Designs of True-Time-Delay Lines and Phase Shifters Based on CRLH TL Unit Cells

Electromagnetic (EM) Metamaterials have specific EM properties that cannot be found in nature (Caloz & Itoh, 2006). These specific EM properties are obtained by the artificial structures, rather than the composition of the metamaterials, and affect the propagations of EM waves when the average structure sizes are much smaller than the guided wavelengths ┣g, i.e., at least smaller than ┣g/4. Since the propagation of an EM wave is related to its electric and magnetic fields, the EM properties of Electromagnetic (EM) Metamaterials can be described by using its permittivity ε and permeability ┤.

shows the four possible combinations of permittivity and permeability of materials. In quadrant I, we can find materials such as isotropic dielectrics which have ε > 0 and > 0. In quadrant II, where ε < 0 and > 0, we can find materials like plasmas to have such properties. While in quadrant IV, we also can find ferromagnetic materials to have ε > 0 and < 0. However, in quadrant III where both permittivity and permeability are negative, i.e. ε < 0 and < 0, there is no natural material having such properties. However, one can construct artificial structures that have negative permittivity and permeability, and these artificial materials are called left-handed (LH) materials as will be explained in the following sections.

Left-handed (LH) materials
When an EM wave propagates in a conventional material, the electric field E and magnetic field H are orthogonal to each other and also orthogonal to the wave-vector k which has the same direction as the power flow density (also known as Poynting vector S). These three vectors, E, H and k, form a right-hand (RH) triplet, so conventional materials can also be called right-handed (RH) materials. In the 1960s, Russian physicist Viktor Veselago theoretically investigated the existence of materials with negative permittivity ε and also negative permeability (Veselago, 1968). He speculated that such materials would also satisfy Maxwell's equations but allow the electric field E, magnetic field H and wave-vector k of an EM wave to form a left-handed (LH) triplet. For this reason, the term 'left-handed' was used to describe these theoretical materials. Based on the fact that, in these materials, E,

Wave propagation in LH materials by Maxwell's equations
The general form of time-varying Maxwell's equations can be written as (Ulaby, 2004): The relationships between the field intensities E and B, flux densities D and H and current density J are (Ulaby, 2004): where ε, and σ are the electric permittivity (also called the dielectric constant), permeability and conductivity, respectively, of the material under consideration.
Consider a wave having a single frequency ω. Then by introducing the time factor e +jωt to (1), the time derivatives in Maxwell's equations of (1) can be replaced by jω and Maxwell's equations can be re-written as: In free space which is lossless, J, σ and ρ are all zero and (3) becomes: It can be readily shown from (4) that 22 EE 0 k ∇+ = (5a) 22 HH 0 k ∇+ = (5a) where k = 2π/λ is the wave number (which is real if ε and are real) with λ being the wavelength.
(5) is known as the wave equation which has many solutions. A plane wave is a wave having a constant phase over a set of planes, while a uniform-plane wave is a wave having both magnitude and phase constant. An EM wave in free space is a uniform-plane wave having the electric field E and magnetic field B mutually perpendicular to each other and also to the direction of propagation, i.e., a transverse electromagnetic (TEM) wave. For convenience and without lost of generality, a s s u m e t h a t t h e E M w a v e c o n s i d e r e d i s propagating in the +z direction in free space. Under these conditions, the solution for (5) is (Ulaby, 2004): The power flow density of an EM wave, also known as the Poynting vector, is defined as (Ulaby, 2004): (9) indicates that the power flow density is only determined by E and H but not the signs of ε and . Thus in both RH and LH materials, the triplets (E, H, S) have the same form of orthogonality, i.e., following our right hand, as shown in Figs. 2(a) and 2(b), and the directions of energy flow are the same.
The group velocity v g of an EM wave is given by (Ulaby, 2004 which expresses the velocity of power flow and so has the same direction as the Poynting vector S, as shown in Fig. 2. The phase velocity v p is the velocity of wave-front given by (Ulaby, 2004): and so has the same sign as k, i.e., v p > 0 for k > 0 in RH materials and v p < 0 for k < 0 in LH materials. As a result, the v p in LH materials and in RH materials are anti-parallel as indicated in Fig. 2.

