A CONCEPTUAL RESEARCH AND ANALYTICAL STUDY BASED ON ANTENNAS &
ELECTROMAGNETIC WAVE PROPAGATION TECHNIQUES Dr. Rajiv Sinha
Principal, Parwati Engineering College, Madhepura, Bihar
1 FUNDAMENTAL OF ANTENNAS 1.1 How antennas radiate
Recieving wires are the interface between radio recurrence circuits and engendering electromagnetic waves (Balanis, 2005;
Rudge et al., 1986). They are utilized in all radar and remote correspondence frameworks. At the point when the electric flows on conveyors change, that is, the point at which they are rotating flows, electric and attractive fields are set up.
These fields transport energy away from the conductor as electromagnetic waves. Figure 1 shows the electric field circles that are spreading away from a dipole radio wire that is portrayed in Segment 2. The circled idea of the electric field is normal for radiation. On account of the dipole radio wire, the energy spreads from the sides of the dipole, and little energy emanates away in accordance with the dipole wires. All radio wires have this property of transmitting in explicit ways, which brings about the property known as directivity that is examined in Section 1.2.
The opposite activity happens on gathering. On the off chance that electromagnetic waves are occurrence on a radio wire, flows are actuated on the channel. The interaction is altogether proportional. On the off chance that the wave hits the recieving wire from the side of the wire, solid flows are instigated on the wire. On the off chance that the wave is occurrence toward the wire, very little current is instigated. Impedance is the proportion of voltage-to-flow in an electrical circuit. In getting electrical energy from a generator, for example, a hifi intensifier, to a heap, like a heap speaker, ensure that the impedance of the generator is equivalent to that of the heap. Most radio recurrence circuits, utilized in radars, are intended to have an impedance of 50 ohms. The practically equivalent to boundary in an
electromagnetic wave is the proportion of electric-to-attractive field. When the wave is well away from the radio wire and is proliferating in what is called free space then its impedance is around 377 ohms.
The distinction in these two numbers clarifies that the recieving wire is additionally filling in as an impedance transformer. What's more, as most transformers that utilization coupled loops of wire on iron centers and that work at lower frequencies, it has an impedance change esteem what's more, a misfortune or productivity boundary.
1.2 Antenna boundaries
The idea of impedance change and mandate radiation prompts significant boundaries that characterize the presentation of radio wires.
Figure 1. Radiation from dipole antenna The first of these is input impedance.
Radiation is a deficiency of energy and is addressed by a radiation obstruction.
Moreover, there will be resistive misfortune in the radio wire itself because of blemished conductivity of the metal and because of misfortune in any dielectric materials utilized. The impedance will likewise have a responsive part, either capacitive or
inductive, which commonly will change rapidly with recurrence, especially in full receiving wires like the dipole. It is significant that this impedance is coordinated to that of the link that interfaces the radio wire to the transmitter.
Much of the time, this will be 50 ohms, and any contrast between the radio wire impedance and this worth will imply that a portion of the energy from the transmitter will be reflected once again into the
transmitter. On the off chance that this reflection is critical, it might detune the transmitter. Insurance gadgets, for example, isolators or circulators might be utilized to forestall this issue. Most radio wires are complementary. This implies that their properties are something very similar on communicate and on get. The get impedance of the radio wire is equivalent to the send impedance, and coordinating is similarly significant.
Figure 2. Radiation pattern of a typical directive antenna. (a) Definition of important parameters; (b) comparison of antenna pattern with uniform (dotted) and tapered (solid) excitation amplitude distribution.
Figure 2a shows the radiation example of an average radio wire, displayed on a polar plot. The distance of the bend from the middle addresses the measure of electromagnetic energy transmitted toward that path. It tends to be seen that a large portion of the energy is coordinated inside a tight scope of points. This scope of points is known as the primary shaft. A radio wire with this kind of radiation design is called mandate, and it has order acquire. An Omni-order radio wire will emanate similarly every which way on this plot, and its radiation example will be a circle. Away from the fundamental pillar, radiation is more vulnerable, and pinnacles happen, got back to side flaps and projections. The points between the flaps are known as nulls. The bar width of the radio wire is determined as the point between the focuses in the principle shaft where the force emanated is decreased to one half.
The invalid to-invalid bar width is likewise now and again utilized.
In huge radio wires, for example, the exhibit or reflector portrayed later, the side flaps can be constrained by tightening the adequacy of the excitation conveyance across the recieving wire region. This implies that the sufficiency is more noteworthy at the middle than the edges.
