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Corrugated HornsMotivation: - reduce cross-polarization levels produced by reflector feeds

- produce nearly identical E- and H-plane patterns of feeds

Contents1. General horn antenna applications

2. Types of horns

3. Edge diffraction

4. Corrugated horns

5. Types of corrugations

6. Dual-band horns

Literature[1] A.D. Olver, P.J.B. Clarricoats, A.A. Kishk, L. Shafai, Microwave Horns and Feeds, IEEE Press, 1994[2] P.J.B. Clarricoats, A.D. Olver, Corrugated Horns for Microwave Antennas, Peter Peregrinus Ltd, 1984[3] C.A. Balanis, Antenna Theory – Analysis and Design, 2nd ed, John Wiley and Sons, 1997[4] C.A. Balanis, Advanced Engineering Electromagnetics, John Wiley and Sons, 1989

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1. General horn antenna applications

2) Reflector antenna feeds-Terrestrial point to point communications- Radio-astronomy- Sat-com such as VSAT (Very Small Satellite Antenna Terminal)

and DBS (Direct Broadcast by Satellite)- Radar systems

1) “Stand alone” applications : - LMDS (Local Multipoint Distribution Systems)- Beam forming arrays- Calibration horns

Wide-band corrugated hornAstro Research Corporation, Yokohama, Japan

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2. Types of horns

2) Corrugated Horns- Developed in response to the need for

horns with symmetric radiation patterns and low cross polarization

- Hybrid type aperture modes- Used in demanding applications due to

good performance

1) Pure Mode Horns- TE and TM type aperture modes- Inferior performance to later developed horns- Used in arrays and as calibration horns

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3) Choked Waveguide Horns- Developed to approach corrugated horn performance with a geometry that is easier tomanufacture

- Can yield high efficiency over an acceptablebandwidth

4) Aperture-Matched Horns- Outer flange is contoured to minimize

diffractions and to match waveguide modes to radiating modes

- Performance can be comparable to corrugated horns if specifications are reduced

Curved surface attached to horn walls

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5) Dielectrically Loaded Horns- A metal horn partially filled with dielectric is used to generate hybrid modes

- Useful at millimeter wave frequencies- Phase center sensitivity of short wide angle horns is improved with dielectric lenses

- Dielectric rod radiators operate with hybrid modes

6) Multimode Horns- Not just the dominant mode present in the

aperture fields- Higher order modes used to compliment the

dominant mode and improve performance- Typically narrow band in operation due to

frequency sensitive structures in horn that generate higher order modes

7) Dual-band Horns- Support two separate frequency bands of operation- Increased level of complexity in horn design- Frequency band separation may imply overmoding of the structure for the

higher band- Necessitates propagation separation of the two bands

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3. Edge diffractionRegular horn antennas excite a significant amount of cross polarization due to diffraction from the edges of the horn. In the aperture, the electric field is truly vertical only in the center planes. At off-center locations, the field is slightly curved, thus leading to diffracted fields in many directions.

E- and H-plane diffraction at edges of aperture, horn and reflector antennas [4]

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4. Corrugated hornsCorrugated horns create a hybrid-mode pattern in the aperture which “straightens out” the E-field and reduces diffractions from the edges. Ideally, the wave radiating from the aperture is no longer bound by the aperture edges and, therefore, does not cause edge diffraction.

In addition to low cross polarization, horn antenna requirements are:

• Symmetrical radiation pattern

• Coinciding E- and H-plane phase centre

• Optimized radiation pattern taper for illumination and spillover efficiency

• Feed horn with hybrid mode aperture fields preferable, to match to reflector focal

fields

In order to achieve a symmetrical radiation pattern with low sidelobes and low cross polarization, a nearly linear horn aperture field distribution is required.

