Resonant resistance of probe- and microstrip-line-fed
circular microstrip patches
D. Guha, Y.M.M. Antar, J.Y. Siddiqui and M. Biswas
Abstract: The input resistance at resonance of the microstrip antenna is an important parameter to
be determined to design the feed and its location for achieving the optimum performance. The
authors propose an improved design formula for circular microstrip to meet this requirement for
both probe- and microstrip-line-fed designs. A modified admittance boundary has been applied to
improve the cavity model formulation available in the open literature and the computed results are
verified with several measurements showing very close approximation compared to other methods.
The generalised formula is applicable to designing circular microstrip antennas with and without an
airgap between the substrate and the groundplane, where the feeding can be realised by a coaxial
probe or by planar microstrip line fed at the edge.
1
Introduction
The microstrip patch is a highly resonant structure with
narrow bandwidth and, as such, near resonance it becomes
mainly resistive with zero or small input reactance. Hence,
to excite a microstrip patch with a particular mode, either
by a coaxial feed or by a planar edge-fed microstrip line, we
have to account for its resonant resistance at the feed point
for efficient impedance matching. The better the matching
between the feed and the radiating patch, the better is the
antenna performance. The problem of determining the
input impedance of a circular microstrip patch has been
taken up by several researchers employing various
approaches such as the Green’s function technique [1, 2],
cavity model analysis [3–7] and the equivalence principle [8].
Lo et al. [9] particularly examined microstrip-line-fed
circular patches. Some experimental studies on circular
microstrip antennas (CMA) were also reported in [10, 11].
The cavity model formulation [6, 7], provides an easy
approach to compute the resonant resistance as less
mathematical steps and computational time are involved,
and, hence, it is ideal for design purposes. However,
recently, while working with a probe-fed circular patch for
a practical application, we observed a major discrepancy
between the measured input resistance at resonance and the
calculated values in [7] as a function of feed positions.
Further examination of the theory in [7] and comparison
with some previous measurements [3, 4] also showed similar
disagreement, as will be discussed in Section 3.
In this paper, we address the problem in order to improve
the design formulations in [6, 7], while maintaining their
merits and simplicity. Indeed, we propose a modification
r IEE, 2005
IEE Proceedings online no. 20045161
doi:10.1049/ip-map:20045161
Paper first received 18th November 2004 and in revised form 1st July 2005
D. Guha, J.Y. Siddiqui and M. Biswas are with the Institute of Radio Physics
and Electronics, University of Calcutta, Acharya Prafulla Chandra Road,
Calcutta 700 009, India
Y.M.M. Antar is with the Department of Electrical Engineering, Royal Military
College of Canada, Kingston, Ontario, Canada K7K 7B4
E-mail: dgirpe@yahoo.co.in
IEE Proc.-Microw. Antennas Propag., Vol. 152, No. 6, December 2005
considering the admittance boundary problem of a microstrip patch in a simple and general way. The proposed
modification is used to improve the formulations to provide
accurate estimation of the resistance as the function of
frequency and feed location. The computed results are
compared with different measurements and theories reported earlier for conventional circular patches and their
variants [5] fed by a coaxial probe or a microstrip line.
Results for the dominant and higher-order TMnm modes are
also examined theoretically and experimentally. The theory
is also verified with our new measurements with a probe-fed
antenna designed for a 50 O matched location.
2
Theoretical formulations
The probe-fed CMA is shown in Fig. 1a, where h2 is the
variable airgap below the substrate. This configuration
degenerates to a conventional microstrip structure when
h2 ¼ 0, i.e. h ¼ h1. A microstrip-line-fed CMA is shown in
Fig. 1b. The quantity ae represents the effective radius of the
circular patch caused by the fringing electric fields as
derived in [12]. The radiating aperture is thus assumed to be
located at the effective radius ae, and is replaced by a
magnetic wall to simplify the problem of admittance
boundary variation [13] in our analysis. We apply this
admittance boundary to modify the input resistance
formulations [6, 7] of a CMA as
a
2
Jn kr
ae
ð1Þ
RðrÞ ¼ Re; nm
2
Jn ðkaÞ
Here, the new factor a/ae defines the quantity Re,nm as the
input resistance of the TMnm mode when the feed is located
at the magnetic wall boundary with r ¼ ae. The parameter
ka ( ¼ anm) represents the mth zero of the derivative of the
Bessel function of order n.
