element to the left of the feed element in Figure 1 is the reflector. The length of this element is given as R and the distance between the feed and the reflector is SR. The reflector element is typically slightly longer than the feed element. There is typically only one reflector; adding more reflectors improves performance very slightly. This element is important in determining the front-to-back ratioof the antenna.

Having the reflector slightly longer than resonant serves two purposes. The first

is that the larger the element is, the better of a physical reflector it becomes.

Secondly, if the reflector is longer than its resonant length, the impedance of the

reflector will be inductive. Hence, the current on the reflector lags the voltage

induced on the reflector. The director elements (those to the right of the feed in

Figure 1) will be shorter than resonant, making them capacitive, so that the

current leads the voltage. This will cause a phase distribution to occur across the

elements, simulating the phase progression of a plane wave across the array of

elements. This leads to the array being designated as a travelling wave antenna.

By choosing the lengths in this manner, the Yagi-Uda antenna becomes an end-

fire array - the radiation is along the +y-axis as shown in Figure 1. The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements. There can be any number of directors N, which is typically anywhere from N=1 to N=20 directors. Each element is oflength Di, and separated from the adjacent director by a length SDi. As alluded to in the previous paragraph, the lengths of the directors are typically less than the resonant length, which encourages wave propagation in the direction of the directors.

The above description is the basic idea of what is going on. Yagi antenna design is done most often via measurements, and sometimes computer simulations. For instance, lets look at a two-element Yagi antenna (1 reflector, 1 feed element, 0 directors). The feed element is a half-wavelength dipole, shortened to be resonant (gain = 2.15 dB). The gain as a function of the separation is shown in Figure 2.

Figure 2. Gain versus separation for 2-element Yagi antenna.

The above graph shows that the gain is increases by about 2.5 dB if the separation SD is between 0.15 and 0.3 wavelengths. Similarly, the gain can be plotted as a function of director spacings, or as a function of the number of

directors used. Typically, the first director will add approximately 3 dB of overall gain (if designed well), the second will add about 2 dB, the third about 1.5 dB. Adding an additional director always increases the gain; however, the gain in directivity decreases as the number of elements gets larger. For

instance, if there are 8 directors, and another director is added, the increases in gain will be less than 0.5 dB.

In the next section, I'll go further into the design of Yagi-Uda antennas.

The design of a Yagi-Uda antenna is actually quite simple. Because Yagi antennas have been extensively analyzed and experimentally tested, the process basically follows this outline: Look up a table of design parameters for Yagi antennas

Build it (or model it numerically), and tweak it till the performance is acceptable

As an example, consider the table published in "Yagi Antenna Design" by P Viezbicke from the National Bureau of Standards, 1968, given in Table I. Note that the "boom" is the long element that the directors, reflectors and feed elements are physically attached to,

and dictates the lenght of the antenna.

Table I. Optimal Lengths for Yagi-Uda Elements, for Distinct Boom Lengths

d=0.0085

Boom Length of Yagi-Uda Array (in )

SR=0.2

0.4 0.8 1.2 2.2 3.2 4.2

R 0.482 0.482 0.482 0.482 0.482 0.475

D1 0.442 0.428 0.428 0.432 0.428 0.424

D2 0.424 0.420 0.415 0.420 0.424

D3 0.428 0.420 0.407 0.407 0.420

D4 0.428 0.398 0.398 0.407

D5 0.390 0.394 0.403

D6 0.390 0.390 0.398

D7 0.390 0.386 0.394

D8 0.390 0.386 0.390

D9 0.398 0.386 0.390

D10 0.407 0.386 0.390

D11 0.386 0.390

D12 0.386 0.390

D13 0.386 0.390

D14 0.386

D15 0.386

Spacing

Between 0.20

0.20

0.25

0.20

0.20

0.308

directors,

(SD/ )

Gain (dB) 9.25 11.35 12.35 14.40 15.55 16.35

There's no real rocket science going on in the above table. I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it. The spacing between the directors is uniform and given in the second-to-last row of the table. The diameter of the

elements is given by d=0.0085 . The above table gives a good starting point to

estimate the required length of the antenna (the boom length), and a set of lengths

and spacings that achieves the specified gain. In general, all the spacings, lengths,

diamters (including the boom diameter) are design variables and can be

continuously optimized to alter performance. There are thousands of tables that further give results, such as how the diamter of the boom affects the results, and the optimal diamters of the elements.

