**Publication: International Journal of Communication Networks and Information Security***Author: Rajhi, Adenen*

*Date published: April 1, 2010*

(ProQuest: ... denotes formulae omitted.)

1. Introduction

In the last few years the Global System for Mobile communications (GSM), the Universal Mobile Telecommunications System (UMTS) bands, and one of the ISM bands is at 2.45 GHz which is also the same band for the Wireless Local Area Network (WLAN) system and Bluetooth applications have been presented in the published papers [l]-[7].

In the literature, several antennas have been used in a variety of applications for which new and more restrictive requirements in the design of the antenna have been introduced. In particular, for high-precision GSM, UMTS and ISM/WLAN applications, few solutions have been proposed by [8]-[10]. Several approaches are developed in order to design multi-band micro-strip patch antennas such as slot matching concept [1 1],[12], as compact ?-shaped slot configurations [13], as ?-shaped slot with compatible feeding [14], as a U-shaped slot in [15] ,[16], as a square slot antenna fed by two orthogonal feed lines is designed for dual polarized applications in [17], as a micro-strip squarering slot antenna (MSRSA) for UWB (Ultra Wideband) antenna applications is designed [18]; unfortunately, these solutions, it may easily provide the desired electric characteristics, but it becomes impractical due to the operational requirements on size and weight.

The complicated geometries of these various antennas present the problem at the levels of the realization, which require very sophisticated equipments and a higher cost for the designer, and for the integration of these antennas in some applications such as the base station of mobile communication. The proposed antenna presents a simple technique; indeed the use of a simple substrate of low cost and larger height allows a good impedance matching; it is therefore necessary to sweep on the aperture size and the dimension of the antenna (length L and width W) and the juxtaposition of the feed probe position allows us to create new resonant frequencies. Once the dimensions of the resonant antenna are determined, the simulated coefficient of reflection S^sub 11^ is extracted. Furthermore, in order to satisfy the demanded precision and reliability, for a high performance proposed antenna a simple modification on the patch surface has been introduced.

The organization of this paper is as follows, in section 2, the theoretical formulation for micro-strip patch antenna is given; in section 3, the design for the both proposed dualband rectangular patch antenna is presented; in section 4, theoretical and simulation results of the electrical characteristics are discussed for better performances of the proposed antennas. Section 5, contains conclusions, and recommendations for further studies.

2. Theoretical Formulation of the Proposed Antenna

In the literature, the analysis of the patch antenna is based mainly in two approximate methods the transmission line model and the resonant cavity model [19].

The cavity model assumes the rectangular patch to be essentially a closed resonant cavity with magnetic walls and it can predict all properties of the antenna with high accuracy but at the expense of much more computation effort than the transmission line model.

The MW cavity model is considered as two conductive surfaces separated by a dielectric substrate with relative dielectric constant sr and this cavity becomes resonant when the conductive surface is excited by a current density distribution. Therefore the analysis of the proposed radiating element, as shown in figure 1 using the technology of the patch antenna with rectangular slot, can use the concept of multi resonant cavities by dividing the geometry of the radiating element in different surfaces and each one has a current distribution ... which can lead to different radiation characteristics.

The conducting surfaces of the radiating elements for the antennas 1 and 2 can be divided in four subsections (Al, Bl, C 1,Dl) for antenna 1 and (A2,B2,C2,D2) for antenna 2; we note that the subsections(Bl,Cl) and (B2,C2) are similar in the current distribution and have identical dimensions therefore they have the same resonant behaviour.

Finally, the proposed radiation elements (antenna 1 and antenna 2) can be analyzed as a system with 4 cavities; the main cavity with dimension L and W, the cavity with dimension of B^sub i^ (or C^sub i^), the cavity with dimension of Di, the cavity with dimension of Ai with i=l,2. We note that the subsections D] for the antenna 1 and B^sub 2^, C^sub 2^ for the antenna 2 have small dimensions; therefore their resonant frequencies are higher than the considered frequency bands.

The dimensions of the proposed patch are the width W= 8cm and the length L=8.55 cm, with a copper plane on one side; in the patch, a slot is designed with a length equal to y2-y^sub 1^ = 4cm and a width X^sub 0^ = 0.4cm for the antenna 1 , y^sub 3^-y^sub 1^ = 0.4cm and a width x^sub 1^ = 4cm for the antenna 2 and the distance between the probe feed and the slot is d=y^sub 1^-y^sub 0^. The coaxial feed was excited by RF source with impedance of 50 ohm, and the frequency band of analysis ranges from 50 Hz to 3.2 GHz. The substrate used in the simulation is plexy-glass material (ε^sub T^1 =2.55) having the height h= 2.5 cm; and the thickness of the patch is assumed negligible.

The patch antenna can be approximately designed by using the transmission line model. The radiating edges of the patch can be thought as radiating slots connected to each other by a micro-strip transmission line. It can be seen from figure. 2 that the rectangular patch with length L and width W can be viewed as a very wide transmission line that is transversally resonating, with a sinusoidal electric field varying under the patch along its resonant length. The electric field is assumed to be invariant along the width W of the patch. Furthermore, it is assumed that the antenna's radiation comes from fields leaking out along the width, or radiating edges, or the slot of the antenna.

