Phase Compensation of Composite Material Radomes Based on the Radiation Pattern
Chin. J. Mech. Eng.
Phase Compensation of Composite Material Radomes Based on the Radiation Pattern
Peng LI 0 1 2 3
Na LI 0 1 2 3
Wanye XU 0 1 2 3
Liwei SONG 0 1 2 3
0 Key Laboratory of Electronic Equipment Structure Design of Ministry of Education, Xidian University , Xi'an 710071 , China
1 Supported by National Natural Science Foundation of China (Grant Nos. 51475348, 51305322 and 51490660) , Open Foundation of State Key Laboratory of Mechanical Transmissions (SKLMT-KFKT- 201409), and Fundamental Research Funds for the Central Universities of China
2 State Key Laboratory of Mechanical Transmissions, Chongqing University , Chongqing 400044 , China
3 Na LI, born in 1982, is currently an associate professor at Key Laboratory of Electronic Equipment Structure Design of Ministry of Education, Xidian University , China
Some compensation methods have been proposed to mitigate the degradation of radiation characteristics caused by composite material radomes, however most of them are complex and not applicable for large radomes, for example, the modification of geometric shape by grinding process. A novel and simple compensation strategy based on phase modification is proposed for large reflector antenna-radome systems. Through moving the feed or sub-reflector along axial direction opportunely, the modification of phase distribution in the original aperture of an enclosed reflector antenna can be used to reduce the phase shift caused by composite material radomes. The distortion of far-field pattern can be minimized. The modification formulas are proposed, and the limitation of their application is also discussed. Numerical simulations for a one-piece composite materials sandwich radome and a 40 m multipartite composite materials sandwich radome verify that the novel compensation strategy achieves satisfactory compensated results, and improves the distortion of the far-field pattern for the composite material radomes. For one-piece dielectric radome, more than 60% phase difference caused by radome is reduced. For multipartite radome, the sidelobe level improves about 1.2 dB, the nulling depth improves about 3 dB. The improvement of far-field pattern could be obtained effectively and simply by moving the feed or sub-reflector according to phase shift of the radome.
Composite materials; Radome; Phase compensation; Radiation pattern
Composite material sandwich radomes (Fig. 1) generally
include low-density core materials (e.g. resin) and
higherdensity skin materials (e.g. fiber), and they are widely used
in antenna-radome systems due to the high
strength-toweight ratio and good dielectric properties [
]. From the
viewpoint of structure, sandwich radomes are composed of
sandwich panels and fiber skin joints (Fig. 1(a)). The joints
are connected to each other by metal bolts and form the
frame that is solid enough to undertake the load of exotic
]. To get enough stiffness and strength, the
joints should be much thicker than skins. Meanwhile the
sandwich panels should be light in weight and low in
transmission loss of electromagnetic wave propagation in
order to achieve excellent radiation performance.
Radomes not only protect enclosed antennas against
wind, rain, ice, snow and solar radiation, but also reduce
the manufacturing cost and extend the service time of
enclosed antennas [
]. However, from the viewpoint of
electromagnetics, the radomes also lead to the degradation
of radiation characteristics of the enclosed antennas, such
as gain loss, boresight error and the rise in side-lobe level
], which can be represented by the distortion of
radiation pattern. Therefore, minimizing the degradation of
radiation characteristics and maximizing structural
stiffness are the prior purposes in the design of modern
highperformance antenna-radome systems [
One of the main reasons of radiation pattern distortion is
the change of phase difference caused by radome. In order
to mitigate the phase difference, some novel approaches
and materials have been proposed. Virone et al. installed a
special metal periodic structure in the joints to reduce the
phase difference between the joints and planes [
good agreement between the experimental and simulated
results is reported , and the results indicate that their
compensation strategy is valid and effective for mitigating
the degradation caused by radomes. The absorbing
materials is used to reduce the effect of scattered field caused by
induced current of the metal frame by enwrapping the
metal bars [
A shaped reflector antenna is designed to change the
original antenna phase distribution and compensate the
phase distortion caused by dielectric radomes [
shaped radome (nonuniform thickness) can also get a
minimal phase difference and reduce the pattern distortion
]. The degradation caused by glass fiber material error
can be compensated [
] by grinding the geometrical
thickness based on phase equivalent [
The metamaterial is applied to design a radome. By
optimizing the structure parameters of the radome [
transmission coefficient of the plane radome is close to 1,
and the degradation is almost invisible. Another
metamaterial radome which has a planar centrosymmetric
honeycomb-shaped structure can obtain a higher gain about
2.5 dB before the use of this metamaterial radome [
However, all these methods above are not easy to apply
in practice. The methods in [
] need large modifications
of the radomes or antennas and lead to high cost. The
metamaterials radome is not suitable for large
rotatable antenna-radome system.