Following [6], the value of Re,nm is determined in terms of
the equivalent conductance due to the ohmic loss Gcon,
dielectric loss Gdlc and radiation loss Grad in the magnetic
wall cavity under the CMA as
Re; nm ¼ ½Gcon þ Gdlc þ Grad 1
ð2Þ
481
2ae
Rðf ; rÞ ¼
RðrÞ
X ðf ; rÞ ¼ ε
h1
ε0
h2
RðrÞQðf f1 Þ
1 þ Q2 ðf f1 Þ2
ð7Þ
where Q is the quality factor of the magnetic wall cavity
under the CMA as given in [14] or [6], and f is the
normalised frequency f/fnm. The resonant frequency fnm can
be accurately calculated employing a recent theory given
in [12].
2a
ρ
ð6Þ
1 þ Q2 ðf f1 Þ2
h
3
Results and discussions
The computed results of the resonant resistance and VSWR
based on equations (1)–(7) are compared with different
measurements involving the antenna parameters of wide
variations. Most of those measurements were carried out
earlier by different researchers and some have been done by
us with a prototype CMA etched on Taconic substrate and
using a HP 8720C network analyser.
Figure 2 compares the measurements of Davidovitz and
Lo [4] for a set of probe-fed CMAs, for two different
thickness, with the formulations by Abboud et al. [7] as well
as ours. The theoretical curves due to the present model
show close agreement with measured data points for both
substrate thicknesses.
a
2ae
400
2a
resonant resistance, Ω
h
b
Fig. 1
Circular microstrip antennas
a Probe-fed
b Microstrip line-fed
The parameters Gcon, Gdlc and Grad can be evaluated using
the closed-form expressions given in [14].
Although the magnetic wall cavity ideally separates the
interior field from the exterior field [13], the feed, either as a
probe or as a microstrip line, near the patch edge disturbs
the ideal situation. A fraction of the excited field near the
edge is coupled to the exterior medium, and hence, to
determine Re,nm, this effect is accounted for in terms of a
new effective dielectric constant er,eq following the conventional approach as
er; eq ¼ ð1 þ ere Þ=2
ð3Þ
where ere is the equivalent dielectric constant of the
suspended substrate of Fig. 1a derived as [12]
ere ¼
er ð1 þ h2 =h1 Þ
ð1 þ er h2 =h1 Þ
ð4Þ
For zero airgap height in Fig. 1a, the parameter h2 ¼ 0 and
hence ere ¼ er, i.e. the dielectric constant of the substrate
itself.
The relation of the resonant resistance R(r) in (1) also
helps in determining the input impedance of a CMA as a
function of frequency near resonance as [14].
Zðf ; rÞ ¼ Rðf ; rÞ þ jX ðf ; rÞ
482
ð5Þ
300
200
100
0
0
0.2
0.4
0.6
0.8
1.0
0.6
0.8
1.0
/a
a
400
resonant resistance, Ω
ε
measured [4]
our theory
computed [7]
measured [4]
our theory
computed [7]
300
200
100
0
0
0.2
0.4
/a
b
Fig. 2 Resonant resistance against normalised feed location of
probe-fed CMAs with different substrate thicknesses er ¼ 2.62,
tan d ¼ 0.001
a h/l0 ¼ 0.055, h ¼ h1 ¼ 4.7 mm, a ¼ 13 mm
b h/l0 ¼ 0.019, h ¼ h1 ¼ 1.6 mm, a ¼ 14.1 mm
IEE Proc.-Microw. Antennas Propag., Vol. 152, No. 6, December 2005
Usually, 50 O probes are used to excite the microstrip
patches and, as such, a 50 O input resistance point on the
patch surface is the ideal feed location to achieve the
optimum performance. Figure 2 reveals the 50 O resistance
points as r/a ¼ 0.3 for h/l0 ¼ 0.055 and at r/a ¼ 0.27 for
h/l0 ¼ 0.019, respectively, for a typical low dielectric
constant substrate. The input resistance for the matched
location of a prototype circular patch etched on a Taconic
TLY-3-0620 substrate is examined in Fig. 3. Measured
values of VSWR were obtained on a HP 8720C network
analyser with a 50 O SMA probe fed at r/a ¼ 0.27. The
VSWR values were calculated using the standard transmission line equation taking the input impedance Z(r, f )
computed from (5)–(7) as the load attached to an end of a
transmission line with Z0 ¼ 50 O. Very close agreement
between the prediction and the measurement is apparent,
particularly around the resonant frequency where the
VSWR value reaches close to 1.0.
