1

3D-PRINTED ANTENNAS

Enver Shee

1, Tam Wai Yong

2, Gan Theng Huat

3

1Anglo Chinese School Independent, 121 Dover Road, Singapore 139650

2NUS High School of Math & Science, 20 Clementi Ave 1, Singapore 129957

3DSO National; Laboratories, 20 Science Park Drive, Singapore 118230

___________________________________________________________________________

RESEARCH QUESTION

Considering design considerations and modifications, how viable are various rectangular horn

antennas for 3D-printing?

INTRODUCTION

A horn antenna is a category of antenna that has a flaring waveguide shaped as a horn to

direct waves. Horn antennas provide medium gain, a low VSWR, as well as a relatively wide

bandwidth, and are very easy to construct [1] [2]

. However, the horn antenna is limited by its

physical size. The typical gain of a horn antenna ranges from 10dBi to 20dBi [3]

. Although

horn antennas are rather old technology, its versatility allows it to be used in conjunction with

newer technologies, such as 3D-printing.

3D-printing, also known as rapid prototyping or additive manufacturing, is the technique of

fabricating a solid object layer by layer additively. Thermoplastics or metals, like steel,

aluminium or titanium, are usually bound together through the use of a binding agent, or

through melting or sintering [4]

.

Direct metal laser sintering (DMLS) is a technique by which mono-metallic 3D objects can be

printed. The object is built bottom up by using a heat-generating laser to melt and fuse metal

powder a layer at a time according to the instructions of the computer-aided design (CAD)

file. The procedure repeats itself until the final layer is sintered and fused, resulting in a

metallic 3D object [5] [6]

.

3D-printing technology has opened the door for more complex shapes and geometries to be

fabricated, that would have been difficult and tedious to do with traditional fabrication

techniques.

The flexibility and accuracy of 3D-printing has enabled antennas to be more complex and

more compact, allowing for the designing and construction of physically smaller antenna with

on par performance [7]

, as well as fabricating details smaller than a millimetre, that traditional

fabrication techniques cannot achieve [8]

. The accuracy of 3D-printing also enables the high

production quality and accuracy of curved surfaces, for example the surfaces of reflector

antennas and antennas of complex structure [9]

. This precision allows for the conformity of

simulated and empirical data, improving the observed results.

3D-printed antennas have evolved from 3D-printed thermoplastic structure coated with layers

of conductive paint, such as silver, copper or carbon paint [10]

, into 3D-printed steel antennas

coated with layers of copper paint. The performance of these antennas are in large agreement

as well with simulations, with little loss in efficiency [11] [12] [13]

. Obstacles in the fabrication of

wholly mono-metallic 3D-printed antennas include the potentially large surface roughness of

the antenna caused by the printing process, and the numerous design considerations required.

2

The extreme surface roughness of 3D-printed antennas introduce reflections within the

antenna and decrease its efficiency [10]

. However, with the improvement of stereolithography

printing methods and laser printing methods, which can print smoother structures than fused

deposition modelling (FDM) methods [8]

, the effect of surface roughness on the efficiency of

3D-printed antennas has been shown to have a minor effect [14]

. An 8x8 antenna array has

been fabricated in one piece from aluminium, which would be impossible to do with

traditional fabrication techniques, and testifies for the viability of 3D-printed, wholly mono-

metallic antennas [15]

.

This paper presents a study of the compatibility of linear-profile, non-linear-profile, and box

rectangular horn antenna designs with DMLS 3D-printing, as well as the design

considerations and modifications that must be made to allow better compatibility and more

successful printing, and how do these proposed modifications affect the antenna performance.

DESIGN CONSIDERATIONS FOR 3D-PRINTING

Due to the small voxel size of 3D-printing, especially with DMLS, fabrication can be very

accurate. When using metal powder with individual diameters of around 20 microns, there

will be a small tolerance of 20 microns on the x-axis and y-axis. The z-axis has a slightly

larger tolerance due to inconsistencies in the layering of metal powder.

