# Aperture Antennas. Reflectors, horns. High Gain Nearly real input impedance. Huygens Principle

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1 Antennas 97 Aperture Antennas Reflectors, horns. High Gain Nearly real input impedance Huygens Principle Each point of a wave front is a secondary source of spherical waves. 97

2 Antennas 98 Equivalence Principle Uniqueness Theorem: a solution satisfying Maxwell s Equations and the boundary conditions is unique. 1. Original Problem (a): 2. Equivalent Problem (b): outside, inside, on, where 3. Equivalent Problem (c): outside, zero fields inside, on, where To further simplify, Case 1: PEC. No contribution from. Case 2: PMC. No contribution from. Infinite Planar Surface 98

3 Antennas 99 To calculate the fields, first find the vector potential due to the equivalent electric and magnetic currents. In the far field, from Eqs. (1-105), Since in the far field, the fields can be approximate by spherical TEM waves, 99

4 Antennas 100 Thus the total electric field can be found by Let be the aperture fields, then Let Use the coordinate system in Fig. 7-4, then and 100

5 Antennas 101 or in spherical coordinate system Using Eq. (7-8), we have If the aperture fields are TEM waves, then This implies Full Vector Form 101

6 Antennas 102 The Uniform Rectangular Aperture Let the electric field be Then, where Therefore, At principle planes 102

7 Antennas 103 For large aperture ( ), the main beam is narrow, the factor is negligible. The half-power beam width. Also, Example: a Uniform Rectangular Aperture 103

8 104 Antennas 104

9 105 Antennas 105

10 Antennas 106 Techniques for Evaluating Gain Directivity From (7-27), (7-24), (7-61) Thus, for broadside case, Total power Then, In general, for uniform distribution If then where respectively. are the directivity of a line source due to the main beam direction relative to broadside. 106

11 Antennas 107 Directivity of an Open-Ended Rectangular Waveguide: Gain and Efficiencies where : aperture efficiency : radiation efficiency. (~1 for aperture antennas) : taper efficiency or utilization factor. : spillover efficiency. is called : illumination efficiency. : achievement efficiency. : cross-polarization efficiency. phase-error efficiency. Beam efficiency Simple Directivity Formulas in Terms of HP beam width 1. Low directivity, no sidelobe 2. Large electrical size 107

12 Antennas High gain Example 7-5: Pyramidal Horn Antenna (aperture efficiency=0.51) Measured gained at 40 GHz: 24.7 db. A=5.54 cm, B=4.55 cm. Example 7-6: Circular Parabolic Reflector Antenna Typical aperture efficiency: 55%. Diameter: 3.66 m Frequency: 11.7 GHz Measured Gain: 50.4 db. Measured. 1. Computed by aperture efficiency 2. Computed by half power beam width 108

13 Antennas 109 Rectangular Horn Antenna High gain, wide band width, low VSWR H-Plane Sectoral Horn Antenna Evaluating phase error thus the aperture electric field distribution 109

14 Antennas 110 where is defined in (7-108), (7-109) Directivity Figure 7-13: universal E-plane and H-plane pattern with factor omitted, and (a measure of the maximum phase error at the edge) Figure 7-14: Universal directivity curves. Optimum directivity occurs at and From figure 7.13 for optimum case, 110

15 111 Antennas 111

16 Antennas 112 E-Plane Sectoral Horn Antenna The aperture electric field distribution See (7-129) for the resulting Directivity Figure 7-16: universal E-plane and H-plane pattern with factor omitted, and (a measure of the maximum phase error at the edge) Figure 7-17: Universal directivity curves. Optimum directivity occurs at and From figure 7.13, 112

17 113 Antennas 113

18 Antennas 114 Pyramidal Horn Antenna The aperture electric field distribution At optimum condition: Optimum gain For non optimum case, Design procedure: 1. Specify gain, wavelength, waveguide dimension,. 114

19 2. Using, determine from the following equation Antennas Determine from 4. Determine, by, 5. Determine, by, 6. Determine, by, 7. Verify if and, by, Example 7-7: Design a X-band (8.2 to 12.4 GHz) standard horn fed by WR90 ( )waveguide. Goal: at 8.75 GHz. 1. Solve for A: 2. Solve for the rest parameters: 3. Evaluating the gain by Fig and 7-17: (exact phase error) 115

