tunable inductor with Radial Stub (RS). Additionally, RF MEMS Switches is
implemented to make the CRLH TL tunable in order to provide various functionalities
in one component.
  The focus of our design is mainly in impedance matching and balancing of CRLH
TLs. In general, the characteristics of a CRLH TL are dependent on frequency. More
benefits can be provided if their properties are varied by other parameters. Thus many
researchers have proposed a variety of methods to tune the CRLH TL. Though CRLH
TLs can only be matched in a restricted frequency range, however, when a purely right
hand impedance and a purely left hand impedance are equal to the line impedance, the
CRLH  TL can be matched over an infinite bandwidth, while the shunt resonant
frequency is identical to the series one  [6]. In this case, both the IDC and the stub
inductor should be controlled by cantilever RF MEMS switches. When simultaneously
tuning the inductance and capacitance of the unit cell, the state of the CRLH TL can be
changed. In this way, the CRLH TL can work under balanced condition at different
frequency points. Compare to the conventional approach which tunes only one reactive
load at a time, a better impedance matching is achieved. Also, it is advantageous to
realize balanced structure. And the radial stub for grounding helps in avoiding the
complex via penetrating process which deters cost effective fabrication.
This  article  is organized as follows. Section 2 presents the basic theory of our
design, including the theory of CRLH TL and RF MEMS switches. Section 3 explains
the design process of the MEMS-based tunable CRLH TL. The designed components
and devices are then verified theoretically by simulations. S-parameters are then
obtained by both circuit analysis and EM  simulation. Dispersion curve is generated by
ABCD parameters. Section 4 introduces an application of CRLH-TL based Zero-Order
Resonator.    
 
Fig.1 Circuit Model of Transmission Line
The equivalent homogeneous circuit model of purely LH (PLH) and purely RH
(PRH) lossless TL are depicted in Fig.1 (a), and Fig.1 (b), respectively. In general, the PRH TL consists of series inductance (LR) which represents the stored energy of  the
magnetic field and shunt capacitance (CR), which represents the stored energy of the
electric field.   And on contrary, the PLH TL can be represented as the combination of
series capacitance (CL) and shunt inductance (LL).  In reality, a PLH structure is not
possible in a TL approach due to microstrip geometry, name unavoidable RH parasitic
series inductance (LR) and shunt  capacitance (CR) effects. As a result, a realizable
circuit generating LH attributes should be the combined form of RH and LH TLs,
which is called CRLH TL [1] [8]. Fig.1 (c) shows the equivalent homogeneous model
of a CRLH TL unit cell. However, the homogeneous CRLH TL does not appear to exist
in nature.  But when the guided wavelength is much larger than the scale of the
structure, CRLH TL can be viewed as effectively homogeneous. So in a certain range of
frequencies, such kind of CRLH TL can be realized by cascading the band-pass LC unit
cell, shown in Fig.1 (d), in either a nonperiodic or periodic form. Usually periodicity is
preferred for computational and fabrication convenience of the CRLH TL  [1]. It
consists of an inductance LR in series with a capacitance CL and a shunt capacitance CR
in parallel with an inductance LL. In general, Fig.2 (a), Fig.2 (b) and Fig.2 (c) shows the
dispersion diagram of a PRH TL, PLH TL, and CRLH TL [1], which also illustrates that
the CRLH TL's dispersion diagram has both LH and RH region. The fundamental relations for a CRLH TL structure can be derived from standard Design of RF MEMS Based Tunable Cell for CRLH Transmission Line(3):http://www.751com.cn/yingyu/lunwen_1769.html