Radiation Pattern Investigation of n Element Microstrip Patch

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Radiation Pattern Investigation of n Element Microstrip Patch
DUET Journal
Vol. 1, Issue 3, June 2012
Radiation Pattern Investigation of n Element Microstrip Patch Antenna Array
S. M. Mahfuz Alam, Md. Anwarul Abedin, Utpal Kumar Das and Md. Arifur Rahman
Dept. of Electrical & Electronic Engg, Dhaka University of Engineering &Technology, Gazipur, Bangladesh
E-mail: [email protected]
ABSTRACT
Microstrip patch antenna is widely used in aircraft, spacecraft and other application for small size, low cost and light
weight. The fringing field created on patch antenna depends on the dielectric constant of patch element. The desired
directivity of the antenna can be achieved by the proper design of the patch antenna array. In this paper the
generalized equations of electric and magnetic field for n element patch antenna array are analyzed and effect of
dielectric constant of patch element on fringing field are investigated. The results from the derived equations are
compared with PCCAD 5.0 software simulation results and results from experiments. The comparison shows that the
derived equations can be satisfactorily used for any n element patch antenna array and any phase displacement
between two patch elements.
1. INTRODUCTION
In high-performance aircraft, spacecraft, satellite and
missile application, where size, weight, cost, performance,
ease of installation, and aerodynamic profile are
constraints, low profile antennas may be required.
Presently there are many other government and
commercial applications, such as mobile radio and
wireless communications that have similar specifications.
To meet this requirements microstrip patch antennas have
been studied and researched extensively over the past
many years because of its low profile structure, light
weight, and low cost in fabrication. They are extremely
compatible for embedded antennas in handheld wireless
devices such as cellular phones, pagers etc. Some of the
principal advantages of this type of antennas are low
profile in nature, conformability to planar and non planar
surfaces, low fabrication costs and compatibility [1].
Antenna array is used to improve performances such as
gain, directivity etc. In the case of patch antenna array, it
can be used to scan the beam of an antenna system and
perform various other functions which would be difficult
with any single element. Research has been done on
radiation pattern calculation of patch antenna array by
improved induced element pattern method (IIEPM) which
transforms the large array calculation problem into two
small array problems [2]. In this paper, a generalized
equations of both electric and magnetic field for an n
element patch antenna array are derived considering the
phase shift between patch elements without calculating
the radiation pattern by transforming large array into two
Dhaka University of Engineering & Technology, Gazipur
small array and this equation is valid for any number of
array element operating at any frequency.
2. BASIC CHARACTERISTICS OF MICROSTRIP
PATCH ANTENNA
Microstrip patch antenna consists of very thin metallic
strip (patch) placed a fraction wavelength above a ground
plane. The patch is so designed that its pattern maximum
is normal to the patch. For a rectangular patch, the length
L of the element is usually λ/3< L <λ/2, where λ is
wavelength. The patch and the ground plane are separated
by a dielectric substrate of height h as shown in Fig. 1.
L
patch
w
t
Dielectric substrate
h
Ground Plane
Fig.1: Microstrip patch antenna
There are numerous substrates that can be used for the
design of microstrip antennas and their dielectric
constants are usually in the range of 2.2< εr < 12 [1]. The
microstrip line feed is used to feed microstrip patch
antenna. The transmission line model of microstrip patch
antenna is shown in Fig. 2.
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DUET Journal
Vol. 1, Issue 3, June 2012
Be = Y0 tan(β Δl)
(2)
Where Y0, β and Δl are the characteristic admittance,
phase constant and incremental length of the patch due to
fringing effect respectively.
If βΔl<<1 or Δl<< λ
Then the edge capacitance can be approximated as
𝐶𝑒 = 𝑣
𝛥𝑙
(3)
𝑝 𝑍𝑜
Where, 𝑣𝑝 =
Fig. 2: Transmission line model
𝜔
𝛽
, 𝑣𝑝 is the phase velocity and 𝑍𝑜 is the
characteristic impedance.
The field distribution is identical to that of a uniform
transmission line of characteristic impedance Z0 and the
phase voltage Vph . The fringing fields associated with
edges “01” and “23” of the patch are taken into account
by Z0 and Vph. The fringing fields associated with edges
“02” and “13” are represented by lumped admittances Ye
(edge conductance) connected at the two ends [3]. Edge
admittance is given by,
Ye =Ge +jBe
(1)
Where Be =ωCe and Ge,Be, Ce are the edge conductance,
edge susceptance and edge capacitance respectively.
The edge conductance accounts for the power radiated at
the radiating edges (or open ends). The edge susceptance
accounts for the fringing electric field (and hence the
fringing capacitance at the open end) [1].
