New MODULE 3 PART 2 ELECTRONICS ENGINEERING.pptx

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1. Overview of Microstrip Antennas Also called “patch antennas” One of the most useful antennas at microwave frequencies ( f > 1 GHz). It usually consists of a metal “patch” on top of a grounded dielectric substrate. The patch may be in a variety of shapes, but rectangular and circular are the most common.

2. Overview of Microstrip Antennas 2 Common Shapes Rectangular Square Circular Elliptical Annular ring Triangular

3. Advantages of Microstrip Antennas Low profile (can even be “conformal,” i.e. flexible to conform to a surface). Easy to fabricate (use etching and photolithography). Easy to feed (coaxial cable, microstrip line, etc.). Easy to use in an array or incorporate with other microstrip circuit elements. Patterns are somewhat hemispherical, with a moderate directivity (about 6-8 dB is typical). Overview of Microstrip Antennas

4. Disadvantages of Microstrip Antennas Low bandwidth (but can be improved by a variety of techniques). Bandwidths of a few percent are typical. Bandwidth is roughly proportional to the substrate thickness and inversely proportional to the substrate permittivity. Efficiency may be lower than with other antennas. Efficiency is limited by conductor and dielectric losses*, and by surface-wave loss**. Only used at microwave frequencies and above (the substrate becomes too large at lower frequencies). Cannot handle extremely large amounts of power (dielectric breakdown). Overview of Microstrip Antennas

5. x y h L W Note: L is the resonant dimension. The width W is usually chosen to be larger than L (to get higher bandwidth). However, usually W < 2 L (to avoid problems with the (0,2) mode).  r Overview of Microstrip Antennas Rectangular patch W = 1.5 L is typical.

6. Circular Patch x y h a  r Overview of Microstrip Antennas The location of the feed determines the direction of current flow and hence the polarization of the radiated field.

7. Coaxial Feed A feed along the centerline is the most common (minimizes higher-order modes and cross- pol ). x y L W Feed at ( x , y ) Surface current x z Feeding Methods

8. Advantages: Simple Directly compatible with coaxial cables Easy to obtain input match by adjusting feed position Disadvantages: Significant probe (feed) radiation for thicker substrates Significant probe inductance for thicker substrates Not easily compatible with arrays Coaxial Feed x z Feeding Methods x y L W

9. Advantages: Simple Allows for planar feeding Easy to use with arrays Easy to obtain input match Disadvantages: Significant line radiation for thicker substrates For deep notches, patch current and radiation pattern may show distortion Microstrip line Feed Feeding Methods

10. Recent work has shown that the resonant input resistance varies as The coefficients A and B depend on the notch width S but (to a good approximation) not on the line width W f . Y. Hu, D. R. Jackson, J. T. Williams, and S. A. Long, “Characterization of the Input Impedance of the Inset-Fed Rectangular Microstrip Antenna,” IEEE Trans. Antennas and Propagation , Vol. 56, No. 10, pp. 3314-3318, Oct. 2008. L W W f S x Feeding Methods Microstrip line Feed

11. Advantages: Allows for planar feeding Less line radiation compared to microstrip feed Disadvantages: Requires multilayer fabrication Alignment is important for input match Patch Microstrip line Feeding Methods Proximity-coupled Feed (Electromagnetically-coupled Feed)

12. Advantages: Allows for planar feeding Feed-line radiation is isolated from patch radiation Higher bandwidth is possible since probe inductance is eliminated (allowing for a thick substrate), and also a double-resonance can be created Allows for use of different substrates to optimize antenna and feed-circuit performance Disadvantages: Requires multilayer fabrication Alignment is important for input match Patch Microstrip line Slot Feeding Methods Aperture-coupled Patch (ACP)

13. MICROSTRIP ANTENNA In high-performance aircraft, spacecraft, satellite, and missile applications, where size , weight , cost, performance, ease of installation, and aerodynamic profile are constraints , low-profile antennas may be required . To meet these requirements, microstrip antenna can be used. These antennas are low profile, conformable to planar and nonplanar surfaces , simple and inexpensive to manufacture using modern printed-circuit technology. In addition , by adding loads between the patch and the ground plane, such as pins and varactor diodes , adaptive elements with variable resonant frequency, impedance, polarization , and pattern can be designed.

