1. Jugul Kishor Antenna

2. 18.1 Introduction  An antenna is basically a metallic structure that is capable of radiating or receiving electromagnetic signals.  In addition they also perform the task of transforming signal from circuit domain (electrical signal) to field domain (electromagnetic signal) so that the signal can propagate through space or vice versa.  Thus antenna behaves as a transducer between a guided wave and propagating wave.  It also behaves as an impedance matcher between the transmission line and free space impedance.  The antennas generally follow the law of reciprocity and hence a transmitting antenna can also be used to receive signal.

3.  However due to some practical and mechanical requirements some antennas are preferred for transmission while the rests are preferred for receiving signals.  In general antennas can be classified into three categories, namely, (1) conduction current or wire antennas, (2) displacement current or aperture antennas and (3) array antennas.  Out of these the array antennas consist of a number of radiating elements which may be either conduction or displacement current type.  The example of conduction type antennas are dipole antenna, loop antenna, helical antenna etc. whereas the example of displacement current type antennas are horn antennas, slot antennas etc.

4.  The displacement or aperture antennas can be classified into two categories, namely, (1) primary antenna and (2) secondary antennas.  Primary antennas are directly excited by source and can be used independently. Horn antennas are such type of antennas.  Secondary antennas requires an primary antenna as its feed and hence cannot be used independently. Reflectors antennas are the examples of secondary antennas.  When an antenna is excited by a source, two types of fields are generated in its surroundings.

5.  The first is non-propagating field and the rest is propagating field.  The non-propagating field remains close to the antenna and does not contribute to the energy propagation whereas the propagating field remains far from the antenna and contributes to the energy propagation.  The propagation fields are also known as radiation fields or far fields or inverse square field.  The non-propagating fields are reactive in nature and are also called the near-fields.  The approximate distance of the boundary between the near field and far field from the antenna can be approximated as where “D” is the maximum dimension of the antenna and is the operating wavelength.

6.  The total space surrounding the antenna can be divided into three regions.  In the first region reactive field dominates and it extends up to a distance.  This reactive field then begins to diminish and it continues up to the distance.  After this distance reactive field vanishes and far field starts.  Since microwaves are generally used for communication and RADAR purpose therefore microwave antennas are not Omni-directional.  Instead they are highly directive.  In addition microwave antennas are very small in size since the dimension of an antenna is proportional to its wavelength.

7.  Microwave antennas also suffer from some disadvantages like high power requirement.  Since power attenuation increases with frequency, microwave antennas require high power and also high gain.  Large power is also required to overcome the received and system noise. 18.2 Radiation Mechanism  Let us consider that a two wire transmission line connected to a time varying source at one end and left open circuited at the other end.  This will result in a standing wave in the line with current in each wire same in magnitude but opposite in phase.  As the wires are in close proximity the field of one wire will cancel the field of the other wire and no radiation will take place.

8.  Now if the open terminals of the transmission line are bent, the spacing between the wires become significant in comparison to wavelength and complete field cancellation does not happen.  This results in a net radiation by the system.  The separation between the wires can be increased by further bending the wires and at the limiting case it will result in a dipole.

9.  The lines of force created between the arms of a small centre fed dipole, in the first quarter of the period, are shown in figure (a).

10.  If sinusoidal excitation is assumed then at the end of this quarter the charge will reach at its maximum value and the field lines will travel a radial distance of outward.  During the next quarter of the period, the charge density on the conductor begins to diminish and at the end of the quarter the field lines of the first quarter travel an additional and hence a total of distance from antenna.  The diminishing of the charges can be thought of as being accomplished by introducing opposite charges in the line which at the end of the first half of the period have neutralized all the charges on the conductors.  The lines of force created by the opposite charges will be of same strength as original field lines in first quarter and will travel a distance at the end of the second quarter.

11.  Therefore at the end of first half the net result is that there are some lines of force pointed upward with 0 to distance and the same number of lines directed downward within to distance.  Since at the end of the first half the net charge on the antenna is zero, the lines of force will detach from the conductors and unite together to form closed loops.  The process will again repeat in the remaining second half but now in opposite direction.  The field distribution surrounding the dipole at any arbitrary time is shown in figure (d).

12.  The radiation pattern of an antenna is the graphical representation of the filed strength or power per unit solid angle, radiated by the antenna at a given distance, as a function of elevation angle or azimuth angle or both.  If filed strength is plotted as a function of angle then it is called a field pattern whereas if the power per unit solid angle is plotted as a function of angle then it is called a power pattern.  Depending on whether the parameter has been plotted against elevation or azimuth angle, such pattern is also called as elevation or azimuth pattern. 18.3 Antenna Parameters Radiation pattern:

13.  If the parameter is plotted against elevation and azimuth angle then the resultant plot is called 3D pattern.  Since power is proportional to the square of field strength, the power pattern is also proportional to the square of the field strength pattern.  Until and unless it is specified the radiation pattern generally corresponds to field strength pattern.  Depending on the radiation pattern, antennas can be classified as (1) isotropic, (2) omnidirectional and (3) directive antennas.  An isotropic antenna is one that radiates uniform field strength in every direction or any plane whereas an omnidirectional antenna is one that radiates same field strength in a particular plane only.  For a directional antenna the radiated field varies with direction and such antenna generally concentrates its radiated field in a particular direction or some particular directions only.

14.  It may be noted that an omnidirectional antenna is also a kind of directional antenna.  In practice, in electromagnetics, there is no such antenna that truly radiates uniform power in all direction and hence no true isotropic antenna exists.

15.  Radiation lobe:  A radiation lobe is a part of the radiation pattern that is surrounded by different regions of relatively weak radiation intensities.  Depending on the maximum radiated field strength, a lobe can be classified as major lobe or minor lobe.  The major lobe contains the direction of maximum radiation whereas minor lobe is any lobe except a major lobe.  A minor lobe can be classified as side lobe and back lobe.  A back lobe has a direction just opposite to the main lobe whereas a side lobe has a direction other than the direction of main lobe and back lobe.  The minor lobes generally correspond to undesired radiation and hence for a properly designed antenna they should be minimized.