Figure 2b shows the distinction in the example. Tightening will expand the shaft width in any case, more critically, decrease the side flap level, which for a uniform conveyance will be around 13 dB underneath the pinnacle of the principle pillar. The figure shows diminished side projections at in excess of 20 dB beneath the pinnacle.
As side flaps can bring about bogus targets or mistakes in target following, numerous radars have a lot of lower side projections.
As a recieving wire transmits in three
measurements, a subsequent radiation design in a plane at right points to the first is utilized. Subsequently, two shaft widths are expected to totally determine the principle pillar. On the off chance that the radiation designs are circles in the two planes, and, all the more precisely, the recieving wire transmits similarly every which way then it is called isotropic. This condition can't be accomplished by and by however is a helpful base on which to indicate recieving wire acquire. The unit utilized is dBi (dBs regarding isotropic).
Where D is the directive gain and θ1 and θ2 are the beam widths in the two planes in degrees. If the area of the radiating face of the antenna is a then the directive gain is also given by
where λ is the wavelength at the operating frequency. The beam width is related to the size of the antenna. If the size, along one dimension, is a then the beam width in radians is given by
The bandwidth of an antenna is that range of frequencies over which its properties remain acceptable. Electromagnetic radiation is polarized, which means that the radiated electric field oscillates in a specific direction but always at right angles to the direction of radiation. Thus, an antenna may radiate horizontal or vertical polarization, or circular, if the direction rotates as the energy propagates.
2 ANTENNA TYPES 2.1 Wire antennas
Wire antennas are the simplest of all types and form the basis of more complicated ones (Pozar, 1998). The dipole shown in Figure 1 is a wire antenna. Its operation
can be understood by considering a two- wire transmission line, used to feed such an antenna. If the transmission line is open circuited then the mismatch produces a reflected wave back down the line, towards the transmitter. This reflection interacts with the incident power wave to produce what is called a standing wave, shown in Figure 3. Obviously at the open end, the current flowing must be zero as there is an infinite impedance
Figure3. Current standing wave (a) on two-wire transmission line and (b) on dipole antenna fed by the two-wire transmission line.
at the open-circuit point. In any case on a standing wave, there are various current zeroes down the line, each isolated fundamentally a recurrence. In the center these zeroes are zeniths of current. The principle top down the line is a fourth of a recurrence away from the open-circuit end.
If the two-wire transmission line is by and by bent open now, a half-wave dipole is molded. The current spread is undisturbed by the contorting cooperation, and the current at the dipole closes is zero and at the center is at its zenith. The dipole exudes unequivocally and in the level plane is Omni-directional. In its vertical plane, it has a figure of eight radiation plan with a radiation invalid along the dipole heading.
The request obtain is 1.64, and it is stimulated along its length, which suggests
that, for example, a vertical dipole is up hypnotized. The dipole is a resonating radio wire in that if the repeat is changed, the show corrupts quickly. As the circumstance of the top in the standing wave on the open- circuited transmission line is repeat subordinate then the current level at the dipole spot will change with repeat. This hugely influences its data impedance. At its full repeat, the dipole resistance is 73 ohms and there is no responsive part.
As the repeat is changed, the resistance changes a little, anyway more fundamentally the reactance augments quickly. This gives an enormous mix, and it is this that confines the information move ability to several percent. The information move limit can be extended by making the wire thicker or even fixed, which prompts the bowtie recieving wire and its three dimensional same, the biconical radio wire.
In case a metal sheet is familiar commonplace with the dipole wire at the feed point and the lower half of the dipole wiped out, a quarter-recurrence monopole radio wire is formed, as shown in Figure 4a.
It has an information impedance an enormous segment of that of the dipole, and if the metal sheet is boundless, a near radiation plan
Figure 4. Antenna on metal ground plane. (a) Monopole antenna and (b) dipole antenna.
over the ground. On the off chance that the ground plane is limited, there is some radiation underneath, and the example is like the dipole yet hilter kilter beneath or more. The monopole radio wire is utilized generally on vehicles and airplane, as the whip or edge recieving wire. A significant component is that it very well may be taken care of straightforwardly from a coaxial link, which is generally utilized as an association among radio wires and handsets, because of its adaptability and screening properties. Then again, two-wire transmission lines have helpless screening properties. The monopole transmits along the ground plane, which makes it ideal for correspondence type applications yet less fit to radar and different sensors that require radiation away from the beginning. To acquire this kind of activity, a dipole can be utilized upheld by a ground plane as displayed in Figure 4b.
