Many high frequency devices operate at high power, and material losses can lead to significant rise in temperature if left unchecked. In such devices, it is important to know the temperature distribution to determine the performance impact of changes in dimensions and material properties, to ensure that the permitted maximum operating temperature and stresses of the material are not exceeded, and if required, to enable a thermal management system to be designed. Clearly, the simulation of these effects requires the ability to perform electromagnetic, thermal and mechanical analyses on the same physical model. For some time, Opera-3d has been able to perform such Multiphysics simulations, a feature of the tool being that all relevant results are passed from one stage of the analysis to subsequent stages without user intervention. This includes the deformation resulting from the thermal and stress analyses – allowing the effect of dimensional changes to be evaluated immediately. Recent developments have added features that are aimed specifically at accounting for effects that are relevant to high frequency applications.
RF devices often contain various materials of low and high conductivity. The former might be, for example, intentionally lossy dielectric intended to act as a load; the latter includes metallic structures whose loss is unavoidable. The evaluation of thermal loss requires knowledge of the distribution of current within the material. The current decays at a characteristic rate with depth, dependent on the frequency and material properties – leading to the concept of skin depth. Since Opera-3d analyses use finite elements, the normal requirement is that the mesh element size perpendicular to the surface must be small enough to resolve the skin depth.
For materials of low conductivity, less than a few 10’s S/m, the skin depth is of the order of millimetres, even at GHz frequencies. Such distances are typically commensurate with the physical dimensions of RF components, and the current distribution may be captured relatively easily with a practicable mesh size. Even when the physical dimensions are considerably larger than the skin depth, Opera-3d includes features, such as mesh layering and hexahedral/prism elements, that enable these structures to be meshed with high aspect ratio volume elements. However, as the conductivity increases towards that of typical metals, the skin depth becomes so small that these tools are unable to provide adequate resolution of the current distribution, and a different approach must be used.
In Opera-3d, the approach taken is to represent the material properties by a surface impedance boundary condition (SIBC). In this, the surface current density is calculated, and the loss power density then evaluated from the known decay of the current with depth; where the skin depth is much smaller than the physical dimensions, this is an excellent engineering approximation.
The example shown below illustrates Opera’s ability to evaluate the dissipation in devices containing both high and low conductivity materials, and to couple high frequency EM results to thermal and stress analyses. The example chosen is a simple microstrip splitter, similar to many commonly used in RF signal distribution or combination networks.
The splitter is shown in figure 1, below. The track is on an epoxy substrate with a dielectric constant of 4; the input and output tracks and the coax ports are 50. The splitter is mounted in a closed aluminium box, the lid of which has been hidden in the figure. For this example, the base of the box is in thermal contact with a heat sink at ambient temperature; the base is also rigidly fixed mechanically.
The simulation was performed using Opera Multiphysics, which runs electromagnetic, thermal and stress analyses sequentially on the same physical model, automatically transferring relevant results from one stage to the next. Although all materials in this model are treated as isotropic, this is not a limitation – Opera Multiphysics allows anisotropic material properties to be modelled in all stages of the analysis.
As noted above, the model includes materials of both high and low electrical conductivity, the former using the SIBC representation, while the latter are meshed as normal for the EM analysis. In operation, we expect power to be dissipated in the track and substrate, and the temperature to rise. The temperatures that result from the thermal analysis stage of the simulation can be seen in the figure 2.
The temperature rise leads to thermally induced stresses and strains, resulting in deformation of the geometry, as shown in figure 3. As well as deformation, the components of stress and strain are also available.
The deformed finite element mesh from the stress analysis is available for use in subsequent analyses to evaluate its effect of the deformation on RF performance.