14. Major operational disadvantages of microstrip antennas are their low efficiency , low power, high Q (sometimes in excess of 100), poor polarization purity , poor scan performance , spurious feed radiation and very narrow frequency bandwidth, which is typically only a fraction of a percent or at most a few percent . There are methods, such as increasing the height of the substrate, that can be used to extend the efficiency (to as large as 90 percent) and bandwidth (up to about 35 percent ). Basic Characteristics Microstrip antennas, as shown in Figure 14.1(a), consist of a very thin ( t ˂˂ λ , where λ is the free-space wavelength) metallic strip (patch) placed a small fraction of a wavelength ( h ˂˂ λ , usually . 003 λ ≤ h ≤ . 05 λ ) above a ground plane.

15. The microstrip patch is designed so its pattern maximum is normal to the patch ( broadside radiator ). This is accomplished by properly choosing the mode (field configuration) of excitation beneath the patch. End-fire radiation can also be accomplished by judicious mode selection. For a rectangular patch, the length L of the element is usually λ / 3 < L < λ / 2 . The strip (patch) and the ground plane are separated by a dielectric sheet (referred to as the substrate), as shown in Figure 14.1(a).

16. There are numerous substrates that can be used for the design of microstrip antennas , and their dielectric constants are usually in the range of 2 . 2 ≤ ε r ≤ 12 . The ones that are most desirable for good antenna performance are thick substrates whose dielectric constant is in the lower end of the range because they provide better efficiency, larger bandwidth , loosely bound fields for radiation into space, but at the expense of larger element size. Thin substrates with higher dielectric constants are desirable for microwave circuitry because they require tightly bound fields to minimize undesired radiation and coupling, and lead to smaller element sizes; however, because of their greater losses, they are less efficient and have relatively smaller bandwidths .

17. Since microstrip antennas are often integrated with other microwave circuitry, a compromise has to be reached between good antenna performance and circuit design. Often microstrip antennas are also referred to as patch antennas. The radiating elements and the feed lines are usually photoetched on the dielectric substrate. The radiating patch may be square, rectangular, thin strip (dipole), circular, elliptical, triangular , or any other configuration. These and others are illustrated in Figure 14.2 .

18. Square, rectangular, dipole (strip), and circular are the most common because of ease of analysis and fabrication, and their attractive radiation characteristics, especially low cross-polarization radiation. Microstrip dipoles are attractive because they inherently possess a large bandwidth and occupy less space, which makes them attractive for arrays. Linear and circular polarizations can be achieved with either single elements or arrays of microstrip antennas. Arrays of microstrip elements , with single or multiple feeds, may also be used to introduce scanning capabilities

19. Feeding Methods There are many configurations that can be used to feed microstrip antennas. The four most popular are the microstrip line, coaxial probe, aperture coupling, and proximity coupling

20. The microstrip feed line is also a conducting strip, usually of much smaller width compared to the patch . The microstrip -line feed is easy to fabricate, simple to match by controlling the inset position and rather simple to model. However as the substrate thickness increases , surface waves and spurious feed radiation increase , which for practical designs limit the bandwidth (typically 2–5 %). Coaxial-line feeds , where the inner conductor of the coax is attached to the radiation patch while the outer conductor is connected to the ground plane, are also widely used. The coaxial probe feed is also easy to fabricate and match, and it has low spurious radiation . However , it also has narrow bandwidth and it is more difficult to model , especially for thick substrates (h > . 02 λ ) .

21. Both the microstrip feed line and the probe possess inherent asymmetries which generate higher order modes which produce cross-polarized radiation. To overcome some of these problems, non contacting aperture-coupling feeds, as shown in Figures 14.3( c,d ), have been introduced. The aperture coupling of Figure 14.3(c) is the most difficult of all four to fabricate and it also has narrow bandwidth. However , it is somewhat easier to model and has moderate spurious radiation. The aperture coupling consists of two substrates separated by a ground plane.

