DESIGN of BROADBAND MICROSTRIP PATCH ANTENNA

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ABSTRACT. The purpose of this project is to design a broadband microstrip patch antenna to be used in wireless communication systems. This project ...
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DESIGN of BROADBAND MICROSTRIP PATCH ANTENNA Chapter · September 2005

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Design of Broadband Micrstrip Patch Antenna

NORTHUMBRIA U N I V E R S I T Y

SCHOOL OF ENGINEERING & TECHNOLOGY COURSE: Msc ENGINEERING & TECHNOLOGY

Name: Farhat M. Emhemed Registration no: 04956900

PROJECT TITLE:

″DESIGN of BROADBAND MICROSTRIP PATCH ANTENNA”

SUPERVISOR:

PROF. EDWARD KOROLKIEWICZ

YEAR: 2005 SUBMISSION DATE:

20 September, 2005

_______________________________________________________________________________________________________________ FARHAT M. EMHEMED

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Design of Broadband Micrstrip Patch Antenna

ABSTRACT The purpose of this project is to design a broadband microstrip patch antenna to be used in wireless communication systems. This project concentrates on the design of a broadband microstrip patch antenna for a 2 GHz system. Firstly, before embarking on such a design, a description of the microstrip line in microstrip antennae is given. Then, the modeling and design of a 50-ohm microstrip line are derived. Next, all simulations are carried out using MathCAD software and Microwave Office. This permits the analysis of the results of the simulations. In addition, the microstrip patch antenna is introduced, the relevant theory is presented and some feed modeling techniques are also discussed. Secondly, a standard rectangular microstrip patch antenna is designed and modeled to operate at an operating frequency of 2 GHz with a FR4 PCB. It is simulated by using Microwave Office and then, the results are analysed and discussed. It is observed that its bandwidth is limited. Finally, an impedance matched broadband antenna is designed in order to broaden the bandwidth of the microstrip patch antenna. A comparison is made between the standard patch antenna and the broadband antenna via simulation. It is shown that by using optimal impedance -matching network, the bandwidth can be increased.

Introduction Microstrip patch antennaes are widely used in various applications, especially in wireless communications. The microstrip patch antenna consists of a dielectric substrate on one side of a patch with a ground plane on the other side, and wide varieties are possible of design. It has many advantages, such as low profile, lightweight, conformity, low fabrication costs, simplicity of manufacture, and the capability to be integrated with microwave integrated circuits (MICs) [7],[4]. In addition, microstrip antennae can be fed by various techniques. However, their application in many systems is restricted because they have inherently narrow bandwidths. To overcome the inherent limitation of narrow impedance bandwidths, many techniques have been suggested for bandwidth improvement, and these can be classified into the following methods [21]: the implementation of impedance matching, increasing antenna volume (this is accomplished by geometric changes to increase the volume under the patch, e.g. increasing thickness) and using coplanar or multi-layer elements [20]. In this project, broad-band impedance matching is proposed for bandwidth enhancement. This technique means the attachment of a network to the patch antenna and this normally is used in the feed _______________________________________________________________________________________________________________ FARHAT M. EMHEMED

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Design of Broadband Micrstrip Patch Antenna

port of the microstrip antenna which does not alter the radiating element itself. This can be done using a four element matching network.

Chapter 5:

Design of Broadband Microstrip Patch Antenna

5.1 Introduction Microstrip antennae are inherently narrowband. A narrow bandwidth is a major disadvantage of microstrip antennae in practical application. In a patch antenna, the impedance bandwidth can be increased and a broadband microstrip antenna can be achieved. Some recently reported broadband or bandwidth-enhancement techniques are presented for microstrip antennae by using a suitable model of the microstrip-matching network directly coupled to the radiating edge of a rectangular microstrip antenna. In this chapter, the use of the matching networks to achieve broadband microstrip antenna is implemented. A conventional rectangular microstrip patch antenna, which is in very wide use, are compared with broadband microstrip patch antenna using a matching network. Microwave Office and Ensemble software are used in the process of obtaining the effect of the impedance matching network on the microstrip patch antenna.

