CHAPTER 3 THE INVERTED-L ANTENNA AND VARIATIONS
CHAPTER 3THE INVERTED-L ANTENNA AND VARIATIONS3.1 IntroductionAs the demand for portable and convenient wireless devices becomes stronger, theneed for device miniaturization increases. [1] The size of a wireless device is often limitedby the dimensions of the battery and the antenna. [1] Generally, the quarter-wavemonopole antenna is used on portable wireless devices due to its characteristically highradiation efficiency and wide bandwidth. [2] However, the monopole antenna is potentiallyobtrusive. It is desirable that the antenna in a wireless device be as small andinconspicuous as possible while still meeting performance demands. Therefore, a needexists for electrically small, low-profile antenna designs with broad impedance bandwidth,an input impedance that is easily matched to a feed line, omnidirectional radiation, andhigh radiation efficiency. [3]One low-profile antenna design that is used in wireless applications is the InvertedL antenna (ILA). The ILA is a short monopole with the addition of a horizontal segmentof wire at the top. The ILA and a few of its variations are illustrated in Figure 3.1.42
#1#2#3#4Inverted - L Inverted - FPlanarDualAntenna AntennaInverted - F Inverted - FAntennaAntennaFigure 3.1. The Inverted-L Antenna (ILA) and variationsThis chapter presents design issues for the ILA (#1 in Figure 3.1) and itsvariations. In Sections 3.2 and 3.3, closed form solutions for the radiation patterns andinput impedance of the ILA are derived using an assumed current distribution on theantenna. Section 3.4 covers design issues for variations of the ILA, including the InvertedF Antenna (IFA) (#2 in Figure 3.1), the Planar Inverted-F Antenna (PIFA) (#3 in Figure3.1), and the Dual Inverted-F Antenna (DIFA) (#4 in Figure 3.1).3.2 The Far-Field Radiation Pattern of the Inverted-L AntennaThe Inverted-L Antenna (ILA) in Figure 3.2 is an electrically small end-fedmonopole with a section of horizontal wire added at the top as a capacitive load.43
LzxhIoFigure 3.2. The geometry of the Inverted-L Antenna (ILA)The ground plane image of the antenna, shown in Figure 3.2 with dotted lines, is treatedas part of the antenna structure to simplify calculations. [4] The calculations are furthersimplified by rotating the Cartesian coordinate system as shown in Figure 3.3.zArm 2LJ2(z)Arm 1J1(z)Arm 3J3(z)yhxFigure 3.3. The ILA and rotated Cartesian coordinate systemIn Figure 3.3, the vertical element of the ILA is located on the x-axis, and the tophorizontal segment and its image are z-directed with opposing currents. The resonantcurrent distribution on each of the arms is assumed to be sinusoidal. The distributions are[4]44
I1 ( z) I z sin[ k ( L z')] cos( kh) az(3.1)I 2 ( z) I z sin[ k ( L z')] cos( kh) (-az)(3.2)I 3 ( z) I z cos( kx') sin( kL) ax(3.3)Using the current distributions in (3.1) through (3.3), the fields due to each arm aredetermined by calculating magnetic vector potentials, A, and integrating with respect tothe radiation vector. [4] Arm 1 is z-directed with positive running current. The far-fieldmagnetic vector potential on arm 1 isAz e jkr4πrwhere r L0I 1 ( z)e jkz 'cos(θ ) dz' e jkr4πr L0I z sin[ k ( L z')] cos( kh)e jkz 'cos(θ ) dz'(3.4)x 2 y 2 z 2 . Using (3.4), the E-field for an offset z-directed line source iswritten as [4]Ε jωµ sin θ sin( kh sin θ cos φ ) Az aθ(3.5)Substituting (3.4) into (3.5) givesΕ jωµLe jkrsin θ sin( kh sin θ cos φ ) I z cos( kh) sin[ k ( L z ' )]e jkz 'cos(θ ) dz '04πr(3.6)The integration in (3.6) is solved usingcx sin(a bx )e dx ecx[c sin(a bx ) b cos(a bx )]b2 c 2(3.7)using (3.7) in (3.6) leads to [4]45