The separation from the dipole to the ground plane is significant. Assuming it is significantly less than quarter of a frequency, the information impedance will be seriously upset, and there will be little radiation away from the beginning. For a quarter frequency separating, the radiation
from the dipole towards the ground plane encounters two quarter frequencies in heading out to the ground plane and back, and reversal all things being equal, identical to a large portion of a frequency.
When these are added, this regressive wave will be in stage with the radiation from the dipole away starting from the earliest stage, and solid radiation will result. Dipoles supported by a ground plane are utilized broadly in clusters and, specifically, in staged exhibits, as will be portrayed later.
2.2 PRINTED CIRCUIT RADIO WIRES Printed circuit radio wires get from a longing to diminish the thickness of recieving wires, for example, the dipole over a ground plane, which is somewhat thick at low microwave frequencies and thus can't be mounted on airplane and rockets (Waterhouse, 2007). Microstrip is a predominant transmission line vehicle for handset circuits, comprising of a circuit line isolated from a ground plane by a dielectric substrate. A miniature strip transmission line can be made to emanate similarly as the two-wire transmission line.
Figure 5 shows a micros trip fix radio wire.
It comprises of a rectangular fix of metal dispersed away from the beginning by a dielectric substrate that is normally not exactly a 10th of a frequency thick. The fix is energized by a micros trip line and has a length of around a large portion of a frequency. The fix goes about as a resonator shaped by a wide miniature strip line, open circuited at each end. One approach to see how it transmits is to envision a wave skipping to and fro between the open circuits emanating a limited quantity of energy at every reflection.
Numerous reflections accordingly add to a solid radiation. The fix transmits overwhelmingly away from the beginning. It is a limited transfer speed recieving wire like the dipole, since its activity depends on
a half-frequency structure. The data transfer capacity can be expanded by utilizing a thick, low-dielectric consistent substrate, however without uncommon measures its transmission capacity is somewhere in the range of 5 and 10%. It has an increase of 6.4 dBi and is captivated toward the half-frequency measurement.
Numerous variations on the rectangular fix have been proposed, like roundabout and three-sided patches. Roundabout polarization can be effortlessly acquired, and openings in the fix can be utilized to cause it to work at two unique frequencies.
Figure 5. Microstrip patch antenna.
Quite possibly the main highlights of the miniature strip fix is that it tends to be incorporated with the handset circuit. The feed displayed in Figure 5 can interface with channels, speakers, and blenders made on a similar substrate. In any case, as circuits need great factor segments to accomplish high selectivity and affectability, they should be made on slender high dielectric steady substrates. This opposing necessity for substrates for circuits and radio wires implies that joining on a similar substrate is restricted. In any case, a layered methodology displayed in Figure 6 is being utilized for alleged "Shrewd Skin"
conformal staged exhibits. The top thick layer is utilized for the fix recieving wires, the more slender substrate beneath it for the circuit, and underneath that are power supplies and cooling. Microstrip fix recieving wires are instances of printed circuit radio wires. This phrasing clarifies that they can be built utilizing a similar assembling measure utilized for printed circuits, to be specific, photolithography.
This develop cycle likewise can be minimal expense, and strategies for multi layering are additionally accessible albeit the assembling of "Keen Skin" congregations, including distinctive material sorts, is very overbearing.
Figure 6. Cross section of “Smart Skin”
antenna concept.
Figure 7. Parabolic reflector antenna. (a) Parabolic configuration showing horn antenna at focus; (b) rays from focus to aperture travel equal distances giving a field with equal phase at the aperture plane.
2.3 Reflectors and lens antennas
Reflector and focal point recieving wires involve a gathering dependent on quasioptic standards as in they can be perceived by summoning beam optics. Figure 7a shows the idea of an essential center took care of, allegorical reflector recieving wire. The beams, displayed in Figure 7b, exuding from the feed, venture out an equivalent
distance to a plane at the front edge of the reflector and along these lines make a uniform stage wave front that makes a thin pillar as it spreads from the recieving wire.
The feed at the center can be just about as basic as a dipole. For better execution, uncommonly planned waveguide horns can be utilized. Reflectors are easy to deliver and are fit for making thin shaft widths over wide recurrence transmission capacities, with great side flap control. The directivity is given by condition (2), where An is the space of the front substance of the reflector, and the bar widths are given around by condition (3). The feed obstructs a portion of the forward going energy reflected off the parabola, and this decreases the productivity and expands the side projections and cross polarization.
