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IETE Journal of Research
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Input Impedance, Bandwidth and Efficiency of an
Edge-Modulated Microstrip Antenna
a
b
D N Khanra , S K Chowdhury & A K Mallick
a
c
Department of Physics, V S Mahavidyalaya, Manikpara 721 513, India.
b
Department of Electronics and Telecommnication Enggineering, Jadavpur
University, Calcutta 700 032, India.
c
Department of Electronics and Electrical Communication Engineering, Indian
Institute of Technology, Kharagpur 721 302, India.
Published online: 26 Mar 2015.
To cite this article: D N Khanra, S K Chowdhury & A K Mallick (1998) Input Impedance, Bandwidth and Efficiency of an
Edge-Modulated Microstrip Antenna, IETE Journal of Research, 44:1-2, 49-60, DOI: 10.1080/03772063.1998.11416029
To link to this article: http://dx.doi.org/10.1080/03772063.1998.11416029
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IETE Journal of Research
Vol 44, Nos I & 2, January-April 1998, pp 48-58
Input Impedance, Bandwidth and Efficiency of an EdgeModulated Microstrip Antenna
D N KHANRA
Department of Physics, V S Mahavidyalaya, Manikpara 721 513, India.
S K CHOWDHURY
Department of Electronics and Telecommnication Enggineering, Jadavpur University, Calcutta 700 032, India.
AND
Downloaded by [UQ Library] at 13:15 15 July 2015
A K MALLICK
Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology,
Kharagpur 721 302, India.
A sinusoidally edge-modulated microstrip patch antenna has been analysed using the modal
expansion cavity model. The investigations have been carried out to explore the input impedance,
bandwidth and radiation efficiency of the modulated structure against its physical parameters
like the modulation depth and periodicity. The simulated results clearly show that the bandwidth
jncreases with modulation depth under certain conditions of excitation. The analysis further
shows that the modulated structure provides a lot of flexibility in matching the antenna to the
standard feeder lines. Experimental results tally satisfactorily with the theoretical data.
Indexing terms : lmput impedance, Bandwidth, Edge-modulated, Microstrip antenna.
M
ICROSTRIP patch antennas are being increasingly
view, a sinusoidally edge-modulated patch antenna (Fig 1)
has been considered for analysis and studies in order to
improve the bandwidth and radiation characteristics without
increasing the overall size of the antenna structure. The
proposed modulated structure provides some additional
design parameters for controlling the antenna characteristics.
The physical parameters are the modulation factor r,
periodicity p, and average half-width ii2 (half of the average
width). In this paper, the input impedance, resonant
frequency, bandwidth and radiation efficiency of the
modulated patch antenna have been studied for different
modes of excitation with varying modulation factor and
periodicity. Analysis indicates that the physical parameters
of the modulated patch antenna have significant effects over
its antenna characteristics. The beam width of the radiation
pattern widens [IOJ and the bandwidth increases with the
increase in modulation factor, r although the area of the
patch remains the same. It may be noted that the unique
combination of wide beam width and broad bandwidth is an
attracting feature of a microstrip antenna for its use in mobile
communication systems [Ill. Further, the slope of the
resonant resistance versus feed position curve decreases with
the modulation factor r which indicates that matching to a
particular impedance value would be better in the modulated
structure than the conventional rectangular patch. These
improved antenna characteristics may put it across in a more
advantageous position in comparison with the rectangular
patch antennas. Theoretical data have been experimentally
verified and they are in good agreement with each other.
used in microwaves due to their many interesting
physical and electrical properties. In particular, the
rectangular and circular disk structures have been extensively
studied by many a research workers [1-31. The recent trend
in the study of microstrip antennas indicates that various
unconventional shaped patch antennas provided improved
performance and better flexibility in the design. For instance,
an elliptic resonator is preferable over circular disk 141 for
application in harmonic multipliers and parametric
amplifiers where the eccentricity, as a design parameter,
provides additional tlexibility and enhances the usefulness
of this structure. A stripline circulator using an apex-coupled
equilateral triangular resonator [SJ has a bandwidth three
times as large as that of a circular disk. The main drawback
of microstrip antennas is their inherent narrow bandwidth
and broadening the bandwidth is the most challenging task
for research workers. Many efforts have been made to
improve the bandwidth of microstrip antennas. But the
methods used invariably increase the volume and overall
size of the antenna to a large extent either by extending the
radiating surface 16 1 or by increasing the antenna
thickness 171, by coupling additional resonators [SJ or using
parasitic elements 191. The main research aim is clearly to
investigate ways of improving the bandwidth without
sacrificing the conformal planar structure, low volume and
weight, and the operational advantages. With this aim in
Paper No 131-8; received 1995 March 27; revised 1998
April 15; Copyright ©1998 by the IETE.
49
so
IETE JOURNAL OF RESEARCH. Vol44, Nos I & 2, 1998
.I
I
PLANE
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Fig I The sinusoidally width modulated patch antenna
ANALYSIS
There are different analytical and numerical
techniques [l 2- 16l for the analysis of microstrip antennas.
