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# Thermal analysis of Dielectric loaded Waveguide filter

Used Tools:

## Introduction

Rectangular waveguide H-plane filter is one of the most popular HF filter topologies used for communication devices. To improve its capabilities and signal transmission performance, many efforts are being devoted to develop and improve its structural topologies in order to: reduce mass and volume, increase the out-of-band rejection, boost their thermal stability for high power levels, decrease the risk of RF breakdown, etc.

The analyzed H-plane waveguide filter topology is proposed by the Ref [1]. It is made of rectangular coupled waveguide cavities, separated by inductive iris and loaded with cylindrical dielectric posts. These posts are placed in the middle of each cavity like shown in the figure 1. The input and output waveguide ports of the filter, including the resonant cavities are standard WR75 (a=19.05mm, b=9.525mm).

An FEM analysis using HFWorks allows to simulate the electromagnetic and thermal behavior of the studied filter topology for the frequency range of [10.5 GHz-11.5 GHz]. This study is attempting to quantify the effects of dielectric properties of the added loads on the power loss level and the thermal stability of the device.

Figure 1 - a) -3D design and b)- cross section view of the studied filter

## Problem description

An S-Parameters study of HFWorks coupled to the thermal solver will be used to predict the electric and magnetic field intensities and loss distribution across the studied filter for the range frequency of [10.5 GHz-11.5 GHz] .The detailed dimensions and the used material properties are demonstrated by Table 1 and Table 2 respectively.

Table 1 - Dimensions of the studied model
 Part Dimension (mm) W1, W2, W3 12.27 6.4 5.62 l1, l2 10.58 10.47 a, b 19.05 9.525 d1, d2 6.6 7.04 t 2

Table 2 - Material properties
 Material Relative permittivity Dielectric loss tangent Thermal conductivity (W/m. K) Duroid RT6010 10.2 0.0023 0.086 Cooper 1 0 400 Air 1 0 0.024

## Electromagnetic boundary conditions

Wave port: The wave port boundary is applied to the both Entry/Exit WG faces and fed with a 1Watt microwave power.

### Mesh

High accuracy solver is used to get more accurate results fora minimum mesh details. The whole meshed model is showed by the next figure.

Figure 2 - The meshed model

### Results

The S-parameters study simulation of HFWorks gives the next results for the working frequency set to 11GHz: the first plot illustrates the electric field distribution within the studied filter for an excitation power set to 1 Watt:

(a)

(b)
Figure 3 - a)-Electric and b)-Magnetic field density at 11GHz.

The return and insertion losses results are plotted versus frequency sweep in the next figure 4. The measured bandwidth for  is 36% and the return loss is better than 18 dB across the whole bandwidth. HFWorks simulation captures perfectly the rejected band.

Figure 4 - Return and insertion loss results

The loss analysis inside HFWorks involves both conductor and dielectric losses: the next figure is showing the volume and surface loss distributions for an excitation power of 1Watt. The dielectric losses are significant inside the loads compared to the ones across the conductor.

Figure 5 - a)- Volume and b)-surface loss densities

The presence of dielectric posts increases the volume losses inside the studied design, those losses will be converted into heat during the filter functioning. HFWorks coupled to thermal allows to predict its temperature profile for the working frequency of 11GHz. A convection boundary condition is applied to the outer housing at ambient temperature with a convection coefficient set to 10 W/m²K. For low excitation power, steady state temperature achieves a maximum value around 57°C inside the dielectric posts.

Figure 6 -  a)-b)-Temperature distribution results

## Conclusion

In order to improve the performance of metallic enclosure filters, the new topologies being developed are mostly differentiated by the means of coupling: apertures, irises and dielectric posts. The latter coupling tool was investigated by Ref[1] and simulated using HFWorks for the H-plane cavity filter.  Many references confirmed the advantages of these topologies in enhancing the thermal stability for high applications power, in increasing the out of band rejection and in improving the field distribution. Improving field distribution can be explained by lower-voltage magnification factor (VMF). A low VMF allows to get the peaks of electric fields concentrated inside the dielectric loads and reduced outside the dielectric posts. On the other hand, in the case of the all-metallic filter, low VMF can not be obtained. However, the use of high dielectric material properties is directly linked with higher loss level inside dielectric loading, which needs to be carefully chosen.

#### References

[1]. Aghayari, Hassan, et al. "Realization of dielectric loaded waveguide filter with substrate integrated waveguide technique based on incorporation of two substrates with different relative permittivity." AEU-International Journal of Electronics and Communications 86 (2018): 17-24.