Further developed execution can be gotten by the utilization of offset reflectors.
Reflectors were utilized on early radars, utilizing mechanical development to filter the bar heading, are as yet utilized in certain applications like homegrown satellite TV gathering, radio space science, and satellite correspondences. Focal point radio wires work along these lines to optical focal points yet are for the most part made of low-misfortune plastics. They are extremely valuable
Figure 8. Microstrip patch array.
at millimetric wavelengths (30–300 GHz) and above. They have been used in car radars at 77 GHz and missile homing heads at 95 GHz.
2.4 Arrays
Numerous dipole or fix recieving wires can be gathered on a similar ground plane to give a radiation design with a lot more modest bar width and to permit it to be filtered, as in a staged cluster. Figure 8
shows a gathering of fix recieving wires framing a little cluster. Photolithography is ideal for exhibits as the assembling costs for a solitary component or a cluster are comparable.
For huge exhibits, the directivity is approximated by
Where N is the total number of elements and De is the directivity of each element.
Alternatively, equation (2) can be used, where the area A is that occupied by the array elements, namely,
where Nx and Ny are the numbers of elements in the x and y directions, respectively (and both Nx and Ny are greater than 1), and dx and dy are the element spacings in the x and y directions, respectively. More discussion of arrays is given in Section 3.2.
3 BEAM SCANNING 3.1 Mechanical scanning
Actual development of a fixed shaft recieving wire is a minimal expense and viable option to staged clusters. Its essential lack is the sluggish output rate contrasted with the quick bar development of a staged cluster, which can ordinarily reconfigure the shaft Course in a couple of milliseconds.
Figure 9. Phased array operation (phase of excitation of elements, etc., adjusted to offset phase change in distance, d, 2d, etc., so that dotted line is uniform phase front).
Regularly mechanical output in one plane is joined with a staged or various pillar clusters in another.
3.2 Phased arrays
The course of the transmitted bar is dictated by the component dividing d and the general period of the component taking care of ϕ (Mailloux, 1994). Figure 9 shows the math of one element of the variety of Figure 8. The shaft bearing is that wherein the stage contrast of the voltages applied to every component is equivalent and inverse to the stage change experienced by the wave from every component venturing to every part of the distance d. At the point when this is along these lines, the energy from every component shows up at a far off point in stage toward the path shown. The energy along these lines consolidates usefully. Every which way other than this, the blend is part helpful and part ruinous, and the complete is in every case not exactly the pinnacle of the principle shaft.
On the off chance that the stage distinction of the component excitation is adjusted then the pillar course will likewise change.
The component dispersing is to some degree dictated by the size of the components. On account of the fix recieving wire, the size is a large portion of a frequency in the dielectric of the substrate, making it regularly of the request for 0.3–
0.4 frequencies. In the event that the components are excessively close, they couple unequivocally, which disturbs the stage shaft control impact depicted previously. Regularly, spacings somewhere in the range of 0.5 and 0.8wavelength are utilized. For spacings of 0.5 frequencies, pillar examining out to 60◦ might be accomplished. Assuming the shaft is filtered past this, grinding flaps show up.
Grinding projections are extra shafts that show up the other way to the primary bar and may bring about phantom focuses in radar frameworks.
Shaft control in two measurements can be accomplished by applying stage contrasts in the two rule bearings of the variety of Figure 6. Subsequently, on a basic level, discretionary stage taking care of every component is required and giving this is
quite possibly the most requesting and costly pieces of staged cluster plan. For high-power radar, waveguide-based ferrite stage snifters have been utilized. Where lower power is utilized then diode exchanging of line lengths is generally utilized. Commonly 4-cycle shifter, with stage states separated by 22.5◦, will give smooth filtering, albeit in some clusters with exceptionally slender bar widths, more pieces are utilized. To lessen the general expense of a total staged exhibit, component diminishing should be possible, in which not all cluster positions are populated with a component and stage shifter. The impact is to make the checking less smooth and to raise the side flap level.
Nonetheless, adequate execution with under half of the cluster positions filled has been accomplished.
In the above-improved on portrayal, it has been accepted that the entirety of the components are energized with a similar force. While this gives the tightest bar width, it brings about first side flaps just 13 dB down on the pinnacle of the principle bar. For some radars, this is unsatisfactorily high. To decrease the side projection level, tightening the degree of component excitation from the middle to the edge of the exhibit should be possible, yet this somewhat expands the shaft width and diminishes the addition.
