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## A waveguide diplexer is designed using the interface between FEKO and FEST3D. A part of the design is modelled in FEKO and the obtained generalised scattering matrix is used as a component in the FEST3D model. A multipactor analysis is performed using SPARK3D.

### The Interface Between FEKO and FEST3D

FEST3D is a software tool for the analysis of passive waveguide components. It is based on an integral equation technique that is efficiently solved by the Method of Moments. The Boundary Integral-Resonant Mode Expansion (BI-RME) method is used to extract the modal charts of complex waveguides with arbitrary cross-sections. FEST3D uses a network approach and the main building blocks are analysed separately before solving the final linear system of equations. These methods provide an efficient solution for waveguide structures, requiring reduced computational resources (in terms of CPU time and memory) compared to full wave solvers.

The two-way interface between FEKO and FEST3D allows mode data and scattering matrices to be exchanged between these software packages. A waveguide structure can easily be designed and quickly analysed using FEST3D. The structure’s performance can be verified in FEKO, or the mode data can be used for further analysis of more complex, or radiating, structures in FEKO.

SPARK3D is a unique simulation tool capable to determine the breakdown power level in a wide variety of passive devices. Mesh information and fields calculated by FEKO can be imported into SPARK3D to perform further analysis including multipactor and gas discharge (corona) breakdown.

### Waveguide Diplexer Design Example

The classical way of diplexer design is to start with two filters and a waveguide junction which are then combined and optimised for performance.

In the following example FEKO is used to analyse a WR-90 rectangular waveguide T-junction which contains a metallic and a dielectric post [1, Fig. 7]. The calculated generalised scattering matrix (GSM) of the T-junction is written to disk. The GSM is then imported into FEST3D where it is combined with two filters to create a diplexer. The diplexer is optimised and the performance of the final design is verified with FEKO.

The first step in the design is to obtain the GSM of the waveguide junction. FEKO is used for the analysis of the waveguide T-junction with its dielectric and metallic posts. Figure 1 shows the FEKO model and simulation results obtained with the Method of Moments (MoM) and the Finite Element Method (FEM). The results are compared to published measurements [1].

**Figure 1: T-junction [1, Fig. 7] analysed in FEKO with the MoM and the FEM.**

In FEST3D two filters are designed using the band-pass filter synthesis tool. The GSM matrix that was written to disk by FEKO, is imported into FEST3D and connected to the two filters to create a diplexer. The FEST3D schematic of the diplexer is shown in Figure 2.

The diplexer structure is optimised in FEST3D to reduce passband reflections below -20 dB. Figure 3a shows the scattering parameters of the optimised diplexer from Figure 2, plotted in FEST3D. The diplexer is then modelled in FEKO to verify its performance (Figure 3b). Figure 3c compares the S_{11} response of the optimised diplexer calculated by FEST3D (using the FEKO GSM as shown in Figure 2) to the response obtained in FEKO with a FEM simulation. The FEKO model of the final diplexer is shown in Figure 4.

**Figure 3: Optimised diplexer response.**

### Multipactor Analysis

The simulated fields at 9.5 GHz for the T-junction and diplexer are exported from FEKO in order to perform the multipactor analysis with SPARK3D. The results can be seen in Figure 5. Breakdown for the T-junction only occurs at 204 kW, but for the diplexer breakdown is more frequent.

Figure 5: SPARK3D multipactor results for the T-junction (top) and diplexer (bottom).

Once the analysis has been run the initial and end locations of electrons can be visualized in Paraview. Figure 6 shows the diplexer, electron locations and the E-field at 9.5 GHz.

### References

[1] Quesada Pereira, F.D. Perez Soler, F. Gimeno Martinez, B. Boria Esbert, V. Canete Rebenaque, D. Gomez Tornero, J.L. Alvarez Melcon, A., “Efficient Analysis of Inductive Multiport Waveguide Circuits using a Surface Integral Equation Formulation”, Microwave Conference, 2006. 36th European, pp.232-235, 10-15 Sept. 2006

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