8/13/2019 2898_ref4

1/2

A SLOW-WAVE STRUCTURE WITHKOCH FRACTAL SLOT LOOPS

Jung-Hyo Kim, Il-Kwon Kim, Jong-Gwan Yook, andHan-Kyu ParkDepartment of Electrical and Electronics Engineering

Yonsei UniversitySeoul, Korea

Received 3 January 2002

ABSTRACT:In this Letter, a Koch slot loop in the ground plane has beenutilized to obtain slow-wave characteristics, and its electrical performances

are analyzed with the use of the ABCD matrix approach. The validity of

this approach has been verified through experimental results, and this tech-

nique was then applied to microstrip patch antennas in order to obtain a

small antenna size. The cross-sectional areas of this type of antenna are

47% to 65% smaller than those of conventional square patches. 2002

Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 8788, 2002;

Published online in Wiley InterScience (www.interscience.wiley.com).

DOI 10.1002/mop.10381

Key words: Koch fractal slot loop; slow-wave structure; periodic struc-

ture; PBG; small size antenna

INTRODUCTION

The slow-wave structure is not only appropriate to optimize dif-

ferent delay times between various transmission lines in high-

speed digital circuits, but also to reduce overall circuit dimensions.

In order to develop slow-wave structures, various techniques, such

as metalinsulatorsemiconductor (MIS) transmission lines, ferro-

magnetic substrate microstrip lines, and cross-tieoverlay copla-

nar waveguide (CPW), have been introduced and investigated by

many researchers [13]. However, most of these structures use

multilayer or high-cost substrates, thus imposing a high fabrication

cost as well as difficult fabrication procedure. A structure recently

proposed by Lin and Itoh [3] employs periodic slots in the ground

plane and can be fabricated in a simple manner. In this Letter, a

slow-wave structure with Koch fractal slot loops incorporated in

the ground plane is proposed in order to control the slow-wave

factor. This approach is then verified by applying this technique to

useful applications, such as miniaturized microstrip patch anten-

nas. Its characteristics are predicted by using an ABCD matrix

approach.

SLOW-WAVE STRUCTURE WITH KOCH SLOT LOOPS

By increasing capacitive and inductive loading effects, the space-

filling property of Koch fractal geometry contributes to the in-

crease of the effective length of the line. A slow-wave structure

can be designed efficiently by utilizing this property of Koch

fractals. As shown in Figure 1, the unit cell of a Koch slot loop is

printed in the ground plane, and a 50- line is printed on the other

side of the substrate ofr 2.5 and thicknessh 0.508 mm. Two

Koch fractal slot loops were designed; in Case A, the cross-

sectional area isL1 L2 4.5 4.5 mm and the slot width w

0.25 mm; in Case B, the cross-sectional area is L1 L2 3 3

mm, and the slot width w 0.1 mm. The Sparameters of the unit

cell obtained by full-wave electromagnetic simulations or experi-

ments are transformed into ABCD matrices, and then the charac-

teristic matrix equation is deduced. Next, the complex propagation

constant of the unit cell is found by the following equation:

j 1

llnAD

2 AD

2

2

1, (1)wherelis the length of the unit cell, the attenuation constant, and

the phase constant. The sign of the solution must be chosen to

provide a physically meaningful value of. As shown in Figure 2,

Figure 1 Microstrip line with Koch slot loop (fractal factor 0.25)

etched in the ground plane (Case A: L1L2 4.5 4.5 mm, w 0.25

mm; Case B: L1L2 3 3 mm, w 0.1 mm)

Figure 2 Slow-wave factor of unit cell

Figure 3 Equivalent circuit of unit cell

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 34, No. 2, July 20 2002 87

8/13/2019 2898_ref4

2/2

the slow-wave factor (Ff), which is defined as /k0 is higher in

Case A than in Case B. This is due to the fact that a larger slot loop

has higher capacitance and inductance values, and thereby results

in higher impedance. The equivalent circuit of the Koch slot loop

unit cell, including the microstrip line, is shown in Figure 3. The

equivalent circuit parameters of Case A are obtained as follows: Cs

0.5 pF, Ls

0.15 nH, C1

0.14 pF, L1

0.4 nH, C2

0.01pF, C3 0.6 pF, R1 1.2 k, and R2 2.

