Abstract: Recent research has concentrated on different designs in order to increase the bandwidth of patch antennas and thus improve functionality of wireless communication systems. An alternative approach as shown in this paper is to design a matched probe fed rectangular patch antenna which can operate at both dual frequency (1.9 GHz and 2.4 GHz) and dual polarisation. In this design there are four variables, the two dimensions of the rectangular patch, ‘a ’ and ‘b ’ and position of the probe feed ‘Xp ’ and ‘YP’. As there is not a unique solution Genetic Algorithm (GA) was applied using two objective functions for the return loss at each frequency. The antenna was then modelled using AWR software and the predicted and practical results are shown to be in good agreement. Key Words: Genetic algorithm (GA), dual frequency, dual polarisation, probe fed patch antenn

Danaher, Sean

Ghassemlooy, Zabih

Korolkiewicz, Edward

Lu, Qing

Sambell, Alistair

English

Northumbria Research Link

 Optimum Design of a Probe Fed Dual Frequency Patch Antenna Using Genetic Algorithm  Q. Lu, E. Korolkiewicz, S. Danaher, Z. Ghassemlooy and A. Sambell  NCRLab, School of Computing, Engineering and Information Sciences, Northumbria University, Newcastle upon Tyne, NE1 8ST, UK  Abstract: Recent research has concentrated on different designs in order to increase the bandwidth of patch antennas and thus improve functionality of wireless communication systems. An alternative approach as shown in this paper is to design a matched probe fed rectangular patch antenna which can operate at both dual frequency (1.9 GHz and 2.4 GHz) and dual polarisation. In this design there are four variables, the two dimensions of the rectangular patch, ‘a’ and ‘b’, and position of the probe feed, ‘Xp’ and ‘YP’. As there is not a unique solution a Genetic Algorithm (GA) was applied using an objective function based on the return loss at each frequency. The antenna was then modelled using AWR software and the predicted and practical results are shown to be in good agreement.  Key Words: Genetic algorithm (GA), dual frequency, dual polarisation, probe fed patch antenna І. Introduction Patch antennas are used in many communication systems as they are compact, have low profile and their manufacturing costs are reduced by using printed circuit technology. The main disadvantage of these types of antennas is that they have narrow bandwidth and hence current research has concentrated on different techniques to improve the bandwidth so that they can be used in a variety of communication systems [1-4]. The alternative approach to increasing the bandwidth is to design the antenna so that it can operate in different bands or at least in dual mode with different polarisations so that the same unit can be used in different communication systems [5-7]. Dual band patch antennas can be obtained using slots, stacked patches and shorting pins [8, 9].  In this paper, a single probe fed dual frequency rectangular patch antenna is designed using GA to determine the optimum dimensions of the patch and the position of the probe feed to produce a matching at the two frequencies. The expression for the probe feed impedance has been derived in ref [10] and used as the objective function in the optimisation process.   In the application of the GA optimisation process it is necessary to consider very carefully the upper and lower range of the four variables. The range for the width and length of the patch must be such that each dimension of the patch radiates only the required frequency. Due to the inherent symmetry of the patch there are four possible positions for the probe feed to obtain simultaneous matching at both frequencies. Consequently the feed position range should only be suitable to only one of the four possible solutions.   The electrical and physical parameters of the substrate PCB FR4 used are: dielectric constant is 4.3, the height of substrate is 1.575 mm, the loss tangent is 0.019 and the thickness of the copper patch is 0.035mm.  П. Genetic Algorithm   The GA [11, 12] is based on the evolution theory where weak species face extinction but strong ones survive and pass their genes to the next generation. However for the strong species to survive there is also a requirement for random injection of genes. As GA mainly manipulates matrices it is normally implemented using Matlab software. The step by step procedure of generating the software program is shown below.  