# Circular Microstrip Patch Array Antenna for C-Band Altimeter System

Authors: Asghar Keshtkar; Ahmad Keshtkar; A. R. Dastkhosh
Journal: International Journal of Antennas and Propagation
 (2008)

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## Abstract

The purpose of this paper is to discuss the practical and
experimental results obtained from the design, construction,
and test of an array of circular microstrip elements. The aim
of this antenna construction was to obtain a gain of
12 dB, an acceptable pattern, and a reasonable value of
SWR for altimeter system application. In this paper, the
cavity model was applied to analyze the patch and a proper
combination of ordinary formulas; HPHFSS software and
Microwave Office software were used. The array includes four
circular elements with equal sizes and equal spacing and was
planed on a substrate. The method of analysis, design, and
development of this antenna array is explained completely
here. The antenna is simulated and is completely analyzed by
commercial HPHFSS software. Microwave Office 2006 software has
been used to initially simulate and find the optimum design
and results. Comparison between practical results and the
results obtained from the simulation shows that we reached
our goals by a great degree of validity.


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## Body

## 1. Introduction

Microstrip patch antennas are
popular, because they have some advantages due to their conformal and simple
planar   structure. They allow all the advantages of printed-circuit  technology.
A vast number of papers are available in the literature, investigating various
aspects of microstrip antennas [1–5]. Development
of microstrip antennas was initiated in 1981, where a space-borne, light-weight,
and low-profile planar array was needed for a satellite communication system.
Since then, the development of the microstrip antenna has been expanded into
three major program areas: mobile satellite (MSAT) communication, earth remote sensing,
and deep-space exploration. The space segment of the MSAT system required the
development of an efficient, light-weight, and circularly polarized L-band
multiple-beam reflector feed array. In the ground segment, the MSAT required
the development of several low-cost and low-profile car-top-mounted L-band
antennas. In the area of earth remote sensing, several dual-polarized microstrip
arrays are needed for a bistatic radar application, at both the L-band and
C-band frequencies, as well as a 1.5-meter-long array at C-band for the
aircraft interferometer synthetic aperture radar (SAR) application. In
addition, a large Ku-band microstrip planar array (3-meter diameter) has been
proposed for a scatterometer application.Finally, a more recent effort
calls for the development of a Ka-band MMIC array, as the reflector feed for a
future deep-space exploration communication system, as well as a Ka-band array
for the advanced communication technology satellite (ACTS) experiment, as a
mobile terminal antenna. The design and analysis techniques which have been
heavily relied on are the multimode cavity theory and the conventional array
theory. Recently, Luk et al. studied the characteristics of the rectangular patch
antennas mounted on cylindrical surfaces [6]. Assuming the substrate thickness to
be much smaller than wavelength and radius of curvature, they found that the
resonant frequencies and the fields under the patch are not affected by
curvature. Usually the radiation pattern of a single element is relatively
wide, and each element provides low values of directivity. In many applications,
it is necessary to design antennas with very high-directive characteristics to
meet the demands of long-distance communications. This can only be accomplished
by increasing the electrical size of the antenna. One way to enlarge the
dimensions of the antenna without necessarily increasing the size of the
individual elements is to form a set of the radiating elements in an electrical
and geometrical configuration. This new form of disposing element is  designated array.
After the rectangular patch, the next most popular configuration is the
circular patch or disk.


## 2. Materials and Methods

In this paper, an antenna array consisting of four equal circular
elements with equal  spacing, placed in the H-plane, has been examined (Figures1 and 2).Geometry of circular microstrip patch antenna.Figure 2
Geometry of the array of circular microstrip patch elements.In Figure2, the way of arranging circular patches and feedings is shown
(the antenna array is fed from its center). They have the same phase in their
entries considering the shapes of feed lines for each of the circular patches.