5.2 Definition of Bandwidth The bandwidth can be the range of frequencies on either side of the center frequency where the antenna’s characteristics, such as input impedance, radiation pattern, beam width, polarization and gain, are close to those values which have been obtained at the center frequency. The bandwidth of a broadband antenna can be defined as the ratio of the upper to lower frequencies of acceptable operation. Bandwidth can be expressed in two ways, as a ratio and as a percentage. Bandwidth as a ratio is usually used for very wide bandwidth applications. Bandwidth for moderately wideband antennae is usually expressed as a percentage relative to the center frequency fact:

BP =

fU − f L *100 fC

(5.1)

Where = f H upper frequency _______________________________________________________________________________________________________________ FARHAT M. EMHEMED

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Design of Broadband Micrstrip Patch Antenna

= f L lower frequency = f C center frequency The BW is inversely proportional to its quality factor Q, where decreasing the quality factor of the microstrip antenna is also an effective way of increasing the antenna’s impedance bandwidth and is given by[18]: BW =

VSWR − 1

(5.2)

Q VSWR

where VSWR is defined in terms of the input reflection coefficient Γ as:

VSWR =

1+ Γ

(5.3)

1− Γ

How efficiently an antenna is operating over the required range of frequencies is found by measuring its VSWR. A VSWR ≤ 2 (dB RL - 5. 9) ensures good performance.

5.3 Design of Broadband Microstrip Antenna using Three Elements 5.3.1 The π Matching Network Figure 5.1 shows the equivalent circuit for a broadband patch antenna using a π matching network represented by a lumped element, then a microstrip line. The equivalent values were calculated by changing each reactance into a component value of capacitance and inductance at the frequency of 2.1GHz, in order to obtain another broadband peak. The calculations are shown in Appendix B. In this design the load impedance is bigger than the source impedance. So, the Q is: RL > Rs

Q2 =

Q2 >Q1

RL −1 RV

(5.4)

Assume that Q2 = 5

5=

121 −1 RV

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Design of Broadband Micrstrip Patch Antenna

Rv = 4.65 •

Design of the load section:

(A)

(B)

For (A):

Q = 5 = 121 / Xc2

Xc2 = 24.2Ω

For (B):

Q = 5 = XL2 /4.65

XL2 = 23.3 Ω



Design of the source section:

(A)

(B) Q=

Q1 =

RS −1 Rv

50 −1 4.65

Q1 = 3.1 _______________________________________________________________________________________________________________ FARHAT M. EMHEMED

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Design of Broadband Micrstrip Patch Antenna

For (A):

Q1= 3.1 = XL1 / 4.65

For (B):

Q1= 3.1= 50 / Xc1

XL1 = 14.5 Ω Xc1= 16.1 Ω

The final π matching circuit with the impedance values is shown below:

Figure 5.1 shows the equivalent circuit for a broadband patch antenna using a π matching network represented by a lumped element.

PORT P= 1 Z= 50 Ohm

CAP ID= C4 C= 4.7 pF

MLIN ID= TL2 W= 47 mm L= 35.1 mm

IND ID= L2 L= 2 nH

CAP ID= C3 C= 3.13 pF

CAP ID= C1 C= 0.861 pF

RES ID= R2 R= 636.5 Ohm

CAP ID= C2 C= 0.861 pF

RES ID= R1 R= 636.5 Ohm

MSUB Er= 4.3 H= 1.575 mm T= 0.035 mm Rho= 1 Tand= 0.019 ErNom= 4.3 Name= SUB1

Figure 5.1 Equivalent circuit for broadband patch antenna using π network _______________________________________________________________________________________________________________ FARHAT M. EMHEMED

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Design of Broadband Micrstrip Patch Antenna

The physical dimensions for the broadband matching network can be calculated by substituting the impedances in the TXLIN calculator in Microwave Office as shown below.

