AN EXPERIENCE TO INCLUDE ADVANCED OPTIMIZATION

TECHNIQUES IN MICROWAVE UNDERGRADUATE

LABORATORIES

P. L´opez-Espi, S. Salcedo-Sanz, R. S´anchez-Montero and A. Portilla-Figueras

Department of Signal Theory and Communications, Universidad de Alcal´a, Spain

Keywords:

Laboratory subjects, Directional couplers, Evolutionary computation.

Abstract:

In this paper, a method to introduce advanced computational optimization techniques in undergraduate labo-

ratory subjects is presented. The experience proposed consists in using evolutionary algorithms to design a

microwave device (a directional coupler in this case), and then constructing a prototype following the outcome

of the algorithms. The idea is to present the undergraduate student advanced techniques that it is unlikely they

study in their degree, but which may be useful for them in postgraduate courses. The results of the applica-

tion of the experience in the subject Antennas and Microwave Laboratory of Universidad de Alcal´a, Spain, is

presented.

1 INTRODUCTION

Advanced computational techniques are currently a

fundamental part in processes of design, manage-

ment and even deployment of electrical, electronic

and telecommunications systems. Thus, these tech-

niques are taught in almost every university postgrad-

uate courses about electrical engineering. In mod-

ern postgraduate electrical engineering studies there

are speciﬁc subjects which cover the majority of ad-

vanced computational techniques such as evolution-

ary computation, neural networks, advanced heuris-

tics etc. However, in spite of their importance in en-

gineering, these techniques are not usually included in

undergraduate courses. Due to the extensive curricu-

lum to be taught in electrical engineering degrees, it

is very difﬁcult to plan speciﬁc subjects in undergrad-

uate curses which cover these techniques. However, it

is possible to introduce them as part of laboratories or

practices, in which the students can have a ﬁrst con-

tact with these techniques.

This paper presents an experience to include

advanced computational techniques (evolutionary

computation-based techniques in this case) in a lab-

oratory subject of the electrical engineering degree

at Universidad de Alcal´a, Madrid, Spain. Speciﬁ-

cally, a microwave laboratory subject has been cho-

sen to carry out a ﬁrst implementation of the pro-

posed experience. High-frequency circuit design is

an important part of the majority of microwave en-

gineering courses. Among others, microwave ampli-

ﬁers, analog ﬁlters and directional couplers are some

of the most studied devices, due to their importance

in a large amount of electronic systems and circuits

(Pozar, 1998). Speciﬁcally, the ideal directional cou-

pler is a passive, reciprocal, completely matched and

lossless four port network studied in the majority of

undergraduate courses related to microwave systems

design.

The implementation of the experience at Univer-

sidad de Alcal´a has been carried out in the subject

Antennas and Microwave Laboratory. In a laboratory

practice of this subject, advanced optimization algo-

rithms based on evolutionary computation (Yao et al.,

1999), (Eberhart et al., 2001) have been introduced in

the design of a directional coupler. The idea is that

the students are introduced in the use of intelligent

soft-computing algorithms, to optimize any type of

microwave device in this case (a directional coupler).

The fact that the evolutionary-based algorithms are

based on concepts easy to understand (the evolution

of species and survival of the ﬁttest solution), makes

easier the inclusion of these techniques in the labora-

tory. In addition, the fact that usually people who do

not know anything about these kind of algorithms ﬁnd

them very interesting, is an important part of the ex-

perience, because it introduces a novelty in the class

that motivates students to work harder in the labora-

163

López-Espi P., Salcedo-Sanz S., Sánchez-Montero R. and Portilla-Figueras A. (2010).

AN EXPERIENCE TO INCLUDE ADVANCED OPTIMIZATION TECHNIQUES IN MICROWAVE UNDERGRADUATE LABORATORIES.

In Proceedings of the 2nd International Conference on Computer Supported Education, pages 163-166

DOI: 10.5220/0002767701630166

 SciTePress

tory. The speciﬁc experience carried out includes the

design of a directional coupler, the construction of a

prototype following the outcome of the algorithms for

optimization, and the comparison with the simulation

of the device using a commercial software package.

This experience can be extended to any other type of

subject, but it is specially well-suited for laboratories,

where practices can be focus on different advanced

techniques to be presented to the students.

2 ANALYSIS OF THE

DIRECTIONAL COUPLER

PROPOSED IN THE

EXPERIENCE

As it has been mentioned before, several design

topologies for directional couplers can be found in

the literature. The proposed experience could be car-

ried out using any topology difﬁcult enough to involve

the optimization of several parameters. In any other

case, the optimization can be carried out by simple

inspection, and it is not necessary to use advanced

optimization techniques, such as evolutionary compu-

tation. Following this premise, a directional coupler

as the one shown in Figure 1, has been chosen to be

designed. This topology is based on the well-known

branch-line coupler, but diagonal strips are added in

order to include constructive constraints which make

harder the optimization of the device. The proposed

coupler has has double symmetry in x and y axis.