As an example of Yagi-antenna radiation patterns, a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector, 1 driven half-wavelength dipole, 4 directors). The resulting antenna has a 12.1 dBi gain, and the plots are given in Figures 1-3.

Figure 1.E-plane gain of Yagi antenna.

Figure 2.H-Plane gain of Yagi antenna.

Figure 3.3-D Radiation Pattern of Yagi antenna.

The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles. The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely, adding another refelctor). The front-to-back ratio is approximately 19 dB for this antenna, and this can also be optimized if desired.

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency. These antennas have directive patterns that are sharp in both the horizontal and vertical planes.

BEVERAGE ANTENNAS consist of a single wire that is two or more

wavelengths long.

A V ANTENNA is a bi-directional antenna consisting of two horizontal, long

wires arranged to form a V.

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape. This antenna has a wide frequency range, is easy to construct and maintain, and is noncritical as far as operation and adjustment are concerned.

The TURNSTILE ANTENNA consists of two horizontal, half-wire antennas mounted at right angles to each other.

LOG-PERIODIC ANTENNA LOG-PERIODIC ANTENNA

In telecommunication, a log-periodic antenna (LP, also known as a log-periodicarray) is a broadband, multielement, unidirectional, narrow-beam antennathat hasimpedanceandradiationcharacteristics that are regularly repetitive as alogarithmic function of the excitation frequency. The individual

components are often dipoles, as in a log-periodic dipole array (LPDA).

Log periodic antennas are arrays that are designed to be self-

similarand thus arefractal antennaarrays. It is normal todrive alternating elements with a circa 180o (π radian) phase shift from the last element. This is normally done by wiring the elements alternatingly to the two wires in a balanced transmission line.The length and spacing of the elements of a log-

increase logarithmically from one end to the other.The result of this structural condition is that if a plot is made of the input impedance as a function of log of frequency then the variation will be periodic i.e. the impedance will go through the cycles of variation in such a way that each cycle is exactly like its preceding

one and hence the name.

Log.-Periodic Antenna, 250 – 2400 MHz Mutual impedance& self-impedance

The method helps us to compute voltages, currents and impedances in antenna systems. The method understands the voltage, which is observed at the input port of every single antenna element, being induced by the radiation of all the antenna elements (including the own element). The voltage can be composed from contributions of single elements. Each contribution is proportional to the current of the respective

element. E.g., voltage U 1 at the input of the first antenna

element equals to the summation whereI 1, I 2, I 3 are currents at the input ports of single

elements, Z 11, Z12, Z 13 are impedances. Z 11 is self-impedance, Z 1n are mutual impedances between the first element and the other elements in the antenna system. These impedances depend on the mutual position and mutual distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors, which is driven by potential, charge, or an alternating magnetic field (and the associated alternating electric current) at thevertex. The conductors have a commonaxisand vertex.The two cones face in opposite directions. Biconical antennas are broadband dipole antennas, typically exhibiting a bandwidth of 3 octaves or more.

Omnidirectional Biconical Antenna Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board. They are becoming very widespread within the mobile phone market. They are low cost, have a low profile and are easily fabricated.

Consider the microstrip antenna shown in Figure 1, fed by a microstrip transmission line. The patch, microstrip and ground plane are made of high conductivity metal. The patch is of length L, width W, and sitting on top of a substrate (some dielectric circuit board) of thickness h with permittivity

. The thickness of the ground plane or of the microstrip is not

criticallyimportant. Typically the height h is much smaller than the

wavelength of operation.

(a) Top View

(b) Side View

Figure 1.Geometry of Microstrip (Patch) Antenna.

The frequency of operation of the patch antenna of Figure 1 is determined by the length L. The center frequency will be approximately given by:

The above equation says that the patch antenna should have a length equal to one half of a wavelength within the dielectric (substrate) medium.