## 2.1. Theory

In Figure1, if h≪a and h≪λ,
the analysis carried out by Luk et al. [6] showed that, for the rectangular patch, the fields under the cavity are
essentially the same as the planar case. It is reasonable to expect that this
conclusion is independent of the shape of the patch. For the circular patch,
the radial electrical fields of TM modes are given by [6] (1)Eρ=E0Jn(knml)cos[n(β−β0)], while Jm(x) is the Bessel function of the first kind of
order m; and knm
is the  root of Jn′(knma)=0 .
Also, “a” that is shown in
Figure 1 is the diameter of each of the circular
patches. The value of β0 is determined by the position of the
coaxial feed. However, the resonant frequency is (2)fnm=knmca2πaeεr, where c is the speed of light in free space; and ae is the effective radius that is given by (3)ae=a{1+2hπaεr[ln(πa2h)+1.7726]}0.5. Therefore, the
resonant frequency of (2) for the dominant TMz110 should be expressed as (4)(fr)110=1.84122πaeεrc.


## 2.2. Design

For patch design, it is assumed that the dielectric
constant of the substrate (εr), the resonant frequency (fr in Hz), and the height of the substrate h (in cm) are known.Design Procedure
A first-order
approximation to the solution of (3) for a is to find ae using (4) and to substitute it into (3) for ae and a in the logarithmic function. This will lead to
(5)a=F{1+(2h/πεrF)[ln(πF/2h)+1.7726]}0.5, where (6)F=8.791×109frεr. The design of microstrip antenna is done as follows: (7)fr=4.3GHz,h=0.16cm,εr=2.33.By substituting in (5),  a𝔍←1.25cm.Richards et al.  have reported, calculated, and measured values of
the input impedance of a coaxial-feeding rectangular patch withεr𝔍←2.62 and h𝔍←2.62 cm [7]. For a coaxial feed,
matching the antenna impedance to the transmission-line impedance can be accomplished
simply by putting the feed at the proper location. In [8–11], some
formulas have been suggested for computing the input impedance in the resonance
state. Typically with very thin
substrates, the feed resistance is very smaller than resonance resistance, but
in thick substrates, the feed resistance is not negligible and should be
considered in impedance matching determining the resonance frequency. In
general, the input impedance is complex, and it includes both a resonant part
and a nonresonant part which is usually reactive. Both the real
and imaginary parts of the impedance vary as a function of frequency. Ideally,
both the resistance and reactance exhibit symmetrically about the resonant frequency,
and the reactance at resonance is equal to the average of sum of its maximum
value (which is positive) and its minimum value (which is negative). A formula that has been suggested to
approximate the feed reactance, which does not take into account any images, is
[12] (8)xf=−ηkh2π[ln(kd4)+0.577], where d is the diameter of the feed probe.Figure3 shows the reflection
coefficient as a function of frequency simulated with HPHFSS 5.4 software. In
the resonance state, the input impedance is a real value and has its maximum
quantity. It can be shown that coupling between two patches, as coupling
between two apertures or two wire antennas, is a function of the position of
one element relative to the other [13–17]. For two
circular microstrip patches, the coupling for two side-by-side elements is a
function of the relative alignment (Figure 2).
In Figure 4, the coupling value that is measured for two cases in E-plane and
H-plane is plotted. In this figure, the measure of coupling is plotted versus the
distance between centers of two adjacent circular patches.Figure 3
Reflection coefficient
as a function of frequency for circular microstrip antenna at 4.3 GHz.Figure 4
Dominant mode mutual coupling for the
conventional circular microstrip patch antenna [13].It can be seen that the coupling
in H-plane is very small in comparison with its value in E-plane. It is better
to place the elements of the antenna array in H-plane and we showed this in
this paper. In the antenna discussed here, the spacing between circular patches
(s) is 3.8 cm. Considering that the
operating frequency is 4.3 GHz, the wavelength will be 7 cm. Consequently, the
value of s/λ is equal to 1.9,
and then using the plot in Figure 4, the
value of coupling is about−30 dB, that
is very small and negligible.