16.  Half Power Beam Width:  The Half Power Beam Width (HPBW) corresponds to the angle between the two directions in the main lobe at which the field intensity becomes half of the maximum field intensity.  This is also known as 3 dB beam width.  A radiation lobe is often characterized by its 3 dB beam width.  If the antenna has a relatively narrow beam width, in both elevation and azimuth plane, then it is called a pencil beam antenna.  On the other hand, if the antenna has a beam width that is relatively narrow in one plane but much broader in the orthogonal plane then it is called a fan beam antenna.

17.  First Null Beam Width:  The First Null Beam Width (FNBW) corresponds to the angle between the directions of the nulls immediately following the major lobe. Radiation intensity:  The power radiated per unit area by an antenna in a given direction can be calculated from Poynting Vector “P” and can be expressed as Watts/sq mwhere we have assumed and and are orthogonal in a plane normal to radius vector.  Since the surface area per unit solid angle (or sterradian) at a distance “r” is square meter, the radiation intensity in the given direction can be expressed as Watts/unit solid angle.

18.  The total power radiated therefore can be expressed as Watts  Since there are total sterradians in the total solid angle, the average power radiated per unit solid angle is given by Watts/sterradian.  In general represents the radiation intensity of an isotropic radiator radiating the same total power. Directive gain and Directivity:  The directive gain of an antenna, in a given direction, is defined as the ratio of radiation intensity of the antenna in that direction to the average radiated power or radiation intensity of an isotropic radiator. Therefore The directive gain in dB scale is denoted by where  The maximum directive gain of an antenna is known as directivity.  The directivity of an isotropic radiator is unity.

19. Power gain: The power gain of an antenna, in a given direction, can be expressed as Where is the total input power and can be expressed as Where is the Ohmic loss in the antenna. From the above two equations we get  For suitably designed antennas the ohmic loss must be very small and hence the efficiency should be nearly 100%.  For 100% efficient antennas the power gain and directive gain are equal.

20. Effective Area and aperture efficiency: The effective area or effective aperture of an antenna can be defined as  The effective area is basically the ratio of power available at the antenna terminal to the power per unit area of the appropriately polarized incident wave.  If “A” be the physical area of the antenna aperture then the ratio of effective aperture and physical aperture of the antenna is called aperture efficiency. It can be expressed as

21. Antenna efficiency:  If the antenna is not matched with the source impedance then reflection will take place at the antenna input and reflection loss will occur.  As a result, the radiated power from an antenna will not be equal to the power available from the source.  The ratio of these two powers is called antenna efficiency. The efficiency of an antenna, in presence of reflection, is called reflection or mismatch efficiency and can be expressed as where is the reflection coefficient at the antenna input.  In addition to the reflection, power also lost at the imperfect antenna conductor and antenna dielectric.  These loss is very difficult to calculate but can be found be measuring the input and radiated power.

22. The combined conductor dielectric efficiency can be expressed as The combined conductor dielectric efficiency sometimes is also called as radiation efficiency. The overall efficiency of the antenna therefore can be expressed as depends on the external circuitry and not solely on the antenna properties. Antenna gain: It is defined as the product of radiation efficiency and directivity of the antenna and can be expressed as where “D” is the directivity of the antenna. Directivity depends only on the shape of the radiation pattern and not on the efficiency whereas gain includes the loss.

23. Effective noise temperature: The effective noise temperature of an antenna can be expressed as where is the brightness temperature and is the physical temperature of the antenna. Antenna polarization:  The polarization of an antenna is the same as the polarization of the field it radiates and therefore can be classified as: (1) linear (horizontal or vertical), (2) circular (LHCP or RHCP) and (3) elliptical.  For maximum response, the polarization of a receiving antenna must be same to the incident wave otherwise polarization loss will take place.  The polarization loss can be measured as the square of cosine of the angle between antenna polarization and the polarization of the incident wave.

24. Antenna impedance: The impedance of an antenna can be represented as  The reactive part corresponds to the electric and magnetic field close to the antenna that returns energy to the antenna during every cycle.  The resistive part of the impedance consists of two parts, namely, (1) Ohmic resistance and (2) radiation resistance.  The Ohmic resistance results due to heating of the antenna conductor by current flowing through it whereas radiation resistance results due to radiation of energy.  Since Ohmic resistance causes losses, it must be very low. In terms of loss resistance and radiation resistance, radiation efficiency can be expressed as

25. Bandwidth:  The bandwidth of an antenna is defined as the frequency range over which certain antenna characteristics satisfies a given standard.  If antenna impedance is of concern then impedance bandwidth is defined as the frequency range over which antenna impedance lies within a specified value.  It may be noted that since different antenna characteristics varies differently with frequency, there is no unique definition of antenna bandwidth. Effective Isotropic Radiated Power (EIRP):  The Effective Isotropic Radiated Power (EIRP) is the power needed by an isotropic antenna to provide same radiation intensity at a given direction as that of the directional antenna.

26. It can be expressed as Where is the power fed to antenna and is antenna gain. Space loss:  A transmitting antenna radiates power in all direction as per its power pattern.  However since the receiving antenna is positioned at a particular direction with respect to the transmitting antenna, only a part of the transmitted power is accepted by it while the rest of the radiated power is lost.  This loss can be represented by the space loss. The space loss can be expressed as where R is the distance and is the operating wavelength.

27. 18.4 Half-wave Dipole and Quarter-wave Monopole Antennas  Half wave dipole consists of two wires, bent at right angle and fed by a voltage source.  The total length of the antenna is approximately half wavelength and that is why it is called as half wave dipole.  In addition to dipole, monopole is also often used as an antenna element.  A monopole is basically a quarter wavelength wire mounted on a large ground plane.  If the ground plane is large then the radiation pattern of such antenna is similar to half wave dipole but its input impedance is half of a half wave dipole.