But some of them are computationally expensive while some
others are applicable only to regular shapes. The modal
expansion cavity model [l?J on the other hand, is applicable
to rectangular as well as to various other unconventional
shapes whose geometries are specified simply by curvilinear
orthogonal coordinate systems. Moreover, it provides simple
and closed form expressions for the different antenna
characteristics. It provides a good insight into the radiation
mechanism of the antenna. Further, the location of the feed
and the complete spectrum of modes or only the dominant
mode can be considered in the analysis. Keeping all these
in mind, the modal expansion cavity model has been
employed for the analysis of the proposed modulated
structure. In this model the patch antenna is considered as a
thin TM cavity with leaky magnetic walls and the fields
inside the antenna are assumed to be those of the cavity.
Therefore, the first step. of the analysis is to solve the
electromagnetic wave equation to obtain the field
expressions within the cavity. This requires a coordinate
system which is quite natural to the boundary surfaces of
the cavity formed by the modulated patch and the ground
plane. Since, the rectangular or any other standard
coordinate system is· not suitable for this purpose, a new
coordinate system (u 1, u2 , u 3 ) has been established by
coordinate transformation. The relationship between the
rectangular and the new coordinate system for sinusoidal
modulation (Fig 2) is obtained as follows:
21t Lll
y = "'-2 [1- rcos (-p.-)];
(I)
where r is the modulation factor and p is the periodicity as
stated earlier. Under the physical constraint r u2 ! p « 1, the
new coordinate system is orthogonal and the corresponding
wave equation is separable.
The close spacing of the patch conductor to the ground
plane tends to concentrate the fields underneath the patch.
The fields leak out into the air through the substrate
surrounding the patch. The first order approximation to the
microstrip antenna is an enclosed cavity bounded by a
magnetic wall along the edges, and by electric walls from
above and below. Also, for the small height of the cavity
compared to the wavelength, h «~.only the urcomponent
of the electric field and the u 1 and u2-components of the
magnetic field exist in the cavity. Assuming ei 001 time
variation, the electric field £ 3 due to a urdirected current
probe located at (u 1', u2 ') in the patch satisfies the wave
equation:
(2)
where w is the angular frequency, k2 = ail J.lo E 0 E,,
h (u 1 ', u2 ') is the current density at the feed point and V, is
the transverse del operator with respect to urax·is. The
boundary condition satisfied by £ 3 is:
(3)
where, sm is the magnetic wall boundary of the modulated
patch and it coincides· with the outward extensions due to
the fringing effect and n is the unit normal to the boundary.
A solution of eqn (2) may be expressed as:
E3 (ttl, u2)
=L
L
m=O n=O
(4)
DN
KHANRA
eta/:
51
INPUT IMPEDANCE, BANDWIDTH AND EF;;tctENCY OF AN EDGE MoDULATED MtCROSTRIP ANTENNA
where, the Lame's coefficients h; in the (u 1, u2
coordinates are given by:
y
,
u 3)
Thus, eqn (6) reduces to two ordinary differential equation
as given by:
u 1 '"' CONSTANT
(7a)
(7b)
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Now, satisfying the boundary conditions that the normal
component of the electric field is zero on the boundary of
the patch, the solution of eqn (7a) may be obtained by
transforming it to the general form of the Mathieu
equation [IS] as given by:
L
m=O
Am cos (m n u11p)
(8a)
Ul(ul)=--------
~
u1 = CONSTANT
u 2 ..
1
and the solution of eqn (7b) is readily obtained as:
CONSTANT
~
u2 (u 2 ) = n=O
L Bn cos { n n ( w wI 2 + u2 )
(8b)
u,
0
Pig 2 The patch contiguration in respect to the transformed coordinate system (u 1, u 2, u 3 )
where, A11111 are the mode amplitude coefficients and 'I'm 11
are the ttrdirected orthonormalised electric field vectors for
the TM 11111 mode. The mode vectors satisfy the homogeneous
wave equation as given below:
2
}
2
(Y'1 + K 11111
'l'mn
)
= 0 with
d'Jimn
a;;=0
where,
w = 2 u 2 [I- r cos (2 n u 1 I p)].
This w is the width of the modulated patch and it varies
along the u 1-axis. Its minimum value is w 1 (=2 ii 2 (1 - r)
and maximum value is w 2 (= 2 ii 2 (I+ r)) (Fig 1).
For a non-radiating cavity with perfect magnetic walls, the
electric field mode vectors may be expressed as:
(5)
mTr:u 1 )
Xmn
The resonant wavenumber Km 11 is given by K 2 mn
= E 0 = E 0 E r Jl 0 W rn 11 ; W mn being the complex resonant
angular frequency corresponding to the TM 11111 mode.
Now eqn (5) may be solved by employing the separated
solution technique. In an orthogonal curvilinear coordinate
system eqn (5) may be expressed as:
3
L
i =I
+K
()
d U;
2
m n 'I'm n
=0
(6)
li'mn (ul, L12)
co
( s - - cos
~nTr:(w/2+u2 ))
(I
W
=- - - - - - - - - - - - - - - - - -,JJ-rcos(2tru 1 /p)
(9)
where Xmn
=
{
1
V;
m = 0 · and
m= 0 or
m :;tO and
n=O
n=O
n:;tO
But, for the radiating cavity with leaky magnetic walls,
the eigenvalues become complex and the electric field mode
vectors no longer have a zero-normal component on the
cavity walls. However, the perturbation is so small that the
electric field mode vectors are still accurately expressed by
eqn (9) 1191.
