Sizing Optimization of Small Antenna Design by PSO Linking
MATLAB and CST-Microwave StudioNguyen Tuan Hung 1, and Hisashi Morishita 1
11

National Defense Academy, Yokosuka, Japan

Introduction

In recent years, due to the magnificent development ofcalculation ability of computer, optimization design has been
introduced and investigated in many research fields withnumbers of optimization algorithms. In the field of antenna
design (especially design of small antennas), most of current
electromagnetic simulators also have some built-in optimization
tools which can help antenna designers be possible to optimize
their antennas with desirable characteristics. However, there is alimit of these tools which is that users can not express theiroptimization purposes in details by formulating objectivefunctions, which is requisite for every optimization problems.
Therefore, in the case of optimization problems requiring
complicated settings of objective function, it is preferable toformulate objective function in a programming environment.
This paper presents a method of linking programming
language MATLAB [1] and electromagnetic simulator CSTmicrowave studio (CST-MWS) [2], and then apply both of theseto sizing optimization problem of small antenna design by using
particle swarm optimization (PSO) [3]. Firstly, the concept ofPSO and the method of implementing PSO to small antenna
optimization design by MATLAB and CST-MWS will bedescribed. Secondly, as a quoted example, this implementation
will be introduced to optimization design of U-shaped folded
dipole antenna (UFDA) [4] which is assumed to be used inside
an USB dongle for WiMAX (worldwide interoperability for
microwave access).
2PSO Calculation by Linking MATLAB and CSTMicrowave StudioParticle swarm optimization (PSO) is based on a simplifiedsocial model of swarming theory. The flowchart ofimplementing PSO in antenna design is shown in Fig. 1. In anoptimization problem with the design variable X and theobjective function G(X) deal with PSO, coordinate and velocityof each particle are put to X and V respectively, and both X andV are renewed sequentially by exchanging searching
information among all particles in the swarm. At each step,
optimality of coordinate X of every particles is evaluated by theobjective function G(X), and the particle which has the best
objective function value as G(Xelite) is defined as elite particle.
The coordinate Xelite of elite particle is selected at each step, andthis selection is repeated until G(Xelite) is not renewed. WhenG(Xelite) converges to a constant value, the final coordinate Xeliteat the last step is considered as the optimal solution Xopt ofoptimization problem. In Fig. 1, "Model analysis" is executed by
CST-MWS, and the other ones are executed by MATLAB tomake the PSO program run continuously.
33.1

Example of Applying PSO to Optimize U-Shaped
Folded Dipole Antenna for WiMAX
Fundamental Antenna Model

Figure 2 shows the original model of UFDA on a 75 mm ×31 mm GP which represents the shielding plate inside USB
dongle. UFDA is connected to GP by the short strip, and fed
from GP to its feed strip by a coaxial cable. UFDA has been

Start
Initialize coordinates X andvelocities V of particles
Model analysis
Calculate objective function G(X)
Converge of G(Xelite) and Xelite ?
NOYES

Optimalcoordinate Xopt

Update coordinates X andvelocities V of particles

Fig. 1. Flowchart of PSO.
UFDA 30
3.211615z

Short stripyx

Feed strip 75(Coaxial fed)
GP[Unit : mm]

31

Fig. 2. Configuration of fundamental antenna model.
already reported as a wideband antenna for WiMAX [4]. Whenan area about 3.8% of GP is cut, UFDA can cover a wide
frequency band including two WiMAX bands (2.3~2.7 GHz and3.4~3.8 GHz). Here, we adopt PSO to optimize respectively thecutting shape of GP, and the shape of UFDA element when GP
is not cut, by applying two efficient objective functions to PSO.
For optimizing the cutting parameters of GP (case 1), or thedimension parameters of UFDA (case 2), we consider theseparameters as continuous design variables and put them tocomponents of coordinate X of every particles in the swarm ofPSO. Two respective objective functions for each case aredesigned as below.
3.2

Optimization of cutting GP (case 1)

Here, the fundamental shape of UFDA is maintained during
the optimization of cutting GP. Cutting GP is decided by three
cutting parameters, and the design target in this case is to obtain
both a wider resonance band (VSWR≤3) and a smaller cuttingarea than 3.8%. Therefore, the objective function G1(X) of thisproblem is proposed as in Equation (1).
G1(X) = (VSWR1+VSWR2+VSWR3)/6 + [Scut/2S0](1)

In Equation (1), VSWR1, VSWR2, VSWR3 are the values ofVSWR at three frequencies f1=2.5 GHz, f2=3.05 GHz, f3=3.6
GHz where f1 and f3 are two center frequencies of two WiMAX
bands, and f2 is the center frequency between f1 and f3. The
cutting area Scut of GP is normalized with the criterion valueS0=100 mm2. It is assumed that minimizing G1(X) by PSO will
help all VSWR1, VSWR2, VSWR3 and Scut to be minimized
simultaneously, where the reductions of VSWR1 , VSWR 2,

-60

1.2-65
G2 (Xelite)

G1 (Xelite)

1.3

1.1
1.0-70-75
-80

0.9

5-85

10 15 20 25 30 35
Step102030
Step

14.1

234.7

3.3 14.4

10.7

GP[Unit : mm]yz

0.9x50Fig. 5. Values of objective function G2(Xelite).

