Reduced rcs uhf rfid gosper and hilbert tag antennas

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN
6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME
ENGINEERING AND TECHNOLOGY (IJARET)

ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
IJARET
Volume 3, Issue 1, January- June (2012), pp. 35-47
© IAEME: www.iaeme.com/ijaret.html ©IAEME
Journal Impact Factor (2011): 0.7315 (Calculated by GISI)
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REDUCED RCS UHF RFID GOSPER AND HILBERT TAG
ANTENNAS

T. G. Abo-Elnaga 1, *, E. A. F. Abdallah 1, and H. El-Hennawy2
1
Microstrip Dept., Electronics Research Institute
El-Tahrir Street, Dokki 12622
Giza, Egypt, +21006751840, tgaber010@yahoo.com
2
Faculty of Engineering, Ain Shams University, Cairo, Egypt

ABSTRACT

In this paper printed flexible conventional, Gosper and Hilbert loop shape antennas
with reduced structure mode radar cross section RCS are proposed for small object
identification. Conventional wire loop antenna input admittance using Fourier series
analysis for the equivalent half-loop antenna excited with a transverse electromagnetic
(TEM) mode is rearranged to obtain the wire loop input impedance versus loop radius
at 900 MHz. T-matched charts as a method of matching the antenna input impedance
with the chip input impedance is also introduced. The proposed Gosper and Hilbert
shapes have size reduction of 76.26% and 83.75 % compared to conventional
structure. RCS reduction of 99.67 % and 99.12 % are obtained for Gosper and Hilbert
loop antennas respectively, compared to conventional one at 900 MHz. Both Gosper
and Hilbert loop antennas are fabricated, measured and the results are discussed.

1. INTRODUCTION

Radio-frequency identification (RFID) is one of the fastest growing wireless
technologies in recent decades. Recent interest for RFID technologies increases
studies and applications of these devices. Many different purposes of RFID are found
such as warehouse management, access control system, electronic toll collection, etc.
UHF RFID requires three components, a transponder, an antenna and a transceiver.
The transponder, or tag, contains data and is attached to the item. The antenna
transmits the UHF radio signal to the transponder, powering and activating it. The
activated transponder then transmits the data stored on the tag back to the transceiver.
There are many standards for UHF RFID systems and they differ according to the
country [1]. The paper idea is to introduce a flexible RFID tag antennas with reduced
radar cross section to identify object location precisely such as weapons, bullets and
all military stuff. Also, it can be used commercially to identify object location in huge

35


warehouses. Methods aiming to decrease object RCS is of great practical interest and
many solutions have been proposed. Some approaches modify the target shape or
orientation to deflect the scattered energy away from the detecting radar while other
converts the radio frequency energy into heat [2]. Passive and active cancellation
technology could be also used [3]. The radar cross section RCS of an antenna is
determined by an antenna component and by a structural term [3-4]. Our investigation
will focus on the reduction of structural scattering of an antenna. Liquid crystal
polymer LCP substrate with dielectric constant , thickness of 0.05 mm and
loss tangent is used as antenna substrate where flexible, reliable and
low cost features are provided, so the proposed structure gains these features. In this
paper conventional, Gosper and Hilbert loop shape antennas are proposed. Gosper
and Hilbert shapes have size reduction of 76.26% and 83.75 % compared to
conventional structure. RCS reduction of 99.67 % and 99.12 % are also obtained for
Gosper and Hilbert shapes respectively, compared to conventional one at 900 MHz.
The paper is organized as; section 2 introduces conventional loop analyses using
Fourier series analysis, T-matched chart and conventional loop with T-matched
section design. Sections 3 and 4 introduce the design of Gosper and Hilbert loop
antenna. Comparison among the aforementioned proposed antennas is introduced in
section 5. Experimental results are introduced and discussed in section 6. Conclusions
are given in section 7.