52
IETE JOURNAL OF RESEARCH, Vol 44, Nos 1 & 2, 1998
Now, if the antenna is fed by a urdirected current probe
10 of small rectangular cross-section (Llu 1Llu 2),at (u 1', u2 ' ),
A
u 1'+ t::.u 112
J
= .k YJl 0 E 0 E r
mn 1
k2 -k2mn
=]·
{go_h
2pu 2
then· the coefficients of each electric mode vector are
obtained from eqn (9) as given by:
J.
1/lmn
du 1 du 2 tlu3
u 1' - llu 1 /2
kxmn
2
2
lo G m n (ul
k -k mn
,
,
(10)
• U2 )
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where,
{
1 ) . (mnllu 1 )
mnu'
• ( (m+2)nllu 1 )
cos ( -sm
·[ cos ((m+2)nu'1 ) sm
. 2p
+ (L)
. p
2p
p
( m~~ u 1
4
)
·
·
{ (m + ~; Ll u 1
}
Now, substituting the above value ofA m n in eqn (4) the expression for the'u 3- directed electric field is obtained as:
1:
m=O
1:
n=O
(11)
VI- rcos (2 nu 1 I p)
Equation (11) gives the general expression for the ur
directed electric field within the cavity. The cavity is able
to support an infinite set of ™mn resonant modes of
different frequencies with different amplitudes. But the fields
excited by the feed will be dominated by a particular mode
whose resonant frequency is nearest to the excitation
frequency. In practice, the antenna is fed by the resonant
frequency of a particular mode of interest. In that case, the
fields inside the cavity consist of the desired mode along
with some of its harmonics only. Since the resonant
frequencies .of all these modes are far apart in the frequency
spectrum, the chance of overlapping of these harmonics over
the desired mode is remote and the contribution of the
harmonics is insignificant. Thus, the general response of
the patch antenna is controlled by the desired mode only.
Therefore, for all practical purposes the basic analysis of
the patch antenna is done on the assumption that only the
desired mode exists [201,
Input Impedance
The input impedance at the feed point (u'1, u'2 ) is
defined as the ratio of the input voltage and the «urrent as
given by: .
Z. = V in =- h E3 (u't• u'2)
m
Io
lo
(12)
o
In an ideal cavity, the loss-tangent is related to the
quality factor Q by the relation o = 1/Q. In case of the
patch antenna, the power dissipated by it includes the power
absorbed in the loss mechanisms (conductor loss and
dielectric loss) as well as the power radiated into the far
field. The effects of all these. losses are taken into account
by defining an effective loss-tangent, oeff in terms of the
total quality factor, QT. The total Q-factor of the antenna is
the combination of all the Q-factors corresponding to
0
53·
N KHANRA et al : INPUT IMPEDANCE, BANDWIDTH AND EFFICIENCY OF AN EDGE MODULATED MICROSTRIP ANTENNA
radiation, conductor and dielectric losses (viz., QR, Qc and
Q1, respectively). Thus, the "effective loss-tangent" 8eff of
terms of this 8eff• an effective complex wave number, ke.ff is
defined as follows:
the dielectric substrate may be expressed as given below 121 1:
(18)
(13)
The general expression for the different Q-factors of a
microstrip patch antenna is given by:
Substituting this value of the wavenumber and that for
E 3 (u 1 ', u2 ') from eqn (II) in eqn (12) the input impedance
for the TMmn mode may be written as:
z m. = jWJ.L 0 hc2
2p ii2E r
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(14)
where, E.1 is the total energy stored within the antenna at
resonance, Pa is the absorbed power and fr is the resonant
frequency. 'The subscript a denotes radiation, conduction
or dielectric losses, as appropriate, using the symbols R, C
and D respectively. The energy stored in the antenna is equal
to the peak energy stored by the electric or magnetic field
distribution within the substrate, which leads to the formula
as given below:
(15)
where, the surface of integration A is the planar area of the
patch and the height h is constant all over the patch.
x2m n
ro2m n- (1 -
1
jOeff
)ro2
Gm n (u 1 •
21r
1r 12
0
0
j j (IEel2 + IE, 12) R2 sinO dO dt/>
(16a)
2 ).
(19)
Using the simple loss-less cavity model, the computed
resonant frequency is slightly higher than the measured
value. This is due to the fact that the magnetic walls at the
edges are to some extent beyond the actual boundary of the
patch for the fringing effect. The waves travelling in a
particular direction (along± u1 for TM 10 mode and along±
u2-axis for 1M 01 mode) have to cover these extensions. In
other words the effective dimensions of the patch are greater
than their actual values and consequently the resonant
frequency is decreased. Thus, the resonant frequency fr for
the TMmnmode of the modulated patch antenna is given by:
The power dissipated due to different losses in the antenna
are given by:
I
pH= 2 Z o
1
U
(20)
where, Pe.ff and we.ff are the effective dimensions of the
modulated patch structure including the extensions due to
fringing effect and are given by the following expressions.