However, 3D-printing does have some limitations that need to be considered which can affect

the accuracy of the fabricated product, and in some cases cause the product to warp and be

unusable. The crux of these limitations is with gravity, and how the fabricated product has to

be supported, either by itself or with removable supports, in order to be printed well. There

are two simple rules:

Firstly, any overhangs of less than 45° will be considered self-supporting, and will not warp

or collapse during printing (see fig. 1). Any overhangs of 45° or greater though need to be

supported by external supports. These supports are removable, though can be difficult and

tedious to remove as the machine will print the supports using the same materials as the main

design. Printing with steel for example will result in steel supports, which are hard to cut off

cleanly. External supports attached onto very thin walls (around 1mm thin) are likely to

damage the wall during removal, and hence should be avoided as much as possible.

Secondly, the height of the fabricated product must be less than 8 times the shortest length of

the base, to ensure stability and proper support during printing. When printing horn antennas,

the two most efficient ways to orientate the product during printing, either mouth-up-base-

down or mouth-down-base-up. These vertical orientations rely on the mouth of the horn or the

flange of the waveguide to support the structure during printing. Hence, this rule is usually not

a problem for horn antennas, for the mouth is usually large enough to support the horn’s

height, and the flange can be extended if additional support is necessary.

Standard Linear-Profile Horn Antenna

A standard linear-profile rectangular antenna is easy to design, with many techniques and

equations already thoroughly described in books on antenna theory. This paper uses equations

described by J.D.Kraus and R.J.Marhefka in their book [16]

. From them, the optimal

dimensions required to produce a 10GHz linear-profile horn with various decibels of

directivity was calculated. The calculation process is documented in the appendices.

3

Fig. 1 (Left): Any overhangs of less than 45° will be considered self-supporting, and anything greater is not

Fig. 2 (Right): Linear-profiled rectangular horn antenna and its overhang angle

For a standard linear-profile rectangular horn antenna, the largest overhang angle would be

the angle between the pyramidal edge of the horn and the vertical (see fig. 2). This angle is

affected by the size of the horn mouth, the horn base, as well as the horn length. The graph

below (graph 1) shows how the overhang angle of a 8GHz, 10GHz, and 12GHz horn antenna

using a WR90 waveguide (22.86mm x 10.16mm) varies with the directivity (in dBi) of the

antenna.

Graph 1: Overhang Angle/˚ against Directivity/dBi for 8, 10, 12 GHz linear-profile horn with WR90 waveguide

Maximum points can be observed for each series, with a higher frequency corresponding with

a lower maximum overhang angle and a higher directivity before this angle is reached. To

translate directivity to gain, the efficiency of the antenna needs to be considered [2]

. The effect

of this on the graph would be a translation to the left as seen in the graph below (graph 2). The

lower the efficiency, the further to the left the graph is translated.

Therefore, for frequencies 8GHz and below, there will be a range of gains that will result in

the designing of a horn antenna that will be incompatible with DMLS 3D-printing, and

modifications must be made to the antenna’s design to prevent warping and collapse during

printing. Higher frequency antennas do not require any modifications.

5

15

25

35

45

55

4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0

Ove

rhan

g A

ngl

e/°

Directivity/dBi

8GHz

10GHz

12GHz

4

Graph 2: Overhang Angle/˚ against Gain/dBi for 10 GHz linear-profile horn with WR90 waveguide

Non-Linear-Profile Horn Antenna

In order to further optimize and increase the efficiency of a horn antenna, non-linear profiles

can be implemented. Non-linear profiles such as an exponential profile or a hyperbolic profile

provide a better impedance transition from waveguide into flared horn into air, and hence

reduce the amount of reflected power [17]

. Exponential-profile and hyperbolic-profile horn

antennas have better voltage standing wave ratio (VSWR) and higher efficiency than their

linear-profile counterparts, and hence require a smaller size to achieve the same gain [18]

.

However, the non-linear profile of these horn antennas make 3D-printing them more difficult

than linear-profile horns. For exponential-profile and hyperbolic-profile horn antennas, their

widely-tapered mouths tend to have overhangs greater than 45° that require modification in

order to be 3D-printed (see fig.3). The graph below (graph 3) shows the relationship between

the overhang angle at the mouth of an 8GHz, 10GHZ, and 12GHz exponential-profile horn

antenna and the directivity (in dBi) of the antenna. Should the overhang angle of the antenna

be below 45°, the whole antenna should be capable of supporting itself, and would be

compatible with 3D-printing without any modifications.