28.  The current distribution along a half wave dipole or monopole can be assumed sinusoidal and can be written as where is the current maximum. The expression for the vector potential at a point P due to the current element Idz can be written as

29. The total vector potential at P due to all the current can be obtained as, If the observation point is sufficiently large then in the denominator of above equation we can substitute whereas for numerator we can substitute Therefore we get For half wave dipole and we can write,

30. From the above two equations we can write If the current is entirely in the z direction then From the above two equations we can write The electric field for the radiation field therefore can be expressed as The time average value power therefore will be

31. If now monopole is considered then using above equation, the total power radiated through a hemispherical surface of radius r can be derived as Applying numerical methods it can be shown that From the above two equations we can write In above equation is the maximum or peak current. In terms of effective current the radiated power is Therefore the radiation resistance of a quarter wave monopole antenna is 36.5 Ohms.

32.  For the half wave dipole power would be radiated through a complete spherical surface.  Therefore for the same current, the power radiated by a half wave dipole will be twice to quarter wave monopole, and the radiation resistance for the half wave dipole becomes 73 Ohm. For the half wave dipole  Dipoles and monopoles also have several other configurations, like, folded dipole, folded monopole, inverted L antenna, inverted F – antenna etc. that are used at microwave frequencies.  The folded half wave dipole is formed by joining the ends of a half wave dipole whereas folded monopole antenna is formed by bending a monopole antenna.

33.  The inverted L antenna and inverted F – antenna are low profile antennas that are formed by bending quarter wavelength monopole element into an L – shape and F – shape respectively.

34. 18.5 Loop Antennas  A loop antenna is basically a loop of wire that can take several forms like circular, ellipse, rectangular, square, triangle etc.  For electrically small antennas the overall antenna length is usually less than about one-tenth of a wavelength whereas for electrically large loops the loop circumference is about a free space wavelength.  Depending on the electrical length, loop antennas are classified into, (1) electrically small and (2) electrically large.

35.  It can be shown that an electrically small loop circumference is equivalent to an infinitesimal magnetic dipole with its axis perpendicular to the plane of the loop.  For such loops the radiation resistance is usually smaller than the loss resistance and hence they are poor radiators.  Such antennas are generally used as receiving antennas in portable radios, pagers, as probes for field measurements and other applications where antenna efficiency in not as important as signal to noise ratio.  Since an electrically small loop is equivalent to an infinitesimal magnetic dipole, the field pattern of electrically small loop antennas is also similar to that of an infinitesimal dipole.  If the overall length of the dipole is increased the maximum of the pattern gradually shifts from the plane of the loop to the axis of the loop.

36. The radiated power of an electrically small loop antenna, carrying a current, at a distance “r”, can be expressed as  For near field and the second term within bracket of above equation is dominant. This implies that the power is mainly reactive.  In the far field, the second term within the bracket is negligible and the power becomes real. The radiation intensity can be derived as Above equation reveals that the maximum radiation intensity occurs at, and is given by

37. The directivity of the loop can be written as The maximum effective of an electrically small loop antenna can be expressed as The radiation resistance can be found as Where is the circumference of the loop and “S” is the loop area. If the loop consists of “N” turns then equation the expression for radiation resistance modifies as  Above equation reveals that the radiation resistance of the loop can be increased by increasing its perimeter and / or the number of turns.  Alternatively a ferrite core of very high permeability can be inserted within the loop circumference.

38.  The ferrite core will increase the magnetic field intensity and hence the radiation resistance. Such loops are also called ferrite loop. The radiation resistance of the ferrite loop can be calculated using the relation where is the radiation resistance of ferrite loop, is the radiation resistance of air core loop, is the effective permeability of ferrite core, is the permeability of free space and is the relative effective permeability of ferrite core. The radiation resistance of single turn ferrite loop can be written as If there are N-turns in the loop then above equation modifies as where D is the demagnetization factor

39.  The relative intrinsic permeability is very large and hence the relative effective permeability of the ferrite core is approximately inversely proportional to the demagnetization factor which, in turn, is a function of geometry of the ferrite core. For constant current and large loop approximation the expressions for radiated power, maximum radiation intensity, directivity, effective aperture and radiation resistance can be expressed as Most of the applications of loop antennas are in the HF, VHF and UHF bands.

40. 18.6 Helical Antennas  Helical antenna consists of a wire wound in a helical shape in presence of a ground plane.  Such antennas are generally fed with a coaxial probe with its center conductor connecting the helical structure and outer conductor connected to the ground plane.  In practice the ground plane may be of various shapes but most popular of them is circular.  The geometrical configuration of a helix consists of N turns of diameter D and inter turn spacing S.

41. The total length of the helix is The total length of wire required to construct the helix is where  Another important parameter, associated with a helix structure, is the pitch angle that defines the angle formed by a line tangent to the helix wire and a plane perpendicular to the helix axis. The pitch angle is defined by For helical antenna reduces to a loop antenna.  By controlling the electrical dimensions of different helix parameters the radiation characteristic of a helix can be varied.  In general the polarization of the radiated field of a helical antenna is elliptical.

42.  Circular and linear polarization can also be achieved at different frequency ranges.  The input impedance of the helical antenna is a function of pitch angle and wire size, especially near the feed point.  A helical antenna can operate in different modes but out of them normal (broadside) and axial (end fire) are the principal modes.  Further out of these two principal modes, axial mode is most commonly used because it can provide circular polarization over a wide bandwidth.  It is also more efficient. Normal mode:  A normal mode in helix is characterized by a radiation pattern with maximum field radiated in a plane perpendicular to the helix axis and minimum field radiated in a direction along the axis.

43.  Thus the radiation pattern is of figure “eight” shape rotated about its axis.  The normal mode of helix takes place when the helix dimension is small compared to the operating wavelength.  In normal mode, a helical antenna can be assumed as a combination of N small loops and N short dipoles connected together with the planes of the loops parallel to each other and perpendicular to the axis of vertical dipole and the axis of both the loop and dipole coinciding with the axis of the helix.

44.  In normal mode the current throughout the helix length can be assumed to be constant and its relative far field pattern can be assumed to be independent of the numbers of loops and short dipoles.  Thus the total radiated field of a helix can be described by the sum of the fields radiated by a small loop of diameter D and small dipole of length S.  In practice the dipole radiates a field in direction where the loop radiates field in direction. The ratio of and describes the axial ration and is given by The axial ratio ranges between “0” and “ ”.