3.3 Multiple pillar clusters
The need to freely control the time of the sign communicated from each part of an organized group, using contraptions, achieves an extraordinarily massive cost.
Alower-cost elective is the various column display. Figure 10 shows the thought. The display segments are related with a column past that has different ports. Each port gives a shaft a substitute way as shown.
Shaft analyzing can be cultivated by trading a single handset starting with one port then onto the next. Then again various handsets could be used, in which case various orientation can be examined simultaneously. The last arrangement can be useful where incredibly fast targets block the use of bar inspecting.
Figure 10. Multiple beam array concept.
(Application of signal to a beam port excites all antenna elements with the correct phases to produce a radiated beam in a different direction to all other beam ports.)
Figure 11. Schematic of Butler matrix beam former. (Transmission lines can be made in micro strip, strip line, coax, or waveguide.)
The disadvantage with different bar exhibits is the intricacy of the bar previous. This brings about an extremely elaborate plan strategy; however utilization of printed circuit creation methods permits somewhat minimal expense creation. Figure 11 shows the schematic of a Butler network pillar previous with four bars and four exhibit components. The network is somewhat narrowband, and the plan intricacy and misfortune increment rapidly as cluster size is expanded. An option with lower intricacy is the Blass lattice, which is utilized in mix with mechanical filtering in some alarming radars. Wide transfer speed can be
accomplished utilizing the Rotman focal point. The cluster component ports, the pillar ports, and the space between are framed in an equal plate waveguide, made just from the space between an upper and lower ground plane. The data transmission is extremely wide, and these shaft formers are utilized in electronic fighting sticking radio wires.
4 TARGET TRACKING ANTENNAS
Radio wires can be utilized to decide the point of appearance of an approaching sign and subsequently to follow an objective in a radar framework (Hall et al., 1991). Figure 12 shows a radio wire with a pillar
Figure 12. Conical scan target tracking.
(Antenna radiates a beam offset from its axis, which is pointing at the target. As the antenna is mechanically rotated, the beam draws out a cone in space Around the target.)
That is counterbalanced from the bearing of the approaching sign. On the off chance that the recieving wire is turned so its shaft heading portrays a tapered shape then the point between the radio wire and the sign not really settled. As the pillar pivots, the got signal level will differ with a similar period as the turn. Then again, assuming the cone pivot is lined up with the sign heading, there will be no variety. Hence, the plentifulness of the variety is relative to the pointing point blunder, that is, the contrast between the cone pivot and the objective heading.
The overall period of the got signal variety gives the objective situation around the boundary of the cone. This kind of
following recieving wire is called cone like output and was utilized on early radars and rockets. It is, nonetheless, somewhat simple to mislead utilizing clear electronic fighting strategies. In abundancy examination following (see Figure 13), the recieving wire is intended to have four shafts around the cone. By contrasting the sign got in each pillar, the point blunders in two planes can be acquired. At the point when this is utilized in a radar framework, target position can be discovered utilizing one heartbeat. In a cone like output framework, many heartbeats are needed to set up target heading. Thus, this technique is called plentifulness correlation mono heartbeat following. Further developed exactness can be acquired if the general period of the sign in each pillar is looked at, as opposed to the plentifulness.
Figure 13. Amplitude camparison (a) showing two beams in vertical plane displaced from antenna axis; (b) layout of four beams for tracking in both vertical and horizontal planes.
This technique is called stage correlation following. In the event that this is done, the bars don't should be balanced from the funnel shaped pivot, and the full gap can be utilized to frame the bar. The period of the sign got by every one of four quadrants is extricated to decide target course. This procedure is likewise utilized in staged clusters to play out the objective following capacity.
5 RADIO WAVE PROPAGATION 5.1 Propagation models
The simplest form of radio wave propagation occurs when two antennas are isolated from their environment (Barclay, 1986). In so-called free space propagation, the power received by an antenna a distance d from another antenna is given by
where Pt is the force emanated the communicating receiving wire, Gt and Gr are the additions of the two radio wires, and λ is the frequency. The got force can be expanded by expanding the addition of the radio wires or by expanding the frequency (or all in all by decreasing the recurrence).
In particular, the got power tumbles off with the square of the distance. On the off chance that the recieving wires are currently situated over a limitless, consummately directing ground plane then the condition is adjusted to be
Where the radio wire statures ht and hr are significantly less than the division distance d. For this situation, the force tumbles off at the fourth force of the distance. In a reasonable climate, with genuine earth, covered by vegetation, structures, and so on, the force tumble off will fluctuate, contingent upon the recurrence and the particular climate. Misfortunes in the environment will constrict or decrease the got influence. Figure 14 shows the barometrical constriction in a reasonable air with recurrence. The force decrease factor is gotten by increasing the climatic lessening
Figure 14. Atmospheric attenuation.