22. On the bottom side of the lower substrate there is a microstrip feed line whose energy is coupled to the patch through a slot on the ground plane separating the two substrates. This arrangement allows independent optimization of the feed mechanism and the radiating element. Typically a high dielectric material is used for the bottom substrate, and thick low dielectric constant material for the top substrate . The ground plane between the substrates also isolates the feed from the radiating element and minimizes interference of spurious radiation for pattern formation and polarization purity . For this design, the substrate electrical parameters, feed line width , and slot size and position can be used to optimize the design.

23. Methods of Analysis There are many methods of analysis for microstrip antennas. The most popular model is the transmission-line model . The transmission-line model is the easiest of all, it gives good physical insight, but is less accurate and it is more difficult to model coupling . RECTANGULAR PATCH : Transmission-Line Model A rectangular microstrip antenna can be represented as an array of two radiating narrow apertures (slots), each of width W and height h , separated by a distance L . Basically the transmission-line model represents the microstrip antenna by two slots, separated by a low-impedance Zc transmission line of length L .

24. Fringing Effects Because the dimensions of the patch are finite along the length and width, the fields at the edges of the patch undergo fringing. This is illustrated along the length in Figures 14.1( a,b ) for the two radiating slots of the microstrip antenna. The same applies along the width. The amount of fringing is a function of the dimensions of the patch and the height of the substrate. For the principal E -plane ( xy -plane) fringing is a function of the ratio of the length of the patch L to the height h of the substrate ( L/h ) and the dielectric constant I r of the substrate.

25. Since for microstrip antennas L/h ˃˃ 1, fringing s reduced; however, it must be taken into account because it influences the resonant frequency of the antenna. The same applies for the width. For a microstrip line shown in Figure 14.5(a), typical electric field lines are shown in Figure 14.5(b). This is a nonhomogeneous line of two dielectrics; typically the substrate and air. As can be seen, most of the electric field lines reside in the substrate and parts of some lines exist in air. As W/h ˃˃ 1 and ε r ˃˃ 1 , the electric field lines concentrate mostly in the substrate.

26. Fringing in this case makes the microstrip line look wider electrically compared to its physical dimensions. Since some of the waves travel in the substrate and some in air, an effective dielectric constant ε reff is introduced to account for fringing and the wave propagation in the line . To introduce the effective dielectric constant, let us assume that the center conductor of the microstrip line with its original dimensions and height above the ground plane is embedded into one dielectric, as shown in Figure 14.5(c). The effective dielectric constant is defined as the dielectric constant of the uniform dielectric material so that the line of Figure 14.5(c) has identical electrical characteristics, particularly propagation constant , as the actual line of Figure 14.5(a ) .

27. Effective Length Because of the fringing effects, electrically the patch of the microstrip antenna looks greater than its physical dimensions. For the principal E -plane ( xy -plane), this is demonstrated in Figure 14.7 where the dimensions of the patch along its length have been extended on each end by a distance Δ L , which is a function of the effective dielectric constant ε reff and the width-to-height ratio ( W/h ). Since the length of the patch has been extended by 3L oneach side, the effective length of the patch is now ( L = λ/ 2 for dominant TM 010 mode with no fringing ) L eff = L + 2 Δ L

28. Because of the arbitrary current or source distribution of the antenna inside the sphere, its radiated field outside the sphere is expressed as a complete set of orthogonal spherical vector waves or modes . For vertically polarized omnidirectional antennas , only TMm circularly symmetric (no azimuthal variations) modes are required . Each mode is used to represent a spherical wave which propagates in the outward radial direction. This approach was introduced first by Chu, and it was followed by Harrington. Earlier papers on the fundamental limitations and performance of small antennas were published by Wheeler. He derived the limits of a small dipole and a small loop (used as a magnetic dipole) from the limitations of a capacitor and an inductor, respectively. The capacitor and inductor were chosen to occupy , respectively, volumes equal to those of the dipole and the loop.