Transmission line (TL) approach of metamaterials 2.1 Left-handed transmission lines (LH TLs)
A microstrip transmission line fabricated on a substrate is shown in Fig. 3(a). The transmission line is also called a right-handed transmission line (RH TL) because when an EM wave travelling through it, the triplet (E, H, k) forms a RH orthogonality, as will be shown later. The equivalent circuit of the transmission line is shown in Fig. 3(b), where L R models the RH series inductance along the transmission line and C R models the RH shunt capacitance between the transmission line and the ground on the other side of the substrate (Pozar, 2004). To simplify our analysis, we assume that the transmission line is lossless. The complex propagation constant , the phase constant , the phase velocity v p and the group velocity v g of the RH TL are, respectively, given by (Pozar, 2004): By making a duality of the equivalent circuit in Fig. 3(b), i.e. replacing the series inductance L R with a series capacitance C L and the shunt capacitance C R with a shunt inductance L L , we can have the equivalent circuit of a left-handed transmission line (LH TL) (Lai et al., 2004) shown in Fig. 3(c). It is called a LH TL simply because when an EM wave travelling through it, the triplet (E, H, k) forms a LH orthogonality, as will be shown later. Now the complex propagation constant , the phase constant , the phase velocity v p and the group velocity v g of the LH TL can be found as Here the phase constant (= 2π/λ) in (13b) (equivalent to the wave number k used in wave propagation previously) is negative and so the phase velocity v p in (13c) associated with the direction of phase propagation is negative. However, the group velocity v g in (13d) indicating the direction of power flow (Poynting vector S) remains positive. This characteristic agrees with that of LH materials shown in Table 1, so the LC circuit shown in Fig. 3(c) can be used to realize LH materials.

Composite right/left-handed transmission line (CRLH TL)
The transmission line structure shown in Fig. 4(a) was proposed in (Lai et al., 2004) to realize the series capacitance C L and shunt inductance L L in Fig. 3(c) for the LH materials (Lai et al., 2004). The structure consists of a series inter-digital capacitors to realize the series capacitance C L and a via shunted to ground on the other of the substrate to realize the shunt inductance L L . However, when an EM wave travels along the structure, the current flowing along the upper metal trace induces a magnetic field, creating an inductive effect. This effect is modeled by the series inductance L R in Fig. 4(b). Moreover, the potential difference generated between the upper metal trace and the ground plane on the other side produces an electric field, creating a capacitive effect. This effect is modeled by the shunt capacitance C R in Fig. 4(b). Since the inductive and capacitive effects caused by the series inductance L R and shunt capacitance C R , respectively, cannot be avoided in practical implementation of LH TLs, the term "composite right/left-handed transmission line" (CRLH TL) is used to describe such a structure.

Dispersion diagrams
Here, we show that the structure of Fig. 4(a) indeed has LH and RH properties shown in Table 1. The complex propagation constant of the CRLH TL structure in Fig. 4(b) can be written as (Caloz & Itoh, 2006;Lai et al., 2004) j ZY γα β where α and are β are the attenuation and phase constants, respectively. Assume the structure, as represented by Fig. 4(a), is lossless,and so has no attenuation, i.e. α = 0 in (14).
The propagation constant is an imaginary number: www.intechopen.com

