# Tunable RF Filters Based on Liquid Crystal for Space Applications
## 2 Materials and Methods
### Thermomechanics of the Liquid Crystal Container  
The liquid crystal container has two major purposes. First, it must position the liquid crystal in the right place of the resonator, in which the RF electromagnetic field is maximum. Second, it must ensure that the liquid crystal remains in that place at all times and especially that it never penetrates through the container walls to the outside. The latter task presents a considerable challenge, because \"at all times\" includes an applicable temperature range which is typically \(-\)35 \({}^{\circ}\)C/+85 \({}^{\circ}\)C for a satellite. The liquid crystal mixture is incompressible and shows significant volume expansion over temperature, therefore a container consisting of rigid walls and being completely filled with liquid crystal would unavoidably burst even in a much smaller temperature range.  
To overcome a potential burst of the liquid crystal container, a solution is presented in Reference [6]. It consists of a flexible metallic bellow, which is mounted to the liquid crystal container on the container end outside of the RF cavity. Although such a solution has been shown to be feasible, significant hurdles must be overcome:  
1. The variation of the volume of the liquid crystal over temperature is compensated by movement of the bellow. The bellow acts as a spring, with a force increasing with movement of the bellow. This force corresponds to a pressure increase in the liquid crystal volume. Pressures encountered in this application are significant (exceeding 5 bar). Also, thermal stress in the associated container and bellow materials build up.
2. The container material is rexolite, while the bellow is metallic. Hence, the connection between rexolite and bellow is not between similar partners, and therefore it is challenging by nature due to the difference in thermal expansion presenting stress to the connecting mechanism.  
Especially for the application on satellites, considerable effort is needed to proof integrity of this design over its lifetime, and to verify running production. Therefore, an improved solution was developed by introducing a gas bubble into the container making the bellow obsolete. It must be ensured that this gas bubble always remains in the part of the container outside the RF cavity. Since gas is much more compressible than a bellow, much lower pressure is building up over temperature. The container consists of similar materials only, facilitating the connection between the container parts. A simulation of the internal container pressure over temperature was performed (Figure 4), and the pressure increase building up due to temperature is now reduced to a few 100 mbar.  
Figure 4: Simulation of internal container pressure over temperature.  
In this simulation, the internal container pressure change over temperature is calculated analytically for a container with a degree of filling of 50% (remaining volume being filled with the air bubble). For the filling process, typical laboratory conditions are considered with an environmental temperature of 23 \({}^{\circ}\)C and 50% relative humidity. The liquid crystal is assumed as incompressible fluid and the stiffness of the container walls as ideal in the pressure range investigated. The stored air is modeled as mixture of ideal gas, taking into account the saturation of water vapor.