29. Because the spherical wave modes outside the sphere are orthogonal, the total energy ( electric or magnetic) outside the sphere and the complex power transmitted across the closed spherical surface are equal, respectively, to the sum of the energies and complex powers associated with each corresponding spherical mode. Therefore there is no coupling, in energy or power, between any two modes outside the sphere. As a result, the space outside the sphere can be replaced by a number of independent equivalent circuits as shown in Figure 11.16(b). The number of equivalent circuits is equal to the number of spherical wave modes outside the sphere, plus one.

30. The terminals of each equivalent circuit are connected to a box which represents the inside of the sphere, and from inside the box a pair of terminals are drawn to represent then input terminals. Using this procedure, the antenna space problem has been reduced to one of equivalent circuits . The radiated power of the antenna is calculated from the propagating modes while all modes contribute to the reactive power. When the sphere (which encloses the antenna element) becomes very small, there exist no propagating modes. Therefore the Q of the system becomes very large since all modes are evanescent (below cutoff ) and contribute very little power. However , unlike closed waveguides, each evanescent mode here has a real part ( eventhough it is very small).

31. For a lossless antenna (radiation efficiency e cd = 100%), the equivalent circuit of each spherical mode is a single network section with a series C and a shunt L . The total circuit is a ladder network of L − C sections (one for each mode) with a final shunt resistive load, as shown in Figure 11.16(c). The resistive load is used to represent the normalized antenna radiation resistance. From this circuit structure, the input impedance is found. The Q of each mode is formed by the ratio of its stored to its radiated energy. When several modes are supported , the Q is formed from the contributions of all the modes.

32. It has been shown that the higher order modes within a sphere of radius r become evanescent when kr < 1. Therefore the Q of the system, for the lowest order TM mode , reduces to When two modes are excited, one TE and the other TM, the values of Q are halved. Equation above, which relates the lowest achievable Q to the largest linear dimension of an electrically small antenna, is independent of the geometrical configuration of the antenna within the sphere of radius r .

33. The shape of the radiating element within the bounds of the sphere only determines whether TE, TM, or TE and TM modes are excited. Therefore, the above equation represents the fundamental limit on the electrical size of an antenna . In practice, this limit is only approached but is never exceeded or even equalled. The losses of an antenna can be taken into account by including a loss resistance in series with the radiation resistance , as shown by the equivalent circuits of antenna. This influences the Q of the system and the antenna radiation efficiency as given by

34. For antennas with equivalent circuits of fixed values, the fractional bandwidth is related to the Q of the system by where f = center frequency Δ f = bandwidth This relationship is valid for Q ˃˃ 1 since the equivalent resonant circuit with fixed values is a good approximation for an antenna.

35. EFFICIENCY OF ELECTRICALLY SHORT ANTENNA There are fundamental limits as to how small the antenna elements can be made. The basic limitations are imposed by the free-space wavelength to which the antenna element must couple to, which has not been or is expected to be miniaturized. The limits on electrically small antennas are derived by assuming that the entire antenna structure (with a largest linear dimension of 2 r ), and its transmission line and oscillator are all enclosed within a sphere of radius r as shown in Figure 11.16(a).

36. It can be concluded that the bandwidth of an antenna (which can be closed within a sphere of radius r) can be improved only if the antenna utilizes efficiently , with its geometrical configuration, the available volume within the sphere . The dipole , being a one-dimensional structure, is a poor utilizer of the available volume within the sphere . However a Goubau antenna, being a clover leaf dipole with coupling loops over a ground plane (or a double cover leaf dipole without a ground plane), is a more effective design for utilizing the available three-dimensional space within the sphere. A design, such as that of a spiral, that utilizes the space even more efficiently than the Goubau antenna would possess a lower Q and a higher fractional bandwidth.

37. The definition of a small antenna is one that can fit inside a sphere of diameter λ /2 π . For a small antenna the Q is proportional to the reciprocal of the volume of a sphere that encloses it. In practice this means that there is a limit to the bandwidth of data that can be sent to and received from small antennas . As antennas are made smaller, the bandwidth shrinks and radiation resistance becomes smaller compared to loss resistances that may be present, thus reducing the radiation efficiency. For users this decreases the bitrate, limits range, and shortens battery life .

