# Tunable RF Filters Based on Liquid Crystal for Space Applications
## 2 Materials and Methods
### Configuration of Biasing Circuit  
The biasing circuit must supply a static electrical field, which can be oriented in the relevant directions. In one extreme, it must be in parallel to the electrical RF field, with reference to Figures 1 and 2, this is in the z-axis. In the other extreme, it must be at 90\({}^{\circ}\) to the first direction, which is (with reference to Figure 2) in the x-y-plane. The biasing circuit for a resonator consists of four electrodes, which run in parallel to the container and which are arranged around the container, as shown in Figure 5.  
A similar four-electrode configuration has been reported in Reference [8]. One electrode is set to a fixed voltage, \(\mathrm{V_{fix}}\) (with reference to the resonator housing), and the opposite electrode is set to the same value but with opposite polarity: \(-\mathrm{V_{fix}}\) (upper left and lower right in Figure 5). For the remaining pair of opposite electrodes, one electrode is set to a variable voltage, \(\mathrm{V_{var}}\), and the opposite electrode to the same voltage but with opposite polarity: \(-\mathrm{V_{var}}\). When the variable voltage, \(\mathrm{V_{var}}\), is varied between \(-\mathrm{V_{fix}}\) and \(+\mathrm{V_{fix}}\), then the resulting vector of the static electrical field in the center of the liquid crystal container can be adjusted within the full range of being in parallel to the electrical RF field until being perpendicular to the electrical RF field (corresponding to the x and z direction in Figure 4). For the filter discussed in this article, the voltage \(\mathrm{V_{fix}}\) is chosen to be 60 V. An increase/decrease of the voltage results in an increase/decrease of the switching speed, but with the same center frequency being reached. However, a decrease in this voltage of more than about 5 \(\mathrm{V_{fix}}\) will additionally result in a smaller frequency range that can be reached by the resonator. With \(\mathrm{V_{fix}}\) being set, the variable voltage, \(\mathrm{V_{var}}\), can be regarded as a representative for the center frequency of the resonator. Some further points in the design of the biasing circuit deserve attention:  
1. The electrodes necessarily consist of conducting material, and they are exposed to the RF electromagnetic field. The field induces RF current on the electrodes, which is subject to Ohmic losses, which in turn increases the resonator loss. To limit this undesired effect, the electrodes must be designed as small as possible, having a surface with low Ohmic losses (low surface roughness, plated with a good conductor such as silver, thickness exceeding skin depth). The RF losses can be further lowered by using a well-chosen glue in the right amount for the mounting of the electrodes. Figure 5: Arrangement of biasing electrodes (four times black dot) around the liquid crystal container (blue: liquid crystal, yellow: container wall). With respect to Figure 2, this view is in the x-z-plane. The electrodes will exhibit RF eigenmodes for themselves. In order not to disturb the resonator or filter function, these eigenmodes must be shifted sufficiently away from the filter passband. In the current filter design, the eigenmodes are more than 5 GHz away from the filter passband. 3. The electrodes, and especially where they penetrate into the RF cavity of the resonator, are a potential source of EMC leakage. RF energy fed into the filter will to some amount leak to the outside via the biasing electrodes--this amount must be minimized. On the other hand, the environment on a satellite can comprise stray electromagnetic fields within a broad frequency range from 0 to 30 GHz. The amount of those signals that penetrate into the filter via the electrodes and couple into the RF path must also be minimized. The DC harness that delivers the biasing voltage to the electrodes can act as an antenna and enhance these undesired effects. In order to meet the requirement, the following measures have been taken: 1.