L e jkz 'cosθjωµ e jkrsin θ ( SIN ) I z cos( kh) 2Eθ ( jk cosθ sin( kL kz') k cos( kL kz' )) 224π r k k cos θ 0where SIN sin(kh sin(θ) cos(φ)). When evaluated and simplified, this expression yieldsthe θ-component of the E-field produced by the currents on arm 1 of the ILA. The resultis [4]Eθ ωµ e jkrSINcos( kh)Ize jkL cosθ j{cos θ sin( kL) cos( kL)}4πksin(θ )r[](3.8)Since the element is z-directed, Eφ 0.By symmetry, the fields produced by the currents on arm 2 of the ILA are identicalto those produced by arm 1. The fields produced by the currents on arm 3 of the structureare summarized without derivation as [4]Eθ Eφ jωµ e jkrIxsin( kL) cos θ cos φ f (θ , φ , h)4πkrjωµ e jkrIxsin( kL) sin φ f (θ , φ , h)4πkr(3.9)(3.10)wheref (θ, φ, h) sin( kh) COS sin θ cos φ cos( kh) SIN1 sin 2 θ cos2 φin which COS cos(kh sin(θ) cos(φ)) and SIN was defined earlier.The expressions for fields from the various arms of the ILA can be simplified if it isassumed that Ix Iz Io, L λ/4, and h λ. Then the fields from arms 1 and 2 of theILA are re-written asEθ ωµe jkrπ π Iokh cos(φ ) cos cos θ j sin( cosθ ) cos θ 4πkr2 2(3.11)and Eφ 0. The fields due to the currents on arm 3 of the ILA are46
Eθ Eφ jωµ e jkrIokh cos θ cos φ4πkrjωµ e jkrIokh sin φ4πkr(3.12)(3.13)The fields expressed in (3.11) through (3.13) define the radiation fields of the ILAin the three principal planes, x-y, y-z, and x-z. In the x-y plane, θ π/2, and the E-fieldsareEθ 60 I oe jkrkh cos(φ ) from arms 1 and 2,r(3.14)ande jkrEφ j 60 I okh sin φ from arm 3.r(3.15)In the x-z plane, φ 0, and the E-fields areEθ ωµ e jkR ππ Iokh cos cos θ j sin( cos θ ) cos θ from arms 1 and 2, (3.16) 4πk2R 2andEθ jωµ e jkRIkh cos θ from arm 3.4πk o R(3.17)In the y-z plane, there is no field produced by arms 1 and 2. The field due to arm 3 isEφ jωµ e jkRIkh sin φ4πk o R(3.18)Thus, the normalized pattern factors in the x-y plane are, for Eθ,F( φ ) cos( φ ) from arms 1 and 2(3.19)F( φ ) sin (φ) from arm 3(3.20)and, for Eφ,and in the x-z plane47
π πF (θ ) cos cos θ j sin( cos θ ) cos θ from arms 1 and 2 22 (3.21)andF(θ ) cos(θ ) from arm 3.(3.22)and in the y-z planeF(θ ) 1(3.23)The radiation patterns of the ILA are plotted in Figure 3.4 using the normalizedpattern factors given by (3.19) through (3.23).Figure 3.4. The modeled radiation patterns of the Inverted-L Antenna, using the antenna system inFigure 3.3. [4]The coordinate system used in Figure 3.4 was defined in Figure 3.3. Figure 3.4(c) showsthat the radiation pattern of the ILA is omni-directional in azimuth. The patterns areidentical to those of a monopole in the y-z and x-y planes. In the x-z plane, however, twoEθ components are generated, one by arms 1 and 2 and one by arm 3. The components48
vary in phase and have different points of maximum radiation. When the two componentscombine, the nulls in both patterns are filled to give nearly omnidirectional coverage. [4]Figure 3.4 illustrates how the various current components on the ILA affect thefar-field radiation. In the next section, the input impedance of the ILA is derived byassuming a sinusoidal current distribution on the antenna.3.3 The Input Impedance of the Inverted-L AntennaBefore applying Pocklington’s equation to the Inverted-L Antenna (ILA), it isworth while to review the derivation for a z-directed current source. The electric fieldinduced by a distributed current on an antenna structure is written as a combination of avector potential A, and a scalar potential Φ, [5]E jωµ o A Φ(3.24)For a z-directed current, (3.24) can be written in scalar form. The result is [5]Ez jωµ o Az Φ z(3.25)The Lorentz gauge condition for a z-directed current is [5] Az jωε oΦ z(3.26)using the derivative of (3.26) in (3.25), gives [5]Ez 1 2 Az2 2 β Az jωε o z (3.27)where β ω µ o ε o is the phase constant for a plane wave. [5] The free space Green’sfunction is given bye jβRΨ 4πR(3.28)49
where R is defined as the distance between the source point, (x’, y’, z’), and theobservation point, (x, y, z), written asR ( x x ')2 ( y y ')2 ( z z' )2(3.29)For a z-directed element of current, J dv’ [5]dE z 1 2 Ψ ( z , z' ) β 2Ψ( z , z' ) Jdv ' 2jωε o z (3.30)The total contribution to the electric field is the integral of (3.30) over the volumein which the current exists. If the current is running along a cylindrical wire of very highconductivity, such as that illustrated in Figure 3.5(a), nearly all of the current will exist onthe surface of the wire. [5]L2ObservationPointcRaJsIL2(a)(b)Figure 3.5. (a) Surface current on a cylindrical wire with cross sectional curve c. (b) Equivalentfilamentary line source for (a). [5]50