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xE

Analysis

yE

( ) ( )

( )

1 0 2 21

2 21

cos2

sin2

x

y

X YE AJ K AJ K

krX Y

E AJ Kkr

r r f

r f

-= -

-=

Then the electric field of the dominant mode in a hybrid-mode waveguide can be written as:

transverse wavenumber

amplitude coefficients

free-space impedance

1 2,

1F

F

K

A A

ZY

=

=

= =

Fz

Fz

EX j Y

HH

Y j ZE

f

f

= -

=

Let be the co-polarized (desired) polarization and the cross-polar (unwanted) component. Assume that for small flare angles (<20 deg), the corrugated horn can be viewed as a periodically corrugated waveguide.

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A linear field distribution (zero cross polarization) is achieved if X-Y=0:- X and Y are finite and equal- X=0 and Y=0 Balanced hybrid-mode condition

The balanced hybrid-mode condition requires:

0 0

0 0

Fz

Fz

EX j Y E

HH

Y j Z HE

ff

ff

= - = =

= = =

Can be achieved if a sufficient number of corrugations per wavelength is chosen

Can be achieved by corrugations which are a quarter wavelength deep

Also note:

The cross-polar component decays with 1/kr1 .

Therefore, larger apertures exhibit better cross-polar performance. They are also less frequency sensitive.

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Modal characteristics of corrugated waveguide

The HE11 mode is the dominant mode. At the balanced hybrid-mode condition, lower modes (EH11 ) go to high-frequency cut-off. HE11 propagates as a fast wave through the point S=

until it reaches /k=1. Thus the short-circuit condition can be used at the throat of the horn in order to match the circular waveguide’s TE11 mode to the HE11 mode.

S=0: Balanced hybrid-mode condition. Magnitude of ratio Ez / Hz equals free-space wave impedance; high-frequency cutoff for EH11

S=: Waveguide acts as if a continuous metal wall is present at corrugation boundary. Corresponds to a slot depth of /2 and, therefore, is used at throat transition.

fast wave (waveguide)

slow wave (periodic structure)

1

1

k

k

bb

bb

= <

= >

Fast-wave region

Slow-wave region

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Analysis (optimization) of corrugated horns

The Mode-Matching Technique (MMT) is most often used. It provides good results on mode conversion along the length of the horn.

The Method of Moments (MoM) is used to compute radiation characteristics. If the aperture is smaller than 1.5 wavelengths, then the currents on the flange of the horn become significant and need to be accounted for.

Example: Mongiardo, Ravanelli, IEEE Trans MTT, May 1997

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Transition Circular Waveguide to Corrugated Conical Horn

Whenever the physical geometry of a guide changes (here from smooth-wall circular waveguide to corrugated waveguide), there is a potential for higher-order mode excitation.

Since the axial symmetry of the horn is preserved, only modes with similar dependence on can be excited: HE11 can only lead to EH1m and HE1m . Generally, for semi-flare angles of less than 70o, the higher-order modes are in cut-off.

Transition at the throat is done with half-wavelength-deep first corrugations. A smooth conical section before the corrugation improves wide angle horn return loss.

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Transitioning corrugations of different depths

This occurs in the main section of the horn where slot depths are gradually changed into a quarter wavelength. Therefore, higher order modes are generally not in cut- off.

EH1m modes are exited with greater intensity than HE1m modes.

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Corrugation depth limitation

When the corrugation depth is less than a quarter wavelength, the EH11 mode can propagate. This mode, if present in the aperture fields, will radiate a high level of cross-polarized field components.

Excitation of this mode can be reduced by using a gradual change from the half wavelength slot depth to the quarter wavelength depth, over not less than a wavelength.

Change in flare angle

A change in flare angle will excite mainly HE1m modes. The amount of excitation is proportional to the difference in flare angles of adjoining sections. It is almost independent of the actual nominal flare angle values.

Abrupt change in flare anglesContinuous change in flare anglesProfiled corrugated horn

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Higher-order mode radiation characteristics

The EH12 mode is the main contributor to cross polarization.