Phase compensation is a common method and could be
applied to many electronic devices to improve their
electromagnetic performance, such as microstrip crossover
], microwave patch antenna [
reflector antenna [
], and radome [
In order to mitigate the distortion of radiation pattern
caused by composite materials radome, a novel
compensation strategy based on phase compensation is proposed.
Some simulation examples are presented to exhibit the
validity of the novel strategy for multi-band system,
multipartite dielectric sandwich radomes.
2 Analysis Methods of Dielectric Sandwich
The radome transmission coefficient T is used to expressed
the transmission characteristics [
TH2 cos4 b þ TV2 sin4 b þ 2THTV cos2 b sin2 b cos d 1=2
Where d = gH - gV,
u ¼ arctan
TV sin2 b sin d
TH cos2 b þ TV sin2 b cos d
TH or TV is the amplitude of transmission coefficient of
the wave, g is the inserted phase delay (IPD) according to
the incident angles of different points, the subscripts H and
V indicate the horizontal and vertical polarizations of the
wave respectively, and b is the polarization angle.
Transmission coefficient and IPD are the functions of
relative permittivity, loss tangent, thickness of radome
materials d and wavelength k [
The IPD is expressed by
g ¼ x
d cos c;
where x is the initial phase and c is the angle of incidence.
High frequency strategy such as physical optics (PO)
] and geometric optics (GO) [
] are usually used in
electromagnetic analysis of large radomes. In order to get a
balance between the efficiency and accuracy of numerical
analysis, the ray tracing-aperture integration method is
adopted in this study [
], which means the assumption
is infinitesimal wavelength. The electromagnetic field
values of the antenna with a radome in the far field is given
where (h, /) is the spherical coordinates of points in space,
(q, /) is the polar coordinates of points in the reflector
mapping to the aperture, E is the electric field value in
point R of the far field, f and u are the amplitude and phase
distributing functions in the antenna’s original aperture
respectively, T is the transmission coefficient of the
radome, S is the original aperture and S0 is the transmission
aperture. Figure 2 shows the schematic diagram of the
variables in aperture and radome.
3 Compensation Strategy
To reduce the degradation of radiation characteristics, both
transmission coefficient of dielectrics and inducted current
of metal should be cut down. In this study, we mainly paid
attention to the effects of transmission coefficient, and tried
to reduce the phase difference in transmission aperture.
The phase of transmission coefficient T is the key factor
that causes the distortion of radiation pattern. In the
original aperture, the phase of the wave is a constant, namely
the phase difference is 0, and the radiation pattern has no
distortion without the radome. In contrast, with the radome,
the phase of T in the transmission aperture is not a constant,
but varies with the incidence angle c. A different c leads to
a different IPD, thus induces a phase difference of T in the
transmission aperture, and finally causes the distortion of
In antenna-radome systems, radome is an indispensible
part and we cannot remove it, but we could change the
phase distribution in the original aperture. If phase
difference in the original aperture has an inverse trend to that in
the transmission aperture. The wave propagates through the
radome. Thus, the phase change will turn out to be a
constant in the transmission aperture. Finally, an ideal
radiation pattern can be obtained.
