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- 1. Overview of Microstrip AntennasDavid R. JacksonDept. of ECEUniversity of Houston
- 2. Overview of Microstrip AntennasAlso called “patch antennas”• One of the most useful antennas at microwave frequencies(f > 1 GHz).• It consists of a metal “patch” on top of a groundeddielectric substrate.• The patch may be in a variety of shapes, but rectangularand circular are the most common.
- 3. History of Microstrip Antennas• Invented by Bob Munson in 1972.• Became popular starting in the 1970s.R. E. Munson, “Microstrip Phased Array Antennas,” Proc. of Twenty-Second Symp. on USAF Antenna Research and Development Program,October 1972.R. E. Munson, “Conformal Microstrip Antennas and Microstrip PhasedArrays,” IEEE Trans. Antennas Propagat., vol. AP-22, no. 1 (January1974): 74–78.
- 4. Typical Applicationssingle element array(Photos courtesy of Dr. Rodney B. Waterhouse)
- 5. Typical Applications (cont.)Microstrip Antenna Integrated into a System: HIC Antenna Base-Station for 28-43 GHzfilterMPAdiplexerLNAPDK-connectorDC supplyMicro-Dconnectormicrostripantennafiber input withcollimating lens(Photo courtesy of Dr. Rodney B. Waterhouse)
- 6. Geometry of Rectangular PatchxyhLWNote: L is the resonant dimension. The width W is usuallychosen to be larger than L (to get higher bandwidth).However, usually W < 2 L. W = 1.5 L is typical.
- 7. Geometry of Rectangular Patch (cont.)view showing coaxial feedxyLWfeed at (x0, y0)Feed along thecenterline is the mostcommon (minimizeshigher-order modesand cross-pol)x
- 8. Advantages of Microstrip Antennas• Low profile (can even be “conformal”).• Easy to fabricate (use etching and phototlithography).• Easy to feed (coaxial cable, microstrip line, etc.) .• Easy to use in an array or incorporate with othermicrostrip circuit elements.• Patterns are somewhat hemispherical, with amoderate directivity (about 6-8 dB is typical).
- 9. Disadvantages of Microstrip AntennasLow bandwidth (but can be improved by a variety oftechniques). Bandwidths of a few percent are typical.Efficiency may be lower than with other antennas.Efficiency is limited by conductor and dielectriclosses*, and by surface-wave loss**.* Conductor and dielectric losses become moresevere for thinner substrates.** Surface-wave losses become more severe forthicker substrates (unless air or foam is used).
- 10. Basic Principles of OperationThe patch acts approximately as a resonant cavity (shortcircuit walls on top and bottom, open-circuit walls on thesides).In a cavity, only certain modes are allowed to exist, atdifferent resonant frequencies.If the antenna is excited at a resonant frequency, a strongfield is set up inside the cavity, and a strong current on the(bottom) surface of the patch. This produces significantradiation (a good antenna).
- 11. Thin Substrate ApproximationOn patch and ground plane, 0tE = ( )ˆ ,zE z E x y=Inside the patch cavity, because of the thin substrate, theelectric field vector is approximately independent of z.Hence ( )ˆ ,zE z E x y≈h( ),zE x y
- 12. Thin Substrate Approximation( )( )( )( )11ˆ ,1ˆ ,zzH EjzE x yjz E x yjωμωμωμ= − ∇×= − ∇×= − − ×∇Magnetic field inside patch cavity:( ) ( )( )1ˆ, ,zH x y z E x yjωμ= ×∇Hence
- 13. Thin Substrate Approximation (cont.)( ) ( )( )1ˆ, ,zH x y z E x yjωμ= ×∇Note: the magnetic field is purely horizontal.(The mode is TMz.)h( ),zE x y( ),H x y
- 14. Magnetic Wall ApproximationOn edges of patch,ˆ 0sJ n⋅ =ˆnhsJ( )ˆsJ z H= − ×Hence,0tH =xyˆnLWsJˆtAlso, on lower surface ofpatch conductor we have
- 15. Magnetic Wall Approximation (cont.)ˆnhxyˆnLWsJˆt0 ( )tH = PMCSince the magnetic field isapproximately independent of z,we have an approximate PMCcondition on the edge.PMC
- 16. ˆnhxyˆnLWsJˆtHence,PMC0zEn∂=∂( ) ( )( )1ˆ, ,zH x y z E x yjωμ= ×∇( )ˆ , 0n H x y× =( )( )ˆ ˆ , 0zn z E x y× ×∇ =( )( )ˆˆ , 0zz n E x y⋅∇ =Magnetic Wall Approximation (cont.)