(2la)
Pejf= P + 2!:.. P
(2lb)
(16b)
'
h ,
andP"=-CJ
1
. 2
j IE3 J2. d A
- - -EsC1u
e 0 Er
(16c)
where, Zo (=VJJiJ /E 0) is the intrinsic impedance of free space,
Gc is the bulk conductiv·ity of the patch conductor and CJ" is
that of the dielectric substrate. Again, CJ" may be expressed
as CJIJ = 2'/C fr ere 0 8. Thus, combining the eqns (14 ), (15)
and (16) together the Q-factors are expressed as:
The extensio11s in dimensions of the modulated patch
along u1 and u2-axis due to the fringing effect are given by
the wetl known formula !221.
t:..p=0.4l 2 h[Ee.ff(w) +0.3 ][w/h+0.262
w I h + 0.813
Ee.ff(w)- 0.258
where, e e.ff (w) is the effective dielectric constant of the
substrate and is given by:
Er+l
e .. . - ( w
) = - -Er-1
+-e.ll
Q" = 1/oand Qc =h....; J.L o 1Cfr Gc
(17)
The values of Es and PH are computed from eqn (15)
and ( 16) and then the radiation quality factor QH is evaluated
from eqn (14). Thus evaluating the different Q-factors, the
effective loss-tangent, De.ff is obtained from eqn (13). In
]<22)
2
2
10)
( 1+--
WI h
-Jn
(23)
The expressions for t:.w and corresponding e 11./f( p) are
obtained from eqns (22) and (23) respectively by just
interchanging p and w.
The bandwidth of microstrip antenna is normally defined
as:
IETE JOURNAL OF RESEARCH, Vol 44, Nos I & 2, 1998
54
Downloaded by [UQ Library] at 13:15 15 July 2015
BW=[(f12 -j, 1)1f,]x100%
(24)
where, /,1 and f 12 are the frequencies between which the
magnitude of the reflection coefficient of the antenna is
~ 1/3 (which corresponds to a VSWR ~ 2.0). However, in
an another way, the bandwidth may be defined [23 1, which
is suitable to the experimental data. In this case, the patch
antenna is represented by a parallel RLC circuit. According
to this resonant circuit model, the bandwidth is obtained
using only the resistance data as a function of frequency.
Following this definition, fa and /,1 in eqn (24) are the
frequencies where the resistance is 0.67 times the value of
Rnu,x (resistance at resonant frequency) i.e., R (/,1 ) =R Ur2)
= 0.67 Rnu,x- For the special case of a prescribed VSWR =
2.0, this method is equivalent to the analytical expression
BW = (VSWR- I) /QYVSWR. In the present paper, the
bandwidth is calculated according to this projected definition
and the frequencies/, 1 and fr 2 are found from the resistance
versus frequency curve around the resonant frequency
(Fig 3).
The radiation efficiency, 1J is another important
parameter for microstrip antennas. It is defined as the ratio
of the radiated power aod the total power fed to the input of
the antenna. In terms of the different Q-factors of the
antenna, the radiation efficiency may be expressed [241 as
follows:
1J =
Qc QD
Qc QD + Qc QR + QD QR
X
100%
(25)
Thus, the radiation efficiency of the modulated patch antenna
may be evaluated by computing the different Q-factors from
the eqn (14) and (17). From eqn (25) it is evident that high
radiation efficiency is obtained for small QR and large Qc
and Q0 .
RESULTS AND DISCUSSIONS
R,.ll
0.67
~~,. ..
"'E
:z:
0
'!
1%
t,.
fr
FREctUENCY
fra
IN GHz
Fig 3 Variation of R with frequency for a particular set of
parameters and determination of bandwidth
The resonant frequency of the modulated patch antenna
has been computed using eqn (20) for the aforesaid
parameters and modes of excitation. It is observed that fr
for the TM01 mode decreases with r while it remains almost
the same for the TM 10 mode. It may be interpreted that
radiation for the TM 01 mode occurs mostly from the
modulated edges and the separation between these
modulated edges increases with r. On the other hand,
radiation for the TM 10 mode' occurs from the unmodulated
edges and hence fr is invariant of r. Similarly, fr decreases
with p for the TM 10 mode while it remains almost
independent of p for the TM01 mode. The variations in
resonant frequency with the antenna parameters rand p for
different modes are furnished in Tables 1 & 2.
