Analysis on Metamaterials Quasi Standard Transmission Line Unit Cell by Software Tool

Journal of Modern Mathematics Frontier Volume 3 Issue 3, September 2014 doi: 10.14355/jmmf.2014.0303.01

www.sjmmf.org

Analysis on Metamaterials Quasi Standard Transmission Line Unit Cell by Software Tool Cong Wang*1, Nam-Young Kim2 Department of Electronic Engineering, Kwangwoon University 447-1, Wolgye-dong, Nowon-gu, Seoul 139-701, Republic of Korea kevin_wang@kw.ac.kr; 2nykim@kw.ac.kr

*1

Abstract A compact distributed metamaterials quasi standard transmission lines unit cell is proposed in this paper. It consists of interdigital capacitor and single or double spiral inductor based on microstrip transmission lines. The area of the unit cell is much reduced when compared with the conventional microstrip metamaterials transmission lines.

The performance and the fundamental properties of the conventional and the proposed unit cells are verified by 3D planar electromagnetic (EM) simulation, and the electric size is calculated and compared. Transmission lines including 10 proposed unit cells and the traditional transmission lines are simulated by full 3D simulator. The forward and backward waves in the left-handed band from the simulation demonstrate the effectiveness of the proposed metamaterials transmission lines unit cell.

Keywords Metamaterials; Transmission Lines; Unit Cell; Interdigital Capacitor; Spiral Inductor; Sonnet/CST Software Tools

Introduction Metamaterials have attracted considerable attention for many years because their unusual magnetic and electric properties are generally not found in nature.

From the first evidences proved that materials with a negative refractive index were indeed physically realizable, numerous new devices or improvements of existing devices have been reported in the microwave and antenna fields. Metamaterials transmission lines based on metamaterials, which is usually implemented by periodically loading a host transmission lines with series of capacitances and shunt inductances and exhibits both the left-handed (LH) and right-handed (RH) propagation bands. In recent years, different microwave components based on metamaterials have been developed and their applications have been reported using metamaterials transmission lines. When considering planar-type of transmission lines, the coplanar waveguide (CPW) and coplanar stripline (CPS) technology offer more

design freedom, several kinds of topologies of metamaterials transmission lines based on them have been realized. However, in microstrip technology there are seldom new topologies are reported after the first classic one from UCLA group.

In this paper, compact distributed microstrip metamaterials transmission lines unit cell using interdigital capacitor and spiral inductor is proposed.

Single spiral and double spiral inductors are introduced to replace the classic shorted stub inductor.

The whole metamaterials transmission lines can be made totally in the traditional transmission lines area, and no expanded size is needed any more. Firstly, both the conventional unit cell and the proposed unit cell are verified by Sonnet’s 3D planar EM simulator for comparing. The performance and the fundamental properties of the unit cell are then analyzed and presented. And the unit cell with double spiral inductor are also studied and compared with the unit cell with the single spiral inductor. Finally, the transmission lines including 10 proposed unit cells and the traditional transmission lines is evaluated by the full 3D CST simulator. The observed forward wave and backward wave in the left-handed band demonstrate the operation of the proposed metamaterials transmission lines unit cell.

Unit Cell Analysis by Sonnet Software Tool The proposed metamaterials transmission lines unit cell based on the interdigital capacitor and single or double spiral inductor are shown in the Fig. 1 (b) and (c). For comparison, the classic metamaterials transmission lines unit cell is also recalled in Fig. 1 (a), which is based on interdigital capacitor and shorted stub inductor. The Sonnet’s 3D planar EM software (version 12.56) is used for evaluation in this section.

The characteristics of the unit cell can be analyzed by Bloch wave approach based on the simulation results.

The Bloch impedance ZB and Bloch propagation

45

www.sjmmf.org

Journal of Modern Mathematics Frontier Volume 3 Issue 3, September 2014

constant β can be calculated. In the case of reciprocal unit cells, these two quantities can be deduced from transmission matrix (ABCD matrix) of the unit cell of the structure by using the equations

  d  cosh 1  A

(1)

ZB  B C

(2)

where d is the length of the unit cell. On the other hand, in the conventional positive-refractive-index (PRI) transmission lines, the phase lags in the direction of positive group velocity, thus incurring a negative phase. However in the negative-refractive-index (NRI) transmission lines, the phase is just reversed. So the phase value of S21 shows another insight of the nature of metamaterials. The electric size of the unit cell in terms of the guided wavelength in the host transmission lines at the transition frequency is defined as r  d Ig

(3)

We firstly evaluated the classic metamaterials transmission lines unit cell. The reported classic unit cell was implemented on Rogers TR/Duroid 5880 with dielectric constant εr = 2.2 and thickness h = 1.57 mm as report in reference. The unit cell period is 11.4 mm, stub length is 10.9 mm, stub width is 1 mm, interdigital finger length is 10.2 mm, interdigital finger width is 0.3 mm, and spacing between the fingers is 0.2 mm. The simulated S21 result is shown in Fig. 2, which is matched to the reported data in reference.

