Aperture coupled line

5.3. InvestigatedUnitCells andMeasurementResults at35 GHz 99

been devoted to avoiding the unwanted phase distortions that apear at low voltages.

The measured results are shown in Fig. 5.30. Phase distortions are no longer present, and the maximal tunable phase range of 280^◦ is achieved at 31.5 GHz. From Fig. 5.31 can be seen that the losses at 31.5 GHz are between -1 and -7 dB depending on the bias voltage.

To give an overview of the three presented unit cells with stacked patches, their proper-ties have been summarized in Table 5.2.

Table 5.2: Unit cells with stacked patches

Struct.nr. Optimizedfor Upper/Lower Operation Phasefrequency range lossesPeak BWtun BW_tun,rel

1. phase range 2.284 mm/ 33 GHz 300^◦ -8 dB 1.5 GHz 4.5%

2.294 mm

2. bandwidth 2.2 mm/ 33 GHz 275^◦ -10 dB 3.3 GHz 10%

2.3 mm

3. compromise 1.38 mm/ 32 GHz 280^◦ -7 dB 3 GHz 9.3%

2.2 mm

100 5. TunableElementary Cells for Reflectarrays usingLiquidCrystal

The plots presented in Fig. 5.33 show the shift of the phase and magnitude versus the frequency when the control voltage is swept between 0 and 20 V. It can be observed that the resonant frequency is slightly shifted, to 36 GHz. At this frequency, the phase is adjustable over only 240^◦. More concerning, however, is the poor performance in terms of reflection loss, which is between -5 and -16 dB (see Fig. 5.34). The fact that there is high return loss even outside the resonance suggests that a large part of the power is being radiated. The assumption is at hand that some of the power is radiated by the open ended line, and part of it is lost through the bias line, although simulations were used to minimize the influence of the bias line.

Phase Distortions

It has been mentioned that in some of the tuning states, corresponding mostly to low applied voltages, the phase characteristics show distortions from the expected S-shaped characteristic (see Fig. 5.24, Fig. 5.26, Fig. 5.28). This induced the misleading assumption that the low voltage values are the cause, due to not being able to overcome inherent molecular torque [Hu06].

However, the lumped element equivalent circuit presented in section 2.2 helps to un-derstand the mechanism underlying the phase distortions. Indeed, most of the phase distortions that occurred in the measurements were observed at the low-voltage end of the tuning interval. Nevertheless, the real cause for the distortions is the higher loss angle usually associated with this low-voltage states (see Tab. 4.1).

In Fig. 5.35 phase and magnitude plots are shown for three tuning states of a unit cell filled with the novel mixture MDA-03-2844. To better understand the phenomenon, let

(a) Schematic of the unit cell with patch

aperture coupled to a line. (b) Realisation of the unit cell with patch aperture coupled to a line -front and backside view.

Figure 5.32: Unit cell with microstrip patch aperture coupled to a line.

5.3. InvestigatedUnitCells andMeasurementResults at35 GHz 101

(a) Phase of the reflection coefficient for different

tuning voltages. (b) Magnitude of the reflection coefficient for dif-ferent tuning voltages.

Figure 5.33: Unit cell with aperture coupled line filled with MDA-03-2844: measured results.

Figure 5.34: Phase and magnitude of the complex reflection coefficient S₁₁ versus the control voltage at 36 GHz - unit cellfilled with MDA-03-2844.

us suppose the unit cell is first in the state 1, when no phase distortions are present.

The value of the relative permittivity εLC,1 for this state is achieved with the control voltage V₁. If the voltage is now lowered to V₂, the relative permittivity changes to εLC,2, shifting the resonance to higher frequencies, but at the same time the loss angle increases tanδ₁ > _tanδ2. This increase in the loss angle is modeled in the proposed lumped element equivalent circuit by a decrease in the value of R_C, according to the

102 5. TunableElementary Cells for Reflectarrays usingLiquidCrystal

Figure 5.35: Phase Distortions

Figure 5.36: Smith Chart illustrating the shift in the S₁₁ curve as the dielectric losses increase (R_C decreases).

5.3. InvestigatedUnitCells andMeasurementResults at35 GHz 103

relation 2.37.

The increase in loss angle and the shift in the capacitance C cause a shifting of the S₁₁ curve in the Smith chart, as shown in Fig. 5.36. The unit cell is now almost perfectly matched at the resonance frequency, which has shifted from 34.8 GHz to 36.3 GHz. If loss angle increases even further, the S₁₁ curve in the Smith chart, which describes a circular shape, will shrink even further leaving the Smith chart origin (the (1,0) point) outside. Thus, in state 3, the _S11 phasor will not rotate the whole 360^◦. Instead, the phase curve exhibits two inflexion points, corresponding to the points where the phasor is tangent to the S₁₁ curve in the Smith chart.

A similar effect takes place when the metallic losses are considered instead of the di-electric losses. By reducing the metallic conductivity, the S₁₁ curve in the Smith chart is shifted toward the (1,0) point. It is thus proximate to assume that the phase distortions that were observed in the previous section are due to the cumulative effects of dielectric and metallic losses.

Figure 5.37: Smith Chart illustrating the shift in the S₁₁ curve as the wave impedanceZ increases.

104 5. TunableElementary Cells for Reflectarrays usingLiquidCrystal

Besides the losses (dielectric and metallic), another parameter can slightly influence the phase characteristic and can contribute to the occurrence of phase distortions. Consid-ering again the lumped element equivalent circuit, the impedance of the line section that stands for the wave propagation before incidence on the unit cell can change. The wave impedance in the waveguide Z_wg, for a TE mode, is different from the free space impedance η₀ =₃₇₇Ω, namely according to the formula [Wei99]:

Zwg =_η0 ¹ 1− ^λ_λ⁰_c²

(5.10)

withλ0the free space wavelength andλc =₂athe cut-off wavelength for the considered mode, in this caseTE₁₀. Moreover, as the voltage is lowered, the resonance shifts toward higher frequencies, to which correspond lower values for λ0 and accordingly higher values for Zwg. Fig. 5.37 shows the influence of a change in the wave impedance on the characteristic in the Smith chart. Combined with an increase in dielectric losses, an increase of the wave impedance favors the appearance of phase distortions, since the characteristic moves closer to the (1,0) point.

5.4 Investigated Unit Cells and Measurement Results at 77