A) Liquid crystal

LC at its nematic phase is a continuously tunable dielectric. If an external static or low-frequency electric field $\vec{E}_{DC}$ is applied, the LC molecules reorient parallel to the field and thus, the LC varies its effective permittivity. The dominant direction of the LC molecules is determined by their director vector $\vec{n}$ [Reference Goelden, Gaebler, Mueller, Lapanik, Haase and Jakoby15]. Depending on the direction of the director $\vec{n}$ , the permittivity of the LC will differ. As depicted in Fig. 1, in absence of an external static field $\vec{E}_{DC}$ , the molecules are positioned perpendicular to the RF electric field $\vec{E}_{RF}$ , providing a permittivity of ε _r⊥. When a static electric field $\vec{E}_{DC}$ is applied, the molecules rotate until their director $\vec{n}$ is parallel to $\vec{E}_{RF}$ providing a permittivity of ε _r∥ as shown in Fig. 2. In this work, LC TUD-649 with ε _r⊥ = 2.43, ε _r∥ = 3.22 and tanδ ≤ 0.0066 at 19 GHz is used. The variable effective permittivity of the LC can be employed to tune the phase constant β and the radiation angle ψ, as seen in (1). Thus, the dielectric material tunability τ _LC has a direct impact on the beam scanning. The material tunability of the LC used in this work is

(2) $${\tau _{LC}}=\displaystyle{{{\varepsilon _{r{\rm \parallel }}} - {\varepsilon _{r \bot }}} \over {{\varepsilon _{r{\rm \parallel }}}}}=24.5\%.$$

Fig. 1.

Parallel plate capacitor with ε _{r ⊥} liquid crystal dielectric.

Fig. 2.

Parallel plate capacitor with ε _r∥ liquid crystal dielectric.

B) Tunable IDC

The tunability of the LC material can not be completely transferred to a component, i.e. an implementation of a tunable LC-based capacitor shows smaller tunability than the material itself. To determine the limitation of the beam scanning of the presented LWA based on the dielectric material tunability and the main components of its unit cell, an IDC is presented and analyzed. This IDC is the prior design step to the CRLH unit cell design that conforms the LWA. The layout of the IDC and its dimensions are presented in Fig. 3. An approximate characterization of the IDC can be done using the equivalent circuit depicted in Fig. 4 [Reference Bahl16]. For this model, and assuming that the series inductance L and the shunt capacitance C _sh are extracted from the microstrip line theory [Reference Bahl16], the inductance L is

(3) $$L=\displaystyle{{{Z_0}\sqrt {{\varepsilon _{re}}} } \over {{c_0}}}l\comma \; $$

and the shunt capacitance C _sh

(4) $${C_{sh}}=\displaystyle{{\sqrt {{\varepsilon _{re}}} } \over {2{Z_0}{c_0}}}l\comma \; $$

where l represents the length of the IDC, c ₀ is the velocity of light in free space, Z ₀ the characteristic impedance of the corresponding microstrip line, and ε _re its relative effective permittivity. The series capacitance C _se of the IDC can be calculated as [Reference Bahl16]

(5) $${C_{se}}=2{\varepsilon _0}{\varepsilon _{re}}\displaystyle{{K\lpar k\rpar } \over {K^{\prime}\lpar k\rpar }}\lpar N - 1\rpar l\comma \; $$

where N = 6 is the number of fingers and

(6) $$\displaystyle{{K\lpar k\rpar } \over {K^{\prime}\lpar k\rpar }}=\displaystyle{\pi \over {\ln [ {2\lcub {\lpar {1+\root 4 \of {1 - {k^2}} } \rpar /\lpar {1 - \root 4 \of {1 - {k^2}} } \rpar } \rcub } ] }}\comma \; $$

for the specific IDC presented in this work, where

(7) $$k=\mathop {\tan }\nolimits^2 \left({\displaystyle{\pi \over 8}} \right)\comma \; $$

for the values of w and s specified in Fig. 3.

Fig. 3.

Proposed IDC layout (dimensions in μm: W'=240, l = 654, w = 25, and s = 25).

Fig. 4.

Equivalent circuit of an IDC with tunable dielectric.

The calculation of Z ₀ and ε _re is slightly different to that of a traditional microstrip transmission line considering air and dielectric. In this work, the metal strip is placed between two dielectrics which permittivity differs from vacuum, the tunable LC and the borofloat (BF33) glass substrate with ε _r = 4.65, as depicted in Fig. 5. The elements of the equivalent circuit of the presented IDC obtained for the different LC permittivities are shown in Table 1. Taking into consideration the values of C _se for the unbiased and biased states, it is possible to approximate the maximum tunability of the IDC similarly to (2) by

(8) $${\tau _{{C_{se}}}}=\displaystyle{{{C_{se}}{\vert _{Biased}} - {C_{se}}{\vert _{Unbiased}}} \over {{C_{se}}{\vert _{Biased}}}}=15\%.$$

Fig. 5.