0.77
0.78
0.76 GHz
0.79
0.794
0.80
0.82 GHz
0.81
12
our experiment
theory
10
Fig. 4
Input impedance loci of a microstrip-line-fed CMA
a ¼ 67.5 mm, h1 ¼ 1.5875 mm, er ¼ 2.62, tan d ¼ 0.001,
f11 ¼ 0.794 GHz, FFFF theory, measured [9]
r/a ¼ 1,
SWR
8
600
6
measured [5]
our theory
computed [7]
4
2
3.4
3.5
3.6
3.7
3.8
3.9
frequency, GHz
Fig. 3
CMA
input resistance, Ω
500
SWR against frequency for the TM11 mode of a probe-fed
a ¼ 15 mm, h1 ¼ 1.575 mm,
f11 ¼ 3.62 GHz
er ¼ 2.33,
tan d ¼ 0.001,
400
h 2 = 1.0 mm
h 2 = 0.5 mm
300
200
100
r ¼ 4 mm,
0
1.24
1.26
1.28
1.32
1.34
1.36
1.38
1.40
frequency, GHz
IEE Proc.-Microw. Antennas Propag., Vol. 152, No. 6, December 2005
Fig. 5 Input resistance against frequency for TM11 mode of a
probe-fed CMA with variable airgaps
a ¼ 50 mm, h1 ¼ 1.58 mm, er ¼ 2.32, tan d ¼ 0.0012, r/a ¼ 0.95
500
εr = 10.20, f11 = 1.84 GHz
εr = 2.94, f11 = 3.26 GHz
400
resonant resistance, Ω
The input impedance loci (normalised with respect to
50 O) of a microstrip-line-fed CMA is shown in Fig. 4. The
measurement of Lo et al. [9] is compared with our
computed data for the dominant mode and excellent
agreement between the theory and measurement is revealed.
Figure 5 shows the theoretical and experimental input
resistances of a probe-fed CMA with different airgap
heights (Fig. 1a). The experimental values of Lee et al. [5]
are compared with the present theory and with the previous
theory given in [7]. Our predicted values at resonance
appear much closer to the measurements with slight shift
towards the lower side of the spectrum. The theoretical
resonant frequency calculated from [12] determines the
location of the peak resistance and causes the relative
frequency shift. However, the amount of this shift is
insignificant: 0.7% for h2 ¼ 0.5 mm and 0.4% at
h2 ¼ 1.0 mm. The reason behind the large discrepancy
between the theoretical curves due to [7] and the present
formulation is that the patch is fed near the edge with
r/a ¼ 0.95, and the formula in [7] fails to predict the input
resistance, particularly for large r/a values as already
evident from Fig. 2.
The effects of the antenna parameters in changing the
resonant resistances are examined and a few design data
points based on the commercially available substrates are
presented in Figs. 6 and 7. Figure 6 shows the resonant
resistance against normalised radial distance for different er
εr = 2.20, f11 = 3.71 GHz
300
200
100
0
0
0.2
0.4
0.6
0.8
1.0
/a
Fig. 6 Resonant resistance against normalised radial distance of
CMAs with different dielectric constant substrates
a ¼ 15 mm, h ¼ h1 ¼ 1.575 mm, tan d ¼ 0.001
values. The larger the er, the higher is the resonant resistance
value. The change is significant; not only at the patch edge,
but also near the patch centre where the 50 O probe is
483
resonant resistance, Ω
300
substrate and the metallic groundplane. The ability of this
new formulation in predicting the values for both
electrically thick and thin substrates has also been verified.
A set of design data is also presented for different
commercially available substrate parameters. The formulas,
as functions of the feed location and operating frequency,
will thus help us to design a planar microstrip line to feed
the patch at the edge or to locate the optimum feed position
of the coaxial probe on the patch surface.
h = 1.575 mm, f11 = 3.706 GHz
h = 0.787 mm, f11 = 3.816 GHz
250
h = 0.508 mm, f11 = 3.860 GHz
200
150
100
50
5
0
0
0.2
0.4
0.6
0.8
1.0
/a
Fig. 7 Resonant resistance against normalised radial distance of
CMAs with different substrate heights
a ¼ 15 mm, er ¼ 2.2, tan d ¼ 0.001
usually located for coaxial feeding. Figure 7 reveals the
effect of substrate thickness on resonant resistance, other
parameters being unchanged. Larger thickness causes
higher resonant resistance of the patch. Although the
change in resonant resistance for using different heights of
standard substrates is not too significant around the
r/aE0.3 (RE50 ohm), it is important to account for near
the patch edge for edge feeding by microstrip line. The effect
of the patch dimension in changing the resonant resistance
values was also examined. The effect is only significant near
r/a E 1.All antenna parameters appear to be equally
important in determining the resonant resistance of a
circular patch as a function of its radial distance.
4
Conclusions
The input resistance of a CMA near resonance can be
accurately estimated using the improved formulations
derived in this paper. The calculated values closely agree
with various measurements using different feeding techniques and configurations, which include probe-fed CMA,
CMA fed with a planar microstrip line at its edge and
probe-fed CMA with variable airgap in between the
484
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IEE Proc.-Microw. Antennas Propag., Vol. 152, No. 6, December 2005