Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27–30, 2012 1101
Design and Analysis of a High Performance Triband 20/30/44 GHz
Corrugated Horn
K. K. Chan
Chan Technologies Inc., 15 Links Lane, Brampton, Ontario L6Y 5H1, Canada
Abstract— The design and analysis of a corrugated horn that operates over more than an
octave bandwidth and covering three different frequency bands at 20 GHz, 30 GHz and 44 GHz is
presented. This horn is used together with a dual polarized 6-port feed network to illuminate a
reflector located on a spacecraft platform. Its return loss is better than 30 dB, 33 dB and 27 dB
at K, Ka, and EHF bands respectively and the corresponding worst-case cross-pole levels relative
to the co-pole peak are −33 dB, −40 dB and −26 dB. The slot and tooth widths are designed for
manufacturability and the number of corrugations is minimized so that the horn can be fabricated
at a low cost while still meeting the stringent electrical specifications. A limit on the level of
the next higher order symmetric TE31 mode that can be present at the horn input from the feed
network without deteriorating the cross-pole performance is examined.
1. INTRODUCTION
For future communication satellites, multiple frequency bands may be combined together and
radiated through a common aperture. This will reduce the number of antennas on board the
satellite. The antenna of choice is typically an offset reflector fed by a single high performance
horn. The work reported here is on the development of a single tri-band corrugated horn as
feed for a reflector antenna. The requirements for the tri-band horn are listed in Table 1 for
the three frequency bands, namely, Band 1: 20.2–21.2 GHz, Band 2: 30.0–31.0 GHz and Band 3:
43.5–45.5 GHz. The emphasis here is placed on the 20/30 GHz bands with a slight reduction in
requirement for the 44 GHz band. The high amplitude taper at 20◦ off-axis is chosen to minimize
spillover loss and the back lobe levels. The challenging requirements are the return loss and the
peak cross-pole level, both of which are critical for a frequency reuse feed.
A literature survey of the state-of-the-art in multi-band horn design was carried out. The horn
type that is frequently used to provide dual or tri-band capability is the corrugated horn with dual
depth slots [1] or slots with special shapes such as ring loaded slots or stepped slots. Horns with
dual depth slots typically show −25 to −30 dB peak cross-pole responses in two bands and −20 to
−25 dB in the third band. This is expected since the slots can be made to exhibit approximately
balanced hybrid condition in two bands. While at the third band, if present, the corrugated surface
impedance should hopefully still remain capacitive. Otherwise, the dual depth slots will not give
good tri-band performance. Ring loaded horns can cover a wide bandwidth with frequency ratio
of not more than 1.7 : 1 for peak cross-pole level below −30 dB and return loss level greater than
30 dB. They do not perform well when the bands are widely separated. Granet and James [2] stated
that a corrugated horn could not be easily designed to meet low cross-polarization requirement in
the three bands of interest, i.e., 20/30/44 GHz regardless of the type of corrugations used. They
then introduced two optimized smooth-walled horns with computed peak cross-pole levels in the
Table 1: Specifications and design values of the triband horn.
Parameter
Specification
Band 1: > 30 dB
Return Loss Band 2: > 30 dB
Band 3: > 27 dB
Peak
Band 1: < −33 dB
cross-pole Band 2: < −30 dB
Level
Band 3: < −26 dB
Band 1: < −17 dB
Illumination
Band 2: < −20 dB
Taper @ 20◦
Band 3: < −22 dB
Design Values
30.0 dB @ 20.2 GHz, 32.5 dB @ 20.7 GHz, 30.0 dB @ 21.2 GHz
33.6 dB @ 30.0 GHz, 44.0 dB @ 30.5 GHz, 43.1 dB @ 31.0 GHz
37.8 dB @ 43.5 GHz, 48.9 dB @ 44.5 GHz, 27.1 dB @ 45.5 GHz
−46.1 dB @ 20.2 GHz, −38.9 dB @ 20.7 GHz, −33.7 dB @ 21.2 GHz
−42.0 dB @ 30.0 GHz, −40.8 dB @ 30.5 GHz, −41.7 dB @ 31.0 GHz
−26.1 dB @ 43.5 GHz, −28.4 dB @ 44.5 GHz, −26.2 dB @ 45.5 GHz
−17.5 dB @ 20.2 GHz, −17.6 dB @ 20.7 GHz, −17.7 dB @ 21.2 GHz
−23.6 dB @ 30.0 GHz, −23.6 dB @ 30.5 GHz, −23.6 dB @ 31.0 GHz
−26.1 dB @ 43.5 GHz, −28.6 dB @ 44.5 GHz, −33.8 dB @ 45.5 GHz
PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27–30, 2012
1102
three bands as −28.7/−25/−26 dB and −21/−27/−27.5 dB respectively, but there is no mention
of the return loss performance of the horn. The dual-depth corrugated horn design presented
here, an extension to the previous work by the authors [3], not only shows much better cross-pole
performance but is also about 38% shorter in axial length than that of the smooth-walled horn
reported in [2]. A compact horn is an important attribute on a satellite platform.