- 17. Resonance Frequencies2 20z zE k E∇ + =cos coszm x n yEL Wπ π⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠2 220zm nk EL Wπ π⎡ ⎤⎛ ⎞ ⎛ ⎞− − + =⎢ ⎥⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦Hence2 220m nkL Wπ π⎡ ⎤⎛ ⎞ ⎛ ⎞− − + =⎢ ⎥⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦xyLW(x0, y0)From separation of variables:(TMmn mode)
- 18. Resonance Frequencies (cont.)2 22 m nkL Wπ π⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠0 0 rk ω μ ε ε=Recall that2 fω π=Hence2 22 rc m nfL Wπ ππ ε⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ 0 01/c μ ε=xyLW(x0, y0)
- 19. 2 22mnrc m nfL Wπ ππ ε⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠Hence mnf f=(resonance frequency of(m, n) mode)Resonance Frequencies (cont.)xyLW(x0, y0)
- 20. (1,0) ModeThis mode is usually used because theradiation pattern has a broadside beam.1012 rcfLε⎛ ⎞= ⎜ ⎟⎝ ⎠coszxELπ⎛ ⎞= ⎜ ⎟⎝ ⎠01ˆ sinsxJ xj L Lπ πωμ⎛ ⎞− ⎛ ⎞ ⎛ ⎞= ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠This mode acts as a widemicrostrip line (width W)that has a resonant lengthof 0.5 guided wavelengthsin the x direction.xyLWcurrent
- 21. Basic Properties of Microstrip AntennasThe resonance frequency is controlled by the patchlength L and the substrate permittivity.Resonance Frequency1012rcfLε⎛ ⎞= ⎜ ⎟⎝ ⎠Note: a higher substrate permittivity allows for a smallerantenna (miniaturization) – but lower bandwidth.Approximately,Note: this is equivalent to saying thatthe length L is one-half of awavelength in the dielectric:0 / 2/ 2drLλλε= =kL π=
- 22. The calculation can be improved by adding a“fringing length extension” ΔL to each edge of thepatch to get an “effective length” Le .Resonance Frequency (cont.)1012 ercfLε⎛ ⎞= ⎜ ⎟⎝ ⎠2eL L L= + ΔyxLLeΔLΔL
- 23. Resonance Frequency (cont.)Hammerstad formula:( )( )0.3 0.264/ 0.4120.258 0.8effreffrWhL hWhεε⎡ ⎤⎛ ⎞+ +⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥Δ =⎛ ⎞⎢ ⎥− +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦1/21 11 122 2eff r rrhWε εε−⎡ ⎤+ −⎛ ⎞ ⎛ ⎞= + + ⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦
- 24. Resonance Frequency (cont.)Note: 0.5L hΔ ≈This is a good “rule of thumb.”
- 25. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07h / λ00.750.80.850.90.951NORMALIZEDFREQUENCY HammerstadMeasuredW/ L = 1.5εr = 2.2The resonance frequency has been normalizedby the zero-order value (without fringing):fN = f / f0Results: resonance frequency
- 26. Basic Properties of Microstrip Antennas• The bandwidth is directly proportional to substratethickness h.• However, if h is greater than about 0.05 λ0 , the probeinductance becomes large enough so that matching isdifficult.• The bandwidth is inversely proportional to εr (a foamsubstrate gives a high bandwidth).Bandwidth: substrate effects
- 27. Basic Properties of Microstrip Antennas• The bandwidth is directly proportional to the width W.Bandwidth: patch geometryNormally W < 2L because of geometry constraints:W = 1.5 L is typical.
- 28. Basic Properties of Microstrip AntennasBandwidth: typical results• For a typical substrate thickness (h / λ0 = 0.02), and atypical substrate permittivity (εr = 2.2) the bandwidth isabout 3%.• By using a thick foam substrate, bandwidth of about10% can be achieved.• By using special feeding techniques (aperture coupling)and stacked patches, bandwidth of over 50% have beenachieved.
- 29. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1h / λ0051015202530BANDWIDTH(%)εr2.2= 10.8W/ L = 1.5εr = 2.2 or 10.8Results: bandwidthThe discrete data points are measured values. The solid curves arefrom a CAD formula.
