# Tunable RF Filters Based on Liquid Crystal for Space Applications
## 2 Materials and Methods
### Filter Tuning and Temperature Compensation  
The first step is to set a baseline performance by means of the tuning screws. Such a tuning step is also common for conventional untunable filters, where manufacturing tolerances and imperfect predictions of the simulation software must be overcome. For the liquid crystal filter, in addition, both aspects are magnified by the presence of the biasing electrodes. When establishing this baseline performance, the liquid crystal is in a defined state, meaning that the fixed voltage, V\({}_{\text{fix}}\), of 60 V is applied, and the varying voltage, V\({}_{\text{var}}\), for each resonator has a defined value. Once the baseline performance is set, the conventional tuning screws are no longer operated. Measurement results are shown in Figure 7 (measured at room temperature).  
The initial version of the filter is plotted in green color (dotted). At the center frequency of 19,780 MHz, the filter has an insertion loss of 16.1 dB. The insertion loss was improved by optimizing the bias electrodes according to the points mentioned in Section 2.3. The improved filter properties are plotted in blue color (dashed), the insertion loss at center frequency has been improved to 10.3 dB. In both filter versions, all dimensions (including those of the liquid crystal container) are identical, and the liquid crystal mixture is from the same manufacturing batch. All following measurement results have been obtained with the first filter version (shown in green).  
In a next step, the tuning range of the liquid crystal mixture is explored. For this filter, a tuning range of 190 MHz is achieved by changing the orientation of the liquid crystal with the static electrical field created by the biasing electrodes. The insertion loss at filter center frequency is 1.9 dB less for the lower accessible center frequency compared to the upper center frequency. This range is achieved by varying the variable biasing voltage, V\({}_{\text{var}}\), from \(-60\) V to \(+60\) V (Section 2.3). When the filter is tuned in this way, always wait for at least 90 minutes after the biasing voltage, V\({}_{\text{var}}\), is set to a different value until the new frequency is evaluated. The same waiting time was also applied for all measurements shown later at varying temperature (within the applicable temperature range of -10 \({}^{\circ}\)C to \(+65\)\({}^{\circ}\)C). For tuning at temperatures towards the lower end of the temperature range, this waiting time is needed, while for temperatures towards the higher temperature end, a shorter waiting time would have been  
Figure 7: Measured insertion loss [S21] for the filter shown in Figure 4 (frequency axis is relative to center frequency of 19,780 MHz).  
sufficient. However, tuning time is not an issue in the application envisaged, and no effort was made to reduce this waiting time.  
In yet another step, the filter is measured with fixed biasing voltages applied, but varying temperature. There is a drift of filter center frequency over temperature due to thermal expansion of the materials involved, and due to a change of dielectric constant (of the liquid crystal) over temperature. Within a temperature range of \(-10\)\({}^{\circ}\)C to \(+65\)\({}^{\circ}\)C, a drift of center frequency of approximately 40 MHz is observed (lower frequency at higher temperature). On the other hand, in the application on a satellite, a filter must operate within a certain temperature range (\(-10\)\({}^{\circ}\)C to \(+65\)\({}^{\circ}\)C is a typical range) and must exhibit the same operating frequency at any temperature.