Graph 3: Overhang Angle/˚ against Directivity/dBi for 8, 10, 12 GHz linear-profile horn with WR90 waveguide

Similar to the linear-profile horn antennas, maximum points can be observed for the

exponential-profile antenna series. A higher frequency corresponding with a lower maximum

overhang angle and a higher directivity before this angle is reached. Translating from

directivity to gain would result with similar leftward translations in the graph depending on

the efficiency assumed [2]

.

Therefore, exponential-profile horns designed for certain levels of gain at frequencies 12GHz

and below will require modifications to allow compatibility with 3D-printing and prevent

5

15

25

35

45

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0

Ove

rhan

g A

ngl

e/°

Gain/dBi

E=0.25

E=0.50

E=1.00

5

15

25

35

45

55

65

4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0

Ove

rhan

g A

ngl

e/°

Directivity/dBi

8 GHz

10 GHz

12 GHz

5

warping or collapse during the printing process. Higher frequency antennas will not require

modifications.

Box Horn Antenna

The box horn antenna provides a horizontal step between the waveguide and the flare, and

this increases the modes in which the antenna propagates (TE10 and TE30), increasing the

overall gain for the antenna [19]

. However, due to the structure of a box horn, the two 90˚

overhangs will require support in order to be 3D-printable without risking warping and

collapse (see fig. 4). All box horns, regardless of frequency or desired gain would require

modifications to its design.

PROPOSED MODIFICATIONS FOR 3D-PRINTING COMPATIBILITY

Some rectangular antenna designs like the standard linear-profile horn require minimal

amounts of modification in order to achieve great compatibility with 3D-printing, and produce

greater success and accuracy during printing. However, other designs such as the box horn

require much more modifications to allow it to support itself during 3D-printing, and avoid

warping or collapse. The table below (table 1) summarizes the design considerations and

proposed modifications for each discussed rectangular antenna design.

One could reduce the aperture area of the horn or increase the length of the horn, but these

modifications would directly lead to compromised gain and impact the antenna’s performance [16].

Fig. 3 (Left): Exponential-profiled rectangular horn antenna and its overhang angle

Fig. 4 (Right): Box horn antenna and its overhang angle

However, the proposed modifications above do not directly affect the performance of the

antenna. A larger waveguide can be used to provide the horn antenna better support at the

waveguide-flare transition during printing, and reduce the overhang angle of the antenna

without affecting the aperture area or horn length. Thickening the waveguide also has the

same supporting and overhang-reducing effect as using a larger waveguide. Adding material

to the outer profile of the horn or, providing better support to the mouth of the horn by

thickening the horn walls and reducing the overhang angle.

The effects and implications of these modifications on the performance and radiation pattern

of horn antennas was investigated and evaluated in the sections below.

6

Rectangular Horn

Design

Problematic Areas Proposed

Modifications

Level of Modification

Required

Linear-Profile Overhang of the

pyramidal edge can

exceed 45° and warp

during printing

Larger waveguide

(not very applicable for

box antenna)

Thicken waveguide

(not very applicable for

exponential/

hyperbolic-profile

antenna)

Thicken horn walls to

reduce overhang

Minimal

Non-Linear Profile Overhang at mouth of

the horn can exceed 45°

and warp during

printing

Average

Box Overhang of the sides

of the horn require

support or will warp

during printing

High

Table 1: Summary of design considerations and proposed modifications for various rectangular horn antennas

Effect of a Larger Waveguide

A larger waveguide propagates mainly at a lower frequency, with frequencies not propagated

below a cutoff point defined by:

√

where is the width of the waveguide, while and is the permeability and permittivity of

the waveguide material.

The wanted frequency (ie. 10GHz) would be propagated as a higher mode (eg TM11, TE20),

with the main propagated frequency being transmitted as a lower but unwanted mode. This

would allow for noise in the lower modes (eg. TE10) to be transmitted, lowering the signal-to-

noise ratio (SNR) [20]

.

We simulated the effect of an antenna with a small waveguide (22.86mm x 10.16mm) and one

with a larger waveguide (45.72mm x 20.38mm) in the High Frequency Structural Simulator

(HFSS ver. 15.0.0) software. The larger waveguide resulted in the wanted frequency of

10GHz falling above the cut-off point of TE20. From the simulation results shown below (see

table 2), a gain advantage of 0.62 dB was observed for the horn with the larger waveguide.