The reflector antenna is usually composed of a main
reflector, a sub-reflector, and a feed. There are three ways
to change the original aperture: shaping the main reflector,
moving the sub-reflector and moving the feed, as shown in
3.1 Shaping the Main Reflector
A small displacement of one point in the main reflector
along the axial direction dmz leads to the change of wave
transmission distance from the sub-reflector to the original
aperture. Figure 3 shows (the red line indicates the shaped
reflector, moved feed or sub-reflector). The phase shift at
the corresponding point in the original aperture is obtained
as follows by the geometric relations [
gm ¼ k dmzð1 þ cos nÞ;
where n is the flare angle from the sub-reflector to the main
However, it is not practical to shape the main reflector
for an installed reflector antenna.
3.2 Moving the Feed
Moving the feed along the axial direction dfz (offset focus)
leads to the change of transmission distance from the feed
to the sub-reflector as shown in Fig. 3. The phase shift in
the original aperture is calculated by [
dfz cos n0;
where n0 is the flare angle from the feed to the sub-reflector.
In the center of the reflector, the flare angle n0 minimizes to
0 and the phase shift is -2pdfz/k. In the edge of the
reflector, the flare angle n0 maximizes to n0max and the phase
shift is gf ¼ 2pdfz cos n0max=k. Thus, the phase difference
in the original aperture is
3.3 Moving the Sub-Reflector
Similarly, the change of the wave transmission distance by
moving the sub-reflector along the axial direction dsz
includes two parts: one is from the feed to the sub-reflector
and the other is from the sub-reflector to the main reflector.
Therefore, the phase shift in the aperture is also
compensated by two parts,
gs ¼ k
dszðcos n þ cos n0Þ:
In the center of the reflector, both flare angles n0 and n
minimize to 0 and the phase shift is 4pdsz/k. In the edge of
the reflector, flare angles n0 and n maximize to n0max and
nmax respectively, and the phase shift is
gs ¼ 2pdsz cos nmax þ cos n0max =k. Thus, the phase
difference in the original aperture is
Dgs ¼ k
cos n0max :
At the same point of the sub-reflector, n0max is less than n,
and their relationship is M ¼ tanðnmax=2Þ= tan n0max=2 ,
where M is the amplification factor of the double reflector
antenna, tan (n/2) = D/4f, D is the diameter of the main
reflector, and f is the focal length.
In the aperture S, from the center to the edge, the two
flare angles increase from 0 to n0max and nmax. If dfz is
negative, namely the feed moves to the -Z direction, the
distribution of phase difference in the original aperture is
bigger in the center and smaller at the edge. If dsz is
positive, namely the sub-reflector moves to the ?Z direction,
the distribution of the phase difference is similar to that
with a negative dfz.
For a hemisphere radome in common use, the maximum
cmax locates at the edge of the aperture, and the minimum
cmin is 0 in the center of the aperture. Thus, the phase
difference in the transmission aperture is
DgT ¼ gmax
The distribution of DgT is smaller in the center and
bigger at the edge, which is just inverse to the distribution
of phase difference caused by negative dfz or positive dsz.
Hence, the two-phase difference can offset each other and
realize the compensation of the distortion of radiation
pattern. This means DgT ¼ Dgf or DgT ¼ Dgs.
Then, the value of the offset focus of the feed is
dfz ¼ 2p 1
The value of the offset focus of the sub-reflector is
dsz ¼ 2p 2
From the above analysis, it is known that the offset focus or
T leads to a phase difference in the transmission aperture and
result in the distortion of radiation pattern as well as the
degradation of radiation characteristics. However, if they
work together, the degradation will be mitigated significantly.
Flare angle n0 is less than n at the same point in the
subreflector. To compensate the same DgT, the value of dfz is
larger than that of dsz. Thus, the compensation by moving
the sub-reflector is more appropriate than by moving the
feed in practice. For most reflector antenna in engineering,
both the sub-reflector and feed are fixed by bolts, if we
adjust the bolts, the position of the sub-reflector or feed
could be changed in a small range.
Once dsz is determined, the phase shift ga of each point
in the aperture can be obtained by Eq. (9). Then, substitute
ga into Eq. (3), and the far field of an antenna with a
radome can be expressed by
Eðh; /Þ ¼
T ðq; /Þf ðq; /Þ exp jðuðq; /Þ þ gaÞqdqd/:
By numerical integration, the calculation of Eq. (12) is
4 Simulation Examples
Two antenna-radome systems are used for simulation: (1) a
5.2 m reflector antenna with a 9.14 m one-piece dielectric
sandwich radome (Fig. 1(a)); (2) a 26 m antenna with a
40 m multipartite dielectric sandwich radome (Fig. 1(b)).
