Synthesis of Ultra-Wideband TEM Horn with Inhomogeneous Dielectric Medium

0.77 MB·

by  G. K. Uskov

Synthesis of Ultra-Wideband TEM Horn with Inhomogeneous
Dielectric Medium
G.K.Uskov, P.A.Kretov, V.A.Stepkin, N.S.Sbitnev, and A.M.Bobreshov ∗†
January 5, 2017
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1
0
Abstract
2 horns’ gain and patterns which is based on combin-
ing antennas with dielectric objects. These objects
n
Therewereproposednewformulasforthedielectric usuallyarecomplex-shapedlensmanufacturedfrom
a
J medium permittivity distribution along spatial co- a solid material which are placed at aperture plane
4 ordinates in the space between a linear TEM-horn’s or beyond it[7, 8]; while improving gain and pat-
leafs, which were obtained according to the rules terns, these techniques have a common downside of

] of geometric optics in the assumption of the phase increasingenergyreflectionbacktofeedinglineand,
h
p center being lumped or distributed. The formu- hence,increasingvoltagesteady-waveratio(VSWR)
- las has been checked by FDTD simulation of an at higher frequencies.
s
ultra-wideband signal excitation; two cases were
s However, there is way to improve horn’s direc-
a studied—when dielectric medium is present, and
tivity without sacrificing VSWR level. Its essence
l
c absent. For these both cases, there was obtained
is filling the space between horn leafs by dielec-
. voltage steady-wave ratio, as well as radiation pat-
s tric medium with spatially varying permittivity;
c terns at a set of frequencies up to 20 GHz; the
manufacturing of such filling objects was a major
i
s results comparison was performed. technological problem in near past, which can be
y
h successfullysolvedinpresenttimeusinganumberof
p techniques, including, but not limited to, 3D print-
1 Introduction
[ ing[9,10].Forexample,MolinaandHasselbarth[10]