The radiation admittance for a single slot is given as

With a slot conductance as

And

And the radiation susceptance of a single slot [19] is given as

Where

Where λ^sub 0^ is the free space wavelength, Z^sub 0^ is the characteristic impedance of the micro-strip line with a length L and a width W.

The effects of the medium and the fringing fields at each end of the patch are accounted for by the effective relative dielectric constant, ε^sub eff^, which is given in equation (6);

and the edge extension, AL, being the effective length to which the fields fringe at each end of the patch.

In figure 2, we can deduce that the effective electrical length of the patch is slightly larger than the real length L and this is due to the overlapping of the electric field at the radiating edge of the patch; therefore it is necessary to add two edges extensions 2ΔL.

To determine the radiation impedance of the antenna, we combine the slot admittance with the transmission line theory. Any conducting subsection of the proposed antennas is merely two slots in parallel separated by a transmission line with a specified length, which has a characteristic admittance Y^sub 0^. The input admittance at the radiating edge can be found by adding the slot admittance to the admittance of the second slot by transforming it across the length of the patch using the transmission line equation and it is given by:

Where ... is the propagation constant of the micro-strip transmission line.

At the resonance ..., the imaginary part of (8) disappears and the radiating element behaves like two slots in parallel having an input admittance equal to twice of the slot conductance

From which we can determine the resonant frequency (which is the operating frequency) in terms of patch dimensions:

For the different conducting subsections, the input admittance is calculated for the corresponding dimension of the radiating edge and for the slot position.

From these theoretical considerations equations (I)-(IO), we can display the calculated Sn given by the following expression (11):

And the bandwidth of the considered antenna is defined by:

Where f^sub max^ and f^sub min^ are determined for a specific level (for example at -1OdB) , the resonant frequency^ of rectangular patch antennas is calculated by using resonant cavity model, together with equations for the effective dielectric constant and the edge extension. The resonant frequency f^sub mn^ of a rectangular patch of width W and length L, both comparable to λs 12, where λs is the wavelength in the substrate, is given by

Where m and n take integer values (m=l, n=0 for the dominant mode), and L^sub e^ and W^sub e^ are the effective dimensions. The effective length L^sub e^ and width W^sub e^ are approximated as follows:

In spite of the simple geometry of the patch antenna, the non homogenous medium in the design of the resonant patch antenna let its analysis quiet difficult. Because of these complexities in the analysis, different approximate methods have been proposed in order to determine the electric characteristics of the printed antenna based on the surface current density distribution ....

Among these methods, there are the cavity method and the transmission line method and these two methods are chosen because they take in consideration the physical concepts and giving good arguments for the resonance phenomenon of the considered antenna.

Table 1 presents a theoretical analysis and comparative results for the two considered antennas divided onto 4 conductive surfaces which are treated as sub cavities (Al, Bl, Cl, Dl) for the antenna 1 and (A2,B2,C2,D2) for the antenna 2 and the total dimension of the antenna (L, W) is considered as a main cavity with a surface current density ... which is resonant at 938MHz; from this point of view of multi cavity structure, we can explain the behaviour of multi resonant frequencies. Indeed, the first resonant frequency f^sub r1^ is related to the larger cavity dimension (main cavity) which is in the GSM band; the second resonant f^sub r2^ can be approximated from the approach of sub-cavities Al for the antenna 1 and A2 for the antenna 2 and its value is around 2 GHz covering the UMTS band. The existence of the third resonant frequency can be explained from the similar subcavities Bl, Cl for the proposed antenna 1 and B2, C2 for the proposed antenna 2. We note also that the conducting surfaces Dl and D2 for the two antennas can be considered as electrically inactive because of the total surface current density which is the sum of two current densities in the opposite directions ....

From the point of view of the resonant frequencies, the designed antenna is functioning mainly in the GSM band with a good choice of the slot dimension and the position of the feeding point relatively to the slot; we can give other possibility of the antenna to cover other telecommunication bands for the second and third generation systems.

3. Simulation and Results

Theoretical magnitude of the parameter Sn for the proposed antennas are compared with ADS simulation results in the frequency range from 50MHz to 3.2GHz and are displayed in the figure 3 for the proposed antenna 1 and in the figure 4 for the proposed antenna 2.

It is noted that the return loss level from the theoretical results and simulation are acceptable; indeed in the case when the frequency is relatively low at 900 MHz the return loss presents a light frequency and amplitude shifts which is probably due to errors of the approximation of the theoretical model; but in the relatively high frequency region at 2000MHz, the theoretical and simulated return loss give a significant differences.

A prototype of the both proposed micro-strip patch antenna has been tested by advanced design system, with the above given geometrical dimensions of the patch. The simulation returns loss of these antenna is presented in figure 5 for three different distances between the probe feed and the slot edge (d 1=0.0 lmm d2=lcm, d3=2cm). From this simulation in figure 5-a, we obtain dual bands, the first band is around a resonant frequency f^sub r1^ and the second band can be considered as around two resonant frequencies (f^sub r2^ ,f^sub r3^), in the figure 5a and around f^sub r2^ in figure 5-b. We note that the fr3 for the second antenna does not appear in the simulation results because the dimension of the sub-cavities B2 and C2 are very small; therefore its resonant frequency are higher then the resonant frequency of the sub-cavity Bl or C 1 .