Two examples are used here for different purposes. The
first purpose is to verify the effectiveness of the
compensation strategy and its feasibility for the multi-band
antenna-radome system. The second is to test the validity
of the strategy for multipartite sandwich radomes.
Table 1 gives some information of the examples. The
parameters of the materials are listed in Table 2.
A-Sandwich (Fig. 1(a)) has two layers of skin (glass fiber) and one
layer of core (foam). C-Sandwich (Fig. 1(b)) has four
layers of skin and two layers of core. For all examples, the
original aperture follows an equal distribution of amplitude
and phase, and the enclosed antenna points to the sky.
4.1 5.2 m reflector antenna with a 9.14 m one-piece radome
The one-piece radome means that there is no connected
joint (ignored) between two panels. Hence, the jointed
panels is considered to be a smooth hemisphere. The
enclosed antenna is a Cassegrain antenna, and the focus
diameter ratio is 0.4, with n0max = 31 and nmax = 80 .
Four situations are considered in this example, including
antenna without offset focus, antenna with offset focus,
antenna under radome without offset focus and antenna under
radome with offset focus. Some parameters of radiation
characteristics are listed in Table 3. As can be seen, the power
loss (the change of Emax) is about 0.2 dB at 2.3 GHz, the
sidelobe-level (SLL) degradation is about 0.24 dB, the nulling
depth (ND) degradation is about 16 dB, and the phase
difference (PD) in the transmission aperture is 0.4. The value of
dsz is 0.066k by Eq. (11), and the value of dfz is 0.44k by
Eq. (10). The latter is much larger than the former, which
indicates that moving sub reflector is more appropriate.
After compensation, the power loss is only 0.14 dB,
which is less than the uncompensated value. The
sidelobelevel (SLL) is improved greatly and approaches to the value
of no radome. The nulling depth (ND) increases about
14 dB from -27.18 dB to -41.25 dB. The phase
difference (PD) in aperture is only 0.055, which is much less
than the uncompensated value 0.4.
At 5.3 GHz, the results are similar to those at 2.3 GHz,
but the degradation is relatively obvious. Before
compensation, the power loss is 0.67 dB, the sidelobe-level
degradation is 1.26 dB, the nulling depth degradation is 23 dB,
and the phase difference of aperture is 0.92. Hence, the dsz
will be more than 0.1k, which leads to the degradation of the
enclosed reflector antenna. Previous studies show that if the
value of the offset focus is less than 0.1k, the degradation is
so tiny that can be ignored. In this viewpoint, there is a
limitation for the compensation strategy, that is, the
maximum value of moving the sub-reflector is 0.1k. This means
that if the phase difference of T is too large, it cannot be
compensated completely. In spite of this, a partial
compensation of 0.1k is still available.
Here, after partial compensation, the sidelobe-level
degradation reduces from 1.26 dB to 0.1 dB, the nulling
depth degradation reduces from 23 dB to 5.2 dB, the power
loss reduces from 0.67 dB to 0.4 dB, the phase difference
reduces from 0.92 to 0.32.
For comparison, the results from antenna with offset
focus are also involved in Table 3. They are worse than the
results from antenna without offset focus and those from
antenna under radome with offset focus.
The above simulation results illuminate that, the radome
leads to the degradations of radiation characteristics, and so
does the offset focus. However, if the radome and the offset
focus exist at the same time with appropriate values, the
respective degradation of radome or offset focus can be
significantly reduced. That means that the offset focus can
compensate the degradation caused by radome, especially
for sidelobe-level and nulling depth.
The distribution of phase difference of T is small in
center and large at edge, while that of offset focus is large
in center and small at edge. This result is just consistent
with previous expositions. After compensation, the
maximum phase difference appears in the center and at the edge,
and the minimum is a ring in the aperture. Overall, the
whole phase difference is decreased greatly.