Figure: 5.2 TXLIN calculator

e.g.

W= 4.81mm, L=19.08mm for the series line.

Figure 5.2 shows the microstrip broadband patch antenna modeled by the micrstrip line.

PORT P= 1 Z= 50 Ohm

MLIN ID= TL5 W= 8.73 mm L= 31.6 mm

MLIN ID= TL3 W= 4.816 mm L= 19.08 mm

MLIN ID= TL4 W= 7.199 mm L= 34.48 mm

MLIN ID= TL1 W= 47 mm L= 35.1 mm

CAP ID= C1 C= 0.861 pF

RES ID= R2 R= 636.5 Ohm

CAP ID= C2 C= 0.861 pF

RES ID= R1 R= 636.5 Ohm

MSUB Er= 4.3 H= 1.575 mm T= 0.035 mm Rho= 1 Tand= 0.019 ErNom= 4.3 Name= SUB1

Figure 5.3 Broadband patch antenna using π microstrip network _______________________________________________________________________________________________________________ FARHAT M. EMHEMED

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Design of Broadband Micrstrip Patch Antenna

5.3.2 The T Matching Network In this design, the T matching network model in chapter 4 is used. •

Design of the source section:

(A)

(B) Q1 = √ (Rv / Rs)-1 Q1 = √ (Rv / 50)-1 Rv = 250

For (A):

Q1= QT = 2 = XL1 / 50

XL1 = 100 Ω

For (B):

Q1= 2 = 250 / Xc1

Xc1= 125 Ω



Design of the load section:

(A)

(B)

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Design of Broadband Micrstrip Patch Antenna

Q2 = √ (Rv / RL)-1 Q2 = 1.03

For (A):

Q2= 1.03 = XL2 / 120

XL2 = 123 Ω

For (B):

Q2= 1.03 = 250 / Xc1

Xc2= 242.7 Ω

The final T matching circuit is shown below:

Figure 5.3 shows the equivalent circuit for the broadband patch antenna using T matching network represented by a lumped element.

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Design of Broadband Micrstrip Patch Antenna

PORT P= 1 Z= 50 Ohm

IND ID= L2 L= 7 nH

CAP ID= C3 C= 0.9 pF

MLIN ID= TL2 W= 47 mm L= 35.1 mm

IND ID= L1 L= 9 nH

CAP ID= C1 C= 0.861 pF

CAP RES ID= C2 ID= R2 R= 636.5 Ohm C= 0.861 pF

RES ID= R1 R= 636.5 Ohm

MSUB Er= 4.3 H= 1.575 mm T= 0.035 mm Rho= 1 Tand= 0.019 ErNom= 4.3 Name= SUB1

Figure 5.4 Equivalent circuit for broadband patch antenna using T network

Figure 5.5 shows the broadband patch antenna using the T micrstrip matching network

PORT P= 1 Z= 50 Ohm

MLIN ID= TL2 W= 0.6836 mm L= 20.59 mm

MLIN ID= TL3 W= 1.088 mm L= 31.63 mm

MLIN ID= TL4 W= 0.3677 mm L= 20.9 mm

CAP ID= C1 C= 0.861 pF

MLIN ID= TL1 W= 47 mm L= 35.1 mm

RES ID= R2 R= 636.5 Ohm

CAP ID= C2 C= 0.861 pF

RES ID= R1 R= 636.5 Ohm

MSUB Er= 4.3 H= 1.575 mm T= 0.035 mm Rho= 1 Tand= 0.019 ErNom= 4.3 Name= SUB1

Figure 5.5 Broadband patch antenna using T microstrip network

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Design of Broadband Micrstrip Patch Antenna

5.3.3 Simulation Figures 5.6 and 5.7 show the responses of the broadband patch antenna with three element networks. patch 0

1.9768 GHz -10.03 dB

-10

2.0155 GHz -10.02 dB

-20

DB(|S[1,1]|) & patch antenna -30 1.8

1.9

2 2.1 Frequency (GHz)