20 116 Antennas 116

21 117 Antennas 117

22 118 Antennas 118

23 Reflector Antennas Antennas 119 Parabolic Reflector Parabolic equation: or Properties 1. Focal point at. All rays leaving, will be parallel after reflection from the parabolic surface. 2. All path lengths from the focal point to any aperture plane are equal. 3. To determine the radiation pattern, find the field distribution at the aperture plane using GO. Geometrical Optics (GO) 119

24 Antennas 120 Requirements 1. The radius curvature of the reflector is large compared to a wavelength, allowing planar approximation. 2. The radius curvature of the incoming wave from the feed is large, allowing planar approximation. 3. The reflector is a perfect conductor, thus the reflect coefficient. Parabolic reflector: Wideband. Lower limit determine by the size of the reflector. Should be several wavelengths for GO to hold. Higher limit determine by the surface roughness of the reflector. Should much smaller than a wavelength. Also limited by the bandwidth of the feed. Determining the power density distribution at the aperture by where, PO/surface current method 120

25 Antennas 121 PO and GO both yield good patterns in main beam and first few sidelobes. Deteriorate due to diffraction by the edge of the reflector. PO is better than GO for offset reflectors. Axis-symmetric Parabolic Reflector Antenna For a linear polarized feed along x-axis, the pattern can be approximate by the two principle plan patterns as below. where, are E-plane and H-plane patterns. If the pattern is rotationally symmetric, then. We have Also, the cross-polarization of the aperture field is maximum in the. Leads to cross-polarization. For a short dipole,,, At, only x component exists. 121

26 Antennas 122 Summary: 1. F/D increases, cross-polarization decreases Since the range of decreases as F/D increases, the term. 2. Fields inverted because of reflection from conductor. 3. Cross-polarization cancels each other on principal plane in the far field. 122

27 123 Antennas 123

28 124 Antennas 124

29 Antennas 125 Approximation formula Normalized aperture field Thus, where EI=edge illumination (db) =20 log C ET=edge taper (db)=-ei FT=feed taper (at aperture edge) (db)= Spherical spreading loss at the aperture edge (7-208) Design procedure of axial symmetrical aperture field: 1. Estimate EI by the radiation pattern of the feed at the edge angle of the reflector. 2. Calculate due to the distance from the feed to the edge. 3. Estimate ET at the aperture by adding the EI and. 4. Look up Table 7-1 for a suitable n. Example 7-8: A 28-GHz Parabolic Reflector Antenna fed by circular corrugated horn. 125

30 Antennas 126 Assume, then Use Table 7.1b for n=2 and interpolate, we have ( measured) ( measured) 126

31 Antennas 127 Offset Parabolic Reflectors Reduce blocking loss. Increase cross-polarization. Dual Reflector Antenna Spill over energy directed to the sky. Compact. Simplify feeding structure. Allow more design freedom. Dual shaping. 127

32 Antennas 128 Other types Design example 1. Determine the reflector diameter by half-power beam width. For the optimum -11 db edge illumination, (7-248) 2. Choose F/D. Usually between 0.3 to Determine the required feed pattern using model. (7-249) Example 7-9: From

33 Antennas 129 Choose F/D=0.5, then. From (7.249), find q to approximate the pattern by. Verify EI=-11 db, by (7-208). Note: for feed pattern Consideration of Gain due to taper and spillover: 1. The more taper, the less loss due to spillover, but less taper efficiency. 2. The less taper, the more loss due to spillover, but higher taper efficiency. 3. Optimum efficiency for feed: EI= -11 db. 129

34 130 Antennas 130

35 131 Antennas 131

36 132 Antennas 132

37 Antennas 133 A General Approximate Feed Model for Broad Main Beam and Peak at Assume That is the feed pattern For symmetrical feed, The value of is chosen to match the real feed pattern at (usually ) by Then, For symmetrical feed, the illumination efficiency efficiency, the feed gain and EI are computed by, the spill over 133

38 134 Antennas 134

39 135 Antennas 135

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