SLOW-WAVE MICROSTRIP ANTENNA

A slow-wave structure can be implemented with Koch slot loops

incorporated in the ground plane, thereby reducing the size of the

patch antenna. Figure 4 illustrates a microstrip patch antenna with

Koch slot loops in the ground plane. As summarized in Table 1,

four different antenna configurations with different periods for

Cases A and B are tested. Figure 5 displays the measured return

losses of four slow-wave antennas, as well as that of a conven-

tional one. The fabricated antennas A1, A2, B1, and B2resonate at

5.49, 6.82, 6.35, and 6.78 GHz, respectively, and the conventional

microstrip patch antenna resonates at 8.95 GHz. Hence, with the

same patch size, 24 to 38.7% lower resonance frequencies havebeen achieved compared to the conventional microstrip antenna;

and for the same resonance frequency, 47 to 65% reduction in area

was obtained. Furthermore, the impedance bandwidth is greater

than that of the conventional antenna. The A1, A2, B1, B2, and

conventional microstrip patch antenna have impedance band-

widths of 3.5%, 3.7%, 3.7%, 2.95%, and 1.8%, respectively, on the

basis of VSWR 2:1. This is due to the fact that the apertures in the

ground plane tend to decrease the quality factor of antennas, thus

increasing the bandwidth.

CONCLUSIONS

In this Letter, a slow-wave structure with Koch fractal slot loops is

proposed, and its characteristics are well predicted by the ABCD

matrix approach. The slow-wave factor is proportional to the size

of the Koch slot loops, but it is inversely proportional to the

repetition period. Thus, enlarging the Koch slot loops and placing

them closer together maximizes the size reduction in the microstrip

antenna.

REFERENCES

1. Y.R. Kwon, V.M. Hietala and K.S. Champlin, Quasi-TEM analysis of

slow-wave mode propagation on coplanar microstructure MIS trans-

mission lines, IEEE Trans Microwave Theory Tech MTT-35 (1987),

881890.

2. H. Ogawa and T. Itoh, Slow-wave characteristics of ferromagnetic

semiconductor microstrip line, IEEE Trans Microwave Theory Tech

MTT-35 (1987),14781482.

3. Y.D. Lin and T. Itoh, Frequency-scanning antenna using the crosstie-

overlay slow-wave structures as transmission line, IEEE Trans Anten-

nas Propagat AP-39 (1991), 377380.

4. C.C. Chang, R. Coccioli, Y. Qian, and T. Itoh, Numerical and exper-imental characterization of slow-wave microstrip line on periodic

ground plane, MTT-Symp Digest 3 (2000), 15331536.

5. R. Spickermann and N. Dagli, Experimental analysis of millimeter

wave coplanar waveguide slow wave structures on GaAs, IEEE Trans

Microwave Theory Tech MTT-42 (1994), 1918 1924.

2002 Wiley Periodicals, Inc.

PRESENTATION OF THE SPECTRALELECTRIC AND MAGNETIC FIELDINTEGRAL EQUATIONS USED ING2DMULT FOR ANALYZING

CYLINDRICAL STRUCTURES OFMULTIMATERIAL REGIONS

Jian Yang and Per-Simon KildalChalmers University of TechnologyS-412 96 Gothenburg, Sweden

Received 7 January 2002

ABSTRACT: When dealing with electromagnetic problems of three-

dimensional (3D) elements, such as dipoles, microstrip patches, and

slots, in the vicinity of two-dimensional (2D) structures, it is very effi-

Figure 4 Antenna configuration

TABLE 1 Design Parameters of Slow-Wave MSA and

Conventional MSA (Fractal Factor: 0.25, Patch Size:

10 10 mm)

Slot Size

(mm2)

Slot Width

(mm)

Period

(mm)

Antenna A1 4.5 4.5 0.25 4.75

Antenna A2 4.5 4.5 0.25 5.5

Antenna B1 3 3 0.1 3.2

Antenna B2 3 3 0.1 3.5

Figure 5 Return loss of fabricated microstrip antenna

88 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 34, No. 2, July 20 2002