Figure 1: Example of the directional coupler used in the

application of the method in Universidad de Alcal´a.

Thus, four different S parameters are enough to

describe it. Using these symmetry properties, the cou-

pler can be analyzed by using even and odd modes

recursively. The following equations show the nor-

malized input admittances in the even and odd excita-

tions:

= j

tan(β

· d

) + j

tan(β

· d

) + j

tan(β

· d

)

(1)

= − j

cot(β

·d

)+ j

tan(β

·d

)− j

cot(β

·d

)

(2)

= j

tan(β

· d

) − j

cot(β

· d

) − j

cot(β

· d

)

(3)

= − j

cot(β

·d

)− j

cot(β

·d

)− j

cot(β

·d

)

(4)

Note that d

)

+ (d

)

, so its admittance

depends on four parameters. The even and odd reﬂec-

tion coefﬁcients can be calculated from the previous

admittances as follows:

−Y

(5)

where i and j take the values e or o depending on

the case, Y

stands for the reference admittance value,

Ω

−1

in this case. Finally, the S parameters

are calculated as follows:

· (Γ

+ Γ

) (6)

· (Γ

− Γ

+ Γ

− Γ

) (7)

· (Γ

+ Γ

− Γ

) (8)

· (Γ

− Γ

+ Γ

) (9)

3 DESIGN METHODOLOGY:

EVOLUTIONARY

OPTIMIZATION ALGORITHMS

The four parameters’ optimization of the proposed

coupler must be optimized for different values of the

coupling P, at a given design frequency. The design

frequencyaffects the values of the different design pa-

rameters, whereas the coupling must be speciﬁed in

the objective function of the optimization algorithm.

In this experience two well-known evolutionary com-

putation techniques have been used: An Evolutionary

Programming algorithm (EP) (Yao et al., 1999) and

a Particle Swarm Optimization (PSO) (Eberhart et al.

2001) approach.

The EP and the PSO implementations considered

(the basic ones given in (Yao et al., 1999) and (Eber-

hart et al. 2001)) can be directly applied to solve

the optimization of the directional coupler proposed,

CSEDU 2010 - 2nd International Conference on Computer Supported Education

164

with very few changes: In the case of the EP, the

individual x is x = {d

, d

, Z

, σ

If the PSO algorithm is used, each particle x is x =

, d

, Z

}. The objective function for the opti-

mization process is given, in both cases, by the fol-

lowing expression:

g(x) = |S

+ (|S

− P)

, (10)

where P stands for the desired coupling and S

, S

are given by Equations (6) and (9), respectively.

4 ORGANIZATION AND

EDUCATIONAL ASPECTS OF

THE PROPOSED EXPERIENCE

The structure of the presented method, as it has been

implemented in Universidad de Alcal´a, is the follow-

ing: First, the students are given a brief summarize

of what they have to do (including the analysis given

in Section 2), an outline of the directional coupler

they have to design (similar to the Figure 1), a small

tutorial on evolutionary computation and ﬁnally the

source code (in Matlab) of the EP and PSO algo-

rithms. In this experience it is not intended that the

students learn to program the EP and PSO algorithms,

but they must understand their principles, and how to

apply them to design a given circuit. The students are

requested to theoretically design the coupler by opti-

mizing the objective function given by Equation (10)

using the EP or the PSO, and then to construct a pro-

totype to be analyzed, using the values given by the

EP or PSO. This is the most interesting part of the ex-

perience, where the students must analyze the results

obtained.

4.1 Prototype Construction and its

Analysis

After obtaining the best set of values for the couples,

the students must construct a prototype, according to

the values obtained by optimization algorithm. The

students can choose the value of the design frequency

and the coupling ratio. Figure 2 shows a picture of

the coupler that was constructed in the preparation

of the experience. In this case the design frequency

has been set up to 1 GHz, and the coupling ratio P

has been ﬁxed to 0.75. The prototype was made us-

ing a low-cost FR-4 substrate, the same available for

the students. With this P, the EP obtained the fol-

lowing values of x = {d

, d

, Z

}: d

= 69.41,

= 26.78, Z

= Z

= 51.43 Ω. Using these val-

ues a simulation of the circuit with lossy transmission

lines, but without considering interconnection effects

can be carried out using the Monolithic Microwave

Integrated-Circuit Analysis and Design (MMICAD)

simulator (Safwat et al., 1997). The analysis of the

differences between the constructed and the simulated

coupler is very interesting, and may help the students

to understand the behavior of the circuit.