- 30. Basic Properties of Microstrip Antennas• The resonant input resistance is almost independentof the substrate thickness h.• The resonant input resistance is proportional to εr.• The resonant input resistance is directly controlled bythe location of the fed point. (maximum at edges x = 0or x = L, zero at center of patch.Resonant Input ResistanceLW(x0, y0)L
- 31. Resonant Input Resistance (cont.)Note: patch is usually fed along the centerline (y = W / 2)to maintain symmetry and thus minimize excitation ofundesirable modes.LxW(x0, y0)y
- 32. Resonant Input Resistance (cont.)For a given mode, it can be shown that the resonant inputresistance is proportional to the square of the cavity-modefield at the feed point.( )20 0,in zR E x y∝For (1,0) mode:2 0cosinxRLπ⎛ ⎞∝ ⎜ ⎟⎝ ⎠ LxW(x0, y0)y
- 33. Resonant Input Resistance (cont.)Hence, for (1,0) mode:2 0cosin edgexR RLπ⎛ ⎞= ⎜ ⎟⎝ ⎠The value of Redge depends stronglyon the substrate permittivity. For atypical patch, it may be about 100-200 Ohms.LxW(x0, y0)y
- 34. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08h / λ0050100150200INPUTRESISTANCE(Ω)2.2r = 10.8εεr = 2.2 or 10.8W/L = 1.5 x0 = L/4, y0 = W/2Results: resonant input resistanceThe discretedata points arefrom a CADformula.L xW(x0, y0)y
- 35. Basic Properties of Microstrip AntennasRadiation Efficiency• The radiation efficiency is less than 100% due toconductor lossdielectric losssurface-wave power• Radiation efficiency is the ratio of power radiatedinto space, to the total input power.rrtotPeP=
- 36. Radiation Efficiency (cont.)surface waveTM0cos (φ) patternxy
- 37. Radiation Efficiency (cont.)( )r rrtot r c d swP PeP P P P P= =+ + +Pr = radiated powerPtot = total input powerPc = power dissipated by conductorsPd = power dissipated by dielectricPsw = power launched into surface waveHence,
- 38. Radiation Efficiency (cont.)• Conductor and dielectric loss is more important for thinnersubstrates.• Conductor loss increases with frequency (proportional to f ½)due to the skin effect. Conductor loss is usually moreimportant than dielectric loss.2δωμσ=1sRσδ=Rs is the surface resistanceof the metal. The skin depthof the metal is δ.
- 39. Radiation Efficiency (cont.)• Surface-wave power is more important for thicker substratesor for higher substrate permittivities. (The surface-wavepower can be minimized by using a foam substrate.)
- 40. Radiation Efficiency (cont.)• For a foam substrate, higher radiation efficiency isobtained by making the substrate thicker (minimizing theconductor and dielectric losses). The thicker the better!• For a typical substrate such as εr = 2.2, the radiationefficiency is maximum for h / λ0 ≈ 0.02.
- 41. εr = 2.2 or 10.8 W/L = 1.50 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1h / λ0020406080100EFFICIENCY(%)exactCADResults: conductor and dielectric losses are neglected2.210.8Note: CAD plot uses Pozar formulas
- 42. 0 0.02 0.04 0.06 0.08 0.1h / λ0020406080100EFFICIENCY(%)ε = 10.82.2exactCADrεr = 2.2 or 10.8 W/L = 1.5Results: accounting for all lossesNote: CAD plot uses Pozar formulas
- 43. Basic Properties of Microstrip AntennaRadiation Patterns• The E-plane pattern is typically broader than the H-plane pattern.• The truncation of the ground plane will cause edgediffraction, which tends to degrade the pattern byintroducing:rippling in the forward directionback-radiationNote: pattern distortion is more severe inthe E-plane, due to the angle dependenceof the vertical polarization Eθ and the SWpattern. Both vary as cos (φ).
- 44. Radiation Patterns (cont.)-90-60-300306090120150180210240-40-30-30-20-20-10-10E-plane patternRed: infinite substrate and ground planeBlue: 1 meter ground plane
- 45. H-plane patternRed: infinite substrate and ground planeBlue: 1 meter ground plane-90-4504590135180225-40-30-30-20-20-10-10Radiation Patterns (cont.)
- 46. Basic Properties of Microstrip AntennasDirectivity• The directivity is fairly insensitive to the substratethickness.• The directivity is higher for lower permittivity, becausethe patch is larger.