(a) BF33 substrate with radiating structure and biasing lines printed on bottom and metal block with cavity. (b) Completely mounted antenna with cavity filled with LC.

Table 1.

Equivalent lumped element values for the approximated IDC model.

Hence, although the LC material can be tuned up to a 24.5%, the maximum tunability of the implemented IDC component is 15%.

C) Fabrication technology

For both the IDC and later for the LWA, the RF metalization is made of 2 µm thick gold, and the biasing lines, made of nickel chromium (NiCr), are printed on a borofloat (BF33) glass substrate with ε _r = 4.65 and tanδ = 0.008. This substrate is chosen because of its combination of transparency, which facilitates alignment, and optimal performance at microwave frequencies. A polyimide layer is spin coated with a height of 10 nm and subsequently mechanically rubbed with a velvet cloth to force the LC molecules to return to their initial position when the static field is switched off [Reference Goelden, Gaebler, Mueller, Lapanik, Haase and Jakoby15]. A brass block is used as a ground plane as shown in Fig. 5. The brass block has a 100 µm deep cavity that is closed when the glass substrate with the RF structure on the bottom side is glued on top of it. The cavity is then filled with the LC.

D) Dispersion characteristics of the IDC

In the CRLH unit cell used for the LWA, the IDC is used as a tunable element. To investigate its dispersion characteristics without additional effects of the other CRLH unit cell elements, the phase shift βl is extracted from the IDC in Fig. 3 with a periodic boundary condition in propagation direction. For this simulated IDC, the extracted phase shift βl for the biased and unbiased states is presented in Fig. 6. It can be seen that a shift of 4 GHz occurs along the whole frequency range.

Fig. 6.

Extracted phase shift for biased and unbiased states.

According to the equivalent circuit in Fig. 4, the series branch of IDC consists of a series resonator formed by L _se and C _se . For frequencies below the $\omega_{se}=1/\sqrt{C_{se} L_{se}}$ , the IDC shows capacitive response yielding a stop band for ω < ω _se . For ω _se < ω, a transmission band is obtained. The cutoff frequency of this transmission band can be tuned between 29 and 32 GHz approximately. At a fixed frequency in the transmission band, a phase tuning βl of up to 0.15π can be achieved.

The measured S-parameters of a single fabricated IDC are shown in Fig. 7. The maximum of the transmission band is tuned between 25.5 and 23.8 GHz if a tuning voltage of 60 V is applied. This yields a measured tunability of 9% for the fabricated varactor. The frequency response of the IDC is shifted by around 6 GHz to lower frequencies compared to the simulations. This is due to the combination of fabrication tolerances, especially concerning the IDC finger width, and the applied equivalent circuit, which does not take all parasitic effects into consideration [Reference Bahl16].

Fig. 7.

Measured scattering parameters of a single IDC unit cell.

E) Electric biasing design

In order to distribute the tuning voltage along a structure consisting of several unit cells, highly resistive NiCr lines are implemented to the structure. These NiCr lines have a thickness of 20 nm, a width of 15 µm, and a length of 21.2 mm which leads to a resistance of 141.3 kΩ. They are meander shaped, as shown in Fig. 11, to obtain the maximum resistance for the given unit cell geometry. For the final LWA prototype, the length of the NiCr lines decreases to 10.98 mm which leads to a resistance of 73.2 kΩ. The effect of these NiCr lines on the antenna beam scanning performance can be neglected [Reference Roig, Maasch, Damm and Jakoby17].

A) Unit cell and equivalent circuit

The phase constant of a CRLH unit cell can be calculated as

(9) $$\beta \approx \pm \sqrt {{L_R}{C_R}} \sqrt {\lpar {{\omega^2} - \omega_{se}^2 } \rpar \lpar {{\omega^2} - \omega_{sh}^2 } \rpar } .$$

Figure 8 depicts the working principle of a LWA. For β < 0 the unit cell works in the left-handed propagation band (LHB), where the radiation angle ψ is negative and, thus, the antenna radiates in the backward quadrant. For β > 0, the unit cell works in the right-handed propagation band (RHB) and the antenna radiates in the forward quadrant. If β = 0 for a single frequency point, then the antenna radiates in the broadside direction since the corresponding group velocity v _g = ∂ω/∂β is not zero.

Fig. 8.

Working principle of a LWA.