Step 1: Each variable is assigned a number of binary digits so that the required accuracy of this variable is obtained in the final solution.  Step 2: All the variables in their binary form are grouped into a string which is called a chromosome.  Step 3: Matlab is used to select a fixed number of random chromosomes called a population out of all possible number of chromosomes that are present. This is called the current generation.  Step 4: Converting the digital value of each variable in a chromosome to an analogue value, the objective function (F) is evaluated and the relative fitness of each chromosome (Pi) determined. This relative fitness is defined as [13]:             (1) Step 5: The selective probability is determined by:                                                       (2) The cumulative probability of the chromosomes is given as:                                                                   (3) Then a random number ‘r’ is generated in the range 0 to 1. If qi-1≤ r ≤ qi then select Psi.  Step 6: Crossover is applied for random chromosomes between the parent and next generation to produce new off -springs.  Step 7: The population is mutated by changing in a random way the value of the genes with the least significant bit having the highest probability of mutation and the most significant the least.  The next generation now becomes the parent generation and the above process is repeated until the genetic variation in the population is below a certain threshold.   As the number of generations increases both the cross over rate and the mutation rate are gradually reduced.     Ⅲ. Optimisation of a Dual frequency Dual Polarised Matched Patch Antenna   A rectangular patch antenna is shown in figure 1, where the effective lengths ‘a’ (1.9 GHz), ‘b’ (2.4 GHz) and the probe feed position (Xp, Yp) for matching need to be determined.   Figure 1: Dimensions and feed position of the patch antenna  The probe feed impedance for the rectangular patch antenna is given by [10]: ܼ௣௣ሺ݂ሻ ൌ ݆2ߨ݂µ݄ ቄെ ௖௢௦௔௞ା௖௢௦௞൫௔ିଶ௑೛൯ଶ௕௞௦௜௡௔௞ ൅௕మௐ೛మగయ∑ ቎ቂୱ୧୬ቂ௡ഏ್ቀ௒೛ାೈ೛మቁቃିୱ୧୬ቂ௡ഏ್ቀ௒೛ିೈ೛మቁቃቃమ௡మට௡మିቀ್ೖഏට݊ଶ െ ቀ௕௞గቁమ௦௜௡௛ቈೌഏ್ට௡మିቀ್ೖഏቁమ቉ሾܿ݋ݏ݄ ቈ௔గ௕ቁଶ቉ ൅∞௡ୀଵܿ݋ݏ݄ ቈ൫௔ିଶ௑೛൯గ௕ට݊ଶ െ ቀ௕௞గቁଶ቉ሿ቏ቑ                                                                  (4) where h is the thickness of the dielectric substrate, k2 = ω2 μ ε0 εreff  (1 - j/Q), Q is the total quality factor (which is equal to 43.5),  ε0   is free space dielectric constant,  εreff  is the mutual effective dielectric constant, ω is the angular velocity. The return loss at the two frequencies is shown below,                   ܵ11ሺ1.9 ܩܪݖሻ ൌ 20 log ൬ฬ௓೛೛ሺଵ.ଽ ீு௭ሻିହ଴௓೛೛ሺଵ.ଽ ீு௭ሻାହ଴ฬ൰ dB,                          and                                                                                                 (5) ܵ11ሺ2.4 ܩܪݖሻ ൌ 20 log ൬ฬ௓೛೛ሺଶ.ସ ீு௭ሻିହ଴௓೛೛ሺଶ.ସ ீு௭ሻାହ଴ฬ൰ dB  The weighted average objective function (Objval) used in the GA program is,                )     Objval= S11 (1.9 GHz) + S11 (2.4 GHz) - |S11 (1.9 GHz) - S11 (2.4 GHz)|              (6The consistent optimised values of the four variables are a = 39.4 b = 30.4 mm, Xp = 14 mm and Yp = 10 mm. In applying GA it is necessary to have a good understanding of the relevant theory so that  that only the uencies are radiated at each of the two edges the minimum and maximum  35 mm. can be placed for matching the range for the probe feed position must   Figure 2:   Photograph of the fabricated patch antenna  The frequency responses of the return loss obtained from practical measurements and from the GA are shown in figure 3. The practical measurements were obtained using ‘Agilent’ network analyser (N5230A) and the predicted results were obtained using the GA program (see the appendix). At 1.9 GHz frequency there is an excellent agreement, while at 2.4 GHz there is about 0.05 GHz or 2% difference betw n the predicted and the practical results.  Figure 3: Predicted and practical results for the return Loss  mm, realistic minimum and maximum values for the variables are used. To ensuretwo required freqs for the dimvalue ensions of the antenna are 30 mm ≤ a ≤ 45 mm and  25 mm ≤ b ≤The edge impedances for each mode are high so in order to obtain matching at 50Ω the probe feed must placed away from the edges of the patch. As there are four quadrants of the patch where the probe feed only be within one quadrant. In this design the range for the probe feed was limited to 5 mm ≤ XP ≤ 20 mm and 5 mm ≤ YP ≤ 15 mm. Ⅳ. Comparison of Predicted and Practical Results  A photograph of the fabricated antenna is shown in figure 2.   