- 47. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1h / λ00246810DIRECTIVITY(dB)exactCAD= 2.210.8ε rεr = 2.2 or 10.8 W/ L = 1.5Results: Directivity
- 48. Approximate CAD Model for Zin• Near the resonance frequency, the patch cavity can beapproximately modeled as an RLC circuit.• A probe inductance Lp is added in series, to account for the“probe inductance”.LpR CLZinprobe patch cavity
- 49. Approximate CAD Model (cont.)LpR CL( )01 2 / 1in pRZ j Lj Q f fω≈ ++ −0RQLω=12BWQ= BW is defined here bySWR < 2.0.0 012 fLCω π= =
- 50. Approximate CAD Model (cont.)in maxR R=Rin max is the input resistance at the resonance of thepatch cavity (the frequency that maximizes Rin).LpR CL
- 51. 4 4.5 5 5.5 6FREQUENCY (GHz)01020304050607080Rin(Ω)CADexactResults : input resistance vs. frequencyεr = 2.2 W/L = 1.5 L = 3.0 cmfrequency where theinput resistance ismaximum
- 52. Results: input reactance vs. frequencyεr = 2.2 W/L = 1.54 4.5 5 5.5 6FREQUENCY (GHz)-40-20020406080Xin(Ω)CADexactL = 3.0 cmfrequency where the inputresistance is maximumfrequency where theinput impedance is realshift due to probe reactance
- 53. Approximate CAD Model (cont.)0.577216γ( )( )0002ln2frX k hk aηγπ ε⎡ ⎤⎛ ⎞= ⎢− + ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦(Euler’s constant)Approximate CAD formula for feed (probe) reactance (in Ohms)f pX Lω=0 0 0/ 376.73η μ ε= = Ωa = probe radius h = probe height
- 54. Approximate CAD Model (cont.)( )( )0002ln2frX k hk aηγπ ε⎡ ⎤⎛ ⎞= ⎢− + ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦• Feed (probe) reactance increases proportionally withsubstrate thickness h.• Feed reactance increases for smaller probe radius.
- 55. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Xr0510152025303540Xf(Ω)CADexactResults: probe reactance (Xf =Xp= ωLp)xr = 2 ( x0 / L) - 1xr is zero at the center of the patch, and is1.0 at the patch edge.εr = 2.2W/L = 1.5h = 0.0254 λ0a = 0.5 mm
- 56. CAD FormulasIn the following viewgraphs, CAD formulas for the importantproperties of the rectangular microstrip antenna will be shown.
- 57. CAD Formula: Radiation Efficiency0 0 1 01 3 11/ 16 /hedrrhed s rr deeR Leh pc W hεπη λ λ=⎡ ⎤ ⎡ ⎤⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞+ +⎢ ⎥ ⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠⎝ ⎠⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦wheretan loss tangent of substratd eδ= =1surface resistance of metal2sRωμσδ σ= = =
- 58. CAD Formula: Radiation Efficiency (cont.)whereNote: “hed” refers to a unit-amplitudehorizontal electric dipole.( ) ( )2 20 120180hedspP k h cπλ=11hedsphedr hedhed hedswsp swhedspPePP PP= =++( )33 30 1201 160 1hedswrP k h cπλ ε⎡ ⎤⎛ ⎞⎢ ⎥= −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
- 59. CAD Formula: Radiation Efficiency (cont.)( )30113 1 11 14hedrrek hcπε=⎛ ⎞⎛ ⎞+ −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠Hence we have(Physically, this term is the radiation efficiency of ahorizontal electric dipole (hed) on top of the substrate.)
- 60. 1 21 2/51r rcε ε= − +( ) ( ) ( ) ( )( ) ( )2 4 2220 2 4 0 2 02 22 2 0 03 11 210 560 5170ap k W a a k W c k La c k W k L⎛ ⎞ ⎛ ⎞= + + + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎛ ⎞+ ⎜ ⎟⎝ ⎠The constants are defined as2 0.16605a = −4 0.00761a =2 0.0914153c =−CAD Formula: Radiation Efficiency (cont.)
- 61. CAD Formula: Radiation Efficiency (cont.)11hedr hedswhedspePP=+Improved formula (due to Pozar)( )( ) ( )3/22200 02 21 0 0 114 1 ( ) 1 1rhedswr rxkPx k h x xεηε ε−=+ + − +201 201rxxxε−=−2 2 20 1 0 1 00 2 2121 r r rrxε α α ε ε α α αε α− + + − += +−( ) ( )2 20 120180hedspP k h cπλ=
- 62. CAD Formula: Radiation Efficiency (cont.)Improved formula (cont.)( )0 0tans k h sα ⎡ ⎤= ⎣ ⎦( )( )( )01 0 201tancosk h sk h ss k h sα⎡ ⎤⎡ ⎤= − +⎢ ⎥⎣ ⎦ ⎡ ⎤⎢ ⎥⎣ ⎦⎣ ⎦1rs ε= −
- 63. CAD Formula: Bandwidth10 0 01 1 16 1/ 32sd hedr rR pc h WBWh L eπη λ ε λ⎡ ⎤⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞= + +⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎢ ⎥⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠⎣ ⎦BW is defined from the frequency limits f1 and f2 at whichSWR = 2.0:2 10f fBWf−= (multiply by 100 if you want to get %)
- 64. CAD Formula: Resonant Input Resistance2 0cosedgexR RLπ⎛ ⎞= ⎜ ⎟⎝ ⎠(probe-feed)( )0010 0 041 16 1/ 3edgesd hedr rL hWRR pc W hh L eηπ λπη λ ε λ⎛ ⎞⎛ ⎞ ⎛ ⎞⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠=⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞+ +⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠⎝ ⎠ ⎝ ⎠
- 65. CAD Formula: Directivity( ) ( )tanc tan /x x x≡where( )( )( )2121 13tanctanrrD k hpc k hεε⎡ ⎤⎛ ⎞= ⎢ ⎥⎜ ⎟+⎝ ⎠⎣ ⎦
- 66. CAD Formula: Directivity (cont.)13Dpc≈For thin substrates:(The directivity is essentially independent of thesubstrate thickness.)