38. FRACTAL ANTENNAS One of the main objectives in wireless communication systems is the design of wideband , or even multiband, low profile, small antennas . In order to meet the specification that the antenna be small, some severe limitations are placed on the design , which must meet the fundamental limits of electrically small antennas. The bandwidth of an antenna enclosed in a sphere of radius r can be improved only if the antenna utilizes efficiently, with its geometrical configuration, the available volume within the sphere . Another antenna that can meet the requirements of utilizing the available space within a sphere of radius r more efficiently is a fractal antenna.

39. Fractal antennas are based on the concept of a fractal, which is a recursively generated geometry that has fractional dimensions, as pioneered and advanced by Benoit B. Mandelbrot. He was able to show that many fractals exist in nature and can be used to accurately model certain phenomena . Fractal concepts have been applied to many branches of science and engineering , including fractal electrodynamics for radiation, propagation, and scattering. These fractal concepts have been extended to antenna theory and design, and there have been many studies and implementations of different fractal antenna elements and arrays, and many others.

40. Fractals can be classified in two categories: deterministic and random . Deterministic , such as the von Koch snowflake and the Sierpinski gaskets, are those that are generated of several scaled-down and rotated copies of themselves. Such fractals can be generated using computer graphics requiring particular mapping that is repeated over and over using a recursive algorithm. Random fractals also contain elements of randomness that allow simulation of natural phenomena . Fractal geometries can best be described and generated using an iterative process that leads to self-similar and self-affinity structures

41. The process can best be illustrated graphically as shown for the two different geometries in Figure 11.18( a,b ). Figure 11.18(a) exhibits what is referred to as the Minkowski island fractal, while Figure 11.18(b) illustrates the Koch fractal loop. The geometry generating process of a fractal begins with a basic geometry referred to as the initiator , which in Figure 11.18(a) is a Euclidean square while that of Figure 11.18(b) is a Euclidean triangle . In Figure 11.18(a), each of the four straight sides of the square is replaced with a generator that is shown at the bottom of the figure. The first three generated iterations are displayed. In Figure 11.18(b), the middle third of each side of the triangle is replaced with its own generator. The first four generated iterations are displayed .

42. The trend of the fractal antenna geometry can be deduced by observing several iterations of the process. The final fractal geometry is a curve with an infinitely intricate underlying structure such that , no matter how closely the structure is viewed, the fundamental building blocks cannot be differentiated because they are scaled versions of the initiator . Another classic fractal is the Sierpinski gasket. This fractal can be generated with the Pascal triangle using the following procedure. Consider an equilateral triangular grid of nodes, as shown in Figure 11.20(a ). Starting from the top, each row is labeled n = 1 , 2 , 3 , . . . .., and each row contains n nodes.

43. A number is assigned to each node for identification purposes. If all the nodes whose number is divisible by a prime number p(p = 2 , 3 , 5 , . . . .) are deleted, the result is a self-similar fractal referred to as the Sierpinski gasket of Mod-p . For example, if the nodes in Figure 11.20(a) whose numbers are divisible by 2 are deleted, the result is a Sierpinski gasket of Mod-2 . If the nodes whose number is divisible by 3 are deleted , a Sierpinski gasket of Mod-3 is obtained, as shown in Figure 11.20(b). Sierpinski gaskets can be used as elements in monopoles and dipoles having geometries whose peripheries are similar to the cross section of conical monopoles and biconical dipoles. The Sierpinski gaskets exhibit favorable radiation characteristics in terms of resonance , impedance , directivity, pattern, and so on, just like the other fractals.

44. Fractal antennas exhibit space-filling properties that can be used to miniaturize classic antenna elements, such as dipoles and loops, and overcome some of the limitations of small antennas. The line that is used to represent the fractal can meander in such a way as to effectively fill the available space, leading to curves that are electrically long but compacted into a small physical space , which leads to smaller Qs/larger bandwidths . It also results in antenna elements that, although are compacted in small space, can resonate and exhibit input resistances that are much greater than the classic geometries of dipoles, loops, etc . Hence instead of using an ordinary loop or a dipole, we can use a Koch loop or a Koch dipole as shown below.