The real (R) and imaginary (X) parts of the input
The resonant frequency./, and the input impedance, Z;n . impedance are computed from eqn (19). The studies on the
of the modulated patch antenna are evaluated for different input impedance include the variation of its real (R) and
structure parameters and modes of excitation. In the imaginary (X) components with frequency as well as with
following investigations, the values of the modulation factor,
the feed location. The investigations have been performed
r are arbitrarily chosen as 0.0, 0.2, 0.5 and 0.8 within the
in two steps. In the first step, the effects of the modulation
limits of 0 and 1.0. The values of the parameter, pare fixed
factor, r have been studied when the periodicity,.p is kept
at 3.2 em.; 6.4 em., 9.6 em., 12.8 em. With these values of r constant. In the second step, the effects of p are studied
and p the constraint on the physical parameters of the
modulated patch structure for the condition of orthogonality TABLE 1 Resonant frequency /,(GHz) of the modulated
patch (h = 0.159 em, E r = 2.5 and 0 =0.0018) for
of the transformed coordinates namely (r u 2 )/p<<I is
different
modes with r as the parameter (p = 6.4
satisfied. The modes under study are restricted to the
em)
dominant TM 10 and TM 01 and some higher order modes
0.8
0.0
0.2
0.5
like TM 20 and TMo2·
The theoretically computed results have been
experimentally verified using modulated patches having
modulation factors r =0.0, 0.2, 0.5, 0.8 constructed from
3M-Cu-Clad 250 teflon type-0625-50 dielectric substrate
of thickness h = 0.159 em, relative permittivity E r = 2.5
and loss tangent =0.0018.
o
Mo~
1.446
1.446
1.446
1.446
™o1
TM2o
2.82
2.58
2.325
2.129
2.892
2.892
2.893
2.893
™o2
5.644
5.174
4.65
4.259
TM
10
0
N KHANRA eta[ : INPUT IMPEDANCE, BANDWIDTH AND EFFICIENCY OF AN EDGE MODULATED MICROSTRIP ANTENNA
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TABLE2 Resonant frequency J,(GHz) for different modes
with p (em) as the parameter (r = 0.5)
M~
3.2
6.4
TM 10
2.822
TM 01
9.6
12.8
1.446
0.972
0.732
2.325
2.325
2.324
2.324
TM 20
5.645
2.892
1.944
1.464
TM 02
4.65
4.649
4.649
4.648
keeping r at a constant value. As expected, the reactance
(imaginary component, X) passes through zero and the
resistance (real component, R) shows a peak at the resonant
frequency. It is observed that the peak value of R changes
with r and p. In other words, the slope of the resistance
curve near the resonant frequency depends upon the structure
parameters rand p. Further, the magnitude and position of
the maxima of X also changes with the structure parameters
r and p and thereby bringing a change in the slope of the
curve at the zero crossing. These studies reveal valuable
informations in respect of matching the modulated structure
with a feeder line of any characteristic impedance.
As stated earlier, at resonant frequency the input
impedance is purely resistive or in other words the resistance
is maximum. This maximum value is called the resonant
resistance (R;n). For the TM 10 and TM 20 modes, the antenna
is center fed along the u 1-axis. These modes consist of waves
travelling along the ± u 1 axis between 0 and p. The
impedance characteristics are practically independent of the
exact location of the feed so long as it is along the u2-axis
with no field variation. But, when the feed is moved along
the u 1-axis with nonuniform field for these TM 10 and TM 20
modes, the entire impedance locus changes drastically with
the position of the feed. Similarly, the impedance values
remain unchanged when the feed is moved along the
u 1-side for TM 01 and TM 02 modes but change sharply for
moving the feed along the urside. Variation ofthe resonant
resistance (R;n) with the feed position as a function of r for
the TM 10, TM 01 , TM 20 and TM 02 modes are shown in Figs
4a through 4d. It is observed that the R;n values for the TM 10
and TM 01 m'odes assume their maximum at the patch edges
and gradually decrease to zero as the feed is moved to the
center ofthe patch. But in case of the TM 20 and TM02 modes,
Rin variation shows three peaks with the additional third one
at the middle (u' 1!p 0.5) of the patch.lt is further observed
that, the magnitudes of all these peaks are same for r = 0
(rectangular patch) but the magnitude of the central peak
for r > 0 (modulated patches) is lower than those at the edes.
Moreover, R;n becomes a less sensitive functi-on of the feed
position in between u' 1 lp = 0.25 and 0.75. The variations
of Rin with the feed position for the aforesaid modes have
also been studied as a function of the periodicity, p with a
constant value of r. Figures Sa through 5d depict the
variations of R;n for the different modes. It is seen that, the
nature of the R;n variation curves for these cases of the
=
55
parameter p, are similar but the magnitue of Rin changes in
reverse to the cases of r parameter. Thus, the most noticeable
feature of R;n variation of the modulated patch antenna is
that, more flexibility is obtained in choosing the impedance
by suitably selecting the value of r and p and the mode of
excitation. Further, mechanical tolerances of the feed
location is better managed with higher values of r because
of lower slope of the curve. Thus, the modulated patch
antenna can be more accurately matched to any desired
impedance value than the rectangular or similar conventional
patch antennas.
The bandwidth Df the modulated patch has been
evaluated for TM 10, TM01 , TM 20 , TM 02 modes with different
values of r which are shown in Table 3.