45.  If, i.e.,, then we get horizontal polarization and the helix behaves as a loop antenna whereas if, i.e.,, then we get vertical polarization and the helix behaves as a vertical dipole. A special case happen when Therefore,  When the above condition is satisfied, the radiated field is circularly polarized in all direction except.  If AR has other values except “0”, “1” and “ ”, the radiated field is elliptically polarized with its major axis either horizontally polarized (for AR lying between 0 and 1) or vertically polarized (for AR lying between 1 and ). For normal mode operation the bandwidth is small and efficiency is poor.

46. Axial mode:  The axial mode is more practical for application and also can be generated very easily.  Such mode is characterized by one major lobe along the axis of the helix.  The diameter D and spacing S of the helical structure, in this mode, is a large fraction of the wavelength and the circumference lies in the range.  The range of pitch angle lies within and the diameter of the ground plane is kept at least.  The input impedance of a helical antenna operating in the axial mode is nearly resistive and lies within 100 Ohm to 200 Ohm.  However with proper design, input impedance, nearly 50 Ohm, can also be achieved.

47. The terminal impedance can be expressed as For a helical antenna, operating in axial mode The above relation assumes that,,, the turns are identical and the spacing between the turns are uniform.  Since an elliptical polarization can be represented as a sum of two orthogonal linear components in time phase quadrature, a helical antenna operating with an elliptical polarization can be used as a receiving antenna for a rotating linear polarized wave.  This enables the helical antenna to be used as space probes, in ballistic missiles and as a ground base antenna for receiving signals that have undergone Faraday rotation during its travel through ionosphere in space telemetry applications of satellites.

48. 18.7 Yagi–Uda Antennas  The Yagi uda antenna consists of a half wave dipole or folded dipole as a driven element and several parasitic elements in parallel with it.  The parasitic element in front of the dipole is called director whereas the parasitic elements at the back of the dipole are called reflectors.  The length of the dipole is kept usually in the range (resonant value), and the length of the directors is kept in the range.  The separation between the directors is kept in the range.  The length of the reflector is kept somewhat greater than that of the dipole and the separation between the dipole and the reflector is kept smaller than the spacing between the dipole and the nearest director.  The separation is found to be optimum at.

49. Approximate design formulas of the Yagi Uda antenna are  Above equations show that the length of the reflector is larger than the driven element whereas the length of the director is smaller than the driven element.  Since the length of each director is smaller than its corresponding resonant length, they have capacitive impedance and hence its current leads the induced emf.  The progressive phase shifts reinforce the field of the energized element toward the directors.  The impedance of the reflectors is inductive and the phase of the currents lags those of the induced emfs.

50.  In a multi-reflector Yagi – uda antenna the major role is played by the first element next to the driven elements.  Successive reflectors have a very little role in the performance of the antenna.  That is why most of the Yagi – uda antenna contains a single reflector.

51.  In contrast to the reflectors, considerable performance improvements of the Yagi Uda antenna can be achieved if more directors are used.  However there is also a limit of the number of directors that can be used.  If the number of directors is more than it, very little improvement is achieved because of the progressive reduction in magnitude of the induced currents on the more extreme director elements.  In general most Yagi Uda antenna has about 6 to 12 directors.

52.  Yagi Uda antenna is a very high gain antenna (about 5 to 9 per wavelength or of the order of 14.8 dB – 17.3 dB) and has low input impedance and relatively narrow bandwidth (about 2%).  Improvement in both can be achieved at the expense of others parameters like gain and magnitude of minor lobes etc. 18.8 Log-periodic Antennas  The log – periodic antenna consists of a number of dipoles of different electrical length and spacing, and is fed by a balanced two wire transmission line. Different geometrical parameters associated with log periodic antenna is related by where “d” is the diameter of the dipole.

53.  Since it is very difficult to obtain wires of different diameters and simultaneously to maintain tolerance of very small gap spacing, constant diameter wires are also used in log – periodic dipole array.  This approximation does not degrade the overall performance by a considerable amount.  The spacing factor,, of a log periodic antenna can be expressed as  The relation between apex angle and can be expressed as

54.  For typical log-periodic dipole arrays the half apex angle lies in the range and lies in the range.  The larger values of or smaller values of require a larger number of elements that are close together.  In practice the total length of the log periodic array can be divided into three different regions, namely, (1) loaded transmission line region, (2) active region and (3) reflection region.  In the loaded transmission line region the dipole elements are short compared with the resonant length and present relatively high capacitive impedance.  Therefore the small dipole current leads the voltage by approximately.

55.  In addition due to the phase reversal introduced by the transposition of the transmission line, adjacent elements are nearly out of phase.  In practice, each dipole current leads the preceding dipole currents approximately by an amount, where d is the element separation and is the phase shift constant along the line.  In contrast to transmission line region, the element lengths in active region approach the resonant length and present a resistive component.  The dipole current in this region is large and nearly in phase with the base voltage.  More precisely, the dipole current is slightly leading just below resonance and slightly lagging just above resonance.  As before the phase of current in a given element leads that in the preceding element by an angle.  In practice this phase difference may be approximated as radians.

56.  In the reflection region the dipole lengths are greater than the resonant length and hence present inductive impedance.  The dipole currents therefore lag the voltage which is quite small because all of the energy transmitted down the line has been radiated by the active region.  It can be shown that the transmission line characteristic impedance becomes reactive in this region and hence the incident energy is reflected back towards the source.

57.  The input impedance of a log periodic antenna repeat periodically with logarithm of the frequency and hence it is called as log – periodic.  In practice to achieve a truly log-periodic configuration infinite dipole elements will be required.  However this is not a practical condition and the structure is truncated at both ends.  This limits the infinite bandwidth of a log periodic antenna to a finite, but still large, bandwidth.  The cut-off frequencies or wavelength of the bandwidth can be determined by the electrical lengths of the longest and shortest dipole elements of the structure.  In general the lower cut off wavelength is approximately double the length of the longest dipole element whereas the high cut-off wavelength is approximately double the length of the shortest dipole element.