This is due to the more uniform illumination of the aperture area [21]

.

Waveguide Size/mm Simulated Peak Gain/dBi Return Loss/dBi

22.86 x 10.16 (normal) 12.4936 -21.90

45.72 x 20.38 (large) 13.1136 -24.90 Table 2: Normal and larger waveguide comparison, full simulation results in appendices

Effect of Thicker Walls

Thickening the walls of a horn antenna can provide it more support during 3D-printing, but it

also creates more surfaces for currents to oscillate on [16]

. However, studies have shown that

this will not affect the antenna, as the thickness of 3D printed metal by mechanical

consideration is much thicker than that of the depth of penetration (see graph 5) by 2-3 orders

of magnitude [22]

. It is also known that thicker edges result in less edge-diffraction and smaller

radiation side-lobes than thinner edges [23] [24]

. Therefore there should be no concern of the

7

thicker horn walls affecting antenna performance if the additional material only changes the

outer profile of the horn.

Graph 5: Depth of Penetration/μm against Frequency/GHz for copper, aluminium, and stainless steel (st. steel)

Nonetheless, a simulation was done with three linear-profile horns with wall thicknesses of

3mm, 1mm, and without thickness (completely flat). The graph below (graph 6) shows that

the gain of the main lobe is not affected, and has a peak gain of 12.4936 dBi regardless of the

thickness.

Graph 6: The peak gain at theta=0 and phi=0 (red and purple lines above ) is 12.4936dBi across all three horns

However, it is to be noted that adding material to thicken the horn walls only provides support

against gravity when the orientation of the antenna during printing is mouth-up-base-down. In

the mouth-down-base-up orientation, the thicker walls provide no additional support, and the

horn will still warp and collapse during printing. As such, the use of this modification restricts

the orientation of the horn antenna during 3D-printing.

COMPARISON OF VARIOUS ANTENNA DESIGNS

In order to assess the viability of the various rectangular horn antenna designs to be used in

conjunction with 3D-printing technology, not only must the level of modifications required

and the effects of these modifications be considered, but the performances of the various

antenna designs must be considered as well.

0.00000

5.00000

10.00000

15.00000

20.00000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

De

pth

of

Pe

ne

trat

ion

/μm

Frequency/GHz

St. Steel

Copper

Aluminium

8

Using HFSS, a linear-profile, exponential-profile, and box horn antenna of similar dimensions

were simulated and compared (see fig. 5). The dimensions of the antennas were optimized to

obtain 10dBi gain at 10GHz assuming a 50% efficiency (13dBi directivity). The calculation

process is documented in the appendices.

Horn Antenna Design Simulated Peak Gain/dBi Return Loss/dB

Linear-Profiled 12.4936 -21.90

Exponential-Profiled 12.2163 -30.40

Box Horn 12.6021 -23.65 Table 3: Comparison of various rectangular horn antenna, full simulation results in appendices

From the simulation results (see table 3), the gain remains fairly constant for all horns except

the boxed horn. It can be observed that the box horn has the best performance. The box horn’s

0.11dBi gain advantage over the linear-profile horn shows that the design possibly has its

merits, although it requires significantly more modifications than linear-profile horn antennas

before it can be 3D-printed. It can also be observed from the simulation results that the

exponential-profile and box horn had return losses less than that of the linear-profile horn.

This is likely due to the exponential-profile horn’s smoother transition from the waveguide to

air, and the box horn’s more uniform aperture illumination.

CONCLUSION

This paper has presented the design considerations required for linear-profile, non-linear-

profile, and box rectangular horn antennas to be compatible with DMLS 3D-printing. It was

found that the box antenna would require the greatest amount of modification to allow 3D-

printability and prevent warping and collapse. Three proposed modifications were

investigated, and found to have an insignificant effect on antenna performance. Considering

this, the viability of the 3 horn antenna designs were evaluated, with the exponential-profile

and box horn showing lower return losses, and the box horn showing slightly greater gain.