It is found that the bandwidth for the TM 10 and TM 20
modes increases with r. This is a most significant aspect of
the modulated patch antenna. It is well known that the
bandwidth of rectangular microstrip antennas increases with
its area. But here, in the case of the modulated patch, the
bandwidth for the TM 10 mode increases with the modulation
factor r, nevertheless the area of the patch remains the same
for all values of r. Not only that, the rate of increase (Fig 6)
of the bandwidth of the modulated patch is higher than that
of its rectangular counterpart whose width b is equal to the
maximum width w 2 of the modulated patch antenna
(Fig I). The bandwidth for the TM 01 and TM 02 modes
decreases as r is increased. But the rate of decrease is very
low. The bandwidth of the modulated patch antenna also
depends on the periodicity, p. The variation in bandwidth
with p for different modes has been studied keeping the
modulation factor, r at a constant value and the results are
shown in Table 4.
It is found that the variation Df bandwidth with p is
reverse to that with the parameter r, i.e., the bandwidth for
TM 10, TM 20 modes decreases while for TM 01 and TM 02
modes increases with increasing p.
The radiation efficiency, T) of the modulated patch
antenna has also been evaluated as a function of its structure
parameters. It is found that, T) increases with r for TM 10 and
TM 20 modes while it decreases for the TM 01 and TM 02
modes (Fig 7a). On the other hand, T) increases with p for
TM 01 and TM 02 modes but decreases for TM 10 and TM 20
modes (Fig 7 b). It may be noted that the variation of radiation
efficiency with the structure parameters are just opposite to
that of the bandwidth. This trade off between the bandwidth
and radiation efficiency of the modulated patch antenna may
be utilized for selecting the physical parameters depending
upon the requirements in its specific uses. Thus, it is observed
that, the modulation factor, r and the periodicity, p have
their significant effects on the resonant frequency, input
impedance, bandwidth and radiation efficiency of the
modulated patch antenna. Further, by suitably selecting the
values of r and p, one can have to his desire, a broader or
narrower bandwidth with respect to an quivalent rectangular
JETE JOURNAL OF RESEARCH, Vol 44, Nos I & 2, 1998
1000
COHPUTED
HEASURED
..
•
400
MEASURED COHPUTEO
p , 6.4cm
h = 0.159cm
r• o
r • 0.2
r • o. 5
r. o.e
800
p •
E,,
2.5
h : 0.0018
r • o.o
r = o. 2
r • 0. 5
r = 0. 8
•
6./o(lll
h .. 0,159
A·
•
Clll
X
E, : 2. 5
6 :
300
0.0018
6 00
Vl
2:
:r
0
.,;
:r
:r
z
-
200
0
::!"
.!:
a:
400
"
0:
100
Downloaded by [UQ Library] at 13:15 15 July 2015
200
0
0
0.25
0
0.25
0
1.0
0.75
0.50
(c)
250
.
•
X
200
1.0
u; /p
(a)
COHPUTED
HEASURED
0.75
0.50
ul/ p
00
r =o
r • 0.2
r. 0.5
r. o.e
p = 6.4
p : 6.4 Clll
h = 0.159clll
em
= 0.159cm
Er = 2.5
& = 0.0018
h
MEASURED COMPUTED
a.
r = 0.0
f,=
&
I
2.5
: 0.0018
•
r = 0.2
r • 0.5
r "' 0.8
•
)C
10
I
Vl
2:
150
\.
Vl
:z:
60
2:
:r
0
0
:z;
-
::!"
c
a:
c
a:
100
50
0
-0.50
40
20
-0.25
0.25
0
0.50
0
-0.50
0
-0.25
(h)
Fig 4 Yarjation of resonant resistance (R; 11
(c) TM 20 mode, and (d) TM 02 mode
0.25
0.50
u;/w
uil W
(d)
)
with feed location as a function of
r. (p =
6.4 em).
(a)
TM 10 mode, (b) TM 01 mode,
0 N KHANRA
l'/
a/:
51
INPUT IMPEDANCE, BANDWIDTH ANIJ EFFICIENCY OF AN EDGE MODULATED MICROSTRIP ANTENNA
1400
500
COMPUTED
MEASURED
1200
•'
P•3.2em
p = 6.4 em
p=9.6 em
X
p:12.8 em.
•
COMPUTED
MEASURED
p • 3.2 ern .
r = o.s
h = 0.1S9cm
Er = 2.5
1000
P= 6.4 ern.
X
p =12.8 em.
•
400
I
•'
p = 9.6 ern
x/
r. = o. s
I
h = 0.1S9ern
Er = 2.5
0 = 0.0018
6 =
300
~ 800
:r
Vl
0
::1:
0.0018
:r
0
c
a:
600
c
0:-
200
400
Downloaded by [UQ Library] at 13:15 15 July 2015
100
200
0.25
0.50
0.15
0
1.00
0
u;'l p
0.25
0.50
200
300
..
MEASURED
COMPUTED
MEASURED
p=3.2
p• 6.4
p = 9.6
p =12.8
2 so
1.0
(c)
(a)
'
•
0.75
u;tt>
em.
em.
em.
em.
COMPUTED
P
•
p
I(
p
•
= 3.2
&
em.
6.4 em .
P= 9.6 e"'
=12.8 em
160
r "' 0.5
r
h : 0,159em
Er: 2.5
5 :: 0.0018
= 0.5
h • 0.1S9em
Er = 2.5
~ c 0.0018
100
120
Vl
Vl
::1:
::1:
:r
:r
0
0
150
z
c
a: 10
a:
,
100
I
I
I
I
I
40
so
•I
I
I
.