The width W of the antenna controls the input impedance. For a square patch fed in the manner above, the input impedance will be on the order of 300 Ohms. By increasing the width, the impedance can be reduced. However, to decrease the input impedance to 50 Ohms often requires a very wide patch. The width further controls the radiation pattern. The normalized pattern is approximately given by:

In the above, k is the free-space wavenumber, given by . The magnitude

of the fields, given by:

The fields are plotted in Figure 2 for W=L=0.5 .

Figure 2.Normalized Radiation Pattern for Microstrip (Patch) Antenna.

The directivity of patch antennas is approximately 5-7 dB. The fields are linearly polarized. Next we'll consider more aspects involved in Patch (Microstrip) antennas.

Spiral antenna

In microwave systems, a spiral antenna is a type of RF antenna. It is shaped as a two-

arm spiral, or more arms may be used.[1]

Spiral antennas operate over a wide frequencyrangeand have circularpolarization. Spiral antennas were first described in 1956.

Applications

A spiral antenna transmits EM waves having a circular polarization. It will receive linearly polarized EM waves in any orientation, but will attenuate signals received with the opposite circular polarization. A spiral antenna will reject circularly polarized waves of one type, while receiving perfectly well waves having the other polarization.

One application of spiral antennas is wideband communications. Another application of spiral antennas is monitoring of the frequency spectrum. One antenna can receive over a wide bandwidth, for example a ratio 5:1 between the maximum and minimum frequency. Usually a pair of spiral antennas are used in this application, having identical parameters except the polarization, which is opposite (one is right-hand, the other left-hand oriented).

Spiral antennas are useful for microwave direction-finding.[2]

Elements

The antenna includes two conductive spirals or arms, extending from the center outwards. The antenna may be a flat disc, with conductors resembling a pair of loosely-nested clock springs, or the spirals may extend in a three-dimensional shape like a screw thread. The direction of rotation of the spiral defines the direction of antenna polarization. Additional spirals may be included as well, to form a multi-spiral structure. Usually the spiral is

cavity-backed, that is there is a cavity of air or non-conductive material or vacuum, surrounded by conductive walls; the cavity changes the antenna pattern to a unidirectional shape. The output of the antenna

Measuring Radiation Pattern

and an Antenna's Gain

Antennas (Home)

Antenna Measurements Previous: Measurements

Home

Ranges

Now that we have our measurement equipment and an antenna range, we can perform some measurements. We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction. The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known.

Due to reciprocity, the radiation pattern from the test antenna is the same for both the receive and transmit modes. Consequently, we can measure the radiation pattern in the receive mode for the test antenna.

The test antenna is rotated using the test antenna's positioning system. The received power is recorded at each position. In this manner, the magnitude of the radiation patternof the test antenna can be determined. We will discussphasemeasurementsandpolarization measurementslater.

The coordinate system of choice for the radiation pattern is spherical coordinates.

Measurement Example An example should make the process reasonably clear. Suppose the radiation pattern of a microstrip antenna is to be obtained. As is usual, lets let the direction the patch faces ('normal' to the surface of the patch) be towards the z-axis. Suppose the source antenna illuminates the test antenna from +y-direction, as shown in Figure 1.

Figure 1. A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction.

In Figure 1, the received power for this case represents the power from the angle:

. We record this power, change the position and record again.

Recall that we only rotate the test antenna, hence it is at the same distance from

the source antenna. The source power again comes from the same direction. Suppose we want to measure the radiation pattern normal to the patch's surface (straight above the patch). Then the measurement would look as shown in Figure 2.

Figure 2. A patch antenna rotated to measure the radiation power at normal incidence.

In Figure 2, the positioning system rotating the antenna such that it faces the source of illumination. In this case, the received power comes from direction

. So by rotating the antenna, we can obtain "cuts" of the radiation

pattern - for instance the E-plane cut or the H-plane cut. A "great circle" cut is

when =0 and is allowed to vary from 0 to 360 degrees. Another common

radiation pattern cut (a cut is a 2d 'slice' of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees. By measuring the radiation pattern

along certain slices or cuts, the 3d radiation pattern can be determined.

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna. For instance, if the source is horizontally polarized (see polarization of plane waves), and the test antenna is vertically polarized, the resulting radiation pattern will be zero everywhere. Hence, the radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization). See also cross-polarization.