eeReturn Loss -20-15-10-50 Loss (dB)-40-35-30-251.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8Frequency  (GHz)ReturnPractical ResultPredicted Result   Simulated polar patterns at 1.9 GHz and 2.4 GHz shown in fig. 4 were obtained where the red polar pattern is for 1.9 GHz and the blue polar pattern is for 2.4 GHz. In fig. 4(a) the polar pattern is in the E-plane and in fig. 4(b) it is in the H-plane. As can be seen an excellent isolation of over 64 dB between the two modes has been obtained.                                                                               (a)                                    (b)  Figure 4: Polar patterns at (a) E-plane and  (b) H-plane        Ⅴ. Conclusions  Equal weighted functions for the return loss at each frequency were used in the objective function in the  GA program in the design of a matched, dual frequency probe fed rectangular patch operating at 1.9 GHz and 2.4 GHz. An excellent return loss has been obtained at the two frequencies (approx -30 dB). The predicted results for the feed impedance were compared with those obtained from the transmission line model and from practical measurements. A very good agreement has been obtained for all results.   References   [1] H. S. Noh, J. S. Yun, J. M. Kim, and S.-I. Jeon, "Microstrip patch array antenna with high gain and wideband for Tx/Rx dual operation at Ku-band," in IEEE Antennas and Propagation Society International Symposium, 2004. Monterey, California 20-25 June 2004. [2] B. Cakiroglu, P. J . Terzuoli, "Multi-scale triangular patch high impedance  to improve the bandwidth of conformal bow-tie antennas," in IEEE Antennas and Propagation Society International Symposium, 2008. AP-S 2008., 5-11 July 2008. ] B. Cakiroglu, P. J. Collins, M. J. Havrilla, K. Sertel, and A. J. Terzuoli, "Fabrication of Multi-Scale Triangular Patch High Impedance Ground Planes to Improve the Bandwidth of Conformal Bow-Tie Antennas for Remote Sensing," in IEEE International Geoscience and Remote Sensing Symposium, 2008. IGARSS 2008. , 7-11 July 2008. S. Mridula, C. K. Aanandan, and P. Mohanan, "A new microstrip patch antenna for mobile communications and bluetooth applications," Microwave and ] F.-S. Chang, K.-C. Chao, C.-H. Lu, and S.-W. Su, "Compact vertical patch antenna al-band WLAN operation," Electronics Letters, vol. 44, pp. 612-613, 2008. y operation of microstrip antennas using [9] ring slot," IEEE Transactions on Antennas and Propagation, vol. 51, pp. [10] ersity, May 2007.  [12] g multiobjective genetic optimization," in IEEE Proceedings of the . Collins, M. J. Havrilla, K. Sertel, and A. Jground plane[3[4] B. Paul, Optical Technology Letters, vol. 33, pp. 285 - 286, 2002. [5] S.-L. S. Yang, A. A. Kishk, K.-F. Lee, K.-M. Luk, and H.-W. Lai, "The design of microstrip patch antenna with four polarizations," in 2008 IEEE Radio and Wireless Symposium, 22-24 Jan. 2008. [6] S. M. Kim, K. S. Yoon, and W. G. Yang, "Dual-band circular polarization square patch antenna for GPS and DMB," Microwave and Optical Technology Letters, vol. 49, pp. 2925 - 2926, 2007. [7for du] F. Croq and D. M. Pozar, "Multifrequenc[8aperture-coupled parallel resonators," IEEE Transactions on Antennas and Propagation, vol. 40, pp. 1367-1374, 1992. J.-Y. Jan, "Single-layer single-feed dual-frequency circular microstrip antenna with an offset open-3010- 3012, 2003. S. K. Lee, "The application of the segmentation method in the design of compact single-feed circular polarized microstrip patch antennas," in School of CEIS. vol. Ph. D Newcastle upon Tyne, UK: Northumbria Univ[11] B. Aljibouri, A. J. Sambell, and B. S. Sharif, "Application of genetic algorithm to design of sequentially rotated circularly polarised dual-feed microstrip patch antenna array," Electronics Letters, vol. 44, pp. 708-709, 2008. R. Kumar, P. P. Parida, and M. Gupta, "Topological design of communication networks usin2002 world congress on computational intelligence-WCCI’02 Honolulo,HI, USA, 12-17 May, 2002. B. Aljibouri, "Applications of the Genetic Algorithms Op[13] timization Approach in the  Design of Circular Polarized Microstrip Antennas," in School of CEIS. vol. Ph. D Newcastle upon Tyne, UK: Northumbria University December 2004.  