Notably, it is impossible to reduce the phase difference
to zero by the compensation of offset focus, since the
curvatures of the radome and the reflector are generally
4.2 26 m antenna with a 40 m multipartite dielectric radome
In practice, one-piece radomes are extremely rare, and most
radomes are multipartite dielectric ones, especially for large
radomes. In this simulation, both the panels and joints
(composed of glass fiber) are included. The metal bolts are
ignored. The effect of metal bolts is extremely small, since
the area blocked by the bolts is so small as a literature
]. The thickness of joints is 30 mm. The joints
are considered as thick dielectrics with an analysis strategy
of ray tracing. The diameter of the enclosed antenna is 26 m,
M is 3, and focus diameter ratio is 0.3.
Three situations are considered in this example: ideal
antenna without offset focus and radome, antenna under
radome without offset focus, and antenna under radome
with offset focus. Some parameters of the 40 m radome
before and after compensation are listed in Table 4. The
degradation of radiation characteristics is serious owing to
the radome thickness and the high frequency. The side-lobe
level degradation is more than 2 dB which can not satisfy
the design requirements. Since the phase differences of the
radome exceeds the limitation, the value of the offset focus
is set as 0.1k. The results are listed in Table 4.
After compensation, the phase difference in the
transmission aperture reduces from 2.65 to 2.26, the side-lobe
level varies reduces from -12.45 dB to -13.65 dB and the
degradation reduces from 2.1 dB to 0.9 dB. The SLL can
satisfy the design requirements. Meanwhile, the nulling
depth is improved by about 3 dB from -13.51 dB to
-16.47 dB. Owing to the asymmetry of radome joints, the
right and left SLLs are different.
The radiation patterns under three situations are shown
in Fig. 4. As can be seen, the improvements of the
sidelobe level and the nulling depth are very illustrious. By
careful observation, the improvement in beam width can
also be detected. Related data are given in Table 4.
The distribution of phase differences of T, offset focus
dsz, and compensated transmission aperture S’ are shown in
Fig. 5. The horizontal axis is the diameter of the aperture,
and the vertical axis is the phase difference. The difference
in phase difference of panels and joints is illustrated in the
first picture. Because the thickness of joints is much less
than that of panels, the phase difference of joints looks like
a mesh in the bottom of the picture. After compensation,
the reduction of phase difference is not obvious because of
the 0.1k limitation, but this does not overthrow the
effectiveness of the compensation.
The simulation results indicate that the offset focus can
compensate the degradation of dielectric sandwich
radomes and have a good potential application for
metalspace frame radomes, especially the distortion of radiation
For the one-piece dielectric radome (9.14 m radome),
more than 60% phase difference caused by radome is
reduced, and more than 80% of the radiation
characteristics degradation is compensated by the
proposed compensation method, since the main reason of
the degradation is the phase difference of the radome.
For the multipartite radome (40 m radome), although
there are more reasons lead to the degradation (such
as joints, frame and large phase difference of a
practical radome), a satisfied results can still be
achieved by the compensation strategy, about 50%
of the degradation is reduced, especially for the
sidelobe level and nulling depth.
For the case of the large phase difference, the
degradation is reduced partly by the proposed
method. Because there is a limitation of the
adjustable range of the sub-reflector or feed.
The method is only useful for a reflector antenna
with a standard parabolic dish. For a modified
parabolic reflector antenna, reflector shaping is a
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Peng LI, born in 1981, is currently an associate professor at Key
Laboratory of Electronic Equipment Structure Design of Ministry of
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Education , Xidian University, China. He received his PhD degree from Xidian University, China, in 2011 . His research interests include numerical computation of mult-field-coupled problem of electronic devices . Tel: ? 86 - 29 -88203040; E-mail: yinhong0523@ 163 . com Wanyen XU , born in 1989, is currently an lecturer at Xidian University, China. He received his PhD degree on mechanical engineering at Xidian University, China, in 2015 .
Liwei SONG , born in 1981, is currently an associate professor at Key Laboratory of Electronic Equipment Structure Design of Ministry of Education , Xidian University, China.