2. CONVENTIONAL LOOP ANTENNA

In this section Fourier series analysis is used and rearranged to obtain the wire loop
input impedance versus loop radius at 900 MHz and a suitable radius is chosen. T-
matched chart as a method of matching the antenna input impedance with the chip
input impedance is also introduced. Conventional printed T-matched loop is designed.

2.1 Conventional loop antenna analyses
Fourier series analysis for the equivalent half-loop antenna excited with a transverse
electromagnetic (TEM) mode assumed in the aperture of the coaxial line was used to
obtain the input admittance of the wire loop antenna [5]. The antenna has radius R,
resonant wavelength λo , constructed from a perfectly conducting wire of radius ai ,
and β o = 2π λo . The wire circular loop input admittance Yin is
found as:
Yin = G + jB = I (0) Vo ) =  I o + 2∑ I n  Vo
∞

  (1)
 n =1 
− jVo bn
In = n = 0,1,2,... (2)
ξ oπ a n
βoR n2 (3)
an = (K n +1 + K n −1 ) − Kn
2 βo R

1 a 2 a 2 1  2( 2 2
)
0.5

Kn = B0  i n 2 − (βo R )  H 0  i n 2 − (β o R )  + γ + ln 4 n − β o R 
π R  R  π  
2β R
2 n −1 1 1 o (4)
− ∑ − ∫ [Ω2 n ( x) + jJ 2 n ( x)]dx
π m = 0 2m + 1 2 0

36


a
bn =
1
( B0 i (n + 1)2 − (βo R )2  ⋅ {H 0  ai (n + 1)2 − (βo R )2 
ln(ao ai )  R



R


a
− H0  o (n + 1)2 − (βo R )2 } + B0  ai (n − 1)2 − (β o R )2 
   (5)
R  R 
a
⋅ {H 0  i (n − 1)2 − (βo R )2  − H 0  ao (n − 1)2 − (βo R )2 })
  
R  R 

In Eqs. (1) to (5), G and B are the input conductance and susceptance
respectively, B0 and H 0 are the modified Bessel functions of the first and second
kinds and order zero, Ω 2 n is the Lommel-Weber function of order 2n, J 2 n is the
Bessel function of the first kind and order 2n, Euler's constant γ = 0.57722 and
ξ o = µo ε o with µ o and ε o are free space permeability and permittivity,
respectively. This method is rearranged and programmed for the wire circular loop
antenna radii prediction in free space at the 900 MHz resonant frequency, Fig.1.

2.2 T-matched chart
The T-matched chart is a method to match the chip input impedance with dipole input
impedance . Referring to Fig. 2, a dipole of length is connected to a second dipole
of length , placed at a close distance b from the first and larger one. It can be
proved, that the impedance at the source point is given by [6]:
(10)
Where

b
3500
Real
Imag
3000

2500

2000

ad
(1+α) :1
1500
Impedance (Ω)

2
l Za 2Z
1000 t

500

0
2w'
-500

-1000

-1500
10 20 30 40 50 60 70 80 90 2w
R (mm)

Fig. 1 Circular loop antenna input impedance Fig. 2 T-matched configuration for
versus different radii with = 0.5 mm planar dipoles and equivalent circuit.
(fabrication purpose), coaxial outer raduis =
1.15 mm at 900 MHz.