2.2

2.3

Figure 5.6: Reflection coefficient of the broadband antenna using π network

T network 0

-5

1.9879 GHz -10.01 dB

2.0185 GHz -10.01 dB

-10

-15 DB(|S[1,1]|) & Schematic 4

-20 1.8

1.9

2 2.1 Frequency (GHz)

2.2

2.3

Figure 5.7: Reflection coefficient of the broadband antenna using T network

5.3.4 Discussion It can be seen from the above plots that the simulation results are slightly different from the results obtained from a broadband antenna, and are nearly the same as the patch antenna. This indicates that the π and T networks are useful for narrow band matching. _______________________________________________________________________________________________________________ FARHAT M. EMHEMED

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Design of Broadband Micrstrip Patch Antenna

5.4 Design of Broadband Microstrip Antenna using Four Elements Impedance Many configurations have been proposed to extend bandwidth. The use of four element wideband impedance–matching networks in order to broaden narrowband antennae was chosen for this study. Wideband antenna can be realized if an impedance matching network is achieved over a wide frequency range. In figure 5.8 a mask layout of a coplanar multiresonator configuration is shown, and consisting of rectangular microstrip patch antenna with coplanar microstrip impedance matching network. The structure is designed as the rectangular microstrip antenna element itself and the other two resonators are open stubs, at a half wavelength at resonant frequency with quarter–wavelength interconnecting lines. The patch radiator with microstrip matching circuit is etched on to an inexpensive FR4 substrate with dielectric constant of εr = 4.3 and thickness h=1.575mm. Other parameters are necessary for analysis of the transmission line such as thickness of patch conductor=0.035mm and loss tangent of substrate tan δ =0.019. The length of the rectangular patch is 35.1mm and the width is 47mm at fo = 2.002 GHz. The calculations are shown in Appendix A using MathCAD software.

Figure 5.8: Plane view of standard rectangular patch antenna with wideband matching network

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Design of Broadband Micrstrip Patch Antenna

The four elements modelling in chapter 4 will be used to design the matched broadband antenna. The virtual impedance is expressed as:

Rv = Rs RL Rv = 50 *121 =77.78Ω

The loaded Q of the network is given by:

Q=

RV −1 = RS

RL −1 RV

Rs=50 Ω, RL=121 Ω Q= 0.75 The input (L) section on the input side of the network, Xp1 and Xs1 can be calculated as:

Q=

RS X p1

X S 1 = Rv Q

X p1 =

50 = 67 Ω 0.75

X S 1 = 77.78 * 0.75 = 58 Ω

Now for the L section on the load end, to find Xp2 and XS2 we get:

X p2 =

Rv Q

X S 2 = RL Q

X p2 =

77.78 = 104 Ω 0.75

X S 2 = 121* 0.75 =90Ω

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Design of Broadband Micrstrip Patch Antenna

Figure 5.9 shows the equivalent circuit for broadband patch antenna represented by lumped element.

IND ID= L2 L= 4 nH

IND ID= L1 L= 7 nH

CAP ID= C4 C= 1.18 pF

CAP ID= C3 C= 0.76 pF

PORT P= 1 Z= 50 Ohm

MLIN ID= TL1 W= 47 mm L= 35.1 mm

CAP ID= C1 C= 0.861 pF

RES ID= R2 R= 636.5 Ohm

CAP ID= C2 C= 0.861 pF

RES ID= R1 R= 636.5 Ohm

MSUB Er= 4.3 H= 1.575 mm T= 0.035 mm Rho= 1 Tand= 0.019 ErNom= 4.3 Name= SUB1

Figure 5.9: Equivalent circuit for broadband patch antenna

5.5 Modelling and Simulation of Microstrip Broadband Antenna In this section, broadband rectangular microstrip patch antenna will be modelled. The simulation will be carried out using microstrip line, Microwave Office and Ensemble software using substrate FR4 PCB.The simulation results are compared between the standard rectangular microstrip patch antenna and the wideband antenna. By using MathCAD calculations, the dimensions of the patch antenna are calculated as shown in Appendix A. The impedances of the matching network were obtained from the calculations, then the widths and the lengths of these elements can be determined using TXLine from Microwave Office. The dimensions of the matching network have been tuned in order to obtain suitable bandwidth response at the centre frequency.