FIG. 1 MICROSTRIP METAMATERIALS TRANSMISSION LINES UNIT CELL OF (A) CLASSIC STRUCTRURE, (B) THE PROPOSED UNIT CELL USING SINGLE SPIRAL INDUCTORS, AND (C) THE PROPOSED UNIT CELL USING DOUBLE SPIRAL INDUCTOR

We can see the zero phase point of the S21 is located at 2.4 GHz from Fig. 2. That means at this frequency the right hand transmission lines and the left hand transmission lines are just compensate for each other.

Left hand band is lower than this transient frequency, which corresponds the positive phase of S21. And the right hand band is higher than this transient frequency, which corresponds the conventional negative phase of

46

S21. The calculated homogeneity factor based on equation (3) is 0.136. The Bloch impedance ZB calculation can be directly realized in the Sonnet software by the user defined equations. In the lower left hand band impedance is about 40 Ohm which is not perfectly matching to the required 50 Ohm Bloch impedance and the higher right hand band impedance is about 54 Ohm which is a much better matching. The calculated image parts in both the left and right hand band are almost zero, which is very useful for the request of the proposed design.

FIG. 2 THE S21 RESULTS OF THE CLASSIC METAMATERIALS TRANSMISSION LINES UNIT CELL

FIG. 3 THE S21 RESULTS OF THE PROPOSED METAMATERIALS TRANSMISSION LINES UNIT CELL USING SINGLE INDUCTOR

In order to compare with the classic metamaterials transmission lines, the proposed metamaterials unit cell is studied based on the same microstrip substrate and almost the same character of the interdigital capacitor part is used in the proposed metamaterials unit cell. Firstly, the scattering parameters of the interdigital capacitor and spiral inductor are determined by full-wave Sonnet simulation, respectively. For the interdigital capacitor, we extract the serial capacitance from the Y21 of Y parameters. For

Journal of Modern Mathematics Frontier Volume 3 Issue 3, September 2014

the spiral inductor, we extract the shunt inductance from the Y11 of Y parameters. The detailed S21 parameter results are shown in Fig. 3. From Fig. 3 it is noted that the realized transition frequency is located at 2 GHz, which is smaller than the classic one using short stub. The Bloch impedance is also calculated by equation (2). In the lower left hand band impedance is about 48 Ohm and in the higher right hand band impedance is around 56 Ohm which is a little better matching than the classic one. The calculated homogeneity factor of the proposed unit cell is 0.146 which is similar to the classic unit cell, but the proposed metamaterials transmission lines is no extended short stub to form a quasi standard trasmission lines as shown in Fig. 4. The total area of the proposed metamaterials transmission lines are much saved when compared to the classic ones. The detailed parameters of the designed metamaterials quasi standard transmission lines unit cell are shown in Fig. 5.

www.sjmmf.org

or microelectromechanical systems (MEMS) technology to reduce the effect of the insertion loss of both the magnitude and phase.

Metamaterials TML Simulation In order to more effectively demonstrate the proposed metamaterial transmission lines unit cell, transmission lines including 10 proposed unit cells using the spiral inductor and the traditional transmission lines plotted in Fig. 5 is simulated by full 3D CST simulator.

Theoretically in the left-handed band, the backward wave should be seen in the metamaterials unit cells part, and the forward wave should be seen in the traditional transmission lines part. The Snapshots of the simulated distributions of y-component of the magnetic field in the connected right-handed transmission lines and left-handed transmission lines at different time instants are plotted and shown in the Fig. 7. The phenomenon is well matched with the theory, which further confirms the proposed metamaterials transmission lines unit cell.

FIG. 4 THE UNIT CELL OF THE CLASSIC (LEFT) AND THE PROPOSED (RIGHT) COMPOSITE RIGHT/LEFT-HANDED TRANSMISSION LINE 0.3 0.2

11

0.6

0.3

0.3

3

1.7

0.7

0.7

unit : mm

2 2.7

FIG. 6 THE S21 RESULTS OF THE PROPOSED METAMATERIALS TRANSMISSION LINES UNIT CELL USING DOUBLE SPIRAL INDUCTOR

FIG. 5 THE COMPOSITE RIGHT/LEFT-HANDED TRANSMISSION LINE UNIT CELL WITH THE DETAILED PARAMETER VALUES

The unit cell with the double spiral inductor as shown in Fig. 1 (c) is also studied for comparing with the unit cell with the single spiral inductor. The zero phase point of the S21 is further move to the lower frequency, which means the total area of the unit cell may be further reduced as shown in Fig. 6. However the double spiral structure introduces the more losses compared with the normal single spiral structure. For gigahertz application, the single spiral inductor is more easily to design and realize. For requirement of more compact size, the double spiral structure may be used with low temperature co-fired ceramics (LTCC)