From the findings above, it can be concluded that although non-linear-profile horns and box

horns require greater levels of modification in order to achieve compatibility with 3D-

printing, their improved performance over the linear-profile horn allow them to be just as

viable for use in conjunction with 3D-printing technology as the linear-profile horn. Overall,

all three horn antenna designs are very viable, with the linear-profile horn needing least

modifications to achieve compatibility, and the box horn requiring more modifications but

achieving greater gain and lower return loss.

However, there is room for the further investigation of other horn antennas such as ridged

horns, conical horns, etc. A wider range of modifications for allowing 3D-printing

compatibility can also be explored. As 3D-printing technology improves, and the minimum

thicknesses of printed walls decreases, the depth of penetration could become significant, and

its implications may need to be investigated too. This investigation has also been mostly

focused on the Ku and X band, and has not explored thoroughly into the lower microwave

bands.

9

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at the European Conference on Antennas and Propagation (EuCAP 2013), Gothenburg,

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[23] R.E. Lawrie, and L. Peters Jr. (1966). “Modifications of Horn Antennas for Low

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[24] P.M. Russo, R.C. Rudduck, and L. Peters Jr. (1965, March). “A method for

11

computing E-plane patterns of horn antennas”. IEEE Trans. Antennas Propagation, Vol. AP-

13, pp. 219-224. doi:10.1109/tap.1965.1138418

12

APPENDICES

Raw Data

Comparison between using a normal-sized waveguide or a larger waveguide

HFSS (ver.15.0.0) simulation of rectangular linear-profile horn antennas with a normal

waveguide (22.86mm x 10.16mm) in fig. 5 and a twice-as-large waveguide (45.72mm x

20.38mm) in fig. 6. Both aperture sizes were fixed at 42.82mm x 33.85mm, with horn lengths

of 19.10mm. The target frequency is 10GHz.

Fig. 5: Normal-sized waveguide horn antenna (a) 3/4 view (b) side view (c) top-down view

13

Fig. 6: Larger waveguide horn antenna (a) 3/4 view (b) side view (c) top-down view

The simulated results are shown below:

14

Graph 7: Normal-sized waveguide horn simulated gain, with peak at 12.4936dBi

Graph 8: Larger waveguide horn simulated gain with peak at 13.1136dBi

-200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00Theta [deg]

-62.50

-50.00

-37.50

-25.00

-12.50

-0.00

12.50Y

1HFSSDesign3XY Plot 1m1

Curve Info

dB(GainPhi)Setup1 : LastAdaptiveFreq='10GHz' Phi='0deg'

dB(GainPhi)Setup1 : LastAdaptiveFreq='10GHz' Phi='90deg'

dB(GainTheta)Setup1 : LastAdaptiveFreq='10GHz' Phi='0deg'

dB(GainTheta)Setup1 : LastAdaptiveFreq='10GHz' Phi='90deg'

Name X Y

m1 0.0000 12.4936

-200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00Theta [deg]

-70.00

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

-0.00

10.00

20.00

Y1

HFSSDesign9XY Plot 1

m1

m2

Curve Info

dB(GainPhi)Setup1 : LastAdaptiveFreq='10GHz' Phi='0deg'

dB(GainPhi)Setup1 : LastAdaptiveFreq='10GHz' Phi='90deg'

dB(GainTheta)Setup1 : LastAdaptiveFreq='10GHz' Phi='0deg'

dB(GainTheta)Setup1 : LastAdaptiveFreq='10GHz' Phi='90deg'

Name X Y

m1 0.0000 13.1136

m2 0.0000 -46.8147

15

Graph 9: Return loss comparison between normal waveguide (-21.90dB) and larger waveguide (-24.90dB)

The data was simplified into table 2.

Waveguide Size/mm Simulated Peak Gain/dBi Return Loss/dB

22.86 x 10.16 (normal) 12.4936 -21.90

45.72 x 20.38 (large) 13.1136 -24.90 Table 2: Normal and larger waveguide comparison, full simulation results in appendices

Comparison between horn antennas of various wall thicknesses

HFSS (ver.15.0.0) simulation of rectangular linear-profile horn antennas with wall thicknesses

of 3mm, 1mm, and 0mm (completely flat) as shown in the figures below (fig. 7, fig. 8, and

fig. 9 respectively). All aperture sizes were fixed at 42.82mm x 33.85mm, with horn lengths

of 19.10mm. The target frequency is 10GHz.