45. Loop Antennas Another simple, inexpensive, and very versatile antenna type is the loop antenna. Loop antennas take many different forms such as a rectangle, square, triangle, ellipse, circle , and many other configurations. Because of the simplicity in analysis and construction , the circular loop is the most popular and has received the widest attention. It will be shown that a small loop (circular or square) is equivalent to an infinitesimal magnetic dipole whose axis is perpendicular to the plane of the loop. That is, the fields radiated by an electrically small circular or square loop are of the same mathematical form as those radiated by an infinitesimal magnetic dipole.

46. Loop antennas are usually classified into two categories, electrically small and electrically large . Electrically small antennas are those whose overall length (circumference ) is usually less than about one-tenth of a wavelength (C < λ/ 10 ) . However , electrically large loops are those whose circumference is about a free-space wavelength ( C ∼ λ) . Most of the applications of loop antennas are in the HF (3–30 MHz), VHF ( 30–300 MHz), and UHF (300–3,000 MHz) bands. When used as field probes, they find applications even in the microwave frequency range.

47. Loop antennas with electrically small circumferences or perimeters have small radiation resistances that are usually smaller than their loss resistances. Thus they are very poor radiators, and they are seldom employed for transmission in radio communication. When they are used in any such application, it is usually in the receiving mode, such as in portable radios and pagers, where antenna efficiency is not as important as the signal to noise ratio. They are also used as probes for field measurements and as directional antennas for radio wave navigation. The field pattern of electrically small antennas of any shape (circular, elliptical, rectangular, square, etc.) is similar to that of an infinitesimal dipole with a null perpendicular to the plane of the loop and with its maximum along the plane of the loop.

48. As the overall length of the loop increases and its circumference approaches one free-space wavelength, the maximum of the pattern shifts from the plane of the loop to the axis of the loop which is perpendicular to its plane . The radiation resistance of the loop can be increased, and made comparable to the characteristic impedance of practical transmission lines, by increasing (electrically) its perimeter and/or the number of turns. Another way to increase the radiation resistance of the loop is to insert, within its circumference or perimeter, a ferrite core of very high permeability which will raise the magnetic field intensity and hence the radiation resistance . This forms the so-called ferrite loop .

49. Electrically large loops are used primarily in directional arrays, such as in helical antennas, Yagi- Uda arrays and so on. For these and other similar applications, the maximum radiation is directed toward the axis of the loop forming an end-fire antenna. To achieve such directional pattern characteristics, the circumference (perimeter) of the loop should be about one free-space wavelength. The proper phasing between turns enhances the overall directional properties.

50. Loop antennas can be used as single elements, as shown in Figure 5.1(a), whose plane of its area is perpendicular to the ground. The relative orientation of the loop can be in other directions, including its plane being parallel relative to the ground. Thus , its mounting orientation will determine its radiation characteristics relative to the ground. Loops are also used in arrays of various forms. The particular array configuration will determine its overall pattern and radiation characteristics. One form of arraying is shown in Figure 5.1(b), where eight loops of Figure 5.1(a) are placed to form a linear array of eight vertical elements.

51. Radiated Fields

52. A comparison of above equations with those of the infinitesimal magnetic dipole indicates that they have similar forms. In fact, the electric and magnetic field components of an infinitesimal magnetic dipole of length l and constant “magnetic” spatial current I m are given by

53. These can be obtained, using duality, from the fields of an infinitesimal electric dipole. They indicate that a magnetic dipole of magnetic moment I m l is equivalent to a small electric loop of radius a and constant electric current I provided that where S = πa 2 ( area of the loop). Thus , for analysis purposes, the small electric loop can be replaced by a small linear magnetic dipole of constant current. The geometrical equivalence is illustrated in Figure 5.2(a) where the magnetic dipole is directed along the z -axis which is also perpendicular to the plane of the loop.