- 67. CAD Formula: Radiation Patterns(based on electric current model)The origin is at thecenter of the patch.Lrεhinfinite GP and substratexThe probe is on the x axis.cossπxˆJ xL⎛ ⎞⎟⎜= ⎟⎜ ⎟⎜⎝ ⎠yLW E-planeH-planex
- 68. CAD Formula: Radiation Patterns (cont.)( ) 22sin cos2 2( , , ) , ,22 2 2y xhexi iy xk W k LWLE r E rk W k Lπθ φ θ φπ⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥ ⎢ ⎥⎜ ⎟ ⎜ ⎟⎛ ⎞ ⎝ ⎠ ⎝ ⎠⎢ ⎥ ⎢ ⎥= ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎛ ⎞⎛ ⎞−⎢ ⎥ ⎢ ⎥⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎣ ⎦⎣ ⎦0 sin cosxk k θ φ=0 sin sinyk k θ φ=The “hex” pattern is for a horizontal electric dipole in the x direction,sitting on top of the substrate.ori θ φ=The far-field pattern can be determined by reciprocity.
- 69. ( ) ( )0, , coshexE r E Gθ θ φ φ θ=( ) ( )0, , sinhexE r E Fφ θ φ φ θ=−where( ) ( )( )( )( )( ) ( )002tan1tan secTEk h NFk h N j Nθθ θθ θ θ= + Γ =−( ) ( )( )( )( )( )( ) ( )002tan coscos 1tan cosTMrk h NGk h N jNθ θθ θ θεθ θθ= + Γ =−( ) ( )2sinrN θ ε θ= −0004jk rjE erω μπ−⎛ ⎞−= ⎜ ⎟⎝ ⎠CAD Formula: Radiation Patterns (cont.)
- 70. Circular PolarizationThree main techniques:1) Single feed with “nearly degenerate” eigenmodes.2) Dual feed with delay line or 90o hybrid phase shifter.3) Synchronous subarray technique.
- 71. Circular Polarization: Single FeedLWBasic principle: the two modes are excited with equalamplitude, but with a ±45o phase.The feed is on the diagonal.The patch is nearly (but notexactly) square.
- 72. Circular Polarization: Single FeedDesign equations:0 CPf f=0112xf fQ⎛ ⎞= ⎜ ⎟⎝ ⎠∓0112yf fQ⎛ ⎞= ±⎜ ⎟⎝ ⎠Top sign for LHCP,bottom sign for RHCP.x yR R R= = Rx and Ry are the resonant input resistances of the two LP (x and y)modes, for the same feed position as in the CP patch.LWxy12BWQ=(SWR < 2 )Resonant frequencyis the optimumCP frequency⎫⎪⎬⎪⎭0 0x y=
- 73. Circular Polarization: Single Feed (cont.)Other variationsLLxyPatch with slotLLxyPatch with truncated cornersNote: diagonal modes are used as degenerate modes
- 74. Circular Polarization: Dual FeedLLxyPP+λg/4 LHCPPhase shift realized with delay line
- 75. Circular Polarization: Dual FeedPhase shift realized with 90o hybrid (branchline coupler)LLxyλg/4LHCPλg/40Z0 / 2Zfeed50 Ohm load0Z0Z
- 76. Circular Polarization: Synchronous RotationElements are rotated in space and fed with phase shifts0o-90o-180o-270oBecause of symmetry, radiation from higher-order modes tends to bereduced, resulting in good cross-pol.