Figure 9 shows the cascaded equivalent circuit of the proposed unit cell for the LWA. The series branch, formed by the inductance L _R and capacitance C _L together with the shunt branch, implemented by the inductance L _L and the capacitance C _R , provide the CRLH behavior. To this basic CRLH configuration a further capacitance C _DC is added that works as a blocking capacitor for biasing purposes. When the DC voltage V _DC is applied to tune C _L and C _R , this extra capacitance is needed to avoid a DC short circuit in the shunt branch. To minimize the effect of C _DC at the working frequency range, this capacitance has to be as large as possible, so the presented circuit behaves as a classical CRLH unit cell in the frequency range of interest [Reference Roig, Maasch, Damm, Karabey and Jakoby18]. The highly resistive biasing network that distributes the different voltages needed to tune the LC is represented by the resistances R _bias .

Fig. 9.

Equivalent circuit and electrical biasing scheme.

The layout of the unit cell and its dimensions are presented in Fig. 10. The series branch is represented by the main IDC consisting of six fingers. The shunt branch is realized with the meander line, which corresponds to the left-handed inductance L _L and the DC blocking capacitor C _DC . The distributed shunt capacitance C _R is created between the complete unit cell and the ground plane below it.

Fig. 10.

Proposed unit cell layout (dimensions in μm: l = 725, W = 161, f _L = 643, f _w = 21, gap = 7, l ₁+···+l ₁₀=1900, f′ _L =340, f′ _W =19, gap′ = 10).

Figure 11 shows how the unit cell is cascaded up to 32 times to form the LWA. As for the IDC case, the NiCr meander shaped lines distribute the applied tuning voltage along the antenna to each unit cell.

Fig. 11.

Periodical repetition of the CRLH unit cell and highly resistive NiCr biasing lines.

B) Dispersion characteristics

Scattering parameters are obtained by means of fullwave simulation in Agilent Advanced Design System (ADS) including dielectric and metallic losses as well as radiation effects. The highly resistive lines are also included in the simulations. The antenna is simulated and measured for both tuning states. To obtain the corresponding radiation angles at each state, vectorial network analysis measurements are carried out. Both RF signal and biasing voltage are applied by means of coaxial connectors mounted on the glass substrate of the LWA. A taper with the same thickness and material properties as the antenna RF metalization, and specifically designed for this purpose, delivers both signals to the antenna. From the obtained S-parameters, the phase constant β is calculated and the corresponding radiation angles extracted using (1) for the unbiased and biased states. For the electric biasing, DC voltages between 0 and 60 V are applied.

Figure 12 shows the simulated and measured input reflection at the biased and unbiased states. By varying the biasing voltage the transmission bands of the antenna are shifted by around 1.5 GHz.

Fig. 12.

Simulated and measured input reflection for biased and unbiased states.

In the simulated biased state, where the LHB spans between 23 and 25.5 GHz, the matching degrades the lower the frequency due to the vicinity of a stopband for frequencies below 23 GHz. This effect is also visible in the unbiased state where the LHB covers from 23 to 27 GHz. The input reflection increases in the stopband up to −3 dB for the biased state, between 26 and 27.8 GHz, and up to −5 dB for the unbiased state, from 28 to 29 GHz, respectively.

For the measured input reflection, the stopband between the LHB and the RHB is drastically reduced in the biased case and even disappears for the unbiased case. This is due to the anisotropy of the LC, which cannot be taken into account in the simulations and provokes the series and shunt frequencies ω _se and ω _sh $=1/\sqrt {C_{sh}L_{sh}}$ to be shifted in opposite directions.

Figure 13 shows the measured and simulated unit cell phase shift for biased and unbiased states. In the simulations a slight change in the slope of the phase shift curve. This is caused by the fact that ω _se and ω _sh do not cancel each other completely. The frequency shift between unbiased and biased states is approximately 1.8 GHz for simulation and measurements. This yields a measured tunability of 7%. At 26.7 GHz, the measured phase shift per unit cell can be tuned between βl = − 0.025π for the unbiased state and βl = +0.012π for the biased state. This means that, at 26.7 GHz it is possible to continuously scan the beam from ψ = [− 11.7]° to ψ = [+5.34]°. For lower frequencies, the phase shift curves diverge due to fact that the unit cell size is not infinitely small compared to the wavelength of the propagating signal.

Fig. 13.

Measured and simulated unit cell phase shift for both biased and unbiased states.

C) Radiation pattern

Figure 14 shows the measured radiation pattern of the 32-unit-cells LWA at 26.7 GHz. The radiation patterns are normalized to the maximum power level of the main beam. The far field pattern shows that the antenna radiates with a main beam direction of ψ = − 5° for the unbiased state and ψ = 9° for the biased state. The side lobe level of the presented LWA is better than −13 dB and can be improved by increasing the number of unit cells. The maximum power deviation in the main beam direction is 2 dB when beam scanning is performed.

Fig. 14.

Measured far field patterns normalized to maximum power level of the main beam at 26.7 GHz for the two tuning states.

The half-power beam width and gain of the LWA can also be improved by increasing the number of unit cells. This has no effect on the beam scanning capabilities.