## 3. Results and Discussion

## 3.1. Numerical Results and Simulation

The aim of this project is to develop an antenna
with a directional pattern and a gain at least equal to 12 dB. An antenna array
with equal spacing and uniform excitation was designed. The circular microstrip antenna was simulated by Ansoft Ensemble 8 that
is based on the method of moment. For obtaining pattern of this antenna array (N=4),
we have the following [18]: (9)AF=A0sin(Nψ/2)Nsin(ψ/2)=A0sin(2ψ)4sin(ψ/2),(10)ψ=α+βdsin(θ)cos(φ),(11)βd=(2πλ)(s)=(2π7)(3.8)=π. Here, α=0 is the phase difference between elements. Figure 5 shows  the array factor. The  first null beam width is
[18]Array factor for 4 linear elements [18]: (a) H-plane cut and  (b)
3D pattern.
(a)(b)(12)BWFN=22λNd=22×7×10−24×3.8×10−2=115°,HPBW=20.886λNd=20.8867×10−24×3.8×10−2=76°, where
AF
in (9) is the array factor and beta = (2*pi/lambda), where lambda is the wavelength.
“HPBW” is the half-power-beam width, and “BWFN” is the beam
width between first nulls.These quantities are used to obtain a whole antenna pattern by
considering the pattern of a circular microstrip element. The pattern is almost
symmetric (in both E-plane and H-plane), and side lobes are very small (Figure6).
A plot
of the directivity of the dominant TMz110 mode as a function
of the radius of the disk is shown in Figure 7. The measurement of antenna
parameters by theoretical calculations is somehow difficult, but we can
calculate them easily by softwares, such as HPHFSS. In general, the dependence
of antenna parameters to their physical parameters can be mentioned. The
bandwidth is inversely proportional to εr.
As we know, the total directivity is equal to multiplication of patch
directivity and to the array directivity. From the diagrams in Figures 5 and 7,
the value of directivity factor of circular microstrip antenna is about 5 dB,
and then a directivity of 13 dB at 4.3 GHz is achieved with the main lobe in
the broadside direction, with the 50-degree HPBW, and 25 dB SLL below the main
lobe.Figure 6
Computed (based on moment method and cavity models) E-plane and H-plane patterns of circular microstrip patch antenna: E-plane (ϕ=0°,180°), H-plane (ϕ=90°,270°).Figure 7
Directivity versus effective radius for circular microstrip patch
antenna operating in dominantTMz110 mode
[12].The circular microstrip patch array
antenna was simulated by Ansoft Ensemble 8 and is  shown in Figure6.In contribution
to our discussion, we consider the results of the simulation. In the analysis
of this antenna by HPHFSS software, three-dimensional pattern of this antenna is obtained. It
is shown in Figure8, and its pattern in E-plane and H-plane is also shown in
Figure 9.Three-dimensional pattern of the array antenna with the circular microstrip patches
simulated with the HPHFSS 5.4: (a)ϕ=0°, (b) ϕ=90°.
(a)(b)Figure 9
E-plane and H-plane patterns of the array antenna with the
circular microstrip patches simulated with the HPHFSS 5.4.Considering the obtained value of input impedance
by HPHFSS software, we can obtain the matching impedance by Microwave Office
software (or analytic methods). Considering the feed lines, the circular
patches have the same phase at their entries, as can be seen in Figure2, we
specify the impedance in each line by varying the width of lines until we
obtain the amount of input impedance equal to 50 Ω. The value of VSWR for this antenna that is
obtained by Microwave Office software is shown in Figure 10, and the value of
reflection coefficient that is obtained by HPHFSS software is shown in Figure
11. Regarding the simulation with HPHFSS 5.4 software, the input impedance of
the antenna is 55+25j, and so we have (13)|Γ|=|Zl−Z0Zl+Z0|=0.2362=−12.5dB,VSWR=1+|Γ|1−|Γ|=1.6.Figure 10
VSWR as a function of
frequency simulated by Microwave Office.Figure 11
Reflection coefficient versus frequency of the
array antenna with the circular microstrip patches simulated with the HPHFSS
5.4.


