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Thermal analysis of 100 GHz waveguide Band-pass filter

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Introduction

Rectangular waveguide structures for bandpass filters with inductive irises are the most suitable and popular solutions for the THz (Terahertz) region. They are indispensable components of microwave links for satellite and radio communication systems to reduce the occurring interference signal and to filter the desired frequencies. The metallic iris between the resonant cavities are used as an equivalent inductance in the circuit topology structure of the filter.

Such structures have an easily fabricated compact sizes with high power handing capacity, low loss, and easy interconnection with other systems over planar transmission line structures.

In this study, a 100 GHz rectangular waveguide band-pass filter with two transmission zeros symmetrically located at both ends of the structure, is presented. The four-pole filter is composed of two dual-mode resonators with unequal width, two WR-10 standard waveguide interfaces with rounded corner for inductive irises in series. The thermal behavior of the BPF is investigated by computing the temperature, temperature gradient, and heat flux due to the thermal loads caused by the conductor losses in our case.

The next figure is showing the schematic illustration, cross-section view and 3D design of the studied BPF with its outer metallic cover.

Figure 1 - a)- The schematic illustration [1] b)- cross-section view and c)-3D design inside SOLIDWORKS of the studied BPF

Table 1 - Dimensions of the BPF

Dimension	d1	d2	d3	d4	a1	a2	a3	a4	t1	t2	t3	r1	r2	r3	l1	l2	l3	b
Value (mm)	1.165	2.695	2.82	1.165	2.54	5.345	5.02	2.54	0.33	0.92	0.25	0.14	0.24	0.09	1.346	1.14	1.19	1.27

Simulation Setup

The S-parameters solver of HFWorks is used, coupled to the thermal coupling case for a working frequency range of [94 GHz-106 GHz]. The properties of the used materials are summarized in table 2.

Table 2 - Material properties

Material	Relative permittivity	Dielectric loss tangent	Electrical conductivity (S/m)	Thermal conductivity (W/m. K)
Copper	1	0	5.96E+7	401

Electromagnetic boundary conditions

Wave port: The wave port boundary is applied to the input and output of the WR-10 cavity ports.

Figure 2 - Wave port boundary condition

Thermal boundary conditions

For an excitation power of $p subscript i n end subscript equals 1 W$ applied to the input port at 100 GHz, a thermal boundary convection is applied to the outer faces of the air cavity of the BPF at an ambient temperature of 22°C and a convection coefficient set to $10 W divided by m squared. C$

Thermal convection boundary condition

Figure 3 - Thermal convection boundary condition

Mesh

In HFWorks, Mesh control refers to specifying different element sizes at different regions in the model. A smaller element size in a region improves the accuracy of results in that region. You can specify mesh control at faces, components and edges.

In this case, a fine mesh control was applied to the whole air cavity body like shown in the next figure of the meshed model.

Figure 4 - The meshed model

Results

The S-parameter module of HFWorks is the basic module needed for most high frequency passive microwave structures and it covers a wide range of applications.

A fast sweep S-parameters study for the frequency range of [94 GHz-106 GHz] revealed the next results for a resonant frequency around 100 GHz:

The electric and magnetic field distributions are presented by the next fringe 3D plot:

Figure 5 - a) Electric and b) Magnetic field distribution at 100GHz

The next figure is showing the return and insertion losses plot versus frequency. As shown, the center frequency of the filter is 100.36 GHz with a bandwidth under 10dB equal to 28.33%, and two transmission zeros are at 97.6 GHz and 102.64 GHz, respectively. The return loss is better than ?14 dB across the whole bandwidth.

An acceptable agreement between simulation and measurement is presented when we compare both results, as shown below. It includes a center frequency of 100.6GHz, two transmission zeros at 97.77 GHz and 103.1 GHz and a return loss better than -14dB across the whole pass band.

The deviation of insertion and return loss results could be caused by uneven surface error or unclose connection between the filter structure and the network measurement analyzer [1].

Figure 6 - Return and insertion loss results versus frequency compared to measurements.

A steady state thermal analysis coupled to the S-parameters study is used to perform the thermal behavior of the studied BPF. It gives the next results:

- The first Figure is showing the temperature distribution results across the filter`s air cavity with an average value of 35,87°C.

Figure 7 - Temperature distribution at 100 GHz

- Figure 8: is showing the Heat flux density with a maximum value located at the rounded corners of the inductive irises.

Figure 8 - Heat flux distribution at 100 GHz

The accurate thermal maps obtained by HFWorks allows to predict the thermal behavior of the BPF under a fixed power excitation. It helps to make the right choice of materials in the early stages of design and to avoid any failure of the final product.

Conclusion

Waveguide based cavity filters are a practical solution for signal transmission at extremely high frequency. They are enabling a perfect microwave filter of desired frequencies with a lossless power, low dielectric effects and supporting high transmitting power.

The simulated characterizations with respect of bandwidth, location of zeros and return loss results present a good agreement with experimental results when considering the errors coming from the fabrication and the accuracy of measurements.

References

[1]. Xin, Wang, et al. "100 GHz waveguide band-pass filter employing UV-LIGA micromachining process." Microelectronics journal 69 (2017): 101-105.

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