37


2.3 Conventional T-matched loop antenna design
As a prototype design, wire circular loop antenna with external radius of 57 mm
which has an input impedance of (63.16 + j8.14) would be suitable for conjugate
matching with chip input impedance of 13.9 - j143.6 at 900 MHz. This is mainly
referred to the fact that the loop antenna input impedance does not change very much
when R is within the range from 50 mm to 64 mm, Fig. 1. It should be mentioned that
the operating frequency for the chip will cover the band from 860MHz to 960 MHz,
and its input impedance varies from 15.69 - j152.6 Ohm at 860 MHz to 12.61 - j137 at
960 MHz [7]. Chip input impedance of 13.9 - j143.6 at 900 MHz is chosen as the
value to be matched with the designed antenna. By choosing this value the designed
antenna input impedance will be remain in an acceptable level of variation relative to
the variance of the chip input impedance with frequency. Transform the structure to
planar one [8] and using the IE3D simulator, the input impedance of the loop antenna
is calculated using an LCP substrate with 50 substrate thickness and of 2.9. It is
found to be (130.5 - j44.3) at 900 MHz (difference between input impedance
predicted by IE3D and that obtained from Fig. 1 may be attributed to the approximate
wire to planar transformation formulae and the presence of LCP material). This value
is used as input impedance for the T-matched circuit. The T-matched chart is shown
in Fig. 3 which indicates that the matching condition with the chip could be met with
and ranges from 0.11 to 0.18. IE3D simulator was used and final
optimized dimensions are shown in Fig. 4 which indicates that on average
and . The power reflection coefficient, shown in Fig. 5, indicates that a
frequency band from 780 MHz to 1122.2 MHz is covered which is suitable for UHF
universal tag application. As shown in Fig. 6, RCS of 0.182 at 900 MHz is
obtained indicating that the tag antenna is detectable. CMF of 0.837 is obtained at 900
MHz, as shown in Fig. 7, indicating that conjugate matching is at a good level. Fig. 8
shows the radiation pattern which is almost figure of 8 at the E-plane and H-plane.
Other antenna parameters such as conjugate match gain and radiation efficiency are
given in table 1.

5
Imag
Real
41.29
143.2

182 1.922
24.73597

44.49266

4.5
6
.789 1
56
761
30.9
64.24935

5

202
123.5

82.5
823
10.3558

.54

4
84.00

51 .6.03
16 3

486
194

62
088 8
103.7
604

20.6 627

72
2

.23
691

3.5
53
b/2w

18 61
41
14

3
2.7 .92
.29 1
24.73597

3.2
44.4926

89 21
56
76

5
30
64.2

.98
12
3.5

51 3
16
23

2.5
6

493

10.

84

.6.03
19

0 82
.00
355

4
5

88
10
20 .76
604
8

3
.66 27

2
91

30
1.5 12 .98
3.5 23
44 19
.4 64 4
92 .24 10 84 .0 2
10 3 0 .6
.35
66 93
5 58 0 604 .7 6 6 91
27
1
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
ad / l

Fig. 3 Conventional printed circular loop antenna T-matched chart
( )

38


m
55 m

m
m
57
R=

=
R
us
dius

di
ra
r ra

t er
u
O
Inne
Fig. 4 Conventional printed circular loop antenna T-matched circuit section.

3

0

-3

-6
PRC (dB)

-9

-12

-15

-18

-21
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Frequency (GHz)

Fig. 5 PRC versus frequency for Fig. 6 RCS versus frequency for
conventional printed loop antenna with T- conventional printed loop antenna with
matched circuit (R=55mm). T-matched circuit (R=55mm).

Fig. 7 CMF versus frequency for Fig. 8 Conventional printed loop
conventional printed loop antenna with T- antenna with T-matched circuit
matched circuit (R=55mm). radiation pattern at 900 MHz
(R=55mm).

39


2. GOSPER LOOP ANTENNA
The Gosper curve is a space filling curve discovered by William Gosper, an American
computer scientist, in 1973, and was introduced by Martin Gardner in 1976. The
Gosper curve is a recursive curve constructed by recursively replacing a dotted arrow,
called the initiator, by seven arrows, called generator, Fig. 9 [9].

Fig. 9(a) Gosper curve Fig. 9(b) Gosper curve Fig. 9 Gosper curve
initiator, generator initiator, generator initiator, generator
replacement for n=1. replacement for n=2. replacement for n=3.