If infinite conductivity is assumed, all of the current exists on the surface of the wire, andthe volume integral reduces to [5] 2 Ψ( z , z ' ) 1 β 2Ψ( z, z ') J s dzdφ 2 jωε o c L / 2 z L/2Ez (3.31)where c is the cross sectional curve of the wire in Figure 3.5(a), and Js is the current onthe surface of the wire. If the surface current is observed from a point along the wire axisin Figure 3.5(b),R ( z z ')2 a 2(3.32)where a is the radius of the wire. If the wire is sufficiently thin, so that a λ,circumferential current does not exist, and the longitudinal current is nearly uniformaround the circumference of the wire. Using this thin wire approximation, (3.31) reducesto [5] 2 Ψ ( z , z' ) 1 β 2Ψ( z , z ') I ( z ')dzEz 2 jωε o L / 2 z L/ 2(3.33)that is the integration of current over the equivalent filamentary line source illustrated inFigure 3.5(b). Although the integration is over an infinitely thin filament of current, thecross sectional area of the wire is included since the wire radius, a, is included in (3.32)and thus in (3.28) and (3.33). [5]The expression in (3.33) gives the scattered field. [5] At the surface of theperfectly conducting wire, the scattered field is equal to the incident or impressed field. [5]Therefore, Ezs -Ezi, and1 Ez jωε oi 2 Ψ( z, z ') β 2 Ψ( z , z ') I ( z ')dz 2 z L /2L/ 2(3.34)This is the general form of Pocklington’s integral equation, valid for z-directed currentswith the thin wire approximation. [5]51
Pocklington’s integral equation is formulated to express the fields radiated by anelectrically small ILA by using the z-directed currents on the vertical segment as well asthe x-directed currents on the horizontal segment. In Figure 3.2, the ILA is modeled withan infinite perfectly conducting ground plane. The ground plane image of the ILA istreated as part of the antenna structure. Currents flow on the ILA in both the x and zdirections. Therefore, the vector magnetic potential, A, exists in the x and z directions andthe scalar potential, Φ, includes the x and z dimensions. [6] The vector magnetic potential,and scalar potentials are related to one another by the Lorentz gauge equation: [6] Ax Az jωεΦ 0 x z(3.35)Differentiating with respect to z yields Φ1 2 Az Ax zjωε z 2 z x (3.36)Substituting this expression into (3.25) givesEz 2 Az Ax 1 2βA z z 2 z x jωε (3.37)The derivation of Pocklington’s integral equation in two dimensions is the same as that forthe general form of Pocklington’s equation, except that (3.25) is replaced by (3.37). Theresult is the electric field in the z direction due to both the x and z-directed currents on theILA and its image. A two dimensional form of Pocklington’s integral equation that is validfor radiation problems involving the ILA is [6] Ez ih 2 ψ z ( z , z ') 1I(z') β 2ψ z ( z , z ') dz 'z 2 jω 4πε h z 52
L a1 ψ xt ( x , x ', z ) I xt ( x' ) dx'a xjω 4πε z L a1 ψ xb ( x, x ', z ) I xb ( x ') dx 'a xjω 4πε z(3.38)where the current distributions on each arm of the ILA, Iz(z’), Ixt(x’), and Ixb(x’) areunknown and the Green’s functions areψ z ( z, z ' ) e jβRte jβRbe jβR, ψ xb ( x , x ', z ) , ψ xt ( x , x', z ) RRtRbwhereR ( z ' z )2 a 2Rt ( h z )2 ( x ' x )2Rb ( h z )2 ( x ' x )2If the ILA is electrically small (kh 0.5 and kL 0.5 for k 2π / λ) , the currentsvary linearly with a maximum at the generator and zero at the free end. [6] Thus, theunknown current distributions in (3.38) are replaced by z' I z ( z ' ) Io 1 for -h z’ h h L (3.39) x a h I xt ( x' ) Io 1 for a x’ L a and z’ h h L (3.40) x a h I xb ( x ' ) Io 1 for a x’ L a and z’ -h h L (3.41)An accurate analysis of the current in the bend between the vertical and horizontalsegments is not performed. However, the current entering the bend must equal the currentleaving the bend. Therefore, the current at z’ h is equivalent to that at x’ a. [6]Once the current distribution on the ILA is assumed, the radiated electric fields53