A new microstrip patch antenna for mobile communications and bluetooth applications,&quot;

Application of genetic algorithm to design of sequentially rotated circularly polarised dual-feed microstrip patch antenna array,&quot;

Applications of the Genetic Algorithms Op [13] timization Approach in the Design of Circular Polarized Microstrip Antennas,&quot;

Dual-band circular polarization square patch antenna for GPS and DMB,&quot;

Fabrication of Multi-Scale Triangular Patch High Impedance Ground Planes to Improve the Bandwidth of Conformal Bow-Tie Antennas for Remote Sensing,&quot;

Microstrip patch array antenna with high gain and wideband for Tx/Rx dual operation at Ku-band,&quot;

Multi-scale triangular patch high impedance to improve the bandwidth of conformal bow-tie antennas,&quot;

Single-layer single-feed dual-frequency circular microstrip antenna with an offset open3010- 3012,

The design of microstrip patch antenna with four polarizations,&quot;

Topological design of communication networks

Optimum design of a probe fed dual frequency patch antenna using genetic algorithm

Northumbria Research Link
Citation: Lu, Qing, Korolkiewicz, Edward, Danaher, Sean, Ghassemlooy, Zabih and Sambell, Alistair  
(2009) Optimum design of a probe fed dual frequency patch antenna using genetic algorithm. In:  
Proceedings of the ARMMS RF and Microwave Society, 20-21 April 2010, Rockingham Forest Hotel, 
Corby, UK. 
URL: 
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Optimum Design of a Probe Fed Dual Frequency Patch Antenna Using 
Genetic Algorithm 
 
Q. Lu, E. Korolkiewicz, S. Danaher, Z. Ghassemlooy and A. Sambell 
 
NCRLab, School of Computing, Engineering and Information Sciences, Northumbria University, Newcastle 
upon Tyne, NE1 8ST, UK 
 
Abstract: Recent research has concentrated on different designs in order to increase the 
bandwidth of patch antennas and thus improve functionality of wireless communication 
systems. An alternative approach as shown in this paper is to design a matched probe fed 
rectangular patch antenna which can operate at both dual frequency (1.9 GHz and 2.4 GHz) 
and dual polarisation. In this design there are four variables, the two dimensions of the 
rectangular patch, ‘a’ and ‘b’, and position of the probe feed, ‘Xp’ and ‘YP’. As there is not a 
unique solution a Genetic Algorithm (GA) was applied using an objective function based on 
the return loss at each frequency. The antenna was then modelled using AWR software and 
the predicted and practical results are shown to be in good agreement. 
 