Figure 5-a demonstrates that a good input match has been obtained for both the GSM/UMTS bands and LAN operations. The optimal proposed antenna is for d2=lcm which covers the required bandwidth respectively of the GSM 900, UMTS 2000 bands and WLAN 2450 operations. For GSM 900, a wide operating frequency range of 890 to 995 MHz is obtained, and the impedance bandwidth determined from -10 dB return loss can reach 105 MHz (or 11.37 % referenced to 923 MHz). For UMTS 2000, a much wider operating frequency range of 1900 to 3100 MHz can be obtained, and the impedance bandwidth determined from -10 dB rerum loss can even reach 1200 MHz (or 55.88 % referenced to 2150 MHz).

The simulated return losses for the antenna 2 are shown in figure 5-b, two distinct resonant modes at 920 MHz and 2250 MHz are obtained. The lower impedance bandwidth is 103 MHz (886-989 MHz), which meets the requirement of the GSM system. The upper impedance bandwidth reaches (for d3) 462 MHz (1888-2350 MHz), which covers the UMTS operating bandwidth.

By analyzing the ADS simulation results of the reflection coefficient of the both proposed antennas, in one hand we can conclude that the antenna 1 has three resonant frequencies (f^sub r1^ ,f^sub r2^ , and f^sub r3^); and for the different distances, the frequency f^sub r1^ is almost the same, but the other frequencies f^sub r2^ and f^sub r1^ changes by changing the distance d. On the other hand, the second antenna has two resonant frequencies (f^sub r1^, f^sub r1^), and we can note that the bandwidth and the resonant frequency depend on the slot position.

In figure 5, the return loss of the two antennas are displayed for three different distances (dl=0.1cm d2=lcm, d3=2cm) and we note that the first resonant frequency is almost the same and it is around 900MHz and this is explained by the fact that L and W are fixed dimensions, and the existence of the slot at different positions explains the different behaviour for the other bands. For the antenna 1 at -1OdB, it covers the UMTS/ WLAN bands and it has two other resonant frequencies f^sub r2^ andf^sub r3^.

The simulation results of the electrical characteristics for the proposed antenna 1 are summarized in the tables 2-4.

Table 2, presents the bandwidth around the first f^sub r1^ resonance frequency and it is noted that the resonant frequency f^sub r1^ and the bandwidth are almost the same one for the different distances d.

Table 3 and Table 4, present respectively the bandwidth around the resonance f^sub r2^ and f^sub r3^ frequencies and it is noted that the bandwidth depends on the distance d. Indeed, one notes for d= 1cm the micro-strip patch antenna present a large bandwidth and more performance around resonance frequency.

By analyzing the ADS Simulation results of the reflection coefficient of the proposed antenna, we can conclude that the antenna has three resonant frequencies (f^sub r1^ ,f^sub r2^, and f^sub r3^); and for the different distances, the frequency f^sub r1^ is almost the same, but the other frequencies f^sub r2^ and f^sub r3^ changes by changing the distance d.

The resonant frequency f^sub r1^ given by Equation (10) can be calculated from the fundamental TM 10 mode of the patch antenna with the dimensions (W = 8cm, L = 8.55 cm), to intend GSM band.

In order to investigate the dependence at the second resonant frequency f^sub r2^ and at the third resonant frequency f^sub r3^ according to the different values of d which represent the distance between the probe feed and the slot, figure.6 and figure.7 are presented to explain this dependence.

Figure.6 and Figure.7 show how the both resonances frequencies f^sub r2^ and f^sub r3^ , depend respectively from the distance d between the slot and the probe feed, indeed, these variations of f^sub r2^ and f^sub r3^ have inverse behaviours if f^sub r2^ increases then f^sub r3^ decreases and vice versa.

4. Conclusion

A simple design of dual band antenna functioning in the second and third generation mobile telecommunication systems, based on the slot matching concept is presented and analysed and the ADS simulation results are given. The main quality of the proposed antenna 1 is that it allows an effective design maintaining all the advantages of microstrip antennas in terms of size, weight and easy manufacturing. Moreover, this antenna has a good effectiveness on the totality of the three covered bands respectively, GSM, UMTS and WLAN frequency bands. This work has to be studied further to have more precise expressions for the dependence of the second and third resonant frequencies (fr2 and /5 ) with the distance d between the slot and the feed probe.

References

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Author affiliation:

Adenen rajhi1, Said Ghnimi2 and Ali Garssallah3

1 Ecole supérieure de technologie et de l'informatique, Tunis, Tunisia.

Adnen.Rajhi@esti. rnu. tn

2 Unité de recherche - Systèmes et circuits électronique hautes fréquences, FST, Tunisia.

3 Unité de recherche - Systèmes et circuits électronique hautes fréquences, FST, Tunisia.