Because of the fringing effect, the effective length of the
patch of the microstrip antenna looks greater than its
physical dimension as shown in Fig. 2. The dimension of
the patch along its length have been extended on each end
side by a distance 𝛥𝑙, which is a function of dielectric
constant, 𝜖𝑟 and width to height ration (w/h) and can be
expressed as [1]
Normalized length,
𝛥𝑙
ℎ
= 0.412
𝑤
ℎ
𝜖 𝑟 +0.3 ( +0.264)
(4)
The Normalized Length vs. Normalized Width Curve is
drawn in Fig. 4 for various values of dielectric constant,
𝜖𝑟 .
0.7
0.65
The edge capacitance, Ce is represented in terms of an
equivalent line length extension as shown in the Fig. 3.
𝜖𝑟 = 1
0.6
0.55
normalised length
The transmission-line model gives good physical insight.
Basically the transmission line model represents the
microstrip patch antenna by two slots, separated by a low
impedance (𝑍𝑜 )transmission line of length L [3].
𝑤
ℎ
𝜖 𝑟 −0.258 ( +0.8)
𝜖𝑟 = 1.5
0.5
𝜖𝑟 = 2.45
0.45
𝜖𝑟 = 5
0.4
0.35
1
2
3
4
5
6
7
8
9
10
normalised width
Fig. 4: Normalized length vs. normalized width
Fig. 3: Transmission Line Model, Edge Capacitance
From the theory of open ended transmission line, the edge
susceptance of microstrip patch can be expressed as [3]
Dhaka University of Engineering & Technology, Gazipur
From Fig. 4 it is seen that for a fixed normalized width,
the normalized length increases with the decrease in
dielectric constant and for a fixed dielectric constant the
24
DUET Journal
Vol. 1, Issue 3, June 2012
normalized length increases with the increase in
normalized width.
3. EXPRESSIONS OF E-FIELD AND H-FIELD OF
PATCH ANTENNA
EФ = A
e −jk o r
r
ejψ/2 2 cos⁡
(1 2 (k o dsinѲsinΦ + P)) (11)
And the magnetic field equation becomes
HѲ = {A
e −jk o r
r
jψ
e 2 2 cos⁡
(1 2 (k o dsinѲsinΦ + P))}/𝜂 (12)
4. RESULT AND DISCUSSION
The electric and magnetic field radiation patterns for
single element patch antenna operating at 10 GHz are
plotted using MATLAB program in Fig. 6 and Fig. 7
respectively. These results are compared with the
experimental results (Fig. 8 and Fig. 9). Fig. 10 shows
PCCAD 5.0 software result.
cos Ѳ
2
Where, k0 = phase constant = 2π/λ and 𝜂 is the intrinsic
impedance
For n element patch array the electric field intensity can
be expressed as:
Assuming, θ1 = θ2 = θ
e −jk o r
EФ = A{
r
+
e −j(k o r 1 −β )
e −j(k o r n −(n −1)β )
rn
where, A =
+
r1
e −j(k o r 2 −2β )
r2
r
90
}
× ej
270
+ ⋯+
5e-008
120
(7)
60
4e-008
3e-008
150
30
2e-008
1e-008
Finally the generalized equation becomes
e −jk o r
5e-006
Fig. 6: E field radiation pattern for single element patch
antenna (theoretical)
jk o Im hw
cosѲ
sinѲ
sin⁡(k o w
)
4π
2 k w cosѲ
o
2
EФ = A
300
30
(6)
240
sin Ѳ
ko w
210
)
(5)
180
2
cos Ѳ
2
1e-005
cos Ѳ
ko w
1.5e-005
e−jk o r sin⁡
(k o w
sin Ѳ
2
150
4π𝔶o r
cos Ѳ
2e-005
jk o I m hw
e−jk o r sin k o w
90
HѲ =
4πr
120
jk o I m hw
60
Fig. 5 shows a rectangular patch antenna array of nelements separated from each other by a distance d. The
magnetic field intensity and electric field intensity of a
single element patch antenna can be expressed as
EФ =
330
0
Fig. 5: Patch antenna array
180
(nψ /2)
n−1 ψ/2 sin ⁡
sin ⁡
(ψ/2)
0
(8)
where, ψ = k o dsinθsinΦ + 𝑃
(9)
210
330
P is the total phase shift between two patch elements.
Hθ =
EФ
η = {A
e −jk o r
r
240
×
sin ⁡
(nψ /2)
ej n−1 ψ/2
}/𝜂
sin ⁡
(ψ/2)
(10)
Finally the electric field equation for two element array
can be written as
Dhaka University of Engineering & Technology, Gazipur
300
270
Fig. 7: H field radiation pattern for single element patch
antenna (theoretical)
25
DUET Journal
Vol. 1, Issue 3, June 2012
150
210
120
240
90
270
2e-006
4e-006
6e-006
8e-006
60
300
30
330
0
From the above figures, it is clear that the radiation
patterns satisfy both the experimental and simulation
results.