Key Words: Genetic algorithm (GA), dual frequency, dual polarisation, probe fed patch 
antenna 
І. Introduction 
Patch antennas are used in many communication systems as they are compact, have low 
profile and their manufacturing costs are reduced by using printed circuit technology. The 
main disadvantage of these types of antennas is that they have narrow bandwidth and hence 
current research has concentrated on different techniques to improve the bandwidth so that 
they can be used in a variety of communication systems [1-4]. The alternative approach to 
increasing the bandwidth is to design the antenna so that it can operate in different bands or at 
least in dual mode with different polarisations so that the same unit can be used in different 
communication systems [5-7]. Dual band patch antennas can be obtained using slots, stacked 
patches and shorting pins [8, 9]. 
 
In this paper, a single probe fed dual frequency rectangular patch antenna is designed using 
GA to determine the optimum dimensions of the patch and the position of the probe feed to 
produce a matching at the two frequencies. The expression for the probe feed impedance has 
been derived in ref [10] and used as the objective function in the optimisation process.  
 
In the application of the GA optimisation process it is necessary to consider very carefully the 
upper and lower range of the four variables. The range for the width and length of the patch 
must be such that each dimension of the patch radiates only the required frequency. Due to 
the inherent symmetry of the patch there are four possible positions for the probe feed to 
obtain simultaneous matching at both frequencies. Consequently the feed position range 
should only be suitable to only one of the four possible solutions.  
 
The electrical and physical parameters of the substrate PCB FR4 used are: dielectric constant 
is 4.3, the height of substrate is 1.575 mm, the loss tangent is 0.019 and the thickness of the 
copper patch is 0.035mm. 
 
П. Genetic Algorithm  
 
The GA [11, 12] is based on the evolution theory where weak species face extinction but 
strong ones survive and pass their genes to the next generation. However for the strong 
species to survive there is also a requirement for random injection of genes. As GA mainly 
manipulates matrices it is normally implemented using Matlab software. The step by step 
procedure of generating the software program is shown below. 
 
Step 1: Each variable is assigned a number of binary digits so that the required accuracy of 
this variable is obtained in the final solution. 
 
Step 2: All the variables in their binary form are grouped into a string which is called a 
chromosome. 
 
Step 3: Matlab is used to select a fixed number of random chromosomes called a population 
out of all possible number of chromosomes that are present. This is called the current 
generation. 
 
Step 4: Converting the digital value of each variable in a chromosome to an analogue value, 
the objective function (F) is evaluated and the relative fitness of each chromosome (Pi) 
determined. This relative fitness is defined as [13]: 
            (1) 
Step 5: The selective probability is determined by: 
                                                      (2) 
The cumulative probability of the chromosomes is given as: 
                                                                  (3) 
Then a random number ‘r’ is generated in the range 0 to 1. If qi-1≤ r ≤ qi then select Psi. 
 
Step 6: Crossover is applied for random chromosomes between the parent and next 
generation to produce new off -springs. 
 
Step 7: The population is mutated by changing in a random way the value of the genes with 
the least significant bit having the highest probability of mutation and the most significant the 
least. 
 
The next generation now becomes the parent generation and the above process is repeated 
until the genetic variation in the population is below a certain threshold.  
 
As the number of generations increases both the cross over rate and the mutation rate are 
gradually reduced. 
 