58.  The later is valid when the active region of the antenna is very narrow.  The active region of log-periodic dipole array is determined by the elements whose lengths are nearly or slightly smaller than the half of the operating wavelength.  Therefore the role of the active elements is passed from the shorter to the longer elements as the frequency decreases.  In practice the energy travelling toward the longer inactive elements from the shorter active elements decreases very rapidly.  Thus a negligible amount of energy is reflected from the truncated end.  The input impedance of a log periodic dipole array repeats periodically with the logarithm on the frequency.

59.  In practice the periodicity of the structure does not ensure broadband operation but if the impedance variation within one cycle can be kept within acceptable range for the corresponding bandwidth then broad band response can be achieved.  The total bandwidth of the antenna is determined by the number of repetitive cycles for the given truncated structure.  The relative frequency span of each cycle can be expressed as  In a log periodic dipole array the phase velocity of the wave travelling along the structure is about 0.6c where c is the free-space velocity.  This corresponds to about phase change for every free-space length of transmission line.

60.  The smaller phase velocity, mentioned above, results from the shunt capacitive loading of the line by the smaller elements in the active region.  It may be noted that since there are larger spacing between the longer elements the loading is almost constant per unit length.  Apart from the log periodic dipole array different other log periodic antenna structures also exist.  For such log periodic antenna we can write and Log periodic antennas are widely used for TV reception and for all round monitoring.

61. 18.9 Horn Antennas  Unlike an open ended transmission line that reflect all the incident power at the open termination, an open ended waveguide behaves as an antenna and radiates some power into space.  However due to high amounts of reflection only a small amount of incident energy can be radiated into space by this way.  In addition the diffraction around the open edges of the waveguide makes its radiation patter non-directional.  The above problems can be overcome if the open end of the waveguide is flared in the form of a horn.  In practice there are several types of horn antennas like E – plane horn, H – plane horn, pyramidal horn, conical horn, corrugated horn, Hog - horn etc.

63. For the horn antenna we can write, where is called flare angle. Further In practice the optimum value of and are and For an optimum designed horn must lie in the range to. The directivity, power gain of pyramidal horn can be expressed as and

64. The E – plane and H – plan half power beam Width can be expressed as The gain of a circular horn can be expressed as  The basic properties of a horn antenna depend on the flare angle,.  If the flare angle is small then it will result in a shallow horn and the wavefront leaving the antenna will be spherical instead of plane.  The radiation pattern also will not be directive.  In practice the flare angle should have an optimum value, depending on the flare length “L” measured in terms of wavelength.  Practically varies from when to when.  In the former case the beam width and gain is about and 40 whereas in the later case they are about and 120 respectively.

65.  Pyramidal and conical horn antennas can give pencil like beam with pronounced directivity in both horizontal and vertical plane.  Fan shaped beam can also be resulted if one dimension of the horn aperture is much smaller than the other. Therefore sectoral horns can be used for this purpose.  In general the wavefronts, leaving the horn, are not plane wave front.  A plane wavefront, however, can be obtained by using a Hog horn.  A Hog horn is basically a combination of a parabolic reflector and horn antenna.  In Hog horn antenna the receiving point does not move while the antenna is rotated about its axis.

66. Horn antennas are often used as a standard antenna for laboratory measurement and reflector antenna feed. 18.10 Reflector Antennas  Reflector antennas basically consists of a feed antenna like, horn, dipole etc. and a passive reflector that collimate or directs the beam in a specified direction.  Depending on the geometrical shape of the reflector it can be classified as (1) corner reflectors and (2) parabolic reflectors. Corner reflector antenna:  A corner reflector generally consists of two flat metallic plates kept at arbitrary angle from each other.

67.  A special case occurs when the angle between the plates becomes equal to.  Under such circumstance the reflector reflects the signal exactly in the same direction as it received.  Such reflectors are often used as a passive target for RADAR applications.  Again due to this reason it prompts the military ships and vehicles designers to keep minimum sharp corners to reduce their detection by enemy RADARs.  Half wavelength dipoles or an array of collinear dipoles, placed parallel to the vertex and at a distance “s” away, is used as a feed.  If the wavelength is large compared to tolerable physical dimensions, the surface of the corner reflector can be replaced by grid of wires.

68.  Such modification reduces wind resistance and also system weight.  To simulate the solid, the grid spacing “g” must be less than one tenth of the operating wavelength.  For a corner reflector the aperture dimension is kept between one and two wavelengths whereas the length of the sides (l) is kept twice the distance between the vertex and the feed.  For reflectors with smaller included angles the sides may be much longer.

69.  The feed to vertex distance (s) is generally kept at an optimum value between and because if this spacing becomes too small then the radiation resistance will decrease and will become comparable to the loss resistance of the system.  This will make the antenna inefficient.  On the other hand, if this spacing becomes very large then the system will produce undesirable multiple lobes and hence its directional characteristics will lost.  Increasing the dimension of the sides of the reflector, in general, increases the band width and radiation resistance and does not affect the beam width and directivity greatly.  In order to reduce radiation toward the back region from the ends, the height of the reflector (h) is usually taken to be about 1.2 to 1.5 times greater than the total length of the feed element.

70. Parabolic reflector antenna:  If a point source is placed at the focal point of a paraboloid reflector then all the waves coming out of the source will be in phase and parallel to each other along the axis of the parabola, after reflection from the paraboloid reflector.  Alternatively if a parallel beam or plane wave incident on the parabolic reflector along its axis then they will be concentrated at the focal point of the paraboloid after reflection from its surface.  Waves reflected towards or coming from other directions will cancel each other because of path differences.  These properties of parabola is used to design a highly directive transmitting or receiving antenna known as parabolic reflector antenna or dish antenna.