follow immediately from (3.38). Substituting (3.39) through (3.41) into (3.38) gives theimpressed, or incident z-directed electric field, -Ezi, in terms of an unknown current at thegenerator, Io Iz(0).Given the impressed electric field, the input impedance of the ILA is derived usingthe equivalent circuit in Figure 3.6.ZA-I o ZL-VTFigure 3.6. Equivalent circuit of the ILA [6]In Figure 3.6, ZA is the input impedance of the antenna, and the current source atthe feed point of the ILA is replaced by a complex impedance, ZL. The Thevenin voltage,VT, is the phasor potential across ZL when ZL is infinite. [6] To determine the phasorpotential, VT, the ILA radiation problem is related to a scattering problem usingsuperposition. That is, Ezi is treated as the z-directed electric field induced by a plane wavepolarized opposite the spherical unit vector aθ. [6] The situation is illustrated in Figure3.7.zEθaθθIoxFigure 3.7. A center fed ILA, and the spherical unit vector aθ. [6]54
The Thevenin voltage induced by the plane wave in Figure 3.7 is VT Eθ Lθ whereLθ is the component of the vector equivalent length of the ILA in the direction of Eθ. [6] IfEθ approaches perpendicular to the x-axis (θ π/2), the vector equivalent length of theILA is [6]h π Lθ ,0 h 2 2 h L (3.42)Assuming a lossless current source (ZL 0), the current Io in Figure 3.6 is Io VT / ZA EθLθ / ΖΑ -EziLθ / ΖΑ and an expression for input impedance follows directly as[6] Ez i Z A Lθ Io (3.43)which is in terms of the unknown current Io Iz(0). The expression in (3.38) for impressedelectric field, -Ezi, is also in terms of Io. Thus, a solution for Io is necessary to determinethe z-directed electric field and input impedance of the ILA.A point matching technique is used to solve for Io. It is known that the magnitudeof the tangential electric field at the boundary of a perfect conductor is zero. Thus, at anypoint on the vertical segment of the ILA, the z-directed electric field must go to zero.This boundary condition is enforced by setting Ezi in (3.38) to zero at z h / 2. Bysymmetry, this enforces the same condition at z -h / 2. [6] Solving (3.38) using theboundary condition yields an approximation for Io.Using the point matching approximation for Io, the expression in (3.38) isintegrated to derive Ezi. The exponenitals in the free space Green’s functions are estimatedusing third order MacLaurin series representations such as [6] ( kR )2 j( kR )3 e jkR 1 jkR 2!3! (3.44)55
The results of the integration are expressions for the input resistance and reactance of anelectrically small ILA. The expression for input resistance is [6]h 10 ( h2 53 L2 65 h( L a ) 2 RL 15( kh)2 2 9h L ( h L )2 (3.45)and the reactance is [6]XLh 6 0 h 2 h L k ( h L )2 k 2 h 2 2 ln 3h 3h 2 0 a a 9h2 1 L 1 l n h 4h4 h2 4La T La 2k 2h 23h a 8LaT3h 234 3( k h )89h2La 2 4L 213k 2 h 2 a2 h48 9h2h2 La La 2 La La 2 2 2k h4 3k h T ln 4T ln h3h 88 a a 22 22L 29 a2h4 (3.46)where La L a and T 1 - a / h.It is also possible to estimate the input resistance of the ILA using Poynting’stheorem and the current distributions in (3.39) through (3.41). The complex Poyntingvector is integrated over all points in the far field of the antenna, and the result is the totalradiated power from the antenna, PR. The result of the integration is used in2I RPR o LP2(3.47)where RLP is the input resistance of the ILA. If terms of the order [kh]4, [kL]4, and[(kh)2(kL)2], and smaller are dropped from the result of the integration of the Poyntingvector, the input resistance of the ILA is h RLP 40( kh) 1 2( h L ) 22(3.48)The input impedance of the ILA is calculated using (3.45) and (3.48). The resultsare given in Figure 3.8 which shows that when Pocklington’s integral equation is used to56
model the input resistance of the ILA, the results depend on wire diameter. Poynting’stheorem, however, is independent of wire diameter. There is a 20% discrepancy betweenthe results predicted by Pocklington’s equation (see (3.45)) and by Poynting’s theorem(see (3.48)). The input resistance of the ILA is small, below 7 Ω, and there is a sharpdecrease in input resistance as the size of the ILA is reduced.Figure 3.8. (a) Input resistance of the ILA illustrated in Figure 3.2 calculated using (3.45) and(3.48) with kh 0.3, with a/h 0.01 and a/h 0.1. (b) Input resistance of the ILAcalculated using (3.45) and (3.48) with kh 0.5, with the same variations ina/h used in (a). [6]The accuracy of equations (3.45) and (3.46) is limited by the point matchingtechnique used to estimate Io. If the boundary condition is enforced on the verticalsegment of the antenna at a point z 0, the symmetry of the antenna enforces anothersample point below the ground plane. It is possible to simplify (3.46) by enforcing theboundary condition at z 0. However, the increased precision due to antenna symmetry islost. The modeled input reactance of the ILA with the boundary condition enforced atz 0 is57