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Design of Broadband Micrstrip Patch Antenna

4 5

1

2 3

Table 5.1 shows the overall design dimensions of the matched broadband antenna. No in Fig.

W(mm)

L(mm)

1

47

35.1

2 3 4 5

2.0 1.06 2.2 0.549

18.88 25.5 32.3 25.3

Table 5.1 Dimensions of the matched antenna

Figure 5.10 shows the microstrip broadband patch antenna modeled by microstrip line.

PORT P= 1 Z= 50 Ohm

MLIN ID= TL7 W= 0.549 mm L= 25.3 mm

MLIN ID= TL5 W= 2.2 mm L= 32.3 mm

MLIN ID= TL2 W= 1.06 mm L= 25.5 mm

MLIN ID= TL1 W= 2.2 mm L= 18.88 mm

CAP ID= C1 C= 0.861 pF

MLIN ID= TL6 W= 47 mm L= 35.1 mm

RES ID= R2 R= 636.5 Ohm

CAP ID= C2 C= 0.861 pF

RES ID= R1 R= 636.5 Ohm

MSUB Er= 4.3 H= 1.575 mm T= 0.035 mm Rho= 1 Tand= 0.019 ErNom= 4.3 Name= SUB1

Figure 5.10 Microstrip broadband patch antenna

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Design of Broadband Micrstrip Patch Antenna

5.5.1 Results Obtained from Microwave Office Software Microwave Office was used to model and simulate the microstrip patch antenna. It can be also used to calculate and plot the S 11. The measured return loss plots of the antenna with and without matching network are shown below in Figures 5.11and 5.12.

Broadband

0

-5

1.9344 GHz -10.02 dB

2.0444 GHz -10.01 dB

-10

-15

-20 DB(|S[1,1]|) & wwww

-25 1.8

1.9

2 Frequency (GHz)

2.1

2.2

Figure 5.11: Reflection coefficient of the rectangular broadband antenna

Graph 7

0

1.982 GHz -10.1 dB

-10

2.0218 GHz -10.02 dB

-20

-30 DB(|S[1,1]|) & Schematic 5

-40 1.8

1.9

2 Frequency (GHz)

2.1

2.2

Figure 5.12: Reflection coefficient of the rectangular patch antenna S11 (dB)

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Design of Broadband Micrstrip Patch Antenna

Figure 5.13 shows the considerable effect of the matching network. The bandwidth can be calculated from the return loss (RL) plot. The bandwidth of the antenna can be said to be those range of frequencies over which the RL is greater than -10 dB(VSWR ≤ 2).

Broadband

0

-10

2.0461 GHz -9.485 dB

1.9333 GHz -9.493 dB

-20

-30

DB(|S[1,1]|) & broadband antenna DB(|S[1,1]|) & patch

-40 1.9

1.8

2 Frequency (GHz)

2.1

2.2

Figure 5.13: Comparison between normal patch and patch with matching

impedance 2. 0

6 0.

0.8

1.0

Swp Max 2.2GHz

0. 4

0 3. 4.0 5.0

0.2

10.0

4.0 5.0

3.0

2.0

1.0

0.8

0.6

0.4

0

0.2

10.0

-10.0

2 -0.

-4. 0 -5. 0

-3 .0

.0 -2

-1.0

Z[1,1] * broadband antenna

-0.8

-0 .6

.4 -0

Swp Min 1.8GHz

Figure 5.14: Input impedance

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Design of Broadband Micrstrip Patch Antenna

5.5.2 Results Obtained from Ensemble Software Figures 5.15 and 5.16 show the reflection coefficient of the rectangular broadband antenna and variation of VSWR with frequency using Ensemble software.