71.  In dish antenna the paraboloid structure is not the main radiator but it behaves only as a reflector.  Therefore all dish antenna needs at least an antenna, like horn or dipole, to serve as a feed to the reflector.  For a non-directional feed or primary antenna, a parabolic reflector produces a beam width given by in degree. where is the operating wavelength and “ ” is the mouth diameter of the reflector.  The beam width between the nulls will be

72.  The maximum power gain of an antenna using a parabolic reflector, with respect to a resonant half wave dipole, is given by If the focus and vertex of a parabola is apart, where “n” is an even number, then the direct radiation in axial direction will be in opposite phase with the reflected wave and will be cancelled.  Above expressions assumes an Omnidirectional feed antenna so that the whole reflector is illuminated uniformly.  If the intensity of illumination at the reflector falls of at the edges then above equation is modified as For effective operation the mouth diameter of a parabolic reflector should be at least. That is why parabolic reflectors are not so common in lower microwave and VHF region.

73.  It has been already mentioned that the dish antenna requires a feed or primary antenna as a source of radiation and the most preferred location of the feed is at the focal point of the reflector.  This should result in a narrow beam and hence a high overall directivity of the system.  However in many cases the radiation from the feed tends to spread out in all directions.  This radiation is added with the preferred reflected fields from the reflector and thus spoils the overall directivity.  In practice there are several techniques that can be used to avoid the above problem.  One of them is to use a spherical / parabolic sub-reflector that redirect all such radiation back to the main parabolic reflector.

74.  In addition to the above feeds, Cassegrian feed is also sometimes used in parabolic reflector antennas.  In such feed system the feed antenna generally lies behind the main reflector and a hyperboloid surface is used as a sub-reflector.  One of the foci of the sub-reflector coincides with the focus of the primary paraboloid reflector.

75.  The radiations from the feed antenna incite on the hyperboloid sub- reflector and suffer reflection by it.  Since the focus of the hyperboloid overlaps with the focus of the parabola, this reflected beam appears to the primary reflector as coming from a virtual source placed at its focus point.  The primary reflector then produces a plane wave, as desired. Cassegrian feed system is often used for low noise receivers where the losses in the transmission line are not tolerable.  Cassegrain feed system also has advantages like (1) reduction in spill over and minor lobe radiation, (2) ability to obtain an equivalent focal length that is much greater than physical length and (3) ability to place the feed in proper location so that the rays do not suffer any interference.  In addition beam broadening can also be achieved with Cassegrain feed by moving one of the reflecting surfaces.

76.  It may be noted that Cassegrain feed system suffers from a serious disadvantage – aperture blockage by the sub-reflector.  This can cause a major problem in the antenna operation, especially when small parabolic reflectors are used.  In practice the dimension of the hyperboloid is determined by the distance of the feed horn from it and mouth aperture dimensions of the feed horn.  Since the mouth aperture dimensions of the feed horn depends on the operating wavelength therefore the size of the hyperboloid is also a function of the operating wavelength.  To avoid this problem large paraboloid reflector can be used with the horn placed as close as possible to the sub-reflector.  However this may not be applicable in certain cases.

77.  In such cases vertically polarized wave source (feed) can be used along with a vertical bar hyperboloid sub-reflector.  If the reflected field by the sub-reflector can be changed to horizontal polarization by some mechanism at the primary reflector then the reflected wave by the primary reflector will pass freely through the vertical bars of the sub-reflector and the problem of aperture blockage will be removed.  Like the Cassegrian feed system, the feed horn in ordinary feed system also causes some aperture blocking.  But that is negligible if the horn is placed at the focus of the parabolic reflector. In addition to its classical forms, Cassegrain feed system also employs a variety of main reflector and sub-reflector surfaces like concave, convex and flat shapes.

78.  In addition to the Cassegrain form, Gregorian form is also employed in reflector antenna to feed the primary reflector.  In Gregorian forms, the focal point of the main dish is moved in the region between the primary parabolic reflector and an elliptical sub reflector.  In practical applications full paraboloid is often not used as primary reflector. Instead several other types of paraboloid can be used.  Each of them has their own advantage but at the cost of non-directional beam in one of the plane.  For example for the pill box reflector the beam is very narrow in H - plane but not in E - plane.

79.  The cylindrical paraboloid reflector produces a narrow beam in E – plane but wide beam in H – plane.  This may be disadvantage in some applications but also finds some good application like ship to ship communication / RADAR where azimuth directivity must be very good but the elevation directivity is immaterial.

80. Field reflected by the main antenna may be coupled to the feed antenna and thus may cause antenna mismatch. To get rid of it offset feed techniques are often used. An offset feed also solves the problem of aperture blockage.  Dish antenna systems also have some limitations as pointed below:  Theoretically the beam of the reflector system should be a pencil beam but in practice the main lobe is surrounded by several side lobes.  In practice the fabricated reflector is not true paraboloid rather its surface deviates from the required paraboloid shape. For satisfactory operation this deviation should not exceed.  In parabolic reflector antennas diffractions also occurs around the edges of the reflector. This is added with the diffraction caused at the horn supports..

81.  The primary size of the feed antenna influences the beam width.  Since the feed antenna is not a true point source it cannot be placed precisely at the focus of the parabolic reflector. This causes aberration, i.e., broadening of main beam and reinforcement of side lobes.  Since the primary antenna does not radiate evenly at the reflector, distortions occurs in the system. This is prominent if dipole is used as a primary antenna since it radiates more in one plane than the other. Such problem can be avoided if a circular horn is used as a feed but even then, because of the gradual tapering of the illumination towards the edges, complete surface of the parabolid is not illuminated uniformly.

82. The non-uniform illumination of the antenna aperture effectively results in a virtual area that is smaller than the actual area of the antenna. This effective area of the antenna is called capture area and is calculated from the power received and its comparison with the power density of the received signal. The capture area simulates an antenna surface that is uniformly illuminated and produces the same signal power at the primary antenna.  If “A” is the actual antenna area, is the capture area then where “k” is a constant and is equal to 0.65 for a half wave dipole feed and 0.9 for Mattress antenna.  Therefore the gain is

83.  For k = 0.65 above equation reduces to  For uniformly illuminated circular aperture k = 1 and we get  For uniform illumination and large circular aperture we can write,  The distance of the parabola from its focus is not uniform and this leads to amplitude tapering at the edges.  To make the power distribution at the reflector aperture uniform especial feed arrangement is required. 18.11 Microstrip Patch Antennas  Microstrip antennas are basically a very thin metallic patch placed above a ground plane.

