Thermal Analysis of a Two-Cavity Dual-Mode Bandpass Filter

The CST EM STUDIO™ (CST EMS) Thermal Solver has been applied to the simulation of the temperature distribution in a dual-mode filter. The current density distribution inside lossy conductive metals is precomputed by CST MICROWAVE STUDIO® (CST MWS) and acts as the thermal source.

The dual-mode filter used in this application consists of two cavities separated by a thin wall containing a coupling slot. Tuning stubs enable the adjustment of the two orthogonal modes and the 45-deg slanted stubs allow for a proper tuning of the coupling bandwidth. The stubs have radiators mounted outside of the cavity. The metallic walls have a finite thickness with a finite electrical conductivity assigned which accounts for the surface currents.

Prior to the thermal analysis the filter needs to be tuned for proper band pass behaviour. The tuning process was performed by varying the lengths of the tuning stubs: the group-delay response method was used to tune each stub individually. The final S-parameter response is shown in Fig.2 for a relative filter bandwidth of 1%. At the lower skirt of the reflection coefficient (at approximately 0.5% off the center frequency) a current density monitor was defined.

The selection of the frequency for a harmonic current denisty monitor is rather critical since the distribution of the currents varies greatly with frequency. At the lower side of the passband the current density monitor was assigned at a frequency of 99.5% off the center frequency. The current density distribution for this frequency is shown in Fig. 3. Note that the magnitude of the current density is scaled to 1 W peak and/or 0.5 W rms. Since the transmitted RF-power in reality is 5kW, a scaling factor of 1e4 has to be applied for the proper magnitude of the thermal heat source. 

The next stage entails the definition of the thermal properties of the model. The HF simulation results are used for the thermal source . Thermal conductivities were assigned to the housing, cooling elements and tuning stubs (brass, copper, aluminum). For this study, the slot wall is assumed to be made of Invar with a rather low thermal conductivty of 13 W/(Km), which is about 30 times less than copper. Within CST EMS, thermal surface properties can be assigned to surfaces of thermal conductive materials. A thermal surface property definition describes the radiation and convection losses from a surface. At the outer walls of the housing a heat transfer coefficient of 5 W/(m^2.K) was assigned to take convection into account. In this filter example the thin separating wall is of low thermal conductance, thus most of the heat needs to be transported via air convection. The air near the coupling slots heats up and begins to rise forming a convection loop. To take this convection effect approximatively into account, another transfer coefficient of 15 W/(m^2K) has been assigned to the thin separation wall. The model is completely embedded into air with a low thermal conductivity. For the thermal boundaries, a fiixed thermal temperature of 273 K was assigned to the bottom face, the top face was assigned to a constant floating temperature and the four vertical boundaries adiabatic  (no heat transfer across).

In Figs. 4,5 and 6 the contour-plots of the temperature are depicted.   

"Heat flow density" is a further post processing quantity of the thermal solver within CST EMS. Figs. 7 and 8 show contour and arrows plot at a user given cutplane respectively.

Convection mechanisms are always connected to medium transportation. To take these effects properly into account, a computational Fluid Dynamics (CFD) program is required. As mentioned above, due to the heat generated at the separation wall, the air starts to circle around forming a convection loop. Fig. 9 shows the air-speed distribution in the dual mode filter [1]. (with courtesy and permission  of the "Spinner GmbH, Feldkirchen-Westerham, Germany")

It has been demonstrated that in a co-simulation of CST MWS and CST EMS the thermal analysis of a filter can be performed. The temperature of, for example, the hot spot in the vicinity of the separating wall computed by CST EMS (approx. 420K) is in a good agreement with the CFD-code "Fluent" showing 405 K. 

References: Dr.Spaeth, Dr. Lorenz : "CFD- Simulations at Spinner", Spinner Spotlight 4/2005, Page 4-6