Matlab code for Gosper curve generation of any order is built and Gosper curve of
order 2 is shown in Fig. 10. The resonance frequency of the aforementioned
conventional circular loop was found to be 1.25 GHz. Gosper loop antenna was
designed at the same resonance frequency using IE3D simulator. Its radius was found
to be 26.8 mm. Gosper loop antenna achieves size reduction of 76.26% compared to
conventional loop antenna. It was chosen as a prototype to complete the T-matched
circuit design at 900 MHz. At 900 MHz, the input impedance is (8.15 + j103.95) .
We considered the structure as asymmetric dipole loaded by Gosper loop antenna.
50

45

40

35
Gosper width (mm)

30

25

20

15

10

5

0
-20 -15 -10 -5 0 5 10 15 20 25 30 35 40
Gosper length (mm)

Fig. 10 Gosper loop antenna (n = 2)

The T-matched diagram shown in Fig. 11 was used as an indicator for the total input
impedance performance. It should be noted that conjugate matching condition with
the chip input impedance is difficult to obtain. As a starting point was
chosen and varying through changing the length till matching condition was
reached. IE3D simulator was used to get the optimum design dimensions, Fig. 12. The
power reflection coefficient is shown in Fig. 13 and clearly covers the frequency band
from 884 MHz to 936 MHz which is suitable for the bands of 920.5 - 924.5 MHz in
China, 920 - 925MHz in Singapore and 902 - 928 MHz in USA, Canada, Mexico,

40


Puerto Rico, Costa Rica, Latin America. As shown in Fig. 14, RCS of 0.0006 at
900 MHz is obtained indicating that the tag antenna is detectable. We should mention
that this small RCS is useful in small targets in package identification. As shown in
Fig. 15, CMF is 0.62 at 900 MHz, indicating that conjugate matching is at acceptable
level. Fig. 16 shows the radiation pattern which is almost omnidirectional at the H-
plane and figure of 8 at the E-plane. Other antenna parameters such as conjugate
match gain and radiation efficiency are given in table 1.

Fig. 11 Gosper loop antenna T-matched chart ( 8.15 + j103.95 )

Fig. 12 Optimum dimensions of Gosper loop antenna with T-matched circuit.

41


3

0

PRC (dB) -3

-6

-9

-12

-15
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Frequency (GHz)

Fig. 13 PRC versus frequency for Gosper Fig. 14 RCS versus frequency for Gosper loop
loop antenna. antenna.

Fig. 15 CMF versus frequency for Gosper Fig. 16 Radiation pattern at 900 MHz for
loop antenna. Gosper loop.

4. HILBERT LOOP ANTENNA

In 1891 Hilbert defined a space filling curve [10]. The general idea is to divide, at step
n, the unit square in 4n equal subsquares each of them containing an equal length part
of the curve (except the first and the last ones which contain a part of length 1/2). A
Matlab program is built to draw Hilbert curve of any order n. Hilbert curve of order 4,
Fig. 17 is simulated using IE3D and input impedance of (10.78 + j53.17) is
obtained at 900 MHz. T-matched chart for that input impedance is shown in Fig. 18.
Choosing and varying from 0.35 to 0.55 till matched condition
was obtained. The optimum structure is shown in Fig. 19. The PRC is shown in Fig.
20 which covers the frequency band from 901 MHz to 928 MHz which is suitable for
the UHF RFID application at China (920.5 - 924.5 MHz), Singapore (920 - 925MHz),
USA, Canada, Mexico, Puerto Rica, Costa Rica and Latin America (902 - 928 MHz).
RCS, Fig. 21 of 0.0016 at 900 MHz is obtained indicating that the tag antenna is
detectable and is useful at small target identification. As shown in Fig. 22, CMF of
0.49 is obtained at 900 MHz. Fig. 23 shows the radiation pattern which is almost

42


omnidirectional at the H plane and figure of 8 at the E plane. Other antenna
parameters such as conjugate match gain and radiation efficiency are given in table 1.

Fig. 17 Hilbert mean curve (n = 4).