84.  Such antennas are low weight, highly compact and efficient and are widely used at microwave frequencies for low power application.  In practice there are different types of patch antennas but out of them rectangular and circular patches are simpler and also common.  Rectangular patch antenna is a rectangular patch of length L and width W.  The thickness of the dielectric is kept below where is the guided wavelength in the dielectric. The radiation edges of a microstrip patch antenna can be assumed as radiating slots connected to each other by a microstrip transmission line.

85. The radiation conductance and susceptance of such slot can be expressed as and where If be the slot admittance then the input admittance of the antenna can be calculated as where At resonance

86.  From the above two equations we get  The resonance frequency can be calculated as,  In patch antenna “W” is not much critical but its value can be selected as  Microstrip patch antennas can be fed in different ways.  However the four most popular feeds are (1) Microstrip line feed, (2) coaxial probe feed, (3) aperture coupling and (4) proximity coupling.  Both the microstrip line feed and the coaxial probe feed have inherent asymmetries and hence generate higher order modes which, in turn, produce cross-polarized radiation.  To overcome some of these problems aperture coupling feed is used.

87.  In addition to rectangular patches, circular patched are also widely used as a radiating element.  To design a circular patch antenna the following equations can be used and where h is in cm and is in Hz.  The rectangular and circular patch antenna generally produce linearly polarized waves with conventional feed arrangement.  However, using modified feed arrangements, circular and elliptical polarizations can also be obtained.

88. 18.12 Lens Antennas  The geometrical theory of optics describes that the diverging rays, coming out of an optical source, placed at the focus of a convex lens, becomes parallel after passing though it and alternatively parallel rays, coming from a optical source placed at infinity, get collimated at the focal point of a convex lens after passing through it.  The above property of light wave is used in microwave to design lens antenna.  The lens antenna thus can be used as a plane wave source during transmitting mode and collimator in receiving mode.  The function of a lens antenna is based on the property that the electromagnetic waves travels relatively slow through a higher dielectric constant material.

89.  This implies that for a specified time, the ray passing through the center region of a dielectric lens will travel less distance than the rays travelling through the edges of the convex lens.  Therefore if a spherical wave approaches the lens, it will be straightened by the lens.  The lens antennas are generally made of polystyrene materials, though other materials can also be used for their fabrication.

90.  One of the major drawbacks of lens antenna is the excessive lens thickness, especially below 10 GHz.  To avoid this problem “zoning“ or “stepping” is often done.  This also reduces lens weight and total absorption of the field passing through it.  But it is associated with a reduced antenna bandwidth. Unstepped dielectric lens antennas can provide 12% bandwidth whereas zoned lens antennas provide only 5% bandwidth.

91.  It may be noted that lens antenna cannot directly radiate electromagnetic energy but instead can correct a curved waveform or collimate electromagnetic energy at a point.  So lens antennas are always associated with a primary antenna like horn.  They are often directly mounted at the face of the horn to correct the curved wave front at the face of horn.  Lens antenna can also be used in place of a parabolic reflector at higher frequencies. Such system does not face any aperture blockage due to the feed.  In general Lens antennas can be divided into two categories, namely, (1) Delay lenses and (2) Fast lenses.

92.  In delay lenses the electrical path length is increased by the lens medium whereas the reverse is true for fast lenses.  Dielectric lenses and H-plane metal plate lenses are the examples of the delay type lenses whereas E-plane metal plate lenses is the example of the fast lenses.  The dielectric lenses also may be divided into two groups: (1) Lenses constructed of non-metallic dielectrics and (2) Lenses constructed of metallic or artificial dielectrics. Non-metallic dielectric lens antenna: To achieve a plane wave at the plane “AB”, the electrical path length of the waves reaching this plane from the source “O” must be equal.

93. Therefore Now, Therefore, If “c” be the velocity of wave in air and “v” be the velocity of wave in lens medium then from the figure and above equation we can write, where n is the refractive index of the lens medium and. Now from the triangle From the above two equations we get

94.  Above equation defines the curvature of the Plano - convex lens.  In general this equation represents a hyperbola with the asymptotes of the hyperbola at an angle with respect to the axis.  can be determined by letting. For this assumption For a point source at “O”, the 3D lens surface should be a spherical hyperbola where as for an in-phase line source the lens surface should be a cylindrical hyperbola. For zoned lenses the thickness of dielectric can be expressed as  It may be noted that since there is an impedance mismatch at the lens surfaces, reflection results from them.  These reflections may directly approach the feed and thus may cause interference problem.

95.  In practice the reflections from the convex surface does not return to the feed, except from points at or near axis.  Thus it does not cause a major problem.  The main problem comes from the reflections at the flat ends which directly collimate at the feed. In general the reflection coefficient can be expresses as  Thus to reduce the effect of reflection “n” must be close to unity. The reflections can also be minimized by adding a quarter wavelength plate of refractive index at the flat lens surface.  This plate behaves as a quarter wave transformer between the lens and air and thus reduce reflection from the flat surface.

96.  An alternative way is to tilt the lens slightly, so that reflected wave collimate at some offset point. Artificial dielectric lens antennas:  In addition to the use of ordinary dielectrics as lens materials, metallic dielectrics or artificial dielectrics can also be used.  The artificial dielectric consists of discrete metal particles of macroscopic size.

97.  Such particles are generally small compared to the operating wavelength to avoid resonance effect and are placed less than a wavelength apart to reduce diffraction effect.  The basic structure and operation of an artificial dielectric lens antenna, made using metal spheres.  The EM wave from the feed antenna induces surface current on the metal spheres during passing through the lens.  The metal sphere thus resembles to the oscillating molecular dipoles of ordinary dielectrics.  It may be noted that disks, strips or rods can also be used in place of metal sphere for the fabrication of artificial dielectric.  In practice disks are often preferred over spheres due to the less weight.  If strips are used they may be continuous in a direction perpendicular to the electric field.