Metamaterial 480
In the equivalent circuit of Fig. 4(b), the components C L and L R form a series-tune circuit with a resonant frequency at 1/ RL LC . At frequencies larger than 1/ RL LC , the circuit is inductive. While the components C R and L L form a parallel-tune circuit resonating at 1/ LR LC . At frequencies larger than 1/ LR LC , the circuit is capacitive. Thus, at frequencies max(1 / ,1 / ) , the series-tune circuit is inductive and the parallel-tune circuit is capacitive. The CRLH TL structure will have an equivalent-circuit model similar to one shown in Fig. 3(b) and so behaves like a RH TL. Under this condition, from (12b), the propagation constant is a positively imaginary number, i.e., = j , and so () 1 s ω =+ in (16). At frequencies less than 1/ RL LC , the series-tune circuit formed by C L and L R is capacitive. At frequencies less than 1/ LR LC , the parallel-tune circuit formed by C R and L L is inductive. Thus at frequencies min(1 / ,1 / ) , the series-tune circuit is capacitive and the parallel-tune circuit is inductive. Now the CRLH TL structure has an equivalent-circuit model similar to one shown in Fig. 3(c) and so behaves like a LH TL. Under this condition, from (13b), the propagation constant is a negatively imaginary number i.e., = -j and so () 1 (16). Between these two limits, i.e., (15c) is purely imaginary and so the propagation constant is purely real at = . There is only attenuation in the CRLH TL structure which behaves as a stop-band filter. This stop band is a unique characteristic of the CRLH TL.
Therefore, the propagation constant of a CRLH TL structure can be re-written from (15) The dispersion diagrams of the RH TL, LH TL, and CRLH TL plotted using (12b), (13b) and (17), respectively, are shown in Fig. 5 (Caloz & Itoh, 2006;Lai et al., 2004). For the RH TL, Fig. 5(a) shows that the group velocity (i.e., v g = dω/d ) is positive and has values only for > 0. Since phase velocity is defined as v p = ω/ , Fig. 5(a) shows that the RH TL has v p > 0. Fig. 5(b) shows that the LH TL also has a positive group velocity (v g = dω/d ) but only for < 0 which leads to v p < 0 (because v p = ω/ ). These characteristics agree with those of the RH and LH materials shown in Table 1. Thus the circuit models in Figs. 3(b) and 3(c) realized using transmission lines have the EM properties of the RH and LH materials, respectively. In Fig.  5(c), the regions for > 0 and < 0 are known here as the RH and LH regions, respectively. Now, consider the dispersion diagram in Fig. 5(c). It can be seen that the CRLH TL behaves like a LH TL for < 0 (v p < 0, v g >0) and like a RH TL for > 0 (v p > 0, v g >0). Thus the circuit of Fig. 4(b) indeed has both the LH and RH properties. Fig. 5(c) shows that the CRLH TL has quite small group velocities in the LH region and much large group velocities in the RH region. The LH region with low group velocities can be used to implement TTDLs with high time-delay efficiencies as described later. Moreover, the CRLH TL has a stopband in the frequency range: min , where = 0, leading to a zero group velocity v g and meaning zero power flow.

True-time-delay lines (TTDLs) using CRLH TL unit cells 3.1 Introduction
True-time-delay lines (TTDLs) are widely employed in various microwave devices and subsystems. They find applications in phased arrays, feed-forward amplifiers, delay-lock loops, phase noise measurement systems and oscillators (Lee, 2004). There are different approaches to implement the TTDLs. For example, in magnetostatic wave (MSW) TTDLs (Fetisov & Kabos, 1998) and surface-acoustic wave (SAW) TTDLs (Smith & Gerard, 1969), the group velocities were slowed down by transferring the microwave signals into the www.intechopen.com magnetostatic waves and surface acoustic waves, respectively. These designs have quite high time-delay efficiencies, but the bulky and complicated transducers required are not conducive for planar microwave circuits. Moreover, SAW TTDLs have extremely narrow bandwidths of only several MHz and MSW TTDLs have very large insertion losses. Optical TTDLs (Xu et al., 2004) have very small insertion losses, so we can use very long optical fiber cables to achieve very large TDs. However, optical TTDLs also need complicated transducers to transfer the microwave signals into the optical waves.
Microstrip lines, with the advantages of simplicity in feeding and compatibility with planar circuits, are widely used in communications systems, particularly for small communications devices. A simple RH TL can also be used to implement TTDL. However, due to the low time-delay efficiency, it is difficult to achieve a long TD using RH TL. To increase the timedelay efficiency of RH TL, various slow-wave structures have been proposed. Some employ periodic discontinuities such as the Electromagnetic Bandgap Structures (EBG) (Kim & Drayton, 2007) and defected ground structure (DGS) (Woo et al., 2008). Others use periodic equivalent LC networks (Zhang & Yang, 2008;Zhang et al., 2011). All of these designs adapt the same basic concept,of increasing the series inductance and shunt capacitance per unit length, hence the effective dielectric, to reduce the guided wavelength of the EM waves.
As described previously, the CRLH TL has a unique dispersion characteristic, i.e., having small group velocities in the LH region. Thus a CRLH TL operating in the LH region can be used to realize a TTDL with a high time-delay efficiency. In this section, a TTDL using four symmetrical CRLH TL unit cells is studied.

