free [11]. However, through the similar analysis as the Galerkin
testing, the line testing also suffers the low frequency breakdown.
Instead of walking through the similar mathematical proof, numer-
ical experiments are presented to confirm the phenomenon. For the
thick rectangular loop previously shown in Figure 2, it has been
demonstrated that EFIE in double precision breaks down at the
frequency of 10
-4
GHz when the Galerkin testing is in use. In this
situation, the self interaction of the (1, 1) element is as follows:
L
0
v
(1,1) = (-1.982027095940055E-013, 9.196015336656657E-006),
L
0
s
(1,1) = (6.203428645183186E-014, -1468677925.16896),
L
0
(1,1) = (-1.361684231421736E-0130, -1468677925.16895).
Here, the subscript 0 refers to the free space, L
0
(1,1) is the (1, 1)
element of the EFIE matrix, which has two terms L
0
v
(1,1) and
L
0
s
(1,1) . Apparently, the element is dominated by the imaginary
part and the smooth term has no contribution to the final result. The
same numerical experiment is applied to the line testing. The
corresponding results are
L
0
v
(1,1) = (-1.982027168700083E-013, 1.078885059767963E-005),
L
0
s
(1,1) = (6.203428645183186E-014, -1818280941.36972),
L
0
(1,1) = (-1.361684304181764E-013, -1818280941.36971).
The line testing method also loses the smooth term. Further
comparisons are collected in Table 3. Both testing methods break
down at 10-4 GHz. The testing scheme does not change the low
frequency behavior of EFIE.
8. CONCLUSION AND GUIDELINE
It can be concluded that high precision computation can postpone
the low frequency breakdown for the RWG-based EFIE. The low
frequency limit is determined by the electrical size of the basis
functions, that is, the mesh element. For example, the electrical
size of the mesh element should be larger than 10
-8
of the
wavelength for the double precision computation. Such a conclu-
sion can serve for a guideline for the application of EFIE with the
RWG basis function in the full-field regime.
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© 2008 Wiley Periodicals, Inc.
NEW BANDWIDTH ENHANCEMENT
AND MULTIRESONANCE TECHNIQUE
FOR MICROSTRIP PATCH ANTENNA
Patra Pradyumna Kumar, Dr. S. S. Pattnaik, Swapna Devi,
Ch. Vidyasagar, G. V. R. S. Sastry, and K. M. Bakward
Department of ETV and ECE, National Institute of Technical Teachers’
Training and Research Center, India; Correspondence to:
pk_dalu@yahoo.co.in
Received 4 October 2007
ABSTRACT: The quality factor, bandwidth, and efficiency are anten-
na’s figures of merit and these are interrelated. There is no typical
method that gives full freedom to optimize these independently. Here we
proposed a novel and new method to optimize bandwidth with respect to
radiation quality factor Q
r
. Slicing a substrate into two thin layers sub-
strate, an impedance bandwidth of 12% is achieved while reducing the
volume by 44.5%. The technique proposed shows that instead of single
thick substrate, if two thin substrates are used, an enhancement of im-
pedance bandwidth takes place while maintaining high antenna gain
and radiation efficiency. This is a new and novel technique for band-
width enhancement in microstrip patch antenna and is quite different
from stacked antenna. In this article, we sliced a substrate into two thin
substrates each of 1-mm thick to achieve a bandwidth of 12% and radi-
ation efficiency of 80.5549 with an overall volume reduction of 44.5%.
While a single substrate of thickness 2.5 mm which is more than the
total thickness of the discussed structure gives only 5% bandwidth for
same antenna dimensions. The proposed structure will find potential
application in MIMO antenna system due to its volume reduction and
other enhanced features. © 2008 Wiley Periodicals, Inc. Microwave Opt
Technol Lett 50: 1162–1165, 2008; Published online in Wiley Inter-
Science (www.interscience.wiley.com). DOI 10.1002/mop.23323
Key words: IE3D; microstrip antenna; slicing substrate; wideband
width; multiresonace
TABLE 3 Comparisons Between the Galerkin Testing and
the Line Testing with Double Precision for the Thick
Rectangular Loop
Frequency
(GHz)
Galerkin Testing Line Testing
(L
) I{Y
in
} (L
) I{Y
in
}
1E-4 6.40E17 -4.86E2 1.73E18 -4.89E2
1E-3 2.48E17 -4.84E1 2.92E17 -4.80E1
1E-2 2.65E14 -4.84 3.81E14 -4.80
1E-1 2.48E12 -4.84E-1 3.46E12 -4.80E-1
1162 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 5, May 2008 DOI 10.1002/mop