9.00 9.25 9.50 9.75 10.00 10.25 10.50 10.75 11.00Freq [GHz]

-28.00

-26.00

-24.00

-22.00

-20.00

-18.00

-16.00Y

1

waveguide LXY Plot 3_1Curve Info

w aveguide normalImported

w aveguide largeImported

16

Fig. 7: 3mm wall thickness horn antenna (a) 3/4 view (b) side view (c) top-down view

Fig. 8: 1mm wall thickness horn antenna (a) 3/4 view (b) side view (c) top-down view

17

Fig. 9: 0mm wall thickness (completely flat) horn antenna (a) 3/4 view (b) side view (c) top-down view

The simulation results are shown below (graph 6):

Graph 6: The peak gain at theta=0 and phi=0 (red and purple lines above) is 12.4936dBi across all three horns

18

Comparison between various rectangular horn antenna designs

HFSS (ver.15.0.0) simulation of rectangular linear-profile, exponential-profile, and box horn

antennas as shown in the figures below (fig. 10, fig. 11, and fig. 12 respectively). All aperture

sizes were fixed at 42.82mm x 33.85mm, with horn lengths of 19.10mm. The target frequency

is 10GHz.

Fig. 10: Linear-profiled horn antenna (a) 3/4 view (b) side view (c) top-down view

19

Fig. 11: Exponential-profiled horn antenna (a) 3/4 view (b) side view (c) top-down view

20

Fig. 12: Box horn antenna (a) 3/4 view (b) side view (c) top-down view

The simulation results are shown below:

Graph 10: Linear-profiled horn simulated gain, with peak at 12.4936dBi

-200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00Theta [deg]

-62.50

-50.00

-37.50

-25.00

-12.50

-0.00

12.50

Y1

HFSSDesign3XY Plot 1m1

Curve Info

dB(GainPhi)Setup1 : LastAdaptiveFreq='10GHz' Phi='0deg'

dB(GainPhi)Setup1 : LastAdaptiveFreq='10GHz' Phi='90deg'

dB(GainTheta)Setup1 : LastAdaptiveFreq='10GHz' Phi='0deg'

dB(GainTheta)Setup1 : LastAdaptiveFreq='10GHz' Phi='90deg'

Name X Y

m1 0.0000 12.4936

21

Graph 11: Exponential-profiled horn simulated gain, with peak at 12.2163dBi

Graph 12: Box horn simulated gain, with peak at 12.6021dBi

Graph 13: Return loss comparison between exponential (-30.40dB) and linear (-21.90dB) profiles

-200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00Theta [deg]

-62.50

-50.00

-37.50

-25.00

-12.50

-0.00

12.50Y

1

Exponential 1mmXY Plot 1m1

Curve Info

dB(GainPhi)Setup1 : LastAdaptiveFreq='10GHz' Phi='0deg'

dB(GainPhi)Setup1 : LastAdaptiveFreq='10GHz' Phi='90deg'

dB(GainTheta)Setup1 : LastAdaptiveFreq='10GHz' Phi='0deg'

dB(GainTheta)Setup1 : LastAdaptiveFreq='10GHz' Phi='90deg'

Name X Y

m1 0.0000 12.2163

-200.00 -150.00 -100.00 -50.00 0.00 50.00 100.00 150.00 200.00Theta [deg]

-70.00

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

-0.00

10.00

20.00

Y1

Box 1mmXY Plot 1

m1

Curve Info

dB(GainPhi)Setup1 : LastAdaptiveFreq='10GHz' Phi='0deg'

dB(GainPhi)Setup1 : LastAdaptiveFreq='10GHz' Phi='90deg'

dB(GainTheta)Setup1 : LastAdaptiveFreq='10GHz' Phi='0deg'

dB(GainTheta)Setup1 : LastAdaptiveFreq='10GHz' Phi='90deg'

Name X Y

m1 0.0000 12.6021

9.00 9.25 9.50 9.75 10.00 10.25 10.50 10.75 11.00Freq [GHz]

-32.00

-30.00

-28.00

-26.00

-24.00

-22.00

-20.00

-18.00

-16.00

Y1

Linear 1mmXY Plot 3_2Curve Info

exponentialImported

linearImported

22

Graph 14: Return loss of box horn antenna (-23.65dB at 10 GHz)

The data was simplified into table 3.