h 60h 2 5( kh)2La T hh L 2h aln XL 28k ( h L )2 a hLa h2 k 2 h2 L 2 2h k 2 h2La 21 2 1 ln 2h 2 h a L L 2 h2 k 2 h2a T ln a 2h a (3.49)The input reactances of two electrically small ILAs with different wire diametersare modeled using (3.46) and (3.49) and the results are compared in Figure 3.9.Figure 3.9. Input reactance of the ILA illustrated in Figure 3.2 calculated using (3.46) and (3.49)with kh 0.3 and with a/h 0.01 and a/h 0.1. [6]58
Figure 3.9 shows that agreement between (3.46) and (3.49) improves as L increases. Theestimations are closest for large values of L and small values of a. In the absence ofexperimental data, (3.46) is more accurate due to antenna symmetry.The low input resistance and high input reactance of the ILA make it difficult tomatch to a standard coaxial feedline. One way to tune the input impedance of the ILA is tochange the structure of the antenna. In the next section, a number of variations on the ILAare treated that optimize input impedance and frequency bandwidth.3.4 Variations on the Inverted-L Antenna3.4.1. The Inverted-F AntennaThe ILA consists of a short vertical monopole with the addition of a longhorizontal arm at the top. Its input impedance is nearly equivalent to that of the shortmonopole with the addition of the reactance caused by the horizontal wire above theground plane. [4] The ILA is generally difficult to impedance match to a feedline since itsinput impedance consists of a low resistance and high reactance. Since loss due tomismatch decreases radiation efficiency, it is desirable to modify the structure of the ILAto achieve a nearly resistive input impedance that is easily matched to a standard coaxialline.The ILA structure is commonly modified by adding another inverted-L element tothe end of the vertical segment to form the Inverted-F Antenna (IFA) shown in Figure3.10.59
LhtGround PlaneFigure 3.10. Geometry of the Inverted-F Antenna (IFA)The IFA in Figure 3.10 is identical to a transmission line antenna of length (h L) fed atthe tap point, t. Alternately, the configuration is treated as a small loop inductor,consisting of the feed probe and the inverted-L element behind the feed, resonated withthe capacitance of a horizontal wire above a ground plane.The addition of the extra inverted-L element behind the feed tunes the inputimpedance of the antenna. [4] The impedance is adjusted by changing the tap point. [4]Figure 3.11 illustrates how the input impedance of an IFA changes when the tap point isaltered.Figure 3.11. a) The dimensions of the IFA (in mm) used to determine the effect of tap pointplacement. b) Impedance of an Inverted-F Antenna for various tap points. Points onthe graph are frequency, denoted in MHz. [4]60
The antenna in Figure 3.11(a) was designed to resonate at 730 MHz with ls 7 mm.Figure 3.11(b) shows that moving the tap point away from the short circuit stub increasesthe resonant frequency of the ILA and decreases the input resistance at resonance. [4] Theimpedance tuning feature has made the IFA more popular than the ILA in practical lowprofile applications. [4]One disadvantage of an IFA constructed using thin wires is low impedancebandwidth. Typically, a single IFA element experiences an impedance bandwidth of lessthan 2% of the center frequency. [4] One way to increase the bandwidth of the IFA is toreplace the top horizontal arm with a plate oriented parallel to the ground plane to formthe Planar Inverted-F Antenna (PIFA). The PIFA is the subject of the next section.3.4.2. The Planar Inverted-F AntennaTo improve the narrow impedance bandwidth of the IFA, the thin wire horizontalsegment is replaced by a flat conducting plate oriented parallel to the groundplane. Theresult is the Planar Inverted-F Antenna (PIFA) shown in Figure 3.12. The PIFA is widelyapplied as a low profile antenna design. [4] Specifically, it has found wide spread use inhand-held radio phone units in Japan. [8]Figure 3.12. Geometry of the Planar Inverted-F Antenna (PIFA)61