The HE12 mode is low in cross polarization but contributes to a high sidelobe level in the main polarization

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Beamwidth and bandwidth of corrugated horns

The pattern beamwidth stays relatively constant over frequency.

The rate of change of the surface impedance at the corrugation boundary is relatively slow over frequency.

Therefore, the bandwidth increases proportionally with aperture diameter.

Input impedance matching is usually the limiting factor.

A compromise needs to be reached between input match and generation of higher order modes.

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Beamwidth and bandwidth of corrugated horns

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Example: Ku-band feed horn for offset dual-reflector systemHombach and Kühn, IEEE Trans AP, Sep. 1989

Comparison theory and measurements in 45-degree plane

Cross polarization and return loss in operational frequency bands

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Ku-band offset dual-reflector system (Hombach, Kühn, IEEE Trans AP, 1989)

GTD – Geometrical Theory of Diffraction

PO/PTD – Physical Optics / Physical Theory of Diffraction

Far Field (FF) or Near Field (NF) of subreflector illuminating main reflector

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Example: Ku-band profiled corrugated hornClarricoats, Dubrovka and Olver, IEE Proc. MAP, Dec. 2004

Cross-polar patterns are for 45-degree plane

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Slots in radial direction used for medium to low- flare-angle horns or profiled horns

5. Types of corrugationsThe type of corrugations used in a corrugated horn depends on a number of factors and usually leads to a compromise involving- Design specifications- Space requirements- Fabrication complexity

Slots in -direction or perpendicular to conical geometry – used for wide-flare- angle horns

Slots in axial direction used for ease of fabrication and reduced performance wide-flare- angle horns

Ring-loaded slots used to reduce slot depth, e.g., in throat section.

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Corrugated horn with all ring-loaded slots

Examples:

Horn with ring-loaded slots in throat section only. Note that without ring-loading, slots 1 and 2 would be of depth 2d.

Corrugated horn model in CST’s Microwave Studio

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Example: X-band corrugated horn with coaxial ringsDeguchi, Watanabe, Tsuji, Proc. EuMC, Sep. 2006

Cross-pol measurements at 45 degrees

24Dual-depth corrugated horn (Kühn and Philippou)

6. Dual-band hornsDual-band horns are required when two separate frequency bands of operation are required within the same feed horn structure.Dual-depth corrugated horns can be used when the frequency band separation is small enough to avoid overmoding in the higher frequency band.

Lower band between EH11 and EH12 high-frequency cutoff; upper band beyond EH12 high- frequency cutoff

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Example: 11.9/17.5 GHz dual-band corrugated hornKühn and Philippou, Proc. 14th EuMC,1984

11.9 GHz 17.5 GHz

Amplitude and phase patterns in the 45-degree plane

Due to the negligible phase variation over the main beam, corrugated horns are also referred to as scalar horns.

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Dual-band horns with large frequency band separation

Since a corrugated horn cannot simultaneously support two bands with large frequency separation, the upper frequency band is usually radiated by a dielectric rod antenna.

However, such an arrangement requires a feeding circuitry which diplexes the two frequency bands (OMJ – ortho-mode junction).

James, Clark, Greene, IEEE Trans. AP, May 2003

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Example: Ku/Ka-band FeedThiart, Rambabu, Bornemann, Proc. European Microwave Association, Dec. 2006

Ku-band: 10.7 GHz to 12.75 GHzKa-band: 29.5 GHz to 30.0 GHz Polarization: Vertical and horizontal for both Ku- and Ka-band

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Example: Corrugated Horn Array

Detectors of Planck Space Telescope in the focal region of the reflector system (© ESA).The largest horn (lower right) is for 30 GHz, the smallest (close to center) for 857 GHz.

Jensen, Nielsen,Tauber, Martin-Polegre, AP Mag,Oct. 2011

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Example: Micro-Machined Corrugated Horn Array

100-150 GHz polarimeter application (William Duncan, NIST, Boulder, CO)