2. DESIGN PROCEDURE
For ease of manufacturing, the straight slot corrugated horn is the preferred approach. One can use
tri-depth corrugations, making each slot depth ∼ λ/4 to conform to the balanced hybrid condition
at each band, so as to obtain good performance in all frequency bands. This would make the
thickness of the corrugation very thin. Simulations have shown that to maintain good cross-pole
response, there must be at least 2.5 dual depth corrugations per wavelength at the highest frequency
band of operation or the dual-depth pitch must be less than 0.4 wavelength. A larger pitch would
lead to rapid deterioration of the cross-pole performance. Fitting three corrugations of different
depths into a given pitch would lead to very small slot widths at the input matching section of
the horn in order to meet the return loss requirement. Thus from a manufacturing viewpoint, the
tri-depth slots approach is not be very desirable at these high frequencies.
In the dual slot depth implementation, the slot widths and tooth thicknesses would be larger to
make the fabrication of the horn feasible. There are a number of possible slot depth combinations
in the dual slot depth approach but to meet the present requirements, the following configuration
is preferred: 1st slot depth at ∼ λ/4 for band 1 and ∼ 3λ/8 for band 2 with 2nd slot depth at
∼ λ/4 for band 2 and ∼ 3λ/8 for band 3. In this combination, cross-pole performance will be
excellent at band 1 and 2 and good in band 3. It also has relatively shallower slot depths, which is
an important consideration to reduce the horn wall thickness and overall weight.
The diameter of the horn aperture and the horn flare angle are then determined so that the feed
pattern has the required fall-off at 20 degrees off-axis and the specified on-axis gain with minimum
horn length. Through extensive simulations, a horn with 8.02 cm aperture diameter and a semi-flare
angle of 14 degrees is found to meet the desired goals. A profile of the dual-depth corrugated horn is
shown in Fig. 1. Besides the linear flare profile, a polynomial profile of the horn was also tried. No
improvement in performance was found. Larger deviation from the linear profile led to cross-pole
degradation, raised sidelobes or merged shoulders and beam broadening that are undesirable for
the present application.
Next the pitch of the dual depth slots in the horn section is set. To obtain low cross-pole level,
the largest pitch suitable for the horn is found to be 2.8 mm. A large pitch minimizes the number
of corrugations needed to fill the horn. This pitch value was determined by a series of iterations to
find the largest value possible without exceeding the cross-pole level. The corrugation configuration
is shown in Fig. 1(b).
Finally, the horn input matching section is designed. To provide a very good match into the horn
and to facilitate the setting up of the proper modal content for low cross-pole levels, a corrugated
matching section is required. This matching section is also allowed to flare out at 14 degrees, same
as that of the horn. Altogether five pairs of dual depth corrugations are needed and the pitch has
to be reduced slightly to 2.5 mm from 2.8 mm for the horn section. The consequence of using less
number of corrugations and larger pitches were investigated. They all lead to inferior results. The
(a)
(b)
Figure 1: (a) Triband corrugated horn. (b) Corrugation details of horn and matching sections.
Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27–30, 2012 1103
0
0
freq = 20.2 GHz
-10
peak directivity = 22.48 dBi
-10
-20
-20
E-Plane
D-Plane
H-Plane
relative amplitude (dB)
relative amplitude (dB)
freq = 21.2 GHz
peak directivity = 22.06 dBi
-30
-40
-50
E-Plane
D-Plane
H-Plane
-30
-40
xpol
-50
xpol
-60
-60
-70
-70
0
10
20
30
40
50
60
70
80
90
0
θ (deg)
10
20
30
40
50
60
70
80
90
θ (deg)
(a)
(b)
Figure 2: (a) Co- & cross-pole patterns at 20.2 GHz. (b) Co- & cross-pole patterns at 21.2 GHz.
0
0
freq = 31.0 GHz
freq = 30.0 GHz
peak directivity = 24.48 dBi
-10
-10
-20
-20
-30
relative amplitude (dB)
relative amplitude (dB)
peak directivity = 24.35 dBi
E-Plane
D-Plane
H-Plane
-40
xpol
-30
-40
xpol
-50
-50
-60
-60
-70
E-Plane
D-Plane
H-Plane
-70
0
10
20
30
40
50
60
70
80
90
0
10
20
30
40
50
θ (deg)
θ (deg)
(a)
(b)
60
70
80
90
Figure 3: (a) Co- & cross-pole patterns at 30 GHz. (b) Co- & cross-pole patterns at 31 GHz.
input matching section was designed using a gradient-based optimization program. The twenty
slot widths and depths available as design variables are optimized to give the required cross-pole
level and return loss in all three bands. To help the optimization process converge faster, the first
few slots closest to the circular waveguide input are made ∼ λ/2 deep at the respective frequency
band and the slot widths are kept small at ∼ 0.31 mm. The slot width increases and the slot
depth decreases towards the horn section. With this starting condition, the slot dimensions tend
to converge quickly to the values that meet most of the performance specifications. After a number
of runs, all of the specifications are met. The pitch is fixed throughout the optimization process.