The PIFA in Figure 3.12 consists of a planar element with an off-center probe feed. Thefeed line is coaxial with the outer conductor connected to ground and the centerconductor emerging from beneath the ground plane to contact the planar element. Oneedge of the PIFA is shorted to ground using a plate of width W L1. The physical actionof the PIFA is a combination of the IFA and the short-circuited air substrate rectangularmicrostrip patch (see Chapter 5). [7]In [7], the currents on the PIFA are modeled using a three dimensionalelectromagnetic field time-domain numerical method called the spatial network method(SNM). In the SNM, The PIFA is broken up into a three dimensional grid of cubes. Thedimension of each cube is d. The feed is modeled as a coaxial line with a center and outerconductor. The width of the outer conductor is 2 d. The extent of the gridding affects theresults of the analysis, and is selected so that the numerical results converge. The PIFA isexcited at resonance through the coaxial feed. The resulting electric and magnetic nodecomponents correspond to the amplitude of the electric field and current distribution,respectively.The magnitude of the electric fields in the x, y, and z-planes are modeled using theSNM and illustrated in Figure 3.13. Figure 3.13 shows that the electric field under theplanar element of the PIFA is z-directed. The z-directed electric field, Ez, is zero at theshort-circuit and maximum at the free end of the planar element. [7] The distribution of Ezis similar to that under the rectangular short-circuited microstrip patch antenna. [7] Theelectric fields, Ex and Ey are generated at all open edges of the planar element. Thesefringing fields are a radiating mechanism of the PIFA. [7]The surface current distributions on a resonant PIFA, modeled using the SNM, areillustrated in Figure 3.14 for different widths, W, of the short-circuit plate, and feed pointlocations, F. In Figure 3.14 the distributions in the top row correspond to the current onthe upper side of the planar element. The distributions in the middle row correspond to thecurrents on the lower face of the planar element. The distributions in the bottom row arethe currents that flow back along the ground plane under the planar element. [7] Thecurrents on the short-circuited plate are shown in all cases, and the feed point is denoted62
by a filled black circle. The direction of the current is shown using an arrow and themagnitude of the current is given by the area within the arrow. [7] Figure 3.14 shows thatcurrents flow out along the lower side of the planar element, and return on the surface ofthe ground plane. These currents set up the inner electric and magnetic fields between theplanar element and the ground plane. The currents on the ground plane produce the imageof the PIFA element. [7] The currents on the top face of the planar element are muchsmaller than those on the lower face except at the edges of the planar element. The edgecurrents on the plate contribute to the fringing fields which are a radiating mechanism ofthe PIFA. [7]63
Figure 3.13. Distribution of the electric fields, Ex, Ey, and Ez in the x-y plane calculated using theSNM where the observed plane is 2.5 d above the ground plane for Ez, and 2 dabove the ground plane for Ex and Ey. [7]64
Figure 3.14. Surface current distributions on the PIFA calculated using the SNM for differentwidths, W, of the short circuit stub, and different feed point locations, F. Part c)represents the currents under a quarter-wave rectangular air substrate microstrippatch antenna for reference. [7]Comparison of Figures 3.14(a&b) to Figure 3.14(c) shows that the currents on thePIFA are similar to the currents on the short-circuited rectangular microstrip patchantenna. However, the PIFA has the advantage of a partially shorted edge. As the width ofthe short circuited plate, W, is decreased, the effective path of the current flow on theplanar element increases. The result is a lower resonant frequency, and a correspondingdecrease of L2. [7] For example, if the ratio of the width of the short circuit element to theresonant length of the PIFA is W / L1 0.125, then the resonant length of a PIFA with L1 /L2 2.0 is 60% shorter than the resonant length of the same PIFA with a fully shortededge. If the planar element is square, so that L1 / L2 1.0, the reduction factor is 40%. [7]65