In addition, the radiation pattern is a function of frequency. As a result, the measured radiation pattern is only valid at the frequency the source antenna is transmitting at. To obtain broadband measurements, the frequency transmitted must be varied to obtain this information.

ANTENNA MEASUREMENTS

Measuring Gain

Back: Measurement of Antennas (Home) Antenna Measurements Antenna Radiation

Patterns

On the previous page on measuring radiation patterns, we saw how the radiation pattern of an antenna can be measured. This is actually the "relative" radiation pattern, in that we don't know what the peak value of the gain actually is (we're just measuring the received power, so in a sense can figure out how directive an antenna is and the shape of the radiation pattern). In this page, we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave.

We can measure the peak gain using the Friis Transmission Equation and a "gain

standard" antenna. A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear). The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 2.15 dB) and the pyramidal horn antenna (where the peak gain can be accurately calculated and

is typically in the range of 15-25 dB). Consider the test setup shown in Figure 1. In this scenario, a gain standard antenna is used in the place of the test antenna, with the source antenna transmitting a fixed amount of power (PT). The gains of both of these antennas are accurately known.

Figure 1. Record the received power from a gain standard antenna.

From the Friis transmission equation, we know that the power received (PR) is given by:

If we replace the gain standard antenna with our test antenna (as shown in Figure 2), then the only thing that changes in the above equation is GR - the gain of the receive antenna. The separation between the source and test antennas is fixed, and the frequency will be held constant as well.

Figure 2. Record the received power with the test antenna (same source antenna).

Let the received power from the test antenna be PR2. If the gain of the test antenna is higher than the gain of the "gain standard" antenna, then the received power will increase. Using our measurements, we can easily calculate the gain of the test antenna. Let Gg be the gain of the "gain standard" antenna, PR be the power received with the gain antenna under test, and PR2 be the power received with the test antenna. Then the gain of the test antenna (GT) is (in linear units):

The above equation uses linear units (non-dB). If the gain is to be specified in decibels, (power received still in Watts), then the equation becomes:

And that is all that needs done to determine the gain for an antenna in a particular

direction.

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern without regard to what the gain is. Typically this can be performed by approximated the integral as a finite sum, which is pretty simple.

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity: Hence, once we have measured the radiation pattern and the gain, the efficiency follows directly from these.

In the next section, we'll look at measuring the phase of an antenna's radiation pattern.

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or electromagnetic waves. They are also insulated from exterior sources of noise. The

combination of both aspects means they simulate a quiet open-space of infinite dimension, which is useful when exterior influences would otherwise give false results.

Anechoic chambers were originally used in the context of acoustics (sound waves) to minimize the reflections of a room. Their radiofrequencycounterpart have also been in use for a few decades, for example to test antennas, radars, or

electromagneticinterference.

The wavelength of audible sound in air falls in the same range as that of commonly used radio waves, and their propagation patterns bear many similarities. This is why both typeslook similar.

Anechoic chambers range from small compartments to ones as large as aircraft hangars. The size of the chamber depends on the size of the objects to be tested and the frequency range of the signals used, although scale models can sometimes be used by testing at shorter wavelengths.

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally "free field" conditions. All sound energy will be traveling away from the source with almost none reflected back. Common anechoic chamber experiments include measuring the transfer function of a loudspeaker or the directivity of noise radiation from industrial machinery. In general, the interior of an anechoic chamber is very quiet, with typical noise levels in the 10–20 dBA range. According to Guinness World Records, 2005, Orfield Laboratory's NIST certified Eckel Industries-designed anechoic chamber is "The

quietest place on earth" measured at −9.4 dBA. [1][2]

The human ear can typically detect sounds above 0 dB, so a human in such a chamber would perceive the surroundings as devoid of sound.

The University of Salford has a number of Anechoic chambers, of which unofficially one

is the quietest in the world with a measurement of −12.4 dBA.[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions. Semi-anechoic chambers have a solid floor that acts as a work surface for supporting heavy items, such as cars, washing machines, or industrial machinery, rather than the mesh floor grille over absorbent tiles found in full anechoic chambers. This floor is damped and floating on absorbent buffers to isolate it from outside vibration or electromagnetic signals. A recording studiomay utilize a semi-anechoic chamber to produce high-quality music freeof outside noise and unwanted echoes.