TTDL realized by transmission line (TL)
The true-time delay (TTD) of a transmission line (TL) is the time it takes for an EM wave to travel through it, so a TL can be used to design a TTDL. For a TL with a length of L, the TTD is: where v g is the group velocity given by with β and ω being the propagation constant and frequency in rad/s, respectively. (18) and (19), show that the TTD is inversely proportional to the group velocity v g . For a given length of TL, the smaller is the v g , the longer will be the TD.

Symmetrical CRLH TL unit cell
To design a TTDL with a large TTD, we propose to cascade a number of CRLH TL structures together, each having a small group velocity. For matching purpose, the CRLH TL structure has to be designed so that S 11 = S 22 over the operating frequency band. However, this is not easy to do using the CRLH TL structure shown in Fig. 4(a) because adjusting any of the structural parameters will change both S 11 and S 22 . To overcome such difficulty, we propose a new structure as shown in Fig. 6 which has a symmetrical structure and is here called a symmetrical CRLH TL unit cell (Zhang et al., 2009). Compared with the CRLH TL structure as shown in 4(a), our proposed CRLH TL unit cell has two stubs, instead of one stub, having a grounded via, making the whole structure centrosymmetrical. To deign such unit cell for use in our TTDL, we only need to match the input impedance to a 50-Ω coaxial cable, which is relatively easy to do. Once this matching is designed, due to its symmetrical structure, the two Z-parameters, Z 11 and Z 22 , will be the same and equal to 50 Ω. The symmetry of the unit cell leads to an equivalent-symmetrical π-model shown in Fig.   6(c) in which L R models the RH series inductance along all the horizontal fingers, C L models the LH coupling capacitance between the fingers, 2L L models the LH shunt inductance of each stub having a via at the end to the ground, and C R /2 models the RH shunt capacitance between the fingers and the ground on each side of the unit cell. Here, we will show that the CRLH TL unit cell in Fig. 6(a) has the same dispersion diagram shown in Fig. 5 (c), so that we can have the LH region to operate the unit cell. The expressions for L R , C R , L L and C L in Fig. 6(c) are, respectively, given by (Bahl, 2001;Marc & Robert, 1991;Pozar, 2004 where h is the thickness of the substrate, r is the radius of the ground via, ε r is the relative dielectric constant, ε re is the effective dielectric constant, l' is the distance from the ground via to the port, l is the length of the finger, N is the number of fingers, W is the width of all the fingers together and Z 0 is the characteristic impedance of each of the fingers. To derive the complex propagation constant of this symmetrical CRLH TL unit cell, we separate the L R and C L in Fig. 6(c) into two capacitances 2C L and two inductances L R /2, respectively. This results in two sub-circuits as shown in Fig. 7, each having the same propagation constant '. The total propagation constant is the sum of the propagation constants for these two sub-circuits, i.e., = 2 '. In Fig. 7, the propagation constant of the symmetrical CRLH TL unit cell is: where () 1 s ω =± (21) shows that the propagation constant is exactly the same as (15c). Thus the symmetrical CRLH TL unit cell has the same dispersion diagram shown in Fig. 5(c).