- 77. Circular Patchxyha
- 78. Circular Patch: Resonance Frequencya PMCFrom separation of variables:( ) ( )cosz mE m J kφ ρ=Jm = Bessel function of first kind, order m.0zaEρρ =∂=∂( ) 0mJ ka′ =
- 79. Circular Patch: Resonance Frequency (cont.)mnka x′=a PMC(nth root of Jm′ Bessel function)2mn mnrcf xπ ε′=Dominant mode: TM1111 112 rcf xaπ ε′= 11 1.842x′ ≈
- 80. Fringing extension: ae = a + Δa11 112 e rcf xaπ ε′=“Long/Shen Formula” :a PMCa + Δaln 1.77262rh aahππε⎡ ⎤⎛ ⎞Δ = +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦21 ln 1.77262erh aa aa hππ ε⎡ ⎤⎛ ⎞= + +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦orCircular Patch: Resonance Frequency (cont.)
- 81. Circular Patch: Patterns(based on magnetic current model)( )( )( )111coszJ kρE ρ,φ φJ ka h⎛ ⎞⎛ ⎞⎟⎜ ⎟⎜⎟⎜= ⎟⎜⎟⎜ ⎟⎜⎟⎟⎝ ⎠⎜⎝ ⎠(The edge voltage has a maximum of one volt.)ayx E-planeH-planeIn patch cavity:The probe is on the x axis.2arεhinfinite GP and substrate0 rk k ε=xThe origin is at thecenter of the patch.
- 82. Circular Patch: Patterns (cont.)( ) ( ) ( ) ( )01 1 002 tanc cos sinRθ zEE r,θ,φ πa k h φ J k a θ Q θη=( ) ( )( )( )1 0010 0sin2 tanc sinsinRφ zJ k a θEE r,θ,φ πa k h φ P θη k a θ⎛ ⎞⎟⎜ ⎟=− ⎜ ⎟⎜ ⎟⎜⎝ ⎠( ) ( )( )( )( )( ) ( )02cos 1 costan secTE jN θP θ θ Γ θ θk hN θ jN θ θ⎡ ⎤−⎢ ⎥= − = ⎢ ⎥−⎢ ⎥⎣ ⎦( ) ( )( )( )( )( )02 cos1tan cosrTMrεj θN θQ θ Γ θεk h N θ j θN θ⎛ ⎞⎟⎜ ⎟− ⎜ ⎟⎜ ⎟⎟⎜⎝ ⎠= − =−( ) ( )tanc tanx x / x=where( ) ( )2sinrN θ ε θ= −
- 83. Circular Patch: Input Resistance( )( )21 021in edgeJ kR RJ kaρ⎡ ⎤≈ ⎢ ⎥⎢ ⎥⎣ ⎦a0ρ
- 84. Circular Patch: Input Resistance (cont.)12edge rspR eP⎡ ⎤= ⎢ ⎥⎢ ⎥⎣ ⎦( ) ( )( )( ) ( ) ( ) ( )/22 20 00 02 22 21 0 0tanc8sin sin sinspincP k a k hNQ J k a P J k a dππθηθ θ θ θ θ θ=⎡ ⎤′⋅ +⎢ ⎥⎣ ⎦∫( ) ( )1 /incJ x J x x=wherePsp = power radiated into space by circular patch with maximumedge voltage of one volt.er = radiation efficiency
- 85. Circular Patch: Input Resistance (cont.)200( )8sp cP k a Iπη=CAD Formula:43c cI p= ( )620 20kc kkp k a e== ∑024364851071210.4000000.07857107.27509 103.81786 101.09839 101.47731 10eeeeeee−−−−== −== − ×= ×= − ×= ×
- 86. Feeding MethodsSome of the more common methods forfeeding microstrip antennas are shown.
- 87. Feeding Methods: Coaxial FeedAdvantages:simpleeasy to obtain input matchDisadvantages:difficult to obtain input match for thicker substrates,due to probe inductance.significant probe radiation for thicker substrates2 0cosedgexR RLπ⎛ ⎞= ⎜ ⎟⎝ ⎠
- 88. Feeding Methods: Inset-FeedAdvantages:simpleallows for planar feedingeasy to obtain input matchDisadvantages:significant line radiation for thicker substratesfor deep notches, pattern may shown distortion.
- 89. Feeding Methods: Proximity (EMC) CouplingAdvantages:allows for planar feedingless line radiation comparedto microstrip feedDisadvantages:requires multilayer fabricationalignment is important for input matchpatchmicrostrip line
- 90. Feeding Methods: Aperture Coupled Patch (ACP)Advantages:allows for planar feedingfeed radiation is isolated from patch radiationhigher bandwidth, since probe inductanceproblem restriction is eliminated and adouble-resonance can be created.allows for use of different substrates tooptimize antenna and feed-circuitperformanceDisadvantages:requires multilayer fabricationalignment is important for input matchpatchmicrostrip lineslot
- 91. Improving BandwidthSome of the techniques that has been successfullydeveloped are illustrated here.(The literature may be consulted for additional designsand modifications.)