FIG. 7 SNAPSHOTS OF SIMULATED DISTRIBUTIONS OF YCOMPONENT OF THE MAGNETIC FIELD IN THE CONNECTED RIGHT-HANDED TRANSMISSION LINES AND LEFT-HANDED TRANSMISSION LINES AT DIFFERENT TIME INSTANTS

47

www.sjmmf.org

Journal of Modern Mathematics Frontier Volume 3 Issue 3, September 2014

Conclusion

pp. 1306-1311, September 2006.

A compact new distributed metamaterials quasi standard transmission lines unit cell based on the microstrip technology is proposed. Spiral inductor is introduced in the unit cell for replacing the classic short stub inductor to greatly reduce the total unit cell area. Numerical simulations are carried out to validate the proposed unit cell and compare the performance with the classic unit cell. The phenomenon of backward wave is also observed from the result of the full 3D simulation. It will be very useful in system on chip (SOP) and system in package (SIP) for some novel applications by considering this proposed compact metamaterial transmission lines topology.

ACKNOWLEDGMENT

This work was supported by a grant supported from Korean government (MEST) No. 2012R1A1A2004366 and (MSIP) No. 2014R1A1A1005901. This work was also supported by a Research Grant of Kwangwoon University in 2014.

REFERENCES

A. Sanada, C. Caloz, and T. Itoh. ‚Characteristics of the composite right/left-handed transmission lines.‛ IEEE Microw. Compon. Lett., vol. 14, no. 2, pp. 68-70, February 2004.

J. Perruisseau-Carrier and A. K. Skrivervik. ‚Bloch wave approach to the design of optimally matched noneffective

medium

composite

right/left

handed

transmission lines.‛ IET Microwaves Antennas Propag., vol. 1, no.1, pp. 50-55, February 2007.

R. A. Shelby, D. R. Smith, and S. Schultz. ‚Experimental verification of a negative index of refraction.‛ Science, vol. 292, no. 5514, pp. 77-79, April 2001.

R. Goto, H. Dequchi, and M. Tsuji. ‚Composite right/lefthanded transmission lines based on conductor-backed coplanar strips.‛ IEICE Trans. Electron., vol. E89-C, no. 9,

48

S. G. Mao, M. S. Wu, Y. Z. Chueh, and C. H. Chen. ‚Modeling of symmetric composite right/left-handed coplanar waveguides with applications to compact bandpass filters.‛ IEEE Trans. Microwave Theory Tech., vol. 53, no. 11, pp. 3460-3466, November 2005.

Cong Wang was born in Qingdao, China in 1982. He received the B.S. degree in Automation Engineering from Qingdao Technological University (China) in 2005, the M.S. and Ph. D. degrees in Electronic Engineering from Kwangwoon University (Korea) in 2008 and 2011 respectively. He is currently working at the same university as an assistant professor. He has published more than 110 papers in domestic and international journals and conferences. He is listed in ‘Marquis Who’s Who in the World, 28th Edition (2010)’ for his outstanding contribution in his own field as a researcher and educator. He also has a few semiconductor layout design patents registered in Korea. His major interests include RFIC/MMIC design and semiconductor fabrication development such as GaAs integrated passive device, SU-8 photo resist based fabrication, silicon-based LED module fabrication and packaging, and AlGaN/GaN HEMT and their applications which are emerging technologies of today.

Nam-Young Kim has received two Masters and two Ph.D. degrees from State University of New York at Buffalo and Midwest University: the M.S. and the Ph.D. in Electronic Engineering. He has also received M. Div and D.C.E. degrees in Theology from Midwest University in 2004 and 2006, respectively. He was a research scientist for CEEM at SUNY at Buffalo in 1994. After completing his research at CEEM at SUNY at Buffalo, Dr. Kim joined the Department of Electronic Engineering of Kwangwoon University as an assistant professor in 1994. His main research focus is in RFIC devices and systems, which use wireless application techniques in order to develop high speed structures in GaAs, Si, and other materials. During his career, he has published almost 120 refereed journal papers and 355 refereed conference papers. Dr. Kim has been issued more than 40 patents and 35 semiconductor design patents. His research fields are in the areas of semiconductor device modeling, ASIC, RFIC and MMIC design.