TTDL realization using symmetrical CRLH TL unit cells
From (18) and (19), the TD of a TL is given by where Ang(S 21 ) is the phase of S 21 . Figure 5(c) shows that the CRLH TL has quite small group velocities v g in the LH region and much higher group velocities in the RH region. Thus the LH region with low group velocities can be used to implement TTDLs with longer TTDs and high time-delay efficiencies as indicated in (22). It can be see that (22) also indicate that, for a given length L, the larger is the slope of phase response, i.e., Ang(S 21 )/df, the longer will be the TD or the higher will be the time-delay efficiency. Moreover, by adjusting L R , C R , L L and C L using the structural parameters through (20), the CRLH TL unit cell can also be designed to operate at different frequencies and TDs.

Single CRLH TL unit cell
The proposed symmetrical CRLH TL unit cell shown in Fig. 6 has been designed with a center frequency at around 3 GHz on a Rogers substrate, RO4350, with a thickness of 0.762 and a permittivity of 3.48 using computer simulation. It has a total a length of 6.8 mm. The design is optimized for the criteria for wide impedance bandwidth, small insertion and large phase response. The simulated results on return loss, -10log|S 11 |, and insertion loss, -10log|S 21 |, of the CRLH TL unit cell are shown in Fig. 8(a), while the phase response, (Ang(S 21 )), shown in Fig. 8(b). For comparison, the results of a RH TL with the same length of 6.8 mm are also shown in the same figure. Figure 8(a) shows that the CRLH unit cell has an operating bandwidth of 2.2-4.0 GHz, a return loss of large than 15 dB and insertion loss of less than 1 dB within the operating bandwidth. The slope of phase response, as shown in Fig. 8(b), is 41.3 degree/GHz, about 3 times larger that of the RH TL at 13.3 degree/GHz. Thus we can expect that the CRLH TL unit cell can achieve a TTD 3.1 times longer than that of a RH TL for the same length and so has the time delay efficiency 3.1 times higher than that of the RH TL.

Multi-CRLH TL unit cells
A TTDL constructed by cascading four symmetrical CRLH unit cells, with a total length of 30 mm, is shown in Fig. 9(a). The TTDL has been designed, studied and optimized using computer simulation. The final design has also been implemented on a Rogers substrate, RO4350, with a thickness of 0.762 and a permittivity of 3.48 and measured for verification of simulation results. For comparison, a TTDL implemented using a RH TL with the same www.intechopen.com length of 30 mm, as shown in Fig. 9(b), has also been designed and simulated using the same substrate. The prototype-modules of the two TTDLs with the same dimension of 30 mm×15 mm×2 mm are shown in Fig. 10. The simulated and measured return losses, insertion losses and TTDs of the two TTDLs are shown in Fig. 11. It can be seen that the simulated and measured results show good agreements. Figure 11(a) show that the measured return losses and the insertion losses of the TTDLs are more than 15 dB and less than 1 dB, respectively, across the frequency band from 2.2 -3.7 GHz. The measurement results in Fig. 11(b) show that the TTDL using CRLH TL unit cells achieves a TTD of 510 ps, about 3.2 times larger than the RH TL having a TTD of 160 ps. This result is consistent with the result obtained for a single CRLH TL unit cell. The measurement results in Fig. 11(b) show that the maximum TTD error for the TTDL using the CRLH TL unit cells is about -21 ps or -4.1% at the frequency of 2.4 GHz. For the TTDL using RH TL, although the maximum TD error is about -7.8 ps at the frequency of 2.8 GHz, the percentage is higher at -4.8%.