Figure 2: Picture of the constructed coupler.

Different analysis can be done at this point. For

example it is possible to compare the measured and

simulated responses of the coupler (Figure 3). Figure

3 (a) displays |S

| and |S

|, and Figure 3 (b) |S

and |S

|. At f

= 1 GHz, the simulated |S

|, |S

| and |S

| values are 0.05, 0.476, 0.039, 0.79, and

the measured |S

|, |S

| and |S

| are 0.11, 0.14,

0.13, 0.84, respectively. As shown in Figure 3 (b)

there is a good agreement between the ideal and mea-

sured coupling value (S

). Its behavior is not so good

at high frequencies however, where there are signiﬁ-

cant differences between the expected (simulated) and

measured behavior. This is due to the extremely sim-

ple transmission line model used for the simulations,

which do not take into account the effects of disconti-

nuities and joints. The students must extract their own

conclusions out of this analysis, and it is an important

part of the mark of the laboratory.

4.2 Educational Aspects of the

Experience

The proposed experience has several educational as-

pects which makes it appealing to be implemented in

University courses. First, the main characteristic of

the experience is that it allows the students to have a

ﬁrst contact with advanced computational techniques

(evolutionary-based), applied to an interesting prob-

lem of circuit design in this case. Second, these al-

gorithms introduce a point of novelty to the classical

practices of laboratories. This usually encourages the

students to work harder in the practice, which is also

useful from the lecturer’s point of view. The possi-

bility of extending this experience to other subjects,

AN EXPERIENCE TO INCLUDE ADVANCED OPTIMIZATION TECHNIQUES IN MICROWAVE

UNDERGRADUATE LABORATORIES

165

(a)

(b)

Figure 3: Performance of the designed directional coupler;

(a) |S

| and |S

|; (b) |S

| and |S

and including different advanced algorithms, is an-

other interesting point to take into account.

The experience presented in this communica-

tion has been carried out in Universidad de Al-

cal´a, Madrid, Spain, in an undergraduate subject

called Antennas and Microwave Laboratory, belong-

ing to the Bachelors Degree in Telecommunications.

In this course, 79 students students learned about

microwave circuits design in the ﬁrst part of the

semester, whereas the second part is devoted to an-

tennas. It is important to note that this laboratory

subject has a previous theoretical counterpart, where

the main concepts of microwave circuits systems are

studied. In order to assess the impact of the proposed

experience, feedback was collected by asking the stu-

dents to anonymously complete a questionnaire. Stu-

dents’ opinion about the difﬁculty of the work carried

out, the difﬁculty of using the evolutionary computa-

tion algorithms and to understand how they work, and

their opinion on the level of learning obtained, were

collected. As a summary, about about 80% of the stu-

dents considered the experience carried out as “good”

or “very good”, about 15% considered it “fair” and

5% of students marked it as “bad” or “very bad”. The

majority of students considered the comparison of the

simulated and measured coupler as the most interest-

ing part of the experience, where they have learned

the most.

5 CONCLUSIONS

This paper presents an experience carried out in Uni-

versidad de Alcal´a, consisting in introducing evolu-

tionary computation techniques in an undergraduate

microwave laboratory, as part of the design of direc-

tional couplers. The idea is that this experience can

be generalized to any laboratory subject and differ-

ent computational techniques. This allows to intro-

duce concepts which usually are not taught in under-

graduate courses, as part of practices in laboratories.

Another interesting point of the experience is that it

introduces certain novelty in the laboratory practices,

which encourage the students to work harder. The re-

sults of the application of the experience in the mi-

crowave circuits laboratory mentioned before are an-

alyzed and discussed, offering a ﬁrst result of the pro-

posed experience in a real environment.

REFERENCES

D. M. Pozar (2004). Microwave engineering. John Wiley &

Sons.

R. Eberhart and Y. Shi (2001). Particle swarm optimization:

developments, applications and resources. In Proc.

IEEE Congress on Evolutionary Computation.

X. Yao, Y. Liu and G. Lin (1999). Evolutionary program-

ming made faster. IEEE Transactions on Evolutionary

Computation, vol. 3, no. 2, pp. 82-102.

A. M. Safwat, D. A. Khalil, H. Elhennawy, and H. F. Ra-

gaie (1997). Quasi-Static Analysis of an Optically Il-

luminated Directional Coupler. IEEE Microwave and

Wireless Components Letters, vol. 45, no. 8, pp. 1351-

1357.

CSEDU 2010 - 2nd International Conference on Computer Supported Education

166