- 92. Improving Bandwidth: Probe CompensationL-shaped probe:capacitive “top hat” on probe:
- 93. Improving Bandwidth: SSFIPSSFIP: Strip Slot Foam Inverted Patch (a version of the ACP).microstripsubstratepatchmicrostrip line slotfoampatch substrate• Bandwidths greater than 25% have been achieved.• Increased bandwidth is due to the thick foam substrate andalso a dual-tuned resonance (patch+slot).
- 94. Improving Bandwidth: Stacked Patches• Bandwidth increase is due to thick low-permittivity antennasubstrates and a dual or triple-tuned resonance.• Bandwidths of 25% have been achieved using a probe feed.• Bandwidths of 100% have been achieved using an ACP feed.microstripsubstratedriven patchmicrostrip lineslotpatch substratesparasitic patch
- 95. Improving Bandwidth: Stacked Patches (cont.)-10 dB S11 bandwidth is about 100%stacked patch with ACP feed3 4 5 6 7 8 9 10 11 12Frequency (GHz)-40-35-30-25-20-15-10-50ReturnLoss(dB)MeasuredComputed
- 96. Improving Bandwidth: Parasitic PatchesRadiating Edges Gap CoupledMicrostrip Antennas(REGCOMA).Non-Radiating Edges GapCoupled Microstrip Antennas(NEGCOMA)Four-Edges Gap CoupledMicrostrip Antennas(FEGCOMA)Bandwidth improvement factor:REGCOMA: 3.0, NEGCOMA: 3.0, FEGCOMA: 5.0?
- 97. Improving Bandwidth: Direct-Coupled PatchesRadiating Edges DirectCoupled Microstrip Antennas(REDCOMA).Non-Radiating Edges DirectCoupled Microstrip Antennas(NEDCOMA)Four-Edges Direct CoupledMicrostrip Antennas(FEDCOMA)Bandwidth improvement factor:REDCOMA: 5.0, NEDCOMA: 5.0, FEDCOMA: 7.0
- 98. Improving Bandwidth: U-shaped slotThe introduction of a U-shaped slot can give asignificant bandwidth (10%-40%).(This is partly due to a double resonance effect.)“Single Layer Single Patch Wideband Microstrip Antenna,” T. Huynh and K. F. Lee,Electronics Letters, Vol. 31, No. 16, pp. 1310-1312, 1986.
- 99. Improving Bandwidth: Double U-SlotA 44% bandwidth was achieved.“Double U-Slot Rectangular Patch Antenna,” Y. X. Guo, K. M. Luk, and Y. L. Chow,Electronics Letters, Vol. 34, No. 19, pp. 1805-1806, 1998.
- 100. Improving Bandwidth: E-PatchA modification of the U-slot patch.A bandwidth of 34% was achieved (40% using a capacitive“washer” to compensate for the probe inductance).“A Novel E-shaped Broadband Microstrip Patch Antenna,” B. L. Ooi and Q. Shen,Microwave and Optical Technology Letters, Vol. 27, No. 5, pp. 348-352, 2000.
- 101. Multi-Band AntennasGeneral Principle:Introduce multiple resonance paths into the antenna. (Thesame technique can be used to increase bandwidth viamultiple resonances, if the resonances are closely spaced.)A multi-band antenna is often more desirable than abroad-band antenna, if multiple narrow-band channelsare to be covered.
- 102. Multi-Band Antennas: ExamplesDual-Band E patchhigh-bandlow-bandlow-bandfeedDual-Band Patch with Parasitic Striplow-bandhigh-bandfeed
- 103. Miniaturization• High Permittivity• Quarter-Wave Patch• PIFA• Capacitive Loading• Slots• MeanderingNote: miniaturization usually comes at a price of reduced bandwidth.General rule: maximum obtainable bandwidth is proportional to thevolume of the patch (based on the Chu limit.)
- 104. Miniaturization: High PermittivityIt has about one-fourth the bandwidth of the regular patch.LW E-planeH-plane1rε =4rε =L´=L/2W´=W/2(Bandwidth is inversely proportional to the permittivity.)