Digital-phase shifters using CRLH unit cells 4.1 Introduction
Phase shifters are essential components in radar and phased array systems. In the designs of phase shifters, insertion loss, size and power-handling capability are major factors for considerations. Phase shifters can be classified into passive and active. Passive phase shifters can be implemented using ferrite technology (Adam et al., 2002) to achieve higher power capabilities, but they have large sizes and heavy weights. Active phase shifters implemented using solid-state devices such as FET and CMOS technologies have smaller sizes. However, their low power-handling capabilities and nonreciprocal characteristics limit their applications.
In digital-phase shifters, phase shift is usually obtained by switching between two transmission lines of different lengths or between lumped-element low-pass and high-pass filters (Keul & Bhat, 1991). Usually, the switches are implemented using solid-state devices such as PIN diodes which have typical power-handling capabilities of just a few Watts and this limits the power-handling capabilities of the phase shifters. Moreover, if an n-bit phase shifter is constructed by cascading several phase shifters together to provide the required phase shifts, the physical size and insertion loss will be undoubtedly increased.
Recently, different design approaches of phase shifters based on using metamaterials have been proposed and studied (Antoniades & Eleftheriades, 2003;Damm et al., 2006;Kim et al., 2005;Kholodnyak et al., 2006;Lapine et al., 2006;Vendik et al., 2009;). These designs share one of the major drawbacks, i.e., the power-handling capability is limited by the powerhandling capabilities of the switches, tunable diodes and tunable capacitors used in the designs. A phase shifter based on CRLH TL employing MEMS has also been proposed and studied (Monti et al., 2009), but the reliability of the design needs more studies (Rebeiz et al., 2002).
In this section, we present an approach for the design of n-bit phase shifters using the CRLH TL unit cells. The phase shifters designed using this approach have the advantages of compact size, high power-handling capability, low insertion loss, arbitrary phase-shift range and arbitrary step size. PIN diodes mounted on the fingers of the CRLH TL unit cell are used as switches to control the phase shift. Different phase shifts are achieved by using different states of these switches and the controlling bits are used to select one of those switch states for the required phase shift.

Description of CRLH TL unit cell using ABCD-parameters
The symmetrical CRLH TL unit cell used for the designs of digital-phase shifters is shown in Fig. 12(a) with the equivalent π-model circuit shown in Fig. 12(b). The symmetrical CRLH TL unit cell and the equivalent π-model circuit are similar to those shown in Fig. 6(a), thus the expressions for L R , C R , L L and C L are same as given in (20a)  The transmission ABCD matrix of the π-model circuit in Fig. 12    ω ω − = have been used in (24a)-(24c). As expressed in (20a)-(20d), the structural parameters of the CRLH TL unit cell can be used to determine the values of L R , C R , L L and C L and in turn to determine the phase incursion through (24c) and operation frequency through (24a) and (24b).

Designs of digital-phase shifters using CRLH unit cells 4.3.1 Basic ideas
The symmetrical CRLH TL unit cell in Fig. 12 (a) is used as the basic cell to design digitalphase shifters here. The advantage of using symmetrical CRLH TL unit cells is that when more unit cells are cascaded together to provide a more states, there is no need to perform any matching between adjacent unit cells.
Here, we use Fig.13 to illustrate our proposed idea of using CRLH TL unit cells to design digital-phase shifters. In the figure, we mount four switches on four different fingers of a unit cell. For an n-bit phase shifter, there will be a total of 2 n states, from 0 to 2 n -1, determined by "closed" or "open" states of the switches on the unit cell. The n-controlling bits are used to select a particular state from these 2 n -1 states and hence to provide a particular phase shift. The "closed" or "open" states in the switches determine the values L R , C R , L L and C L through (20a)-(20d) and, in turn, determine the phase incursion Ang(S 21 ) in (24c), so each switch state can be used to provide a particular phase shift, i.e., --switches --via to ground where m is the index (from 0 to 2 n -1) for the switch states, and (S 21 ) m and (S 21 ) 0 are the values of S 21 in the m th -switch and zeroth-switch states, respectively. For convenience and without lost of generality, the zeroth-switch state is taken as the state with all switches closed.
For high power applications such as radars, power-handling capability is one of the important concerns in the design of phase shifters. In our design, the power-handling capacity of the switches (i.e., PIN diodes in our case) used in the CRLH TL unit cell determines the power-handling capacity of the phase shifter. Here, surface-current density distribution is used to study the power-handling capacity of the switches. Computer simulation results on the surface-current density distribution of the CRLH TL unit cell on a Rogers substrate, RO5880, with eight fingers and four switches, are shown in Fig. 14. Figs. 14(a) and 14(b) show the surface-current density distributions with all four switches "opened" or "closed", respectively, at 9.5 GHz. The arrowheads indicate the positions of the switches on the fingers of the CRLH TL unit cell. With all switches "opened", Fig. 14 (a) shows that the largest surface-current density flowing through the switches is about -28 dB below (or 1/25.1 of) those flowing through the input and output ports. While with all switches "closed", Fig. 14 (b) shows that the largest surface-current density flowing through the switches is about -16 dB below (or 1/6.3 of) those flowing through the input and output ports. The width of the finger is only 1/7 of the port, so the largest surface-current through the switches is 16.43 dB below (or 1/44 of) those flowing through the ports. Thus the powerhandling capability of the phase shifter is about 44 times higher than the power-handling capability of a switch (PIN diode).

