Composite Right/Left-Handed Transmission Lines
Among several types of LWAs reported in the literature, one structure particularly stands out due to its unique radiation properties. It is a metamaterial CRLH transmission line LWA [Caloz and Itoh (2006)], which radiates in its n = 0 space harmonic, as compared to n = -1 space harmonic in other conventional LWA structures, and is capable of full-space frequency scanning from backfire to endfire, including broadside.
The general properties of a CRLH structure can be established based on a lumped circuit unit cell model. An ideal left-handed (LH) transmission line consists of a series capacitance and a shunt inductance, and subsequently exhibits anti-parallel phase and group velocities [Ramo et al. (1994)]. However, such a line does not exist in nature because of the presence of parasitic series inductance and shunt capacitance, which are responsible for right-handed (RH) contributions. To take into account these effects, Caloz et al. [Caloz and Itoh (2006)] developed the concept of a CRLH transmission line, which acts as an LH transmission line at low frequencies and RH transmission line at high frequencies.
The CRLH artificial transmission line is composed of RH elements (Lr, CR) and LH elements (Ll, CL~), as shown in Fig. 5.5(a), and is characterized by the following dispersion relation [Caloz and Itoh (2006)]:
where к = LLCr + LrCL , wR = 1ДjLrCr , wL = 1/^JlLCL and p is the unit cell size or period, and by the Bloch impedance
where wse = 1/^JlrCl , wsh = 1Д/LlCr and ZL is the load impedance. Depending on the relative values of the LH and RH contributions, this transmission line can be unbalanced or balanced, i.e., exhibiting a gapless transition between the LH and RH bands.
Figure 5.5 Composite right/left-handed (CRLH) MTMs fundaments. (a) Unit cell transmission model. (b) Dispersion diagram [Caloz and Itoh (2006)].
The typical dispersion relation of a balanced CRLH transmission line, where f is the phase shift across the structure, curves are shown in Fig. 5.5b. As seen in (5.13), the CRLH transmission line offers a certain degree of dispersion (phase) control via the CRLH parameters LR, CR, lL, and CL. Thanks to its dispersive properties and subsequent design flexibility, the CRLH transmission line provides low-loss, compact, and planar dispersion-engineered solutions, avoiding frequency limitations, complex fabrication, cryogenics, circulators, or amplifiers. Moreover, the CRLH transmission line’s operational frequency and bandwidth are dependent only on a single unit cell’s RH/LH capacitor and inductor values [Caloz and Itoh (2006)]. Thus, a compact CRLH transmission line can be designed to operate at high frequencies while also exhibiting wide bandwidth.
Figure 5.6 Frequency-space mapping associated with temporal-spatial dispersion for the CRLH LWA employed in the RTSA. Reprinted with permission from Caloz et al., 2013, Copyright 2013, IEEE.
A CRLH transmission line can also be operated in a radiative leaky-wave mode when open to free-space, since the CRLH dispersion curve penetrates into the fast-wave region, we [wBF, wEF. The resulting LWA radiates from backfire (0 = -90°) to end-fire (0 = +90°), including broadside (0 = 0°) as frequency is scanned from wBF (where b = -k0) to wEF (where b = +k0) [Liu et al. (2002); Caloz and Itoh (2006)], following the scanning law of (5.12a), which is plotted in Fig. 5.6.