reduced rcs uhf rfid gosper and hilbert tag antennas

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –

6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME

35

REDUCED RCS UHF RFID GOSPER AND HILBERT TAG

ANTENNAS

T. G. Abo-Elnaga 1, *

, E. A. F. Abdallah 1, and H. El-Hennawy

2

1 Microstrip Dept., Electronics Research Institute

El-Tahrir Street, Dokki 12622

Giza, Egypt, +21006751840, [email protected] 2Faculty 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

INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING AND TECHNOLOGY (IJARET)

ISSN 0976 - 6480 (Print) ISSN 0976 - 6499 (Online)

Volume 3, Issue 1, January- June (2012), pp. 35-47

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IJARET © I A E M E



36

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 wavelengtho

λ , constructed from a perfectly conducting wire of radiusi

a ,

andoo

λπβ 2= . The wire circular loop input admittance in

Y is

found as:

on

nooinVIIVIjBGY

+==+= ∑

∞

=1

2))0(

(1)

,...2,1,0=−

= na

bjVI

n

n

o

on

πξ

(2)

( ) n

o

nn

o

n KR

nKK

Ra

β

β 2

112

−+= −+

(3)

( ) ( ) ( )

[ ]∑ ∫−

=

+Ω−+

−

−++

−

−=

1

0

2

0

22

5.022222

0

22

0

)()(2

1

12

12

4ln11

n

m

R

nn

oo

io

in

o

dxxjJxm

RnRn

R

aHRn

R

aBK

β

π

βγπ

ββπ

(4)



37

( )( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) )11

11

11(ln

1

22

0

22

0

22

0

22

0

22

0

22

0

−−−

−−⋅

−−+

−+−

−+⋅

−+=

RnR

aHRn

R

aH

RnR

aBRn

R

aH

RnR

aHRn

R

aB

aab

oo

oi

oi

oo

oi

oi

io

n

ββ

ββ

ββ

(5)

In Eqs. (1) to (5), G and B are the input conductance and susceptance

respectively,0

B and 0

H are the modified Bessel functions of the first and second

kinds and order zero, n2

Ω is the Lommel-Weber function of order 2n, n

J2

is the

Bessel function of the first kind and order 2n, Euler's constant γ = 0.57722 and

oooεµξ = with

oµ and

oε 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

10 20 30 40 50 60 70 80 90-1500

-1000

-500

0

500

1000

1500

2000

2500

3000

3500

R (mm)

Imp

ed

an

ce

( Ω)

Real

Imag

w2

'2w

b

l2

da

aZ

tZ2

( ) 1:1 α+

Fig. 1 Circular loop antenna input impedance

versus different radii with = 0.5 mm

(fabrication purpose), coaxial outer raduis =

1.15 mm at 900 MHz.

Fig. 2 T-matched configuration for

planar dipoles and equivalent circuit.



38

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) Ω 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) Ω 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.

24

. 73

597

24

.73

597

44.4

9266

44.4

9266

44.49266

64.2

4935

64.2

4935

64.24935

84

.00

604

84.0

0604

84.00604

103.7

627

103.7

627

103.7627

123.5

194

123.5

194

123.5194

14

3.2

761

143.2

761

163.0

328

163.0328

182.7

895

182.7

895

202.5

462

10.3

558

10.3

558

10.3558

20.6

691

20.66

91

20.6691

30.9

823

30.9

823

30.9823

41

.2956

41.2

956

51.6

088

51.60

88

61.9

221

61.92

21

72.2

353

82.5

486

ad / l

b / 2

w

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.21

1.5

2

2.5

3

3.5

4

4.5

5

Imag

Real

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

( )



39

Inner radius R = 55 mm

Outer radius R = 57 m

m

Fig. 4 Conventional printed circular loop antenna T-matched circuit section.

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

-21

-18

-15

-12

-9

-6

-3

0

3

PR

C (

dB

)

Frequency (GHz)

Fig. 5 PRC versus frequency for

conventional printed loop antenna with T-

matched circuit (R=55mm).

Fig. 6 RCS versus frequency for

conventional printed loop antenna with

T-matched circuit (R=55mm).

Fig. 7 CMF versus frequency for

conventional printed loop antenna with T-

matched circuit (R=55mm).

Fig. 8 Conventional printed loop

antenna with T-matched circuit

radiation pattern at 900 MHz

(R=55mm).



40

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

initiator, generator

replacement for n=1.

Fig. 9(b) Gosper curve



Fig. 9 Gosper curve



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) Ω.

We considered the structure as asymmetric dipole loaded by Gosper loop antenna.

-20 -15 -10 -5 0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

50

Gosper length (mm)

Go

sp

er

wid

th (

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,



41

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 Ω)

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



42

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

-15

-12

-9

-6

-3

0

3

PR

C (

dB

)

Frequency (GHz)

Fig. 13 PRC versus frequency for Gosper

loop antenna.

Fig. 14 RCS versus frequency for Gosper loop

antenna.

Fig. 15 CMF versus frequency for Gosper

loop antenna.

Fig. 16 Radiation pattern at 900 MHz for

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



43

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).

20.4

2183

20

.42

183

35

.98

744

35

.98

744

51

.55

305

51

.55

305

67

.11

865

67

.11

865

82

.68

426

82

.68

426

82.68426

98

.24

987

98

.24

987

98.24987

11

3.8

155

11

3.8

155

113.8155

12

9.3

811

12

9.3

811

129.3811

14

4.9

467

144.9

467

144.9467

16

0.5

123

160.5

123

2. 6

71

21

2.6

71

21

2.67121

5.3

20

82

5.3

20

82

5.32082

7.9

70

43

7.9

70

43

7.97043

10

.62

10

.62

10.62

13

.26

97

13

.26

97

13.2697

15

.91

93

15

.91

93

15.9193

18

.56

89

18

.56

89

18.5689

21

.21

85

21

.21

85

21.2185

23

.86

81

23.86

81

26

.51

77

ad / l

b / 2

w

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.551

1.5

2

2.5

3

3.5

4

4.5

5

Imag

Real

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



44

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

0.80 0.85 0.90 0.95 1.00

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

PR

C (

dB

)

Frequency (GHz)

Fig. 20 PRC of Hilbert loop antenna versus

frequency.

Fig. 21 RCS of Hilbert loop antenna versus

frequency.

Fig. 22 CMF versus frequency for Hilbert loop

antenna.

Fig. 23 Hilbert loop antenna radiation

pattern at 900 MHz.



45

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

Parameter

Conventional

Gosper

Hilbert

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



46

ground plane), simulated PRCs1 was obtained which agree very well with the

measured one, Fig. 24(d).

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

-18

-15

-12

-9

-6

-3

0

3

PR

C (

dB

)

Frequency (GHz)

PRCM

PRCs

PRCSs1

Fig. 24(a) Fabricated Gosper

loop antenna.

Fig. 24(b) Computed and measured PRC of

Gosper loop antenna.

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

-27

-24

-21

-18

-15

-12

-9

-6

-3

0

3

PR

C (

dB

)

Frequency (GHz)

PRCs

PRCs1

PRCm

Fig. 24(c) Fabricated Hilbert

loop Antenna.

Fig. 24(d) Computed and measured Hilbert loop

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.



47

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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

dual-band mobile phone applications", IEEE Antennas and Propagation

Society International Symposium, vol. 3, pp. 3127 - 3130, 2004.

reduced rcs uhf rfid gosper and hilbert tag antennas

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