98.  The designing of an artificial dielectric lens is similar to ordinary dielectric lens but difficulty comes from the determination of the refractive index of the artificial dielectric material.  However this can be determined experimentally by using a slab of such artificial dielectric or can be calculated approximately.  To do this let us consider that an initially uncharged conducting sphere has been placed in an electric field.  As a result positive and negative charges will be induced in the spheres.  These induced charges may be represented by point charges +q and –q separated by a distance l.

99.  This simulates an electric dipole of dipole moment ql.  Since the potential due to the dipole is given by where polarization of the artificial dielectric is given by Where N is the number of spheres per cubic meter.  Now the displacement and effective dielectric constant of the artificial dielectric medium can be expressed as  Therefore Above equation reveals that if the number of spheres per unit volume and the dipole moment of one sphere per unit applied field are known then the effective dielectric constant can be determined.

100. To determine the dipole moment per unit applied electric field we will start with the equation Therefore in a uniform field the potential where is the angle between the radius vector and the field. Therefore the potential outside the sphere can be expressed as At the surface of the sphere the potential must be zero and hence we can write, where “a” is the radius of the sphere. Now where is the effective relative permittivity of the artificial dielectric.

101.  It can be shown that the effective relative permeability of an artificial dielectric of conducting sphere can be  Therefore the effective index of refraction of the artificial dielectric of conducting sphere can be expressed as  For disk or strip-type artificial dielectrics the relative permeability can be approximated as unity and hence the refractive index of artificial dielectrics made from such particles can be expressed as The artificial dielectric lens antennas are of lesser weight than ordinary dielectric lens antennas.

102. E – Plane metal plate lens antennas:  The dielectric lens antennas, discussed above relies on the fact that wave propagates slowly when passing through it.  The opposite is true for E – plane metal plate lens antennas.  The velocity of the wave propagating through the space between two parallel metal plates separated by a distance “b” and oriented parallel to E plane can be expressed as where we have assumed.  Therefore the refractive index of the medium between the parallel plates can be expressed as Above equation revels that n < 1 or c < v.

103.  The above property of the parallel metal plates can be used to design a lens antenna but this time, since the wave is propagating faster than its free space velocity; the geometry of the lens should be Plano – concave rather than Plano – convex.  The figure shows that to obtain a plane wave at the output we must have Where is the guided wavelength of the wave.

104.  Since the velocity of the wave inside the metal plate depends on the plate separation “b”, two types of E – plane metal lens can be designed: (1) lens designed with metal plates of varying thickness but same spacing and (2) lens designed with metal plates of same thickness but varying spacing.

105.  Since the refractive index n depends on the operating wavelength, E – plane metal plate lenses are of narrow bandwidth.  The bandwidth of such lenses can be expressed as where is the maximum tolerable path difference in free-space wavelengths and is the thickness of lens plate at edge of lens in free space wavelength.  In contrast to dielectric lenses, zoning in E – plane metal plate lenses decreases its frequency sensitivity.  Therefore zoning is desirable for E-plane metal plate lens, both to save weight and increase the bandwidth of such lens.  The bandwidth of a zoned E-plane metal plate lens approximately can be expressed as whereK = number of zones. The zone on the axis of the lens being counted as first zone.

106. 18.13 Slot Antennas  Slot milled on the broad or narrow wall of a waveguide behaves as an antenna at microwave frequencies.  Such antennas are called slot antenna.  A single slot, however, is seldom used as antenna.  Instead an array of slots is used to achieve the desired radiation pattern. Such antenna is called a slot array antenna. A properly designed slot array antenna can radiate 90% of the feed power and have a main lobe surrounded by very narrow side lobes.

107. 18.14 Array Antennas and Concept of Phased Arrays  To obtain higher gain, hence directivity, and to control different antenna parameters, antenna elements are often arranged in specific pattern and fed by signals with a predefined amplitude ratio and phase difference.  Such cluster of antenna elements are called array antenna.  There are different ways by which the individual elements of an array can be fed and in general they can be classified as (1) corporate feed and (2) branch feed.  Corporate feed connects all the elements and their phase shifters in parallel with the source whereas the branch feed method uses branching of feed lines into two or more several paths.

108.  For a uniform linear array the signals, fed to the antenna elements, have equal magnitude and uniform progressive phase shift.  Therefore for an N – element array total field can be expressed as where where is the progressive phase shift between the elements and is the phase shift due to the path difference

109. Above equation may be viewed as a geometric progression and can be re- written in the form  Above equation reveals that the maximum value of this expression is equal to “N” and occurs when becomes zero.  This corresponds to principal maximum of the array. Recalling the condition of principal maxima we can write

110.  Above equation reveals that by changing the progressive phase shift between the antenna elements the direction of the major lobe can be changed.  This is the principal of phased array antenna where beam steering is accomplished by changing the progressive phase shift between the antenna elements instead of mechanically rotating the whole antenna structure.  The movement of direction of the main lobe by changing the progressive phase shift is known as electronic scanning. If the inter element spacing, d, is equal to or greater than, there may be more than one principal maximum.

111.  For a broadside array the maximum radiation is directed perpendicular to the line of the array at whereas for an end-fire array the direction of maximum radiation is along the line of the array at.  Substituting these values of in above equation we get for a broadside array and for an end fire array.  The electric field becomes zero when and these values corresponds to the nulls of the pattern.  The first null occurs when k = 1 and we get  The condition for secondary maxima is  The first secondary maximum corresponds to m = 1 and we get  The amplitude of the first secondary lobe can be obtained as

112.  The amplitude ratio of the first secondary maximum to principal maximum is therefore.  Therefore the first side lobe is about 13.5 dB below the principal maximum.  The beam width of the principal lobe can be calculated as twice the angle between principal maximum and first null.  If for a broadside array the angle between principal maximum and first null can be assumed as then asand principal maxima occur at  If is small then above equation can be approximately as  The width of the principal lobe can be expressed as

113.  Similarly for the end-fire array we can write As and principal maxima occur at  If is small, then