Radio-frequency anechoic chambers

An RF anechoic chamber.

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes similar to that of an acoustic anechoic chamber, however, the interior surfaces of the RF anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1]. The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns, electromagnetic compatibility (EMC) and radar cross section measurements. Testing can be conducted on full-scale objects, including aircraft, or on scale models where the

wavelengthof the measuring radiation is scaled in direct proportion to the target size.Coincidentally, many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber, such as attenuation of sound and shielding from outside noise.

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-ionising radiation), as effectively as possible, from as many incident directions aspossible. The more effective the RAM is the less will be the level of reflected RF

radiation. Many measurements in electromagnetic compatibility (EMC) and antenna radiation patterns require that spurious signals arising from the test setup, including reflections, are negligible to avoid the risk of causing measurement errors and ambiguities.

One of the most effective types of RAM comprises arrays of pyramid shaped pieces, each

of which is constructed from a suitably lossy material. To work effectively, all internal surfaces of the anechoic chamber must be entirely covered with RAM. Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests. To be sufficiently lossy, RAM can neither be a good electricalconductornor a goodelectrical insulatoras neither type actually absorbs any

power.Typically pyramidal RAM will comprise a rubberized foam material impregnated

with controlled mixtures of carbon and iron. The length from base to tip of the pyramid structure is chosen based on the lowest expected frequency and the amount of absorption

required. For low frequency damping, this distance is often 24 inches, while high

frequency panels are as short as 3–4 inches. Panels of RAM are installed with the tips pointing inward to the chamber. Pyramidal RAM attenuates signal by two effects:

scattering and absorption. Scattering can occur both coherently, when reflected waves are in-phase but directed away from the receiver, or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength. This incoherent

scattering also occurs within the foam structure, with the suspended carbon particles promoting destructive interference. Internal scattering can result in as much as 10dB of

attenuation. Meanwhile, the pyramid shapes are cut at angles that maximize the number of

bounces a wave makes within the structure. With each bounce, the wave loses energy to

the foam material and thus exits with lower signal strength. [4]

An alternative type of RAM comprises flat plates of ferrite material, in the form of flat tilesfixed to all interior surfaces of the chamber. This type has a smaller effectivefrequency range than the pyramidal RAM and is designed to be fixed to good conductive surfaces. It is generally easier to fit and more durable than the pyramidal type RAM but is less effective at higher frequencies. Its performance might however be quite adequate if tests

are limited to lower frequencies (ferrite plates have a damping curve that makes them most effective between 30–1000 MHz)[2].

There is also a hybrid type, a ferrite in pyramidal shape. Containing the advantages of both technologies the frequency range can be maximized while the pyramid remains small (10 cm)[3].

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy, while

waves of lower frequencies have longer wavelengths and are lower in energy, according

to the relationship λ=v/f where lambda represents wavelength, v is phase velocity of

wave, and f is frequency. To shield for a specific wavelength, the cone must be of

appropriate size to absorb that wavelength. The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation, at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies. Pyramidal RAM is at its most absorptive when the incident wave is at

normalincidence to the internal chamber surface when the pyramid height

isapproximately equal to λ/ 4, where λ is the free space wavelength. Accordingly,

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size.

Installation into a screened room

An RF anechoic chamber is usually built into a screened room, designed using the Faraday cageprinciple. This is because most of the RF tests that require an anechoicchamber to minimize reflections from the inner surfaces also require the properties of a screened room to attenuate unwanted signals penetrating inwards and causing interference to the equipment under test and prevent leakage from tests penetrating outside.

Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the test equipment, the hardware under test and associated cables. For example, the far fieldcriteria sets a minimum distance between the transmitting antenna and the receiving antenna to be observed when measuring antenna radiation patterns. Allowing for this and the extra space that may be required for the pyramidal RAM means that a substantial capital investmentis required into even a modestly dimensioned chamber. For most

companies, such an investment in a large RF anechoic chamber is not justifiable unless it is likely to be used continuously or perhaps rented out. Sometimes for radar cross section measurements it is possible to scale down the objects under test and reduce the chamber size provided that the wavelength of the test frequency is scaled down in direct proportion.

