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Horn antennas
P. Hazdra, M. Mazanek,…[email protected] of Electromagnetic FieldCzech Technical University in Prague, FEEwww.elmag.org
v. 25.4.2016
Outline
• Radiation from open ended waveguide• Phase variation in aperture (linear / quadratic)• Polarization of aperture antennas• Horn antennas• Phase center of aperture antennas
Katedra elektromagnetického pole 2
Acoustic horn antennas
Katedra elektromagnetického pole 3
Rectangular waveguide in free space
4
, cos ′
/2
/2
2 ′ 2 2 ′ 2
Separable amplitude distribution constant * cosinus
Constant phase assumed (real function)
VSWR below 2 for mode at , waveguide itself is a quite good antenna.
Rectangular waveguide - phase
5
100∘
95∘80∘
300∘
phase phase
Impedance at the aperture (along the a)
6
/2/2
≅ 377Ω
/2
Rectangular waveguide in free space
7
, cos ′ ⋅ 1
, ,1 cos
2 cos sin
, ,1 cos
2 cos sin
Consider Huygens source (questionable since , )
, cos ⋅cos 2
1 22
sin 2
2
2 2 sin cos sin cos2 2 sin sin sin sin
polarization
Rectangular waveguide in free space
8
dB scale
E‐plane (YZ), 90∘ , ≅1 cos
2
sin sin sin
sin sin
H‐plane (YZ), 0∘ , ≅1 cos
2cos sin cos
1 2 sin cos
Wider due to sinc function≅ 107∘
≅ 61∘
More accurate model of aperture fields
1 Γ ′ ⋅
1 Γ ′ ⋅
2 /
Phase variation in aperture
9
Including phase variations: consider complex aperture distribution
• linear: ~ ′• quadratic: ~• cubic: ~
~ ′
Linear phase Quadratic phase
Linear phase variation in aperture
10
• constant: • linear: ′
, sin /4
Linear aperture of length a
• HPBW increased by cos• Directivity decreased by 1/ cos
2
sin
Basis to an antenna scanning technique
Quadratic phase variation (error)
11
Constant aperture illumination Tapered aperture illumination
/2 represents a path length deviation of /4from constant phase at the edges of the aperture
• Displacement of the reflector feed from the focus, distortion of reflector or lens• Feeds whose wave fronts are not ideally spherical• Raises side‐lobe levels• Raises level of the minimums (fills nulls)• Loss in gain (widening of main lobe)
0 constant phase
12
∬ , dx′dy′
∬ , dx′dy′ ∬ , dx′dy′
∬ , dx′dy′ ⋅
∬ , dx′dy′
∬ , dx′dy′
Aperture efficiency due to quadratic error
Amplitude efficiency Phase efficiency cos′
/2
• Quadratic phase error –efficiency as a function of
Polarization of aperture antennas
13
Observation point in spherical coordinates , , on a large (radiation) sphere
wave vector points to observation direction
Radiation fields are transversal to (lies in plane T)and can be decomposed into different orthogonalcomponents (polarization bases)
Plane tangent to the observation sphere
Coordinate system
Component 1(co‐pol.)
Component 2(cross pol.)
Field notation
Spherical , , ,
Spherical , , ,
Ludwig3 Horizontal (Y) Vertical (X) , , ,
“co‐polarization is intended to radiate, while the crosspolarization is that which is orthogonal.”
Polarization of aperture antennas
14
, ,
Field components are function of angular position and has jump at z axis ‐ observation of spherical components in such oriented spherical system does not give impression of polarization
Aperture in XY, radiating along Z (default)
Aperture in YZ, radiating along X (rotated)
, ,co‐pol. cross‐pol.
Better but still not the best for polarization definition of aperture antennas
Reference polarization
Cross polarization
Polarization of aperture antennas
15
45∘135∘, ,
sin cos
cos sin
Co‐polarization Y
Cross‐polarization X
LUDWIG‐3
• Ludwig‐3 definition gives zero cross polarization for Huygens source.