Horn Antenna Design Simulated Peak Gain/dBi Return Loss/dB

Linear-Profiled 12.4936 -21.90

Exponential-Profiled 12.2163 -30.40

Box Horn 12.6021 -23.65 Table 3: Comparison of various rectangular horn antenna, full simulation results in appendices

Mathematical Equations and Derivations

Finding optimal dimensions for linear-profile and non-linear-profile rectangular horns

From [16],

Where is the length of the horn, and are the widths of the aperture in the magnetic and

electric field planes respectively, is the gain (non-dimensional), is the efficiency of the

horn, is the maximum magnetic field phase difference, is the maximum electric field

phase difference, and is the signal wavelength in air.

Letting and ,

Therefore,

9.00 9.25 9.50 9.75 10.00 10.25 10.50 10.75 11.00Freq [GHz]

-30.00

-29.00

-28.00

-27.00

-26.00

-25.00

-24.00

-23.00

-22.00

-21.00d

B(S

(1,1

))

HFSSDesign9XY Plot 3Curve Info

dB(S(1,1))Setup1 : Sw eep

23

√

√

For a 10dBi gain rectangular horn antenna at 10GHz assuming 50% efficiency (13dBi at

100% efficiency), the optimal dimensions were found to be:

mm, mm, mm.

Finding the overhang angle for linear-profile rectangular horns

Letting and be the widths of the waveguide in the magnetic and electric field planes

respectively, the overhang distance is calculated by the equation:

(

)

(

)

√( ) ( )

Therefore,

√( ) ( )

Graphs 1 and 2 were generated by inserting WR90 waveguide dimensions (in mm)

and for 8, 10, and 12 GHz ( , , ) over 31 values of

gain/directivity at 0.5dBi increments. Starting gain/directivity value is based on the

gain/directivity of a pure waveguide (no flare).

Graph 1: Overhang Angle/˚ against Directivity/dBi for 8, 10, 12 GHz linear-profile horn with WR90 waveguide

Graph 2: Overhang Angle/˚ against Gain/dBi for 10 GHz linear-profile horn with WR90 waveguide

5

15

25

35

45

55

4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0

Ove

rhan

g A

ngl

e/°

Directivity/dBi

8GHz

10GHz

12GHz

5

15

25

35

45

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0

Ove

rhan

g A

ngl

e/°

Gain/dBi

E=0.25

E=0.50

E=1.00

24

Finding the overhang angle for exponential-profile rectangular horns

For an exponential horn, the profile of the walls are described by the equations:

(

)

(

)

Where and are the widths of the horn in the magnetic and electric field planes

respectively, and is the distance along the horn's length ( at the transition between

waveguide and horn, and at the aperture). The overhang distance, is calculated by the

equation:

(

(

)

)

(

(

)

)

√ (

) (

)

Therefore,

(

(

)

(

) )

(

(

)

(

) )

At the aperture, . Therefore,

√ (

)

(

√ (

))

Where is the overhang angle at the aperture. Graph 3 was generated by inserting WR90

waveguide dimensions (in mm) and for 8, 10, and 12 GHz ( ,

, ) over 31 values of gain/directivity at 0.5 dBi increments. Starting

gain/directivity value is based on the gain/directivity of a pure waveguide (no flare).

25

Graph 3: Overhang Angle/˚ against Directivity/dBi for 8, 10, 12 GHz linear-profile horn with WR90 waveguide

Finding the depth of penetration for various metals

From [22],

√

Where is the depth of penetration, is the signal frequency in air, is the conductivity of

the metal, and is the permeability of free space ( H/m).

Graph 5 was generated by inserting the conductivity of copper, aluminium and stainless steel

( , , and respectively) and frequencies from 0.5

GHz to 15 GHz at 0.5 GHz increments.

Graph 5: Depth of Penetration/μm against Frequency/GHz for copper, aluminium, and stainless steel (st. steel)

5

15

25

35

45

55

65

4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0

Ove

rhan

g A

ngl

e/°

Directivity/dBi

8 GHz

10 GHz

12 GHz

0.00000

5.00000

10.00000

15.00000

20.00000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

De

pth

of

Pe

ne

trat

ion

/μm

Frequency/GHz

St. Steel

Copper

Aluminium