•
'1./
"'
,17·
0
-0.50
-0.25
0
0-25
0.50
0
-0.50
-0.25
0.25
0.50
u21 W
(d)
(b)
Fig 5 Variation of resonant resistance (/?,,) with feed location as a function of p. (r
(c) TM 20 mode, and (d) TM 02 mode
= 0.5
I
em). (a) TM 10 mode, (b) TM 01 mode,
IETE JOURNAL OF RESEARCH, Vol 44, Nos I & l, I 'J':.I!S
58
100
TABLE 3 % bandwidth of the modulated patch for different modes with r as the parameter (p = 6.4 em)
M~
™1o
™o1
™zo
™oz
0.0
0.2
0.5
0.65
0.83
1.35
2.30
2.55
2.12
1.46
1.06
0.90
1.24
2.77
2.94
3.26
3.09
2.88
2.67
0.8
·r--------------------,
--- --- ---
90
80
..
~
10
~
9.6
-
--·
-·-··-
so
12.8
Downloaded by [UQ Library] at 13:15 15 July 2015
M
™1o
™o1
™zo
™oz
3.68
1.35
1.03
0.68
0.92
1.46
1.83
2.06
5.31
2.77
1.44
1.09.
2.15
2.88
3.44
3.65
-·
-·
-·
-·
-· --· -· -·
.-·
60
6.4
.. ..---··-
c::'
TABLE 4 % bandwidth of the modulated patch for different modes withp (em) as the parameter (r = 0.5).
3.2
-
0
p = 6.4 ''"·
u2= 1.6 ''"·
h = O.IS9 em.
™o1
™oz
1 "1o
1 "zo
Er
6
o.z
0
=z.s
=0.0011
0.4
o.a
0.6
(a)
2./.
100
2.0
i
~
0
90
--
1.6
c
·-
---------
10
.c
-o
·-
1.2
Rectangular
3:
10
potch
"0
c
~ 0.8
o--o--o Theory
Expt.
60
Jt-X-X--0(
0.1.
r = O.S
Liz= 1.6
-
''"·
= O.IS9 , •.
€r = z.s
6 = 0.0018
h
so
'·b'
3.0
in em -·-•
Fig 6 Comparison of the bandwidth variation with b for the
TM 10 mode of the modulated patch and its equivalent
rectangular counterpart
=
9.0
12.0
(b)
Fi~
patch antenna. It can also be more accurately matched to
any desired impedance level by properly selecting the values
of r and p. The investigation, therefore, reveals that the
modulated patch antenna provides improved performance
and better flexibility in the design with respect to the
conventional rectangular patch antenna. It is also economical
and cost effective. It may be noted that r 0 always exhibits
the familiar properties of the corresponding rectangular
patch antennas. It may also be noted that the maximum value
ofthe (r ii2 I p) ratio is always kept within a small magnitude
of 0.25 keeping in mind the restriction imposed on these
parameters.
6.0
7 Variation of radiation efficiency with the structure
parameter. (a) parameters r, (b) parameters p
The input impedances have been measured with the help
of a network analyzer (HP-841 OC). It is to note that the
value of the periodicity p is taken to be 6.4 em unless
otherwise specified. The computed data for the resonant
frequencies, input impedances and bandwidths, are in good.
agreement with the measured results.
CONCLUSION
A new shaped (sinusoidally edge-modulated) microstrip
D N KHANRA eta/ : INPUT IMPEDANCE, BANDWIDTH AND EFFICIENCY OF AN EDGE MODULATED MICROSTRIP ANTENNA
patch antenna has been studied in order to get some
additional physical parameters controlling its antenna
characteristics. A new orthogonal coordinate system has
been established to match its boundary and then the modal
expansion cavity model has been employed for the analysis.
The input-impedance, band-width and the radiation
efficiency have been evaluated for different modes of
operation with different values of modulation factor, rand
different values of periodicity, p. The computed data have
been experimentally verified an{l they are in good agreement
with each other. The observations show that the modulation
factor, rand the periodicity, p have their significant effects
on the input impedance, bandwidth and radiation efficiency
of the modulated patch antenna.
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REFERENCES
I.
Y T Lo, D Solomon & W F Richards, Theory and Experiment on Microstrip Antennas, IEEE Trans Antennas
Propagat, vol AP-27, pp 137-145, 1979.
2.
A G Derneryd, A theoretical investigation of the Rectangular Microstrip Antenna Element, IEEE Trans Antennas
Propagat, vol AP-26, pp 532-535, 1978.
3.
A G Derneryd, Analysis of the microstrip disk antenna element, IEEE Trans Antennas Propagat, vol AP-27, no 5,
pp 660-664, 1979.
4.
A K Sharma & B Bhat, Spectral Domain analysis of elliptic
microstrip disk resonators, IEEE Trans Microwave Theory
Tech, vol MTT-28, pp 573-576, 1980.
5.
J Helszajn & D S James, Planar triangular resonators with
magnetic walls, IEEE Trans. Microwave Theory Tech,
vol MTT-26, pp 95-100, 1978.
6.