Fig. 3. Values of objective function G1(Xelite).

13.74031

1.5
3.5

Fig. 6. Optimal shape of UFDA element.

75109876543212.0[Unit : mm]

VSWR3 are expected to be equal to achieving a wide resonanceband. That is to say, minimizing G1(X) makes the design target
be attained.
The convergence of objective function G1(X) in PSO is
decided by Elite particle which has the best coordinate Xelite inthe swarm at each step. Figure 3 shows the convergence ofG1(Xelite) through 35 steps where G1(Xelite) is minimized to its
minimum value as 0.91. This minimum value of G1(Xelite) leadsto the optimal shape of GP as shown in Fig. 4 with three cutting
parameters optimized to 14.1, 0.9 and 13.7 mm, respectively.
According to this, the cutting area Scut here is minimized to 24.7mm2 which is only 1% area of original shape of GP. Figure 7
shows the comparison of calculated VSWR characteristics
before and after optimizing. After optimizing the cutting shapeof GP (the red line with star marks), resonance band of UFDA is
widen much more with the relative bandwidth about 64%(VSWR≤3 in 2.35~4.38 GHz). This result indicates that thedesign target of this case is accomplished perfectly when both
wideband characteristic and small cutting area are obtained
simultaneously.
3.3

Optimization of UFDA Element (case 2)

In this case, we investigate how to optimize the shape ofUFDA element without cutting GP. Shape of UFDA element isdesigned with 8 dimension parameters, and the design target
here is just to cover two WiMAX bands (VSWR≤3 in 2.3~2.7
GHz and 3.4~3.8 GHz). Here, if we adopt function G1(X) with
Scut=0 to PSO like in case 1, there is a possibility that VSWRmay decrease enormously at only one frequency and increaseover 3 at other frequencies. Therefore, the objective function
G2(X) adopted to PSO in this case is defined as the followingEquation (2).
G2(X) = −Nf(2)In Equation (2), Nf is the number of frequency points in two
WiMAX bands which satisfy the condition VSWR≤3. Twobands of WiMAX are divided to 82 frequency points (10 MHzinterval) and so on, the maximum value of Nf is 82. It is
assumed that by using PSO to minimize G2(X) to −82, an
optimal shape of UFDA element that fulfills the design target inthis case will be obtained.
The minimization of G2(X) done by Elilte particle through51 steps is shown in Fig. 5 where G2(Xelite) gets to -82 at 51ststep. According to this, the optimal shape of UFDA is formed asin Fig. 6 with its 8 dimension parameters optimized to 1.5, 3.3,10.7, 3, 4.7, 2, 3.5, 14.4 mm, respectively. Since the width of
every parts of UFDA become smaller after optimizing, thisBefore opt.
After opt. (Case 1)
After opt. (Case 2)VSWR

Fig. 4. Optimal shape of ground plane.

2.5

3.0
3.5
4.0
Frequency [GHz]4.5

Fig. 7. VSWR characteristics before and after optimizing.
optimal shape has the volume as 72% when compared to its
original shape, which means that it is effective for miniaturizing
antenna size. Moreover, the blue line with circle marks in Fig. 7
indicates that after optimizing UFDA element, two WiMAX
bands are covered completely (VSWR≤3 in 2.24~2.99 GHz and3.39~3.81 GHz). That is to say, the design target is alsoachieved perfectly in this case.
4Conclusion

In this study, as a quoted example of small antenna
optimization design by linking MATLAB and CST-MWS, wehave investigated optimization of UFDA design for WiMAX.
By adopting two objective functions to PSO to optimize
respectively the shapes of GP and UFDA have been proposed by
two different effective formulations. First, in the case of
optimizing the cutting shape of GP with the shape of UFDA
maintained, using a combined function that can evaluate bothVSWR value and the cutting area has helped to form an optimal
shape of GP with smallest cutting area as 1% and obtain a 64%
bandwidth including two WiMAX bands. Next, in the case of
optimizing UFDA without cutting GP, using a function thatcounts the number of frequency points satisfying VSWR≤3 hashelped to form an optimal shape of UFDA which has thevolume as 72% of its original shape but can cover completely
two WiMAX bands. Therefore, effectiveness of two objectivefunctions are demonstrated obviously.
References
[1]
[2]
[3]
[4]

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CST Microwave Studio, Ver.2010, Computer Simulation
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G. Venter, and J. S. Sobieski, “Particle Swarm Optimization,”
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N. T. Hung, S. Watanabe, and H. Morishita, “Fundamental studyon U-shaped folded dipole antenna for WiMAX,” Proc. of the 5thEuCAP, pp.1318-1321, April 2011.