5
Imag
Real
2.671 21

26 .51 7
67.11865
20.42183
35.98744
51.55 305

82 .68 426
5.320 82

4.5
21 .21 8
98 .24987
7. 97043

11 3.8 155

7
14 4.9
12 9.3 8
13 .26 97
10 .62

15 .9111

18 .56

5

4
467

16 0.5.86 8
93

89

23
123 1

3.5
b/2w

2.671 21 5

3
35.98744

67 .11 865
20.42183

51 .55 30

82 .68 4
5.320 82

21 .
98 .24
7.970

21 8
11 3

14 4
12 9
13 .2
26

10 .6

5
15..3 81

18 .
987

.8 15
43

2.5
.9 4
91 91
6 97

56 8
2

16 23
67
5

3

9

0.5.8
16 81
23

2

21
1.5 .21
7. 98 . 14 85
2.6

11
82 0 82

12 1 18 4.9
5.

97 24 10 3. 13 9.5 .9
.6

.56 46
32

.62 8 15 .26 9
71

0 4 98 38 1
84

3 7 11 3
9 89 7
21

5 7
26

1
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
ad / l

Fig. 18 Hilbert loop antenna T-matched chart ( 10.78 + j53.17 ).

43


Fig. 19 Optimum structure of Hilbert loop antenna with T-matched circuit structure.

1

0

-1

-2

-3
PRC (dB)

-4

-5

-6

-7

-8

-9
0.80 0.85 0.90 0.95 1.00
Frequency (GHz)

Fig. 20 PRC of Hilbert loop antenna versus Fig. 21 RCS of Hilbert loop antenna versus
frequency. frequency.

Fig. 22 CMF versus frequency for Hilbert loop Fig. 23 Hilbert loop antenna radiation
antenna. pattern at 900 MHz.

44


5. COMPARISON AMONG CONVENTIONAL, GOSPER AND HILBERT
LOOP TAG ANTENNAS

This section introduces a comparison among various proposed loop antenna structures
namely Conventional, Gosper and Hilbert tag antennas. The comparison includes
radiator and T-matched section areas, conjugate match gain, radiation efficiency,
bandwidth, minimum values of PRC, structure RCS and conjugate match factor CMF,
table 1. As indicated by table 1, Gosper antenna introduces the most reduced RCS
compared to the other two antennas’ RCS and area. Also Gosper antenna radiation
efficiency is 99.8 % which is better than the conventional and Hilbert antennas.

Table 1 Comparison among performance of Conventional, Gosper and Hilbert loop
antennas.
Loop Shape Conventional Gosper Hilbert
Parameter
Radiator area ( ) 9503.33 2256.4 1600
T-matched section area ( ) 48 709.8 243.375
Conjugate match gain (dB) -0.29 -1.2 -2.1
Radiation efficiency (%) 80.28 99.8 58
Bandwidth (MHz) 780-1122.2 884-936 901-928
Minimum value of PRC (dB) -20.5 -13.5 -8.1
RCS ( ) at 900 MHz 0.182 0.0006 0.0016
CMF at 900 MHz 0.837 0.62 0.49

6. GOSPER AND HILBERT LOOP ANTENNA EXPERIMENTAL RESULT

Gosper printed loop antenna was fabricated using LCP substrate as shown in Fig.
24(a). The input impedance was measured by measuring half of the structure over
ground plane and multiply the resultant input impedance by two then, power
reflection coefficients are calculated. Since Gosper antenna is asymmetrical at the
excitation, so both halves are considered and the average is used in power reflection
coefficient calculation and denoted as PRCM. As shown in Fig. 24(b), there is a
difference between computed and simulated PRC which may be attributed mainly to
the presence of the air gap between the half Gosper structure and the ground plane
which was difficult to be eliminated due to the flexible nature of the LCP substrate.
So, computed PRC was considered twice once with an air gap with 1 mm inserted at
the excitation symmetrical plane through all the structure, (0.5 mm between half
structure and the ground plane), and the resultant power reflection coefficient is
denoted as PRCs1 and PRCs is the resultant power reflection coefficient in the
absence of that air gap. The obtained PRCs1 agree with the measured PRCM. We
may also refer the difference between PRCM and PRCS1 to the average process in the
measured results. Hilbert loop antenna was also fabricated using LCP substrate, Fig.
24(c) and the input impedance was measured as aforementioned method used in
measuring Gosper antenna input impedance. Also, the difference between simulated
power reflection coefficient denoted by PRCs and the measured power reflection
coefficient denoted by PRCm may be attributed to the presence of the air gap between
the half Hilbert structure and the ground. So, an air gap of 1 mm was inserted at the
symmetrical plane of the proposed structure (0.5 mm between half structure and the