A Henderson, J R James & C M Hall, Bandwidth extension
techniques in printed conformal antennas, Proc Military
Microwave Conf, Brighton, UK, pp 329-334, 1986.
7.
8.
9.
A Sabban, A new broadband stacked two-layer microstrip
antenna, IEEE Antenna Propagat Soc lnt Symp Digest,
pp 63-66, 1983.
G Kumar & K C Gupta, Broad-band microstrip antennas
using additional resonators gap-coupled to the radiating
edges, IEEE Trans Alllennas Propagat, vol AP-32, pp
1375-1379, 1984.
C Wood, Improved bandwidth of microstrip antennas using
parasitic elements, lEE Proc, pt-H, vol 127, pp 231-234,
1980.
I 0. D N Khanra & A K Mallick, Studies on the Radiation Pat-
59
tern of a Sinusoidally Edge-Modulated Microstrip Patch
Antenna, Journal of the JETE, vol 39, no 5, pp 323-327,
1993.
II. Y Ebine, T Matsuoka & M Karikomi, A Wide Beamwidth
and Broad Bandwidth Microstrip Antenna with a Pair of
Short Circuit Patches,/£/C£ Trans on Communication, vol
E74, no 10, pp 3241-3245, 1991.
12. M C Bailey & M D Deshpande, Integral equation formulation of microstrip antennas, IEEE Trans Antenna
Propagat, vol AP-30, no 4, pp 651-656, 1982.
13. A K Sharma et al, Spectral domain analysis of a hexagonal
microstrip resonator, IEEE Trans Microwave Theory Tech,
vol MTT-30, no 5, pp 825-828, 1982.
14. E L Coffey, DFNA analysis of microstrip antennas, Int
Symp Dig, Antennas Propagat Soc, pp 613-616, 1980.
15. K C Gupta & PC Sharma, Segmentation and desegmentation techniques for the analysis .of planar microstrip antennas, Int Symp Dig, Antennas Propagat Soc, pp 19-22,
1981.
16. E N Newman & P Tulyathan, Analysis of microstrip antennas using moment methods, IEEE Trans Antennas
Propagat, vol AP-29, no I, pp 47-53, 1981.
17. K R Carver, A model expansion theory for the microstrip
antennas, IEEE AP-S lnt Symp Dig, pp 101-104, 1979.
18. N W Mclachlan, Theory and application of Mathieu functions, Oxford University Press, Oxford, 1951.
19. P Bhartia & I J Bahl, Millimeter wave Engineering and Applications, Wiley Interscience Publications, pp 603-607,
1984.
20. J R James; P S Hall & C Wood, Microstrip Antenna Theory and Design, Peter Peregrinus Ltd, pp 73, 1981.
21. W F Richards & Y T Lo, An improved theory for
microstrip antennas and applications,/£££ Trans Antennas
Propagat, vol AP-29, pp 38-46, 1981.
22. E 0 Hammerstad, Equations for microstrip circuit design,
Proc 5th European Microwave Conference,. Humburg, pp
268-272.
23. S A Long & W F Richards, An experimental investigation
of electrically thick rectangular microstrip antenna, IEEE
Trans Antennas Propagat, vol AP-34, no 6, pp 767-772,
1986.
24. J R James, A Henderson & P S Hall, Microstrip antenna
performance is determined by substrate constraints, Microwave System News, pp 73-84, 1982.
60
IETE JOURNAL OF RESEARCH. Vol 44, Nos I & 2, 1998
AUTHORS
Downloaded by [UQ Library] at 13:15 15 July 2015
A K Mallick, BEE (Hans), MTech,
PhD was graduated from the
Jadavpur University, .Calcutta, and
received his postgraduate and
doctoral degrees from the Indian
Institute of Technology, Kharagpur.
He is, formally, an Electrical Engineer with specialization in Microwave and Lightwave Engineering.
Dr Mallick served the All India Radio (AIR), Calcutta as
an Assistant Engineer for four years (1962-65) and joined
the
Department
of Electronics
and
Electrical
Communication Engineering of the Indian Institute of
Technology, Kharagpur in the year 1967 as a Lecturer. At
present, he is a Professor of the same Department. He
was the Head and Professor of the Radar and
Communication Center of the Institute from 1984 to 1989.
In his credit, there are a number of superior quality
research papers published in national and international
journals of repute.
His principal research interest is in the areas which
include Electrostatics, Electromagnetics, Microwaves,
Millimeterwaves and Lightwave Engineering. At present,
he is actively engaged in the area of MicrbStrip Antennas,
EMIIEMC, and Fault Diagnosis of Phased Array Antennas.
Dr Mallick is a Fellow Member of the Institution of
Engineers (India), and a Life Member of the Society of
EMC Engineers (India).
*
*
*
D N Khanra, MSc, PhD was born in
1951 the District of Midnapore, West
Bengal. He received the Post
Graduate degree in Physics from
Calcutta University in 1976 and the
PhD
degree
from
Jadavpur
University in 1995.
At present he is working as a
Reader in Physics at V S Mahavidyalaya, Manikpara,
Midnapore.
His area of research interest is Microwaves and
Microstrip Antennas.