- 105. Miniaturization: Quarter-Wave PatchLW E-planeH-planeEz = 0It has about one-half the bandwidth of the regular patch.W E-planeH-planeshort-circuitviasL´=L/2
- 106. Miniaturization: Planar Inverted F Antenna (PIFA)A single shorting plate or via is used.This antenna can be viewed as a limiting case of the quarter-wave patch, or asan LC resonator.side viewfeedshorting plateor via top view/ 4dL λ<
- 107. PIFA with Capacitive LoadingThe capacitive loading allows for the length of the PIFA to be reduced.feedshorting plate top viewside view
- 108. Miniaturization: Slotted PatchThe slot forces the current to flow through a longer path, increasingthe effective dimensions of the patch.top viewlinear CP0o ±90o
- 109. Miniaturization: MeanderingMeandering forces the current to flow through a longer path,increasing the effective dimensions of the patch.feedviameandered quarter-wave patchfeedviameandered PIFA
- 110. Improving Performance:Reducing Surface-Wave Excitation andLateral RadiationReduced Surface Wave (RSW) AntennaSIDE VIEWzbhxshorted annular ringground plane feedaρ0TOP VIEWaρobfeedD. R. Jackson, J. T. Williams, A. K. Bhattacharyya, R. Smith, S. J. Buchheit, and S. A.Long, “Microstrip Patch Designs that do Not Excite Surface Waves,” IEEE Trans.Antennas Propagat., vol. 41, No 8, pp. 1026-1037, August 1993.
- 111. Reducing surface-wave excitation and lateralradiation reduces edge diffraction.RSW: Improved Patternsspace-wave radiation (desired)lateral radiation (undesired)surface waves (undesired)diffracted field at edge
- 112. -90-60-300306090120150180210240-40-30-30-20-20-10-10-90-60-300306090120150180210240-40-30-30-20-20-10-10conventionalconventional RSWRSWMeasurements were taken on a 1 m diameter circular ground plane at1.575 GHz.RSW: E-plane Radiation PatternsMeasurementTheory
- 113. Reducing surface-wave excitation and lateral radiationreduces mutual coupling.RSW: Mutual Couplingspace-wave radiationlateral radiationsurface waves
- 114. Reducing surface-wave excitation and lateral radiation reduces mutual coupling.-100-90-80-70-60-50-40-30-20-1000 1 2 3 4 5 6 7 8 9 10Separation [Wavelengths]S12[dB]RSW - MeasuredRSW - TheoryConv - MeasuredConv - TheoryRSW: Mutual Coupling (cont.)“Mutual Coupling Between Reduced Surface-Wave Microstrip Antennas,” M. A. Khayat, J.T. Williams, D. R. Jackson, and S. A. Long, IEEE Trans. Antennas and Propagation, Vol.48, pp. 1581-1593, Oct. 2000.
- 115. ReferencesGeneral references about microstrip antennas:Microstrip Antenna Design Handbook, R. Garg, P. Bhartia, I. J. Bahl,and A. Ittipiboon, Editors, Artech House, 2001.Microstrip Patch Antennas: A Designer’s Guide, Rodney B. Waterhouse,Kluwer Academic Publishers, 2003.Microstrip and Printed Antenna Design, Randy Bancroft, NoblePublishers, 2004.Microstrip Antennas: The Analysis and Design of Microstrip Antennasand Arrays, David M. Pozar and Daniel H. Schaubert, Editors,Wiley/IEEE Press, 1995.Advances in Microstrip and Printed Antennas, K. F. Lee, Editor, JohnWiley, 1997.
- 116. References (cont.)General references about microstrip antennas (cont.):Millimeter-Wave Microstrip and Printed Circuit Antennas, P. Bhartia,Artech House, 1991.The Handbook of Microstrip Antennas (two volume set), J. R.James and P. S. Hall, INSPEC, 1989.Microstrip Antenna Theory and Design, J. R. James, P. S. Hall, andC. Wood, INSPEC/IEE, 1981.
- 117. Computer-Aided Design of Rectangular Microstrip Antennas, D. R.Jackson, S. A. Long, J. T. Williams, and V. B. Davis, Ch. 5 of Advancesin Microstrip and Printed Antennas, K. F. Lee, Editor, John Wiley, 1997.More information about the CAD formulas presented herefor the rectangular patch may be found in:References (cont.)
- 118. References devoted to broadband microstrip antennas:Compact and Broadband Microstrip Antennas, Kin-Lu Wong,John Wiley, 2003.Broadband Microstrip Antennas, Girish Kumar and K. P. Ray,Artech House, 2002.Broadband Patch Antennas, Jean-Francois Zurcher and FredE. Gardiol, Artech House, 1995.References (cont.)

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