2-bit phase shifter
A 2-bit phase shifter using a single CRLH TL unit cell is shown in Fig. 15(a), where two switches are mounted on two different fingers . The positions of the switches in the "open" and "close" states determine the values of L R , C R , L L and C L of the unit cell through (20a) -(20d) and hence the phase incursion. The state with all switches closed is taken as the zeroth-switch state. Simulation studies are used to determine the positions of the switches on the top and bottom fingers of the unit cell in order to achieve the phase shifts of 45 0 and 22.5 0 , respectively. The phase shifts of 67.5 0 and 0 0 are provided by "opening" and "closing", respectively, both two switches. Table 2 shows the phase shift for different input logic patterns. It should be noted that, although the phase shifts of 0 0 , 22.5 0 , 45 0 and 67.5 0 with equal step size of 22.5 0 are used in our design, other phase shift values and step sizes are just possible and easily be achieved. The layout of the 2-bit phase shifter with the DC bias circuits for the PINs (the switches) is shown in Fig. 15(b), where RF in and RF out are the input and output RF signals, respectively, and the input bits have the DC voltages of 0 and 5 V representing the two corresponding logic levels "1" and "0".   Fig. 16(a) shows a 3-bit phase shifter using a single CRLH TL unit cell where four switches are used to achieve eight different switch states and hence eight phase shifts of 0 0 , 22.5 0 , 45 0 , 67.5 0 , 90 0 , 112.5 0 , 135 0 and 157.5 0 . Note that the number of controlling bits is less than the number of switches on the unit cell because two switches may be used to provide a phase shift. The state with all switches closed is taken as the zeroth-switch state. Again, computer simulation is used to determine the positions of these switches on the fingers in order to achieve these phase shifts. In Fig. 16(a), the two switches on the inner fingers are used to provide the phase shifts of 22.5 0 and 45 0 . The two switches on the outer fingers serving in pair are used to provide a total phase shift of 90 0 . Different switch states www.intechopen.com are used to provide other phase shifts such as 67.5 0 , 112.5 0 , 135 0 and 157.5 0 . When all switches are closed, the phase shift is 0 0 . Table 3 shows the phase shift for different input logic pattern. The layout of the 3-bit phase shifter with DC bias circuit is shown in Fig. 16(b).