Figure 5.15: Reflection coefficient of the rectangular broadband antenna

Figure 5.16: Variation of VSWR with frequency

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Design of Broadband Micrstrip Patch Antenna

Figures 5.17 (a,b and c) show the radiation patterns at different frequencies along the operation band.

Figure 5.17a: Radiation patterns at lower frequency

Figure 5.17b: Radiation patterns at centre frequency

Figure 5.17c: Radiation patterns at upper frequency _______________________________________________________________________________________________________________ FARHAT M. EMHEMED

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Design of Broadband Micrstrip Patch Antenna

5.6 Results and Discussion To be able to judge the performance of this impedance-matched antenna, a standard antenna has been built in the same process as in the chapter 3. This standard antenna is completely identical to the impedance-matched antenna except that the matching network is replaced by a quarter wave transformer. Table 5.1 shows the comparison between the standard antenna and the broadband antenna.

Centre frequency (GHz) Patch antenna Broadband antenna

2.0 1.97

Bandwidth (RL > -10 dB)

Quality factor

(MHz)

40 110

50 18

Table 5.1: Comparison between the standard antenna and the broadband antenna

It is observed from the results above that the rectangular microstrip patch antenna with the impedance–matching network yielded a BW of 110 MHz, which is obtained at -10 dB for (VSWR = 2). By adjusting the widths and the lengths of the impedance matching network microstrip lines, the broadband behavior was obtained by realising the dual-frequency property. It was clear that there were two resonances in the return loss curve, leading to wide bandwidth, determined from the -10 dB return loss points, according to the simulation results in figure 5.13. The standard antenna has its best match at 2 GHz (-38 dB) and within the band of operation, the impedance-matched antenna has its worst match at 1.97 GHz (-10 dB) return loss, but it can be seen that the bandwidth at this level has been increased to a value of 110 MHz, which is about 5.5% of the center frequency at 1.97 GHz, for VSWR ≤ 2. The centre frequency is (fL+fH) /2, where fL and fH are the lower and higher frequencies with -10 dB return loss. The radiation characteristics of the antenna in the operating bands were shown. The radiation patterns for the proposed antenna have been plotted at the centre, lower and upper frequencies. It was found that good radiation patterns were observed, which proves that the matching network, even though it is coplanar with the patch, does not affect the radiation patterns characteristics.

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Design of Broadband Micrstrip Patch Antenna

It can also be seen that increasing the antenna’s bandwidth reduced the quality factor of the antenna. The obtaining broadband microstrip patch antenna has a match increased antenna size compared to a single rectangular microstrip patch antenna. In addition, the planar multiresonator technique uses only with rectangular patch to obtain the bandwidth. The obtained results from the three element networks were slightly different from the results obtained from the broadband antenna.

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Design of Broadband Micrstrip Patch Antenna

Chapter 6

Conclusions

6.1 Conclusion The aim of this project was to design a broadband microstrip patch antenna for use in wireless communication systems. Before designing such an antenna, it was necessary to become familiar with microstrip lines because microstrip patch antennae are derived from them. The simulation and theoretical results of microstrip line have been illustrated. Comparison was made between these sets of results, and it can be concluded that the simulated results obtained are slightly different from the results obtained by theory using MathCAD, due to microstrip losses such as conductor and dielectric losses. It was found that the tolerance of the dielectric constant of FR4 PCB is high, therefore the dielectric loss was greater than the conductor loss. The rectangular patch antenna was designed and modeled using ideal and lossy transmission lines. From the simulation, it was concluded that the characteristic impedance at 2GHz for lossy antenna is less than that obtained from an ideal one, due to the losses in the transmission line patch antennae. For both cases the maximum impedance can be obtained at resonant frequency. It can also be concluded that for the return loss after matching using the quarter wave transformer, a good S11 of -38 was achieved for the rectangular patch antenna. The bandwidth of the antenna obtained was about 40 MHz, which is 2% at the desired frequency 2GHz. It was concluded that the microstrip patch antenna has inherently narrow bandwidth, determined at -10dB return loss. Finally, the broadband microstrip patch antenna has been successfully designed and modeled having a center frequency of 1.97 GHz, by using the attachment of a four-element network to the patch antenna. The achieved impedance bandwidth of the antenna was 110 MHz with 5.5 %, applicable to wireless communications operating continuously over the frequency range 1.93 to 2.04 GHz. An acceptable VSWR of less than or equal to 2:1 was obtained. It was found that the matched antenna has its worst match at 1.97 GHz, but this is reasonable. Radiation pattern plots have been obtained for the desired antenna orientation and the radiation patterns were reasonable. The broadband microstrip patch antenna obtained has increased antenna size compared to the single rectangular microstrip patch antenna. However, impedance matching is a general technique and many other design forms could be devised, which possibly could yield better results. _______________________________________________________________________________________________________________ FARHAT M. EMHEMED