54. SLOT ANTENNA BABINET’S PRINCIPLE Babinet’s principle which in optics states that when the field behind a screen with an opening is added to the field of a complementary structure , the sum is equal to the field when there is no screen . Babinet’s principle in optics does not consider polarization , which is so vital in antenna theory ; an extension of Babinet’s principle, which includes polarization and the more practical conducting screens, was introduced by Booker. Referring to Figure 12.22(a), L et us assume that an electric source J radiates into an unbounded medium of intrinsic impedance η = √ (μ/ ε ) and produces at point P the fields E , H .

55. The same fields can be obtained by combining the fields when the electric source radiates in a medium with intrinsic impedance η = √ (μ/ ε ) in the presence of 1. an infinite, planar, very thin, perfect electric conductor with an opening Sa , which produces at P the fields E e, H e [Figure 12.22(b)] 2. a flat, very thin, perfect magnetic conductor Sa , which produces at P the fields E m , H m [Figure 12.22(c )]. That is, E = E e + E m H = H e + H m The field produced by the source in Figure 12.22(a) can also be obtained by combining the fields of

56. 1. an electric source J radiating in a medium with intrinsic impedance η= √ ( μ/ ε ) in the presence of an infinite, planar, very thin, perfect electric conductor S a , which produces at P the fields E e , H e [ Figure 12.22(b)] 2. a magnetic source M radiating in a medium with intrinsic impedance η d = √ ( ε /μ) in the presence of a flat, very thin, perfect electric conductor S a , which produces at P the fields E d , H d [Figure 12.22(d )] That is , E = E e + H d H = H e − E d

57. The dual of Figure 12.22(d) is more easily realized in practice than that of Figure 12.22(c). To obtain Figure 12.22(d) from Figure 12.22(c), J is replaced by M , E m by H d , H m by − E d, ε by μ , and μ by ε . This is a form of duality often used in electromagnetics (see Section 3.7, Table 3.2). The electric screen with the opening in Figure 12.22(b) and the electric conductor of Figure 12.22(d) are also dual. They are usually referred to as complementary structures , because when combined they form a single solid screen with no overlaps.

58. Using Booker’s extension it can be shown that if a screen and its complement are immersed in a medium with an intrinsic impedance η and have terminal impedances of Z s and Z c , respectively , the impedances are related by To obtain the impedance Z c of the complement (dipole) in a practical arrangement , a gap must be introduced to represent the feed points. In addition, the far-zone fields radiated by the opening on the screen ( E θs , E φs , H θs , H φs ) are related to the far-zone fields of the complement ( E θc , E φc , H θc , H φc ) by

59. Infinite, flat, very thin conductors are not realizable in practice but can be closely approximated . If a slot is cut into a plane conductor that is large compared to the wavelength and the dimensions of the slot, the behavior predicted by Babinet’s principle can be realized to a high degree. The impedance properties of the slot may not be affected as much by the finite dimensions of the plane as would be its pattern.

60. The slot of Figure 12.23(a) will also radiate on both sides of the screen. Unidirectional radiation can be obtained by placing a backing (box or cavity) behind the slot, forming a so-called cavity-backed slot whose radiation properties (impedance and pattern) are determined by the dimensions of the cavity.

61. The slot of Figure 12.24(a) can be made to resonate by choosing the dimensions of its complement (dipole) so that it is also resonant. The pattern of the slot is identical in shape to that of the dipole except that the E - and H -fields are interchanged .

62. When a vertical slot is mounted on a vertical screen, as shown in Figure 12.25(a), its electric field is horizontally polarized while that of the dipole is vertically polarized Changing the angular orientation of the slot or screen will change the polarization .

63. The slot antenna, as a cavity-backed design, has been utilized in a variety of law enforcement applications. Its main advantage is that it can be fabricated and concealed Within metallic objects, and with a small transmitter it can provide covert communications . There are various methods of feeding a slot antenna. For proper operation , the cavity depth must be equal to odd multiples of λg / 4, where λg is the guide wavelength.