 
 
 
Ⅲ. Optimisation of a Dual frequency Dual Polarised Matched Patch Antenna  
 
A rectangular patch antenna is shown in figure 1, where the effective lengths ‘a’ (1.9 GHz), 
‘b’ (2.4 GHz) and the probe feed position (Xp, Yp) for matching need to be determined.  
 
Figure 1: Dimensions and feed position of the patch antenna 
 
The probe feed impedance for the rectangular patch antenna is given by [10]: 
 2 µ
 
∑∞
                                                                  (4) 
where h is the thickness of the dielectric substrate, k2 = ω2 μ ε0 εreff  (1 - j/Q), Q is the total 
quality factor (which is equal to 43.5),  ε0   is free space dielectric constant,  εreff  is the mutual 
effective dielectric constant, ω is the angular velocity. 
The return loss at the two frequencies is shown below,  
                 
11 1.9 20 log .  
.  
 dB, 
                         and                                                                                                 (5) 
11 2.4 20 log .  
.  
 dB 
 The weighted average objective function (Objval) used in the GA program is,  
              
)     Objval= S11 (1.9 GHz) + S11 (2.4 GHz) - |S11 (1.9 GHz) - S11 (2.4 GHz)|              (6
The consistent optimised values of the four variables are a = 39.4 b = 30.4 mm, Xp = 14 
mm and Yp = 10 mm. 
In applying GA it is necessary to have a good understanding of the relevant theory so that 
 that only the 
uencies are radiated at each of the two edges the minimum and maximum 
 35 mm. 
can be placed for matching the range for the probe feed position must 
 
 
Figure 2:   Photograph of the fabricated patch antenna 
 
The frequency responses of the return loss obtained from practical measurements and from 
the GA are shown in figure 3. The practical measurements were obtained using ‘Agilent’ 
network analyser (N5230A) and the predicted results were obtained using the GA program 
(see the appendix). At 1.9 GHz frequency there is an excellent agreement, while at 2.4 GHz 
there is about 0.05 GHz or 2% difference betw n the predicted and the practical results. 
 
Figure 3: Predicted and practical results for the return Loss 
 mm, 
realistic minimum and maximum values for the variables are used. To ensure
two required freq
s for the dimvalue ensions of the antenna are 30 mm ≤ a ≤ 45 mm and  25 mm ≤ b ≤
The edge impedances for each mode are high so in order to obtain matching at 50Ω the probe 
feed must placed away from the edges of the patch. As there are four quadrants of the patch 
where the probe feed 
only be within one quadrant. In this design the range for the probe feed was limited to 5 mm 
≤ XP ≤ 20 mm and 5 mm ≤ YP ≤ 15 mm. 
Ⅳ. Comparison of Predicted and Practical Results 
 
A photograph of the fabricated antenna is shown in figure 2.  
 
ee
Return Loss 
-20
-15
-10
-5
0
 L
os
s 
(d
B
)
-40
-35
-30
-25
1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8
Frequency  (GHz)
R
et
ur
n
Practical Result
Predicted Result
 
 
 
Simulated polar patterns at 1.9 GHz and 2.4 GHz shown in fig. 4 were obtained where the red 
polar pattern is for 1.9 GHz and the blue polar pattern is for 2.4 GHz. In fig. 4(a) the polar 
pattern is in the E-plane and in fig. 4(b) it is in the H-plane. As can be seen an excellent 
isolation of over 64 dB between the two modes has been obtained. 
 
  
 
                                                                          (a) 
 
                                  (b) 
 
Figure 4: Polar patterns at (a) E-plane and  
(b) H-plane 
 
 
 
 
 
 
 
Ⅴ. Conclusions 
 
Equal weighted functions for the return loss at each frequency were used in the objective 
function in the  GA program in the design of a matched, dual frequency probe fed rectangular 
patch operating at 1.9 GHz and 2.4 GHz. An excellent return loss has been obtained at the 
two frequencies (approx -30 dB). The predicted results for the feed impedance were 
compared with those obtained from the transmission line model and from practical 
measurements. A very good agreement has been obtained for all results. 
 