6-bit phase shifter
To design a 6-bit phase shifter, we employ two symmetrical CRLH TL unit cells, as shown in Figs. 17(a) and 17(b), in cascade to provide the required phase shifts . The state with all switches closed is taken as the zeroth-switch state. In the unit cell of Fig. 17(a), we use four switches to achieve sixteen different switch states and hence sixteen different phase shifts. The two switches on the inner fingers are used to provide the phase shifts of 5.625 0 and 11.25 0 . The two switches on the outer fingers are used to provide the phase shifts of 22.5 0 and 45 0 . Different switch states are used to provide other phase shifts such as 16.875 0 , 28.125 0 , 34.75 0 , 39.375 0 , 50.625 0 , 56.25 0 , 61.875 0 , 67.5 0 , 74.125 0 , 78.75 0 and 84.375 0 . Thus these switch states can be used to provide the phase shifts from 0 0 up to 84.375 0 at a step size of 5.625 0 . In the unit cell of Fig. 17(b), we use two switches in a pair to provide the large phase shifts of 90 0 or 180 0 . The pair of switches on the inner fingers provides a phase shift of 90 0 , while the pair of switches on the outer fingers provides a phase shift of 180 0 . The phase shift of 270 0 is achieved by "opening" all four switches. This phase shifter therefore can provide the phase shifts from 0 0 up to 270 0 at a step size of 90 0 . By cascading these two unit cells, any phase shifts at a multiple number of 5.625 0 can be achieved by using the 6 controlling bits according to (25), i.e. the phase shifter can provide the phase shifts from 0 0 up to 354.375 0 at a step size of 5.625 0 . Table 4 shows the phase shift for different input logic pattern. The layout of the 6-bit phase-shifter with DC bias circuits is shown in Fig. 17(c).  The insertion losses of the three phase shifters are all less than 1.3 dB in the frequency band of 9-10 GHz. Figs. 19(a) and 20(a) show that the return losses of the 2-bit and 3-bit phase shifters are more than 15 dB in the frequency band of 9-10 GHz. For the 6-bit phase shifter, Fig. 21(a) shows the return loss is more than 15 dB for the frequency band from 9.2 to 9.8 GHz. Regarding accuracy, the measurement results in Fig. 19(b) show that the maximum error for the 2-bit phase shifter is about -2 0 at the phase shift of 67.5 0 and frequency of 9.73 GHz. For the 3-bit phase shifter, Fig. 20(b) shows that the maximum errors is +4.5 0 at the phase shift of 157.5 0 and frequency of 9.10 GHz. While for the 6-bit phase shifter, it is -6.3 0 at the phase shift of 180 0 and frequency of 9.66 GHz. The power-handling capability of the phase shifters has been studied using a setup with the block diagram shown in Fig. 22. The solid-state transmitter is basically an AM modulator which takes in the signal from the IF signal source, uses it to modulate the carrier signal at a much higher frequency and amplifies the modulated signal to a high-power level. The amplified signal is fed to the phase shifter under tested via an isolator which prevents any high-power signal from reflecting back and damaging the solid-state transmitter. A 40-dB coupler is used to couple a small portion of the high-power signal from the output of the phase shifter and feed it to the frequency spectrograph for measuring the power capability of the phase shifter. Majority of the high-power signal from the phase shifter is fed to a highpower load for power dissipation.  In this study, the maximum transmitted peak power causing a diode to burn off is taken as the power-handling capability of the phase shifter and the results are shown in Table 5.
Since the PIN diodes used in our design have an instantaneous power-handling capability of 34 dBm, the expected power-handling capabilities for the 2-bit, 3-bit and 6-bit phase shifters are about 50.43 dBm, i.e. 44 times higher as described previously. Table 4.4 shows that the power-handling capabilities of the three phase shifters at 9, 9.5 and 10 GHz are over 51.1, 51.1 and 50.9 dBm, respectively, corresponding to about 51.5, 51.5 and 49.2 times of the power-handling capability of the PIN diodes. www.intechopen.com

Conclusions
In this chapter, the EM metamatreials and the realization of EM metamaterials using the transmission line approach have been briefly described. A CRLH TL unit cell with a symmetrical structure has been proposed for the designs of TTDLs and digital-phase shifters. TTDLs using a single unit cell and four unit cells in cascaded have been designed and studied. Simulation and measurement results have shown that the TTDLs have the return losses of more than 15 dB and insertion losses of less than 1 dB. For the same length of 30 mm, the TTDL constructed using four CRLH TL unit cells in cascade can achieve a much larger TD, about 3.2 times larger, than that using the RH TL. Digital-phase shifters constructed using the CRLH TL unit cells have the advantages of small sizes, arbitrary phase-shift ranges and arbitrary step sizes. Three digital-phase shifters, 2-bit, 3-bit and 6-bit, have been designed and studied. Simulation and experimental results have shown that the digital-phase shifters have the low insertion losses of about 1.3 dB and return losses of larger than 15 dB across the operation bandwidths. Moreover, they have the much higher powerhandling capabilities, about 50 times higher, than that of the PIN diodes used as switches in our designs for the digital-phase shifters.