5.3 Investigated Unit Cells and Measurement Results at 35 GHz
5.3.1 Single Patch
88 5. TunableElementary Cells for Reflectarrays usingLiquidCrystal
plane, βg is the guided phase constant in the waveguide simulator and=30 mm is the length of the waveguide simulator.
For the guided wavelength holds [Wei99]:
βg = 2π λg = 2π
λ0
1−
λ0
λc
2
) = 2π
1 λ0
2
− 1
λc
2
=2π
1 λ0
2
− 1
2a 2
(5.6) with
λg = λ0 1− λλ0c2
(5.7)
the guided wavelength.
5.3 Investigated Unit Cells and Measurement Results at 35
mix-5.3. InvestigatedUnitCells andMeasurementResults at35 GHz 89
(a) Schematic of the unit cell with single
patch. (b) Realisation of the unit cell with
simple patch - front and backside view.
Figure 5.16: Unit cell with simple patch
ture specially developed by Merck, known as MDA-03-2844 (see also chapter 4). The control voltage was swept during thefirst measurements between 0 and 40 V, but it was soon observed that a complete resonance frequency shift is achieved at 20 V.
The measurement results are organized as follows: the phase and magnitude of the re-flection coefficient versus frequency are shown for each measurement for all the applied bias voltages. For clarity reasons, and in order to suggest the displacement of the curves as the bias voltage is increased, only a few curves are highlighted and labeled with the respective voltages. Next, a vertical cut is made at the frequency where the maximal phase shift is achieved – designated as the operation frequency of the unit cell – and the phase and magnitude dependence on the bias voltage are recorded in a single plot.
Fig. 5.17 shows the phase and magnitude of the reflection coefficient for the cell filled with K15. There is a very pronounced resonance notch in the magnitude characteristic, varying from about -14 dB for 0 V to -10 dB for 20 V. The variation can be explained with the variation of tanδfrom tanδ⊥ =0.02 to tanδ =0.0048.
The resonance frequency can be tuned between about 32.5 to 34 GHz. The maximal phase shift is achieved at 33 GHz, which represents an error of about 6% with respect to the desired operating frequency of 35 GHz. This can be regarded as a reasonable deviation, considering some factors that caused it:
• The cell has been designed for permittivities of εr,⊥ = 2.3 and εr, = 2.6, there are however uncertainties of the measured values of εr,K15 as high as 4%, as reported in [Mue07].
• There are inevitable etching errors, alignment errors of the cell in the waveguide simu-lator, errors regarding the cavity height, since the used spacer was a soft substrate prone to compression.
90 5. TunableElementary Cells for Reflectarrays usingLiquidCrystal
(a) Phase of the reflection coefficient (b) Magnitude of the reflection coefficient
Figure 5.17: Measured results of the unit cell pair with single patchesfilled with K15
Figure 5.18: Phase and magnitude of the complex reflection coefficient S11 versus the control voltage at 33 GHz - unit cellfilled with K15.
Fig. 5.18 reveals that only about 190◦tunable phase range can be achieved with this unit cell, which is far too little, compared with the at least 300◦ needed.
The measured results of the unit cell with single microstrip patch filled with BL006 are shown in Fig. 5.19. The resonance notch in the magnitude plot can now be tuned between 31.5 GHz and 34 GHz, which is 1 GHz more than with the K15 unit cell, or an improve-ment of 60% in relative terms. The peak return loss is also slightly reduced, it varies between -13 dB and -8 dB compared to -14 dB to -10 dB. The performance improvement,
5.3. InvestigatedUnitCells andMeasurementResults at35 GHz 91
especially the wider tuning of the resonance, is expected because of the better tunability of BL006 compared to K15.
As a consequence, the tunable phase range at 33 GHz increases to about 250◦, as can be observed in Fig. 5.20. At this frequency, the maximal return loss is slightly under -10 dB.
The actual operating frequency is also deviating from the design operating frequency for the same reasons highlighted previously.
As expected, the best result is obtained byfilling the unit cell with the highly anisotropic
(a) Phase of the reflection coefficient (b) Magnitude of the reflection coefficient
Figure 5.19: Measured results of the unit cell pair with single patchesfilled with BL006
Figure 5.20: Phase and magnitude of the complex reflection coefficient S11 versus the control voltage at 33 GHz - unit cellfilled with BL006.
92 5. TunableElementary Cells for Reflectarrays usingLiquidCrystal
mixture MDA-03-2844. Fig. 5.21(b) shows that the resonant notch of the magnitude can be tuned between 33 and 37 GHz, i.e. in a 4 GHz-span compared to 2.5 GHz with BL006 and 1.5 GHz with K15. The return loss remains roughly constant at around -8 dB. The fact that the return loss does not diminish with the increase of the bias voltage, as it was the case with the previous two unit cells filled with K15 and BL006, can be explained with the help of the lumped element equivalent circuit in section 2.2. As the value of
(a) Phase of the reflection coefficient (b) Magnitude of the reflection coefficient
Figure 5.21: Measured results of the unit cell pair with single patches filled with the special mixture MDA-03-2844.
Figure 5.22: Phase and magnitude of the complex reflection coefficient S11 versus the control voltage at 35 GHz - unit cellfilled with MDA-03-2844.
5.3. InvestigatedUnitCells andMeasurementResults at35 GHz 93
the relative permittivity is changed from εr,⊥ = 2.4 to εr, = 3.4, the capacitance C in the equivalent circuit (capacitance between patch and ground) is increased. This makes the value of the impedance of the unit cell Zcell approach the value of the free space impedance η0, which results into a steeper phase curve and higher return loss. This effect is counterbalanced by the simultaneous reduction of the loss factor of the liquid crystal tanδas the voltage increases, from tanδr,⊥ =0.02 to tanδr, =0.007.
As shown in Fig 5.22, at 35 GHz the phase can be now adjusted in a 280◦ range, which is close to the aim of 300◦, the desired value that would allow realization of a large reflectarray without significant loss of performance. The reflection losses are between -1 dB and -8 dB. The peak losses are still very high. However, on a large reflectarray, the losses will be distributed between -1 and -8 dB in accordance with the phase distribution of the elements. Thus, the average loss of power will be considerably lower than the peak losses of a unit cell.
The properties of the measured unit cells with single patches are synthesized in Table 5.1.
Atuning bandwidthis here defined as the frequency interval swept by the resonant mag-nitude notch when the control voltage is varied:
BWtun =|fres,U=0− fres,U=max| . (5.8)
It should not be confused with the operating bandwidth. A tunable unit cell can usually be operated in a much narrower band than the tuning bandwidth. It is however a good measure for the tunability of the unit cell. A relative tuning bandwidth can be readily calculated with:
BWtun,rel = |fres,U=0−fres,U=max|
f0 (5.9)
with f0 the operating frequency.
Table 5.1: Overview: measurements of unit cells with single patches.
Liquid Crystal Frequency Phase range Losses BWtun Rel. BWtun
K15 33 GHz 190◦ -12 dB 1.5 GHz 4.2%
BL006 33 GHz 250◦ -10 dB 2.5 GHz 7.5%
MDA-03-2844 35 GHz 280◦ -8 dB 4 GHz 11.4%
94 5. TunableElementary Cells for Reflectarrays usingLiquidCrystal