45


ground plane), simulated PRCs1 was obtained which agree very well with the
measured one, Fig. 24(d).
PRCM
PRCs
3
PRCSs1

0

-3

-6

PRC (dB)
-9

-12

-15

-18
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Frequency (GHz)

Fig. 24(a) Fabricated Gosper Fig. 24(b) Computed and measured PRC of
loop antenna. Gosper loop antenna.
PRCs
3
PRCs1
PRCm
0

-3

-6

-9
PRC (dB)

-12

-15

-18

-21

-24

-27
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Frequency (GHz)

Fig. 24(c) Fabricated Hilbert Fig. 24(d) Computed and measured Hilbert loop
loop Antenna. Antenna.

7. CONCLUSIONS

In this paper a loop type tag antenna, Conventional, Gosper and Hilbert loop tag
antennas were presented. Both Gosper and Hilbert loop tag antennas were fabricated
using LCP substrate and the measured results agreed with computed ones.
Comparison among Gosper, Hilbert and Conventional loop tag antenna was done and
size reduction relative to conventional one was obtained. Both Gosper and Hilbert
loop antennas had a reduced RCS compared to their physical areas and conventional
loop one. The proposed antennas may be used in tagging a small object where
identifying its location is a must.

46


REFERENCES
[1] Barthel H., “Regulatory status for RFID in the UHF spectrum,” EPC Global,
Brussels, Belgium, March 2009.
[2] Zhang H., Fu Y., and Yuan N., “RCS Reduction of ridged waveguide slot
antenna array using EBG radar absorbing material,” IEEE Antennas Wireless
Propag. Lett., vol. 7, pp.473-476, 2008.
[3] Knott E. F., Shaeffer J. F., and Tuley M. T., Radar cross section, 2nd ed.
Raleigh, NC: SciTech Pub., 2004.
[4] Hansen R. C., “Relationship between antennas as scatterers and as radiators”,
Proc. of the IEEE, vol. 77, no. 5, pp. 659-662, May 1989.
[5] Guangping Z., Glenn S. S., “An accurate theoretical model for the thin-wire
circular half-loop antenna,” Antenna and Propagation Symp. (APS), vol. 39,
no. 8, pp. 1167-1177, 1991.
[6] Chu Q. X., Wang L., Zhou J. K., "A novel folded T-matched dipole in base
station,” Int. Conf. Microwave and Millimeter Wave Technology ICMMT, pp.
1–3, 2007.
[7] Higgs-2 integrated single chip UHF RFID tag IC data sheet, EPC global Class
1 Gen 2, Alien Technology Corporation, July 2008.
[8] Butler C. H., " The equivalent radius of a narrow conducting strip" IEEE Trans.
Antennas and Propagation, vol. AP-30, no. 4, pp. 755 - 758, July 1982.
[9] Fukuda H., Shimizu M. and Nakamura G., "New Gosper space filling curves,"
in Proc. Int. Conf. on Computer Graphics and Imaging, pp. 34–38, 2001.
[10] Azad M., Ali M., "A compact Hilbert planar inverted-F antenna (PIFA) for
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Society International Symposium, vol. 3, pp. 3127 - 3130, 2004.

47

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