 
References  
 
[1] H. S. Noh, J. S. Yun, J. M. Kim, and S.-I. Jeon, "Microstrip patch array antenna with 
high gain and wideband for Tx/Rx dual operation at Ku-band," in IEEE Antennas and 
Propagation Society International Symposium, 2004. Monterey, California 20-25 
June 2004. 
[2] B. Cakiroglu, P. J . Terzuoli, "Multi-scale 
triangular patch high impedance  to improve the bandwidth of conformal 
bow-tie antennas," in IEEE Antennas and Propagation Society International 
Symposium, 2008. AP-S 2008., 5-11 July 2008. 
] B. Cakiroglu, P. J. Collins, M. J. Havrilla, K. Sertel, and A. J. Terzuoli, "Fabrication 
of Multi-Scale Triangular Patch High Impedance Ground Planes to Improve the 
Bandwidth of Conformal Bow-Tie Antennas for Remote Sensing," in IEEE 
International Geoscience and Remote Sensing Symposium, 2008. IGARSS 2008. , 7-
11 July 2008. 
S. Mridula, C. K. Aanandan, and P. Mohanan, "A new microstrip patch 
antenna for mobile communications and bluetooth applications," Microwave and 
] F.-S. Chang, K.-C. Chao, C.-H. Lu, and S.-W. Su, "Compact vertical patch antenna 
al-band WLAN operation," Electronics Letters, vol. 44, pp. 612-613, 2008. 
y operation of microstrip antennas using 
[9] 
ring slot," IEEE Transactions on Antennas and Propagation, vol. 51, pp. 
[10] 
ersity, May 2007. 
 
[12] 
g multiobjective genetic optimization," in IEEE Proceedings of the 
. Collins, M. J. Havrilla, K. Sertel, and A. J
ground plane
[3
[4] B. Paul, 
Optical Technology Letters, vol. 33, pp. 285 - 286, 2002. 
[5] S.-L. S. Yang, A. A. Kishk, K.-F. Lee, K.-M. Luk, and H.-W. Lai, "The design of 
microstrip patch antenna with four polarizations," in 2008 IEEE Radio and Wireless 
Symposium, 22-24 Jan. 2008. 
[6] S. M. Kim, K. S. Yoon, and W. G. Yang, "Dual-band circular polarization square 
patch antenna for GPS and DMB," Microwave and Optical Technology Letters, vol. 
49, pp. 2925 - 2926, 2007. 
[7
for du
] F. Croq and D. M. Pozar, "Multifrequenc[8
aperture-coupled parallel resonators," IEEE Transactions on Antennas and 
Propagation, vol. 40, pp. 1367-1374, 1992. 
J.-Y. Jan, "Single-layer single-feed dual-frequency circular microstrip antenna with an 
offset open-
3010- 3012, 2003. 
S. K. Lee, "The application of the segmentation method in the design of compact 
single-feed circular polarized microstrip patch antennas," in School of CEIS. vol. Ph. 
D Newcastle upon Tyne, UK: Northumbria Univ
[11] B. Aljibouri, A. J. Sambell, and B. S. Sharif, "Application of genetic algorithm to 
design of sequentially rotated circularly polarised dual-feed microstrip patch antenna 
array," Electronics Letters, vol. 44, pp. 708-709, 2008. 
R. Kumar, P. P. Parida, and M. Gupta, "Topological design of communication 
networks usin
2002 world congress on computational intelligence-WCCI’02 Honolulo,HI, USA, 12-
17 May, 2002. 
B. Aljibouri, "Applications of the Genetic Algorithms Op[13] timization Approach in the 
 
Design of Circular Polarized Microstrip Antennas," in School of CEIS. vol. Ph. D 
Newcastle upon Tyne, UK: Northumbria University December 2004. 
 


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Optimum design of a probe fed dual frequency patch antenna using genetic algorithm

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