(Solid line denotes attenuation in clear air, long dashes denote attenuation in
rain, and short dashes denote attenuation in fog.)
in dB/km by the distance between the radio wires. It very well may be seen that at low frequencies, under 1 GHz, the lessening is little and can be overlooked. At higher frequencies, it becomes huge and, as a general rule, increments with recurrence.
There are, in any case, groups in which the weakening is high and these are known as lessening groups. These can be utilized when limit spread to the get radio wire and to forestall recieving wires past that reach getting the sign and in this manner being made aware of its quality. There are additionally groups of low weakening, known as spread windows, and these are utilized when limit the communicate power.
Likewise displayed in the figure is the extra lessening because of precipitation.
This relies upon the precipitation rate and the length of the engendering range that encounters this precipitation. In long radio connections, just piece of the reach might encounter critical constriction because of a confined rainstorm. As a rule, downpour weakening increments with recurrence and turns out to be exceptionally huge when the frequency becomes similar to the raindrop size. Weakening because of mist, cloud and combat zone dust, which will hinder optical proliferation frameworks, as it were becomes significant at extremely high frequencies, and in low recurrence and microwave frameworks might be overlooked.
5.2 PROPAGATION IN DIFFERENT RECURRENCE GROUPS
At extremely low frequencies, below1 MHz, the upper climate goes about as a conductor, and this makes a waveguide between the world's surface and the upper layers. This permits extremely long proliferation goes well past the noticeable skyline and even around the earth. These frequencies likewise proliferate well in seawater and are utilized to speak with lowered submarines.
In the high-recurrence (HF) band (3–
30 MHz), the ionosphere diffracts radio energy back down to the earth, bringing about spread reaches into the great beyond.
All radio wave energy is dependent upon diffraction, which brings about energy being bowed around snags or in energy not voyaging a straight line. As a rule, diffraction diminishes with recurrence. At HF, the collaboration between the ionized particles and the radio energy, and specifically the slope in the molecule thickness with stature, twists the wave downwards. The molecule thickness relies upon various variables, including season of day, season, and area, and the impacts lead to outrageous variety in the proliferation qualities.
In the extremely high-recurrence (VHF) band (30–300 MHz), it is the adjustment of thickness of the climate at lower levels, close to the world's surface, that influences engendering. As at HF, the wave is twisted back towards the earth and
this implies that proliferation into the great beyond is conceivable, albeit, as a general rule, spread ways are a lot more limited than at HF. In arranging radio connections at VHF, the suspicion that the world's sweep is 4/3 times its genuine worth is adequate. Once more, the thickness profile is variable, and uncommon conditions might give extremely long ranges due to ducting marvels. At ultrahigh frequencies (UHFs) (300 MHz–3 GHz) or more, the radio wave is considered to go in an orderly fashion. Nonetheless, reflection and diffraction from articles, for example, structures might be huge.
REFERENCES
1. Balanis, C.A. (2005) Antenna Theory, Analysis and Design, 3rd edn, John Wiley, New Jersey.
ISBN 0-471-66782-X.
2. Barclay, L.W. (Ed.) (1986) Propagation of Radiowaves, 2nd edn, Peter Perigrinus, IET, London. ISBN 0-85296-102-2 & 978-0- 85296- 102-5.
3. Hall, P.S., Garland-Collins, T.K., Picton, R.S. and Lee, R.G. (1991) Radar, Brassey’s Battlefield Weapon Systems and Technology Series, Brassey’s, London. ISBN 0-08-037710.
4. Mailloux, R.J. (1994) Phased Array Antenna Handbook, Artech House, Norwood. ISBN 0- 89006-502-0.
5. Pozar, D.M. (1998) Microwave Engineering, 2nd edn, John Wiley, New Jersey. ISBN 0-471-17096- 8.
6. Rudge, A.W., Milne, K., Olver, A.D. and Knight, P.
(1986) Handbook of Antenna Design, Peter Peregrinus, IET, London. ISBN 0-886341-052-9.
7. Waterhouse, R. (Ed.) (2007) Printed Antennas for Wireless Communications, JohnWiley, Chichester.
ISBN 978-0-470-51069-8.
