Abstract
Composite right-/left-handed (CRLH) transmission lines have gained great interest in the microwave community. In practical applications, such CRLH sections realized by series and shunt resonators have a finite length. Starting from the observation that a high-order Chebyshev filter also exhibits a periodic central section of very similar structure, the relations between finite length CRHL transmission lines and Chebyshev filters are discussed in this paper. It is shown that a finite length CRLH transmission line in the balanced case is equivalent to the central part of a low-ripple high-order Chebyshev band-pass filter, and a dual-CRLH transmission line in the balanced case is equivalent to a low-ripple high-order Chebyshev band-stop filter. The nonperiodic end sections of a Chebyshev filter can be regarded as matching sections, thus leading to an even better amplitude and phase response. It is also shown that, equally to a CRHL transmission line, a Chebyshev filter exhibits negative phase velocity in part of its passband. As a consequence, an improved behavior of finite length CRLH transmission lines may be achieved adding matching sections based on filter theory; this is demonstrated by a simulation example.
Highlights
In the past years, metamaterials [1] have found wide interest in the microwave community
As the normal shunt capacitance and series inductance cannot be avoided in practice, the concept of a composite right/left-handed (CRLH) transmission line was developed, and a number of applications have been demonstrated [4,5,6,7,8,9], for example, for frequency-scanned antennas, directional couplers, power dividers, zeroth-order resonators, and so forth, and further applications of negative refractive index transmission lines for constructing advanced microwave components [10, 11] are envisaged
In the left-handed region, phase angles increase along the nodes, approximating a negative phase velocity. This phase analysis shows the equivalence between a finite length transmission line and a Chebyshev filter with respect to approaching a negative phase velocity, where the filter has a superior amplitude and group delay performance compared to conventional finite length CRLH transmission lines
Summary
Metamaterials [1] have found wide interest in the microwave community. A homogeneous negative refractive index, left-handed, or metamaterial transmission line, does not exist in nature and typically is approached by an artificial structure which is usually constructed from a series of discontinuous sections and operates in a restricted frequency range [2, 3]. The starting points of our considerations were on the one hand, the periodic nature of the central part of Chebyshev filters, and on the other hand, practical problems of implementing finite length CRLH transmission lines into a (typically) 50 Ohm environment. If we design a CRLH transmission line based on the classical filter theory, a better performance of a finite length transmission line section can be achieved To this end, we firstly summarize the characteristic formulas of a CRLH transmission line. We present an example on how to improve the design of CRLH transmissions lines in a simple way
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