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Metamaterial Transmission Lines with Tunable Phase and Characteristic injection-locked active antenna for array applications, IEEE Trans Mi- lable characteristic impedance and dispersion (phase) [15–19]. crowave Theory Tech 50 (2002), 481–486. This can be achieved by loading the line by means of electrically 3. D. Bonefacˇcic´ and J. Bartolic´, Compact active integrated antenna with small reactive elements. Thanks to this controllability and the transistor oscillator and line impedance transformer, Electron Lett 36 small size of the unit cell of such lines, these artificial lines have (2000), 1519–1521. been applied to the design of compact devices with enhanced 4. N.M. Nguyen and R.G. Meyer, Start-up and frequency stability in performance and/or providing new functionalities. Obviously, the high-frequency oscillator, IEEE J Solid-State Circuits 27 (1992), 810– 820. superior characteristics of these artificial lines can be further enhanced by including tuning in the loading reactive elements. © 2009 Wiley Periodicals, Inc. This has led to the design of tunable components based on these artificial lines such as scanning leaky-wave antennas [1], tunable filters and resonators [3, 20, 21], and phase shifters [4], among others. Also, the synthesis of electrically controllable artificial METAMATERIAL TRANSMISSION LINES transmission lines has been applied to impedance matching [5]. WITH TUNABLE PHASE AND Based on split ring resonators or complementary split ring CHARACTERISTIC IMPEDANCE BASED resonators, tunable artificial lines have been designed [3, 22]. In ON COMPLEMENTARY SPLIT RING such lines, the resonant elements (split ring resonators or their complementary counterparts) are loaded with varactor diodes and, RESONATORS hence, the electrical characteristics of these resonators can be Adolfo Ve´ lez, Jordi Bonache, and Ferran Martín electronically controlled. This technique has been applied to the GEMMA/CIMITEC, Departament d’Enginyeria Electro` nica. Universitat design of compact tunable filtering structures [20–22]. However, Auto` noma de Barcelona. 08193 Bellaterra (Barcelona), Spain; rather than being designed with tunable transmission lines, these Corresponding author: [email protected] devices have been actually implemented by using tunable resona- tors. Tunable lines must satisfy one of the following requirements Received 10 November 2008 (or both of them simultaneously): (i) the characteristic impedance and phase can be independently modified for a certain given ABSTRACT: In this article, resonant-type tunable metamaterial trans- frequency (fixed frequency and tunable line characteristics) or (ii) mission lines with independent control over the electrical parameters of the operating frequency can be varied for a certain value of the the line, that is, the electrical length and characteristic impedance, are characteristic impedance and phase shift (fixed line characteristics presented for the first time. Tuning is achieved by loading a host mi- and tunable frequency). To satisfy such requirements, at least two crostrip line with varactor-loaded complementary split ring resonators (VLCSRRs) and varactor diodes. By locating the varactor diodes in se- tuning elements are needed. ries configuration with the line, outside the region occupied by the In this article, tunable metamaterial transmission lines based on VLCSRRs, it is possible to control the characteristic impedance and the complementary split ring resonators are proposed. The target is to electrical length (phase shift), over a wide band. As an illustrative ex- vary the operating frequency over a wide range, leaving the phase ample, a tunable 35 ⍀/90° line functional between 0.4 and 0.8 GHz shift and line impedance unaltered in such interval. To achieve (which represents more than 65% tuning range), is presented and this, we have considered a single unit cell line, with one varactor applied to the design of a transmission line power divider. The de- diode loading the resonant element and two varactor diodes series vice is small and it exhibits reasonable performance. © 2009 Wiley connected to the host line. Specifically, a tunable 35 ⍀/90° has Periodicals, Inc. Microwave Opt Technol Lett 51: 1966–1970, 2009; been designed and applied to the implementation of a microwave Published online in Wiley InterScience (www.interscience.wiley.com). power divider. DOI 10.1002/mop.24480 2. GENERAL CONSIDERATIONS FOR THE DESIGN OF Key words: tunable lines; metamaterials; impedance inverter TUNABLE METAMATERIAL TRANSMISSION LINES Any metamaterial transmission line is a bi-port and, hence, its unit 1. INTRODUCTION cell can be described either by a T- or a ␲-circuit model. In both Tunable microwave components are devices whose electrical char- cases, the dispersion relation is given by the following well-known acteristics can be tailored through external actuation (i.e., a DC expression [23]: voltage). These components are of the greatest interest in modern wireless communication systems. To achieve electronic tuning, Z ͑␻͒ ␾ ϭ ϩ s voltage variable capacitances are generally used in the designs. cos 1 ͑␻͒ (1) Zp Such capacitors can be implemented by means of microelectro- mechanical systems (MEMS), ferroelectric components, or semi- ␻ ␻ where Zs( ) and Zp( ) are the series and shunt impedances, conductor varactor diodes. Many works have been dedicated to the respectively, of the T- or ␲-circuit models, and ␾ is the electrical design of tunable microwave devices by using such variable ca- length of the unit cell. The characteristic impedance is given by the pacitances. following expression: Recently, tunability has been applied to the design of metama- terial-based components and devices [1–10]. Although its defini- Z ͑␻͒ ϭ ͱZ ͑␻͓͒Z ͑␻͒ ϩ 2Z ͑␻͔͒ (2) tion is a little bit vague, metamaterials are artificial materials, B s s p composed of small size (as compared to wavelength) inclusions or if the T-circuit is considered, whereas for a ␲-circuit, the charac- “atoms,” with controllable electromagnetic properties [11–14]. teristic impedance is given by the following: These properties can be made drastically different than those of their constitutive elements and can be engineered through actua- Z ͑␻͒Z ͑␻͒/2 tion on the material and geometry of the inclusions. The metama- ͑␻͒ ϭ s p ZB ͑␻͒ (3) terial concept has been extended to the synthesis of artificial ͱ Zs ϩ 1 ͑␻͒ transmission lines (metamaterial transmission lines) with control- 2Zp 1966 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 8, August 2009 DOI 10.1002/mop In the previous formulas, losses have been excluded, and expres- Thus, the series and shunt variable capacitances, Cvar2(V) and ␾ ␹ ␹ sion (1) is valid in that region, where has a real solution. Cvar1(V), must be selected so that the required values for s and p According to expressions (1) through (3), if we want to design (expressions 8 and 9) can be satisfied by adjusting the bias voltage, a tunable artificial line with the phase shift (unit cell) and charac- V, within the tuning interval. Inspection of expressions 8 and 9 ␾ ϭ ␾ ϭ teristic impedance set to certain values ( o and ZB Zo) over reveals that it is possible to design tunable metamaterial transmis- a certain frequency band, it follows that the series and shunt sion lines by using the model of Figure 1. Namely, these expres- impedances must satisfy the following: sions are monotonic with frequency, so that in a certain frequency interval, it is potentially possible to tune the capacitance by means cos␾ Ϫ 1 of a commercial varactor diode. In this article, we consider a ϭ ͱ o Zs Zo ␾ ϩ (4) different approach, based on the resonant type approach of meta- cos o 1 material transmission lines, which is discussed in the next section. Zo Z ϭ (5) 3. TUNABLE METAMATERIAL TRANSMISION LINES BASED p ͱ 2␾ Ϫ cos o 1 ON CONPLEMENTARY SPLIT RING RESONATORS In this section, it is demonstrated that it is possible to design for a T-circuit, and tunable metamaterial transmission based on complementary split ring resonators. Indeed, tunable artificial lines based on such ϭ ͱ 2␾ Ϫ Zs Zo cos o 1 (6) resonators have been previously reported by the authors. In Ref. 25, a complementary split ring resonator-loaded line was also ␾ ϩ loaded with varactor diodes series connected to the host line, above cos o 1 Z ϭ Z ͱ (7) p o cos␾ Ϫ 1 the position of the complementary split ring resonators. In Ref. 22, o the varactor diode was placed between the inner and outer region of the complementary split ring resonators. By this means, the for a ␲-circuit, and such values must be constant, that is, frequency electrical characteristics of the resonators were tuned, and the independent, over the required frequency interval (which deter- structure was demonstrated to be useful as a tunable filter. In these mines the tuning range). previous works by the authors, only one tuning diode was consid- According to this analysis, the series and shunt impedances of ered (per unit cell). Tuning was achieved, but not in the sense that the equivalent T- or ␲-circuits must exhibit a dependence on the we claim in this article, that is, to preserve line characteristics variable element (capacitance) able to compensate its dependence (impedance and electrical length) over a certain frequency band. on frequency, at least over the tuning interval. Let us consider as To achieve this, at least two tuning elements are required. The an example a tunable artificial line that can be described by the most simple structure based on complementary split ring resonator composite right/left handed T-circuit model (Fig. 1) [13, 24]. In loaded lines and two varactor diodes consists on a combination of such line, the capacitances are bias dependent to provide tuning to the previous tunable lines; that is, a transmission line with a series the structure. Let us also consider that the line operates in the left varactor diode on top of a varactor loaded complementary split handed band. This univocally determines the sign of the series and ring resonator (etched in the ground plane).
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