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Design of Broadband Micrstrip Patch Antenna

6.2 Further work Some Further work and investigation of broadband antenna can be carried out in order to improve the bandwidth of the antenna. •

Instead of using FR4 PCB for antenna, other material such as Durouid 5880 is recommended because which has lower loss tangent if compared with the FR4 PCB.



The obtaining broadband microstrip patch antenna has a match increased antenna size, so it is recommended to reduce the size by putting the matching network under the patch instead of the front.



A probe feed method is preferable where this could reduce the size of the antenna and increase the bandwidth.

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Design of Broadband Micrstrip Patch Antenna

References [1] Microstrip Antennas1

JR James & P S Hall

[2] Foundations of Interconnect and Microstrip Design by T. C. Edwards, M. B. Steer (Hardcover - January 1, 2001) [3] James D. Woermble “soft substrates conquer Hard Design” Microwave January 1982. [4] Microstrip Antennas2

JR James & P S Hall

[5] Pozar and Schaubert; “Microstrip Antennas”, Proceedings of the IEEE, vol. 80, 1992 [6] Microwave Engineering .by David M. Pozar (Hardcover - September 3, 2004) [7] Antenna Theory: Analysis and Design, 2nd Edition / by Constantine A. Balanis ( 1997) [8] www. 4_5 Microstrip Antenna.htm [9] www. Microstrip - Microwave Encyclopedia - Microwaves101_com.htm (03 March 2005) [10] www.Introduction to Common Printed Circuit Transmission Lines.htm (03 March 2005) [11] www. Table Of Contents. Pdf [12] www. Mstrip40LabManual.pdf (04 February 2005) [13] www. mstrip.pdf (03 March 2005) [14] www.RF Cafe - Microstrip Equations Formulas.htm (10 February 2005) [15] www.US Microwaves Application Note 104 - THIN FILM MICROSTRIP TRANSMISSION LINES.htm (03 March 2005). [16] High Frequency and Microwave Engineering, by E.da Silva 2001 [17] Compact and Broadband Microstrip Antennas, by Kin-Ln Wong, 2002 John Wily & Sons, [18] Broadband Microstrip Antennas, by Kumar, Girish , 2003 ARTECH HOUSE, INC. [19] Broadband Patch Antennas, By Zurcher, Jean-Francois, 1995 ARTECH HOUSE. [20] Microstrip and printed Antenna Design / by Randy Bancroft /NOBLE publishing, 2004. [21] IEE ANTENNAS & PROPAGATION

ICAP 2003

[22] IEE ANTENNAS & PROPAGATION, Vol.37, NO.11, NOV.1989

Bibliography [1] RF and Microwave Wireless Systems, by KAI chang, 2000 John Wily & Sons. [2] IEEE Antennas and Propagation Magazine, Vol. 42, No. 4, August 2000 [3] IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 12, NO. 8, AUGUST 2002 [4] IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 49, NO. 7, JULY 2001 _______________________________________________________________________________________________________________ FARHAT M. EMHEMED

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