Corrugation details of the matching section are shown in Fig. 1(b).
PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27–30, 2012
1104
0
0
freq = 45.5 GHz
freq = 43.5 GHz
peak directivity = 25.67 dBi
peak directivity = 24.58 dBi
-10
-10
-20
E-Plane
D-Plane
H-Plane
relative amplitude (dB)
relative amplitude (dB)
-20
-30
-40
xpol
E-Plane
D-Plane
H-Plane
-30
xpol
-40
-50
-50
-60
-60
-70
-70
0
10
20
30
40
50
60
70
80
0
90
10
20
30
40
50
60
70
80
90
θ (deg)
θ (deg)
(a)
(b)
Figure 4: (a) Co- & cross-pole patterns at 43.5 GHz. (b) Co- & cross-pole patterns at 45.5 GHz.
0
80
TE11 & TE3 mode excitation at horn input port
phase patter ns of tri-band hor n
diagonal plane φ = 45 deg.
phase cente r loc. = 4.00 ins.
60
fr eq = 43.5 GHz
-10
relative amplitude (dB)
relative phase (deg)
TE31/TE11 = -15 dB
TE31/TE11 = -20 dB
TE31/TE11 = -25 dB
TE31/TE11 = -30 dB
xpol
40
20
0
-20
20.70 GHz
30.50 GHz
44.50 GHz
-40
-20
-30
-40
-50
-60
-60
0
2
4
6
8
10
12
14
16
18
20
angle of f-axis, θ (deg)
Figure 5: Phase patterns at frequency band centers.
0
10
20
30
40
50
60
θ (deg)
Figure 6: Influence of TE31 mode on the radiation
patterns.
3. PERFORMANCE PREDICTIONS
The horn assembly has three parts — input circular guide, matching section and horn section, as
shown in Fig. 1(a). It has a total of 205 circular waveguide sections. Mode matching software is
used to predict the horn performance. To ensure convergence at the highest frequency of operation,
26 modes are used at the input to represent the fields, which results in 215 modes at the output
aperture. The co-pole and cross-pole patterns in the E-, D- and H-planes at the band edges are
plotted in Figs. 2 to 4 to demonstrate the worst-case performances. As can be seen, the main beam
is Gaussian shape with no sidelobes or merged sidelobes within the 20◦ reflector illumination cone.
Further, the beamwidths in the E-, D- and H- planes are almost the same. Outside this cone, the
sidelobes are below −36 dB. The cross-pole levels are also pleasingly low.
The best phase center location for the three bands is found to be approximately 4.0 inches from
the aperture. A plot of the co-pole phase patterns in the diagonal plane is shown in Fig. 5 at
the center band frequencies. The maximum phase error within the 3-dB beamwidth is ∼ 12◦ and
within the 10-dB beamwidth, the error is ∼ 30◦ .
Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27–30, 2012 1105
The horn is typically connected to a multi-band feed network. The common waveguide manifold
in this network is typically overmoded with symmetric modes at the highest band but not at the
two lower bands. It is also overmoded with asymmetric modes in band 2 and 3. However, by
maintaining symmetry in the feed network design, excitation of the asymmetric modes is avoided.
The symmetric higher order TE31 mode at the input circular guide is typically excited at the
multiplexer and usually cannot be avoided but can be controlled. Shown in Fig. 6 are the diagonal
plane plots with various amplitude ratios of TE31 /TE11 mode at 43.5 GHz. Field matching analysis
of the horn sections must now include the TE3n and TM3n modes at the junction discontinuities.
In order not to degrade the cross-pole performance at band 3, the amount of TE31 mode generated
by the feed network before launching into the horn should be less than −25 dB relative to the TE11
mode.
4. CONCLUSIONS
The design of a corrugated horn that operates in three bands at 20/30/44 GHz has been presented.
The co-pole beams are Gaussian in nature with very low cross-pole levels. Special attention is
placed on the tooth and slot widths so that the horn can be manufactured without difficulty. The
number of corrugations has also been minimized without sacrificing the performance of the horn.
Care must be taken in the feed network design to ensure that the level of the TE31 mode excited at
the horn input does not compromise the cross-pole performance. The horn has significantly better
RF performance and is more compact than comparable smooth-walled horns.
REFERENCES
1. Chan, K. K., S. R. Gauthier, and G. Dinham, “Multifrequency band earth station feed design,”
IEEE AP-S International Symposium, Vol. 2, 960–963, Dallas, Texas, May 1990.
2. Granet, C. and G. L. James, “Optimized spline-profile smooth-walled tri-band 20/30/44 GHz
horns,” IEEE Antennas and Wireless Propagation Letters, Vol. 6, 492–494, 2007.
3. Chan, K. K. and S. K. Rao, “Design of a triband corrugated horn,” Proceedings of the 2003
Asia-Pacific Microwave Conference, Vol. 1, 29–32, Seoul, Korea, Nov. 4–7, 2003.