RF anechoic chambers are normally designed to meet the electrical requirements of one or more accredited standards. For example, the aircraft industry may test equipment for aircraft according to company specifications or military specifications such as MIL-STD 461E. Once built, acceptance tests are performed during commissioning to verify that the standard(s) are in fact met. Provided they are, a certificate will be issued to that effect, valid for a limited period.

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must expose as few metallic (conductive) surfaces as possible, as these risk causing unwanted reflections. Often this is achieved by using non-conductive plastic or wooden structures for supporting the equipment under test. Where metallic surfaces are unavoidable, they may be covered with pieces of RAM after setting up to minimize such reflection as far as possible.

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required. Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior fields which, otherwise, would not be present inside the chamber. This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering. Unnecessary cables and/or poor filtering can collect interference on the outsideand conduct them to the inside. A good compromise may be to install human

interface equipment (such as PCs), electrically noisy and high power equipment on the outside and sensitive equipment on the inside.

One useful application of fiber optic cables is to provide the communications links to carry signals within the chamber. Fiber optic cables are non-conductive and of small cross-section and therefore cause negligible reflections in most applications.

It is normal to filter electrical power supplies for use within the anechoic chamber as unfiltered supplies present a risk of unwanted signals being conducted into and out of the chamber along the power cables.

Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers:

RF radiation hazard Fire hazard Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this not only can cause unwanted reflections from the human body but may also be a radiationhazardto the personnel concerned if tests are being performed at high RF powers. Suchrisks are from RF or non-ionizing radiation and not from the higher energy ionizingradiation.

As RAM is highly absorptive of RF radiation, incident radiation will generate

heat within the RAM. If this cannot be dissipated adequately there is a risk that hot spots may develop and the RAM temperature may rise to the point of

combustion. This can be a risk if a transmitting antenna inadvertently gets too close to the RAM. Even for quite modest transmitting power levels, high gain

antennas can concentrate the power sufficiently to cause high power flux near their apertures. Although recently manufactured RAM is normally treated with

a fire retardant to reduce such risks, they are difficult to completely eliminate.

Safety regulations normally require the installation of a gaseous fire suppression system including smoke detectors. Gaseous fire suppression avoids damage caused by the extinguishing agent which would otherwise worsen damage caused by the fire itself. A common gaseous fire suppression agent is carbon dioxide. Normally the fire detection system is linked into the power supply to the chamber, so that the fire detection system can disconnect the power supply if smoke or a fire is detected.

Propagation Modes

Ground-wave propagation Sky-wave propagation

Line-of-sight propagation Ground-wave propagation

UNIT V

RADIO WAVE PROPAGATION

Follows contour of the earth

Can Propagate considerable distances Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

Signal reflected from ionized layer of atmosphere back down to earth

Signal can travel a number of hops, back and forth between ionosphere and earth’s surface

Reflection effect caused by refraction Examples

Amateur radio CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of sight

Satellite communication – signal above 30 MHz not

reflected by ionosphere

Ground communication – antennas within effective line of site due to refraction

Refraction – bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium, speed changes Wave bends at the boundary between mediums

Optical line of sight

Effective, or radio, line of sight

d = distance between antenna and horizon (km) h = antenna height (m)

K = adjustment factor to account for refraction,

rule of thumb K = 4/3

Maximum distance between two antennas for LOS propagation:

3.57 Κh1 Κh2

h1 = height of antenna one h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance

between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere's interior).

Because spherical geometry is rather different from ordinary Euclidean geometry, the equations for distance take on a different form. The distance

between two points in Euclidean space is the length of a straight line from one point to the other. On the sphere, however, there are no straight lines. In non-

Euclidean geometry, straight lines are replaced withgeodesics. Geodesics on the sphereare the great circles (circles on the sphere whose centers are

coincident with the center of the sphere).

Between any two different points on a sphere which are not directly opposite each other, there is a unique great circle. The two points separate the great circle into two arcs. The length of the shorter arc is the great-circle distance between the points. A great circle endowed with such a distance is the Riemannian circle.