The resonant frequency of the PIFA depends upon the width of the short circuitedstub, W, the height of the element, h, and the dimensions of the planar element, L1 and L2.To derive the resonant frequency of the PIFA, a factor, γ1, is calculated that involves theheight, h, and the length of the planar element, L2. This factor isγ 1 4( L2 h)(3.50)Another factor, γ2, is calculated that treats the effectively lengthened current path due tothe partial short-circuit. The second factor isγ 2 4( L1 L2 h W )(3.51)The factors γ1 and γ2 are substituted into one of the following equations to determine theresonant frequency of the PIFA:fr rc (1 r )c γ1γ2fr r k c (1 r k )c γ1γ2L1 1L2(3.52)andL1 1L2(3.53)where r W / L, and k L1 / L2. [7]The radiation pattern of the IFA and PIFA are the same as that of the ILA if t issmall compared to the length of the horizontal or planar element. The ILA radiationpatterns are in Figure 3.4.The bandwidth of the PIFA can be improved using a proximity coupled feed. Theproximity coupled feed does not touch the planar element of the PIFA. Instead, thefeedline is coupled capacitively to the planar element of the PIFA using a plate at the endof the feedline that is oriented parallel to the planar element. The proximity coupled PIFAis the subject of the next section.66
3.4.3. Proximity Coupled Planar Inverted-F AntennaNormally the Planar Inverted-F Antenna (PIFA) is fed coaxially with the shieldingof the feedline connected to the ground plane and the center conductor attached to theplanar element. [2] An alternative to the contacting feed is the proximity coupled feed. Inproximity coupling, the center conductor of the coaxial line is terminated with a plate thatis oriented parallel to the planar element of the PIFA. Figure 3.15 shows a PIFA with aproximity coupled feed.Planar ElementProximity Coupled FeedGround PlaneCoaxial LineFigure 3.15. Planar inverted-F antenna fed using proximity couplingIn Figure 3.15 the plate at the end of the feedline acts as an additional load that storescharge and makes the current distribution on the feedline more uniform. [1] The proximitycoupled feed adds three degrees of freedom to the impedance matching of the antenna: thelength and width of the feed plate, and the distance between the feed plate and the planarelement. [8] By adjusting these parameters along with the location of the feed, theproximity coupled PIFA can be impedance matched to a transmission line.A proximity coupled feed offers a number of advantages. First it is easier to changethe location of the proximity coupled feed with respect to the planar element since there isnot a direct connection. [8] Second, the loading effect of the capacitive feed causes theproximity fed PIFA to have a lower resonant frequency than a typical PIFA. At resonance,the planar element of the PIFA has a length, L2, slightly less than λ/4. Using proximitycoupling, L2 can be reduced to λ/8. [8]Proximity coupling also has disadvantages. Since the feed plate must be orientedparallel to the planar element and the ground plane, complexity and manufacturing67
tolerances are added to the design. In addition, currents on both sides of the feed platemust be modeled to achieve accurate results. Moment Method codes often neglect thecurrents on one side of a planar element. Therefore, brute force numerical methods suchas the Finite Difference Time Domain (FDTD) theory are sometimes necessary. [2]The primary purpose a proximity coupled feed is manipulation of the inputimpedance of the PIFA. Increasing the distance between the feed plate and th
43 Inverted - L Inverted - F Planar Dual Antenna Antenna Inverted - F Inverted - F Antenna Antenna . F Antenna (IFA) (#2 in Figure 3.1), the Planar Inverted-F Antenna (PIFA) (#3 in Figure . the vertical
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