180
Fig. 8: E field radiation pattern for single element patch
antenna (experimental)
Fig. 11: E field radiation pattern for two element patch
antenna array (Proposed)
90
1e-008
120
60
8e-009
6e-009
150
30
4e-009
2e-009
180
0
210
330
240
300
270
Fig. 9: H field radiation pattern for single element patch
antenna (experimental)
Fig. 12: H field radiation pattern for two element patch
antenna array (Proposed)
Fig. 10: E and H field radiation pattern for single element
patch antenna (PCCAD 5.0)
Fig. 13: E field radiation pattern for two element patch
antenna array (PCCAD 5.0)
Dhaka University of Engineering & Technology, Gazipur
26
Vol. 1, Issue 3, June 2012
180
150
210
120
240
90
270
2e-006
4e-006
6e-006
8e-006
60
300
30
330
0
DUET Journal
Fig. 14: H field radiation pattern for two element patch
antenna array (PCCAD 5.0)
Fig. 17: E field radiation pattern for P=π
90
1e-008
120
60
30
330
0
8e-009
6e-009
150
30
2e-009
2e-006
4e-006
6e-006
60
300
4e-009
0
90
270
180
120
240
210
330
240
300
Fig. 18: H field radiation pattern for P=π
180
150
210
270
Fig. 15: E field radiation pattern for P=π/2
90
6e-010
120
60
Fig. 15, Fig. 16, Fig. 17 and Fig. 18 show the radiation
pattern for different values of P. So, the proposed
equations can be applied successfully for any difference
in phase of excitation as well.
4e-010
150
30
5. CONCLUSION
2e-010
180
0
210
330
240
300
270
Fig. 16: H field radiation pattern for P=π/2
Dhaka University of Engineering & Technology, Gazipur
In this paper, the effect of dielectric constant of patch
element on fringing field is analyzed. Generalized
equations of electric and magnetic field radiation pattern
of n element patch array operating at any frequency are
proposed. The radiation patterns of both single element
and two element patch array, operating at 10 GHz are
compared with the experimental results and PCCAD 5.0
software simulation results. The results from the proposed
equations are identical to the experimental results and the
PCCAD 5.0 software simulation results. The radiation
patterns have been observed for different phase shift in
excitation between two patch elements. All results
27
DUET Journal
indicate that the proposed generalized equations can be
used for any number of patch antenna array operating at
any frequency.
REFERENCES
[1] C. A. Balanis, “Antenna theory analysis and design,”
Jhon Wiley & Sons, Inc. second edition, 1996.
[2] Zhang, S., Gong, S., Gong, Q., Guan, Y. and Lu,
B. , “Application of the Active Element Pattern
Method for Calculation of the Scattering Pattern
of Large Finite Arrays,” Antennas and Wireless
Propagation Letters, IEEE , vol.10, no., pp. 83-86,
2011
[3] Manik Gujral, Tao Yuan, Cheng-Wei Qui, Le-Wei Li
and Ken Takei, “Bandwidth increment of microstrip
patch antenna array with opposite double- E EBG
structure for different feed position,” International
symposium on antenna and propagation ISP-2006.
[4] P. Bhartia, K. V. S. Rao, and R. S. Tomar,
“Millimeter-Wave Microstrip and Printed Circuit
Antennas,” ARtech House, Boston, MA, 1991.
Dhaka University of Engineering & Technology, Gazipur
Vol. 1, Issue 3, June 2012
[5] R. F. Harrington, “Time Harmonic Electromagnetic
fields,” McGraw-Hill Book Co. p. 183, 1961.
[6] E. O. Hammerstad, “Equations For Circuit Design,”
Proc. Fifth European Microwave Conf., pp. 268-272,
September 1975.
[7] N. G. Alexopoulos and I. E. Rana, “Mutual Impedance
Computation Between Printed Dipoles,” IEEE Trans.
Antennas Propagate, Vol. AP-29, No. 1, pp. 106-111,
January 1981.
[8] D. T. Paris, W. M. Leach Jr. and E.B. Joy, “Basic
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[9] J. D. Kraus. “Antennas,” McGraw-Hill, Inc, Second
edition, 1988.
[10] J. A. Edminister, “Electromagnaetics,” McGraw-Hill,
Inc., Second edition, 2006.
[11] Sergey M. Makarov, “Antenna and EM modeling
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edition, 2006.
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