Between two points which are directly opposite each other, called antipodal points, there are infinitely many great circles, but all great circle arcs between antipodal points have the same length, i.e. half the circumference of the circle, or πr, where r is the radius of the sphere.

Because the Earth is approximately spherical (see Earth radius), the equations for great-circle distance are important for finding the shortest distance between points on the surface of the Earth (as the crow flies), and so have important applications in navigation.

A useful way to remember this formula is cos(central angle)= cos(longitude difference CTM ) , where CTM could be taken to mean 'Only the cos terms in longitude angle difference cosine expansion to be multiplied with cos(latitude difference)'.

The central angle is alternately expressed in terms of latitude and longitude differences dlat,dlong, using only cosines, as: arccos( cos(dlat) - cos(lat1)*cos(lat2)*(1 - cos(dlong) ) . The distance d, i.e. the arc length, for a sphere of radius r and given in radians,

is then:

This arccosine formula above can have large rounding errors for the common case where the distance is small, however, so it is not normally used for manual calculations. Instead, an equation known historically as the haversine formula was preferred, which is much more numerically stable for small distances:

[1]

Historically, the use of this formula was simplified by the availability of tables for the haversinefunction: hav(θ) = sin

2(θ/2).

Although this formula is accurate for most distances, it too suffers from rounding errors for the special (and somewhat unusual) case of antipodal points (on opposite ends of the sphere). A more complicated formula that is accurate for all distances is the following special case (a sphere, which is an ellipsoid with equal major and minor axes) of the Vincenty formula(which more generally is a method to compute distances onellipsoids):

[2]

When programming a computer, one should use the ATAN2() function rather

than the ordinary arctangent function (ATAN()), in order to simplify handling of the case where the denominator is zero, and to compute unambiguously in all quadrants.

When using a spreadsheet program such as Excel the arccosine formula is suitable since it is simpler and rounding errors disappears with high precision used. If r is the great-circle radius of the sphere, then the great-circle distance is . Vector version Another representation of similar formulas, but using usingn-vector instead of latitude/longitude to describe the positions, is:

[3]where and

are the n-vectors representing the two positions s and f. Similarly to the equations above based on latitude and longitude, the expression based on arctan is the only one that is well-conditioned for all angles. If the two positions are originally given as latitudes and longitudes, a conversion to n-vectors must first be performed.

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is the chord of the great circle between the points. The central angle between the two points can be determined from the chord length. The great circle distance is proportional to the central angle.

The great circle chord length may be calculated as follows for the corresponding unit sphere, by means of Cartesian subtraction

[4]:

Spherical cosine for sides derivation

By using Cartesian products rather than differences, the origin of the spherical cosine forsides becomes apparent:

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial radius a of 6,378.137 km; distance b from the center of the spheroid to each pole is 6356.752 km. When calculating the length of a short north-south line at the equator, the sphere that best approximates that part of the spheroid has a radius of b

2 / a, or 6,335.439 km, while the spheroid at the poles is best

approximated by a sphere of radius a2/ b, or 6,399.594 km, a 1% difference. So

as long as we're assuming a spherical Earth,any single formula for distance on the Earth is only guaranteed correct within 0.5% (though we can do better if our formula is only intended to apply to a limited area). The average radiusfor a spherical approximation of thefigure of the Earthis approximately6371.01 km (3958.76 statute miles, 3440.07 nautical miles).

LOS Wireless Transmission Impairments Attenuation and attenuation distortion Free space loss

Noise

Atmospheric absorption Multipath

Refraction Thermal noise

Atmospheric absorption – water vapor and oxygen contribute to attenuation

Multipath – obstacles reflect signals so that multiple copies with varying delays are received

Refraction – bending of radio waves as they propagate through the atmosphere

Multipath Propagation Reflection - occurs when signal encounters a surface that is large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that is large compared to wavelength of radio wave

Scattering – occurs when incoming signal hits an object whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases If phases add destructively, the signal level relative to

Noise declines, making detection more difficult Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading Slow fading Flat fading

Selective fading

Rayleigh fading Rician fading

Error Compensation Mechanisms Forward error correction Adaptive equalization Diversity techniques