STUDY OF THE CONVERGENCE OF SEMN METHOD IN ANALYSIS
OF FINITE MICROSTRIP ANTENNAS
1
1
Farzad Tavakkol-Hamedani, Ahad Tavakoli and Lotfollah Shafai
1
Amirkabir University of Technology (Tehran Polytechnic)
424 Hafez Ave., Tehran, Iran
2
University of Manitoba, Winnipeg, Manitoba, Canada, R3T 5V6
2
I. ABSTRACT
The convergence of SEMN (surface equivalence principle and multiple network
theory) method in the computation of input impedance of a probe-fed finite rectangular
microstrip patch antenna is studied. Comparing electric and magnetic field integral
equation (EFIE and MFIE) formulations of SEMN method, it is shown that the MFIE
formulation has a better convergence criterion. Also, it is shown that lower size segments
are required when the substrate or ground plane are extended beyond the patch.
II. INTRODUCTION
SEMN method has been introduced for the analysis of finite structures [1]. Also,
EFIE and MFIE formulations of SEMN method have been utilized for the analysis of
finite rectangular microstrip patch antennas [2]. Here, we have shown that MFIE
formulation has a better convergence criterion. Also, the convergence of MFIE
formulation for three cases: truncated finite microstrip antenna, extended substrate and
extended ground plane is studied.
In each case, the top view of the antenna (involving the feed-point, the origin and x
and y unit vectors of the rectangular coordinate system and the rectangular surface
segments used in the SEMN method) is depicted. Also, the dimensions of the antenna a,
b and c and the number of segments m, n and q in respectively x, y and z directions and
the substrate relative dielectric constant r are presented. The probe diameter is assumed
to be zero.
III. COMPARISON OF EFIE AND MFIE FORMULATIONS
Consider a rectangular dielectric slab with r=2.62 and dimensions a=0.32, b=0.47
and c=0.006 that is fed by a balanced coaxial feed at xs=0.06 and ys=0.015 (all
dimensions are normalized with respect to free space wavelength). Fig. 1 shows in-phase
and quadrature components of magnetic and electric excitation fields on the upper
surface of the dielectric slab. It is seen that magnetic and electric fields have circular and
radial natures respectively and their amplitudes become singular at a sufficiently small
distance from feed-points. However, their amplitudes are zero on feed-points. In antenna
analysis, the feed-point should be modeled by a number of segments whose
electromagnetic excitation fields are assumed to be zero. Using a greater number of
segments for modeling the antenna total surface and feed-points, more accurate
0-7803-6369-8/00/$10.00 ©2000 IEEE
14
numerical results are derived. Comparing the amplitudes of magnetic and electric
excitation fields in Fig. 1, the former has a considerably lower amplitude at a feed-point
neighborhood. This, results in a better convergence criterion for MFIE (in comparison to
EFIE) formulation of SEMN method. In the following sections, MFIE formulation of
SEMN method has been utilized for the analysis of finite microstrip antennas. Also, four
zero-excitation adjacent segments around the feed-points have been used unless its
contrary is mentioned.
IV. TRUNCATED FINITE MICROSTRIP ANTENNA
Fig. 2 shows a truncated finite microstrip antenna and the convergence of its
calculated input impedance for two cases of using four and sixteen zero-excitation
adjacent segments around the feed-points in Figs. 2(b) and 2(c) respectively. Fig. 2(b)
represents that good convergence in the resonance frequency domain of the antenna is
derived by using segments of length 0.042 (=2resonance length of the patch) or less.
Fig. 2(c) represents that better convergences in nonresonance frequency domains are
derived by using greater number of zero-excitation segments around feed-points.
V. EXTENDED SUBSTRATE
Fig. 3 shows the antenna of Fig. 2(a) with extended substrate and the convergence
of its calculated input impedance. Fig. 3(b) represents that good convergence is derived
by using segments of length 0.025 or less. Therefore, lower size segments are required
for deriving accurate numerical results of finite microstrip antennas with extended
substrate. Also, it is seen that the main effects of extended substrate, are considerable
reductions in the resonance frequency and input resistance of the antenna.
VI. EXTENDED GROUND PLANE
Fig. 4 shows the antenna of Fig. 3(a) with extended ground plane and the
convergence of its calculated input impedance. As the previous case, good convergence
is derived by using segments of length 0.025 or less. It is seen that the main effect of an
extended ground plane is a considerable reduction in the input resistance of the antenna.
REFERENCES
[1] F. Tavakkol-Hamedani and A. Tavakoli, “A new approach to analysis of arbitrary
shaped, single or multilayered printed antennas based on surface equivalence
principle and multiple network theory,” in Dig. IEEE AP-S Int. Symp., Montreal, July
1997, pp. 2358-2361.
[2] F. Tavakkol-Hamedani, A. Tavakoli and L. Shafai, “Analysis of finite microstrip
antennas using surface equivalence principle and multiple network theory (SEMN),”
to appear in Proc. AP2000 int. Symp. on Antenna and Propagation.
15
(e) Imaginary electric field lines
(a) Imaginary magnetic field lines
(b) Amplitude of imaginary magnetic field lines
(f) Amplitude of imaginary electric field lines
(c) Real magnetic field lines
(g) Real electric field lines
(d) Amplitude of real magnetic field lines
(h) Amplitude of real electric field lines
Fig. 1. Characterization of magnetic and electric excitation fields of a balanced coaxial
feed on the upper surface of a rectangular dielectric slab.
16
y
a=24 mm,b=12 mm, c=3 mm,
r=3, m=8, n=4, q=1.
x
b
(a)
a
800
1000
m=8, n=4
m=12, n=6
m=16, n=8
m=20, n=10
m=12, n=6
m=16, n=8
m=20, n=10
600
400
500
200
R
R
0
0
X
X
-200
-500
3.6
3.65
3.7
3.75
3.8
3.85
3.9
3.95
-400
3.6
4
3.65
3.7
3.75
3.8
3.85
3.9
3.95
4
Freq. (GHz)
Freq. (GHz)
(b)
(c)
Fig. 2. (a) A truncated finite microstrip antenna and the convergence of its calculated
input resistance (R) and reactance (X) for two cases: (b) using four and (c) using sixteen
zero-excitation adjacent segments around feed-points.
500
R
y
R
400
m=18, n=6
m=24, n=8
m=30, n=8
R
300
x
b
200
100
a
0
-100
Substrate:
Patch:
X
X
X
a=36 mm, b=12 mm, c=3 mm,
-200
3.5
3.6
3.7
3.8
3.9
4
r=3, m=18, n=6, q=1.
Freq. (GHz)
(a)
(b)
Fig. 3. (a) The antenna of Fig. 2(a) with extended substrate and (b) the convergence of its
calculated input resistance (R) and reactance (X).
m=18, n=6
m=24, n=8
m=30, n=8
300
y
R
250
R
R
200
150
x
b
100
50
a
0
X
Grounded Substrate: Patch:
a=36 mm, b=12 mm, c=3 mm,
r=3, m=18, n=6, q=1.
-100
3.5
3.55
3.6
3.65
X
X
-50
3.7
3.75
3.8
3.85
3.9
Freq. (GHz)
(a)
(b)
Fig. 4. (a) The antenna of Fig. 3(a) with extended ground plane and (b) the convergence
of its calculated input resistance (R) and reactance (X).
17