• Pattern measurement using linear probe (the most common case)
• Measurement of satellite antennas (where X‐pol is important issue) involves not only 0, 90∘, but also
45∘.
zero X‐pol: cos sin
sin coscos sin ⋅
Horn antennas
16
• Extension of waveguides (matching Z to Z , larger aperture larger gain)• Primary feeds for reflector antennas (control of aperture distribution by mixing waveguide
modes), radar, satellite, space, radioastronomy• Antennas for microwave measurement, standard horn antennas for gain meas. (gain may be
calculated to within 0.1 dB by known its dimensions)• Basic antenna in microwave region (300 MHz – 100+ GHz)• Special wideband (10:1) horns based on “H” waveguide
4.5 – 50 GHz
www.rfspin.com
mode converter
corrugated horn
dual‐mode horn
Pyramidal “standard horn”
ridged horn
Horn antennas
17
• Bandwidth properties (corrugated horn 2:1, ridged 10:1, standard )• Radiation patterns (E‐, H‐ planes and 45∘ cuts, , ) • Gain and aperture efficiency (standard horn 51%, up to 80% (multimode) )• Phase center (important for measurement and reflector antennas – phase center should be
aligned with reflector focal point)• Polarization (no X‐pol if the pattern is axisymmetrical cos sin )• Input match ‐ two reflection components: a) junction between the feeding waveguide and horn
flare (throat), b) reflection at the aperture due to transition from a guided wave to a radiating field oscillatory return loss
• Fabrication and cost
Home-made horns for WiFi 2.45 GHz
18
15
8
70∘
Horn as a feeder in a reflector antenna
19
50
Horn antennas
20
E/H plane sectoral horns
Flared in E dimension Flared in H dimension
Horn antennas
21
3
6phase
2.7
2.7
Both horns have the same aperture size but the shorter has lower gain due to phase error.
• Optimum design
The H-plane sectoral horn aA
22
2
tan 2
14
… path length from the (virtual) horn apex… axial length… difference in path of travel
cos ′
E field of mode in waveguide (no flare)
• Waves arriving at aperture positions displaced from the aperture center lag in phase relative to those arriving at the center. Aperture phase is uniform in y, but varies in the x‐direction as
• We assume k (valid for relatively large horns)
plane wave
2
1 , for ≪ , that holds for ≪
, cos ′ / Quadratic phase approximation
phase error
Line source radiating cylindrical waves
The H-plane sectoral horn aA
23
/2 2 2
E‐plane
H‐plane
… ∘
Universal radiation pattern for the principal planes of an H‐plane horn
E plane… ‐13.3 dB uniform line source
H plane…‐23 dB cos taper
cos ′
sin
Radiation integral
The H-plane sectoral horn aA
24
• For each value of there is an optimum dimension of the horn giving maximal directivity
≅ 3 8 838
4
For a fixed axial length the directivity increase by virtue of the increased aperture area. Optimum performance is reached for
3/8, which corresponds to a phase lag at the aperture edges of 135∘. As Ais increased beyond the optimum point, the phase deviations across the aperture lead to cancellations in the far field decrease directivity
0.81 0.79 ( )
135∘
⋅
The E-plane sectoral horn bB
25
• For each value of there is an optimum dimension of the horn giving maximal directivity
≅ 2 8 814
4
0.81 0.80 ( )
90∘
⋅
The pyramidal (EH) horn antenna
26
physically realizable for
, cos ′
4 4
≅ 3 ≅ 238
12
H‐plane horn E‐plane horn
0.81 0.80 ( ) 0.79 ( )
0.81 ⋅ 0.80 ⋅ 0.79 0.51Aperture efficiency
Optimum pyramidal horn
⋅
135∘ 90∘
≅ 0.45
≅ 78∘
≅ 54∘
27
The pyramidal (EH) horn antenna
2.7
1.88∆ ≅ 140∘∆ ≅ 90∘
Amplitude
Phase
Pyramidal horn antenna for 2.5 GHz
28
1.21.51.92.3
1.2 1.5 1.9 2.3
2.71.88
Pyramidal horn antenna 2.5 GHz
29
50%
Pyramidal horn antenna
30
Directivity
E/H plane half‐power angles
Matching VSWR<2
≅ 78∘ 28.8∘
≅ 54∘ 28.8∘
28.2∘
26.8∘
Pyramidal horn antenna
31
Pyramidal horn antenna – phase center
32
H‐planeE‐plane
phase
• Apparent center of the spherical waves that emanate from the horn at a given radial distance, usually far – field, important for measurement and reflector antennas – phase center should be aligned with reflector focal point
• Generally different in E/H plane (taking average…)• Phase center is a point when antenna radiates
spherical waves (not true in practice)
Phase of the farfield
33
Farfield origin at phase center (main portion of pattern has constant phase
at the enclosing sphere)
Farfield origin not at phase center
• For horns the phase center is located inside the horn
• Variation with frequency
Literature
• W. L. Stutzman, G. A. Thiele, Antenna Theory and Design, Wiley 2012• C. A. Balanis, Antenna Theory and Design, Wiley, 2005• Y. T. Lo, S. W. Lee, Antenna Handbook, Vol. II, Thomson, 1993• R. F. Harrington, Time‐Harmonic EM Fields, IEEE Press, 2001
Katedra elektromagnetického pole 34