## 3.2. Array Antenna Configuration

The array antenna was constructed as shown in Figure12. The dimensions and
structural diagram of the antenna are shown too in this  figure. The
fabricated patch was designed to  operate at 4.3 GHz. The patch is probe feeding, and the ground
plane is finite for this patch and has the dimensions of 15=m←4cm. By selecting
proper values for microstrip-line
width and length and the position of the feed point, a good impedance bandwidth
can be obtained. An inset feed scheme is employed to match the patch antenna to
a 50Ω coaxial probe feed. The dielectric material
has a permittivity of 2.33 and a thickness of 0.16 cm. The substrate of this
antenna is made of RT/Duroid 5870, fabricated by Rogers Company (Mentor, OH, USA).Figure 12
Pictures of the fabricated antenna and
its geometry. The feeding line is a standard50Ω coaxial probe feed. Other dimensions are W1=0.4cm, W2=0.6cm, W3=0.3cm, W4=0.5cm, W5=0.6cm, W6=0.2cm, L1=3cm, L2=1.9cm.


## 3.3. Results of the Test

In the test process, the antenna pattern and the value of VSWR were obtained.
Antenna  radiation performance was measured and recorded in two orthogonal
principal planes (E-plane and H-plane or vertical and horizontal planes). The
pattern was plotted in
the form of polar coordinates. By definition, near-field tests are done
by sampling the field very close to the antenna on a known surface. From the
phase and amplitude data collections, the far-field pattern was computed in the
same fashion that theoretical patterns were  computed from the theoretical field
distributions. The transformation used in the computation depends on the shape
of the surface over which the measurements are taken with the scanning probe. An
antenna range instrumentation must be designed to operate over a wide range of
frequencies, and it usually can be classified into five categories as follows:(1)
source antenna and transmitting system,(2)
receiving system,(3)
positioning system,(4)
recording system,(5)
data-processing system. This
technique involves an antenna under test which is placed on a rotational
positioned and rotated around the azimuth to generate a two-dimensional polar
pattern. This measurement was done for the two principal axes of the antenna to
determine parameters such as antenna beam width in both the E- and H-planes. The practical results of the test are in
agreement with the desirable results and theoretical analysis. E-plane and
H-plane patterns of the antenna are shown in Figure 13. In the practical test carried out by AGILENT
8510C network analyzer, the value of VSWR in central frequency was 1.5433 that
was well in agreement with the theoretical analysis (Figure 14). Variation in the measured performance is mainly due to
imprecise fabrication by a milling machine. It is important to  calibrate
the network analyzer before doing VSWR measurement. The network analyzer should
be calibrated for a suitable frequency range containing the band where the antenna
will operate. Typical network analyzers have a cable with SMA connector in the end.
Calibration was performed by connecting three known terminations, 50 Ω load, short, and open, to this SMA connector. After calibration the reference plane will be
at the connection point of the SMA connector. To measure the reflection at the
feed point of the antenna, a semirigid coax cable with SMA connector in one end
can be used.Figure 13
Measured E-plane and H-plane patterns of the array antenna with the circular microstrip patches.Figure 14
VSWR as a function of frequency measured by the AGILENT
8510C network analyzer.


## 4. Conclusion

A small microstrip patch antenna
array has been presented. The antenna has been  designed to be used in altimeter
system applications, in the C-band. In fact, this
antenna was designed for 4.3 GHz and 12 dB gain. But as you can see,
4.2 GHz
also has good pattern and  proper VSWR. The design has been accomplished
using commercially available HPHFSS, Ansoft Ensemble 8, and Microwave Office
2006 softwares. The designed antenna has shown good performance in terms of
return losses and radiation (a prototype has been fabricated and tested). Good
agreement has been obtained between simulation and experimental results,
providing validation of the design procedure. Good performance has been
obtained for the envisaged applications.



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*Source: 389418-2008-02-18.xml*