accompanied a planar slot radiator by a dielectric
1 These days TEM-horns of various types are widely
v lense created by layer-by-layer backing a mixture
used as antennas in ultra-wideband (UWB) radi-
6
olocation and communication; TEM-horns earned
7
8 their popularity for having wide range of opera-
0 tional frequencies, while being extremely easy for
0 manufacturing. Unfortunately, these antennas have α
.
1 a number of drawbacks too; for example, they must
0 have relatively large electric size to radiate signals H₂ ϵ B₁
7
efficiently and may have low-gain frequency gaps.
1 H₁
These drawbacks can be partially worked around
: L₁
v by carefully choosing antenna size and shape[1–5]; B₂ L₂
i
X moreover, it is possible to make horn operational
frequency range even wider, usually at the cost of
r
a further antenna size increasing[6].
There is another approach for improving TEM-
∗TheworkwassupportedbytheRussianFederationPres- Figure 1: TEM horn antenna of the interest, with
ident’sgrantforyoungdoctors(projectMD-7902.2016.9). size markers shown. Here α is the aperture plane,
†TheauthorsarewithVoronezhStateUniversity,1,Uni-
(cid:15) is the excitation plane.
versitetskayapl.,394018,Voronezh,Russia.
1
y y
symmetry axes intersect the excitation plane. Also
consider the point F which is the midpoint of the
P P₂ lineformedbyhornleafs’continuationsintersection;
let this F be the lumped phase center.
F z P₁ z
Ifelectromagneticbeamsaresimultaneouslyemit-
ted from F, then after a certain amount of time
theyformasphericalwavefront. Theideaistoslow
down central beams by increasing dielectric permit-
tivity along their trajectories, and, hence, turn the
(a) lumped phase center (b)distributedphasecenter spherical wavefront into a plane.
Let R be the longest possible straight path
max
Figure 2: To the wavefront planarization proce-
from F to the aperture rectangle as R , which
max
dures.
is the line pointing to a leaf’s trapeze apex. Since
that path is the longest, the material along it must
have the lowest dielectric permittivity among all
of alumina ceramic powder and microscopic hollow
beam paths; call it ε . It is safe to assume that
glass spheres. min
ε =1, hence
In this work, for a given TEM horn with flat min
trapezoidal leafs (see Fig.1 for its schematic view) R
t = max
we (a) derive dielectric filling permittivity distri- max c
bution from geometric optics model of radiation
is the time required for a beam to travel along
process, and (b) use time-domain computer sim-
the R path, where c is the speed of light in free
ulation of ultra-short pulse propagation to check max
space.
whether adding this filling actually improves horn
Let’s now consider a beam propagating in arbi-
characteristics.
trary direction inside the horn. Let R be the dis-
tance between F and the point P where the beam
2 Wavefront planarization intersectstheapertureplaneα,sothetimerequired
for the beam to travel to that point is
Let’s assume for the rest of the paper that UWB
R
signals propagate through the space like they are t= ,
v
beams of light. Obviously, this assumption is quite
strong for frequency order of tens gigahertz, but it where v is the speed of electromagnetic wave in the
lets us derive simple, but useful material distribu- dielectric material located along the path.
tions. This approach is not uncommon in antenna FortheR -beamandR-beamtoreachthehorn
max
design[11, 12], either. exit plane simultaneously, the following condition
In the following subsections we present two simi- must be met:
R R
larly obtained distribution formulas. For the first max = .
one, we assumed that the whole electromagnetic c v
wave was emitted from the single point (we call it a Taking into account that ε=(c/v)2, the following
lumped phase center in this paper); for the second expression for the dielectric permittivity inside the
one,weuniformlystretchedthatphasecenteracross horn can be obtained:
horn’s excitation plane to form a distributed phase
R2
center. ε= max. (1)
R2
2.1 Lumped phase center In the coordinate system we introduced above, it
can be stated that
Let’s choose a system of Cartesian coordinates such
that x axis is horizontal, y axis is vertical, and z is R2 = 1(cid:0)B2+H2(cid:1)+(L +l)2,
max 4 2 2 2
TEM-horn’s main direction (as shown in Fig.2a);
R2 =x2+y2+(L +l)2,
and put the origin at the point where the horn’s 2
2
(a) no filling (b) lumped phase center (c) distributed phase center
Figure 3: Electric field magnitude in horn’s horizontal symmetry plane at 15GHz (time-domain simula-
tion).
wherelisthedistancebetweenF andtheexcitation (x ,y ). Let’s additionally require the following
2 2
plane, x and y are the coordinates of a point P, restriction to satisfy:
|x|≤B /2, |y|≤H /2. If we substitute the above
2 2 x x y y
expression into equation (1), we get the following 1 = 2, 1 = 2 . (3)
B B H H
expression: 1 2 1 2
In these new circumstances, R and R values
ε= 14(cid:0)B22+H22(cid:1)+(L2+l)2. (2) can be obtained as max
x2+y2+(L +l)2
2 1(cid:104) (cid:105)
R2 = (B −B )2+(H −H )2 +(L −L )2,
max 4 2 1 2 1 2 1
Equation (2) gives us a formula of material distri-
bution along straight lines connecting F and each R2 =(x2−x1)2+(y2−y1)2+(L2−L1)2.
point at the aperture plane. It can be also rewrit-
If we substitute the above expressions into equa-
ten as the ε(θ) ∝ cos2θ dependence, where θ is
the angle between the beam and the horn’s main tion (1) taking into account that x1 = BB12x2 and
direction. y1 = HH12y2, when the final formula will be
(cid:104) (cid:105)
1 (B −B )2+(H −H )2 +(L −L )2
2.2 Distributed phase center 4 2 1 2 1 2 1
ε= .
(cid:16) (cid:17)2 (cid:16) (cid:17)2
Despite the above section’s approach has proven 1− BB12 x22+ 1− HH21 y22+(L2−L1)2
itself to work in practice, its propagation model is (4)
simplistic and cannot reflect reality very well. Let’s
elaborate the model to make it more adequate.
3 Computer simulation model
Computer simulation shows (Fig.3a) that TEM
horn does not emit waves from just a single point;
In order to check the proposed material distribu-
instead, the irradiation process involves the whole
tions, we made their digital models, suitable for
excitation plane. This means that the phase center
finite-difference time-domain (FDTD)[13] simula-
should not be though as a lumped entity, but as
tion. This model included a simple TEM horn
a continuum of phase centers distributed on the
(Fig.1) with a strip feeding line; the dimensions
excitationplanebetweenhornleafs. So,let’smodify
were chosen as follows:
theformula(2)toconvertlumpedphasecenterinto
distributed. L =30mm, L =30mm
1 2
As in the previous case, we continue to think B =10mm, B =50mm
1 2
about the wavefront as a set of beams, but now H =2mm, H =50mm
1 2
these beams are not required to have a common
origin(formerpointF). Instead,leteachbeamstart In this model, all antenna and feeder surfaces
from the point P =(x ,y ) at the excitation plane were approximated by thin perfect electric conduc-
1 1 1
and intersect the aperture plane at the point P = tors. The whole problem’s geometry was fit into
2
3
68mm × 57mm × 63mm computational domain formulasforgeneratingdielectricfillingsignificantly
and split into 151×135×137 cuboid Yee cells. To increaseshorn’sgainanddirectionalselectivitywith-
prevent radiated signal from reflecting back into out impairing antenna matching.
computationaldomain, four-layerconvolutionalper- Despite the antenna being studied was linear
fectlymatchedlayer(PML)boundarycondition[14] TEM-horn, the same approach can potentially be
was applied to domain edges (each having 5mm as appliedtomorecomplex-shapedhornsby,forexam-
the minimum distance to the nearest conducting ple, subdividing this complex shape into a number
surface). of short linear intervals.
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