Paper Title (use style: paper title) · Web viewNote that while the unit cell simulation yields usable transmission data along the main angle of incidence, Fig. 5, the transmission

Finite Frequency Selective Surface ModellingR. Dickie, R. Cahill and V.F. Fusco

The Institute of Electronics, Communications and Information Technology (ECIT), Queen’s University Belfast, Northern Ireland Science Park,

Queen’s Road, Queen’s Island, Belfast BT3 9DT, Northern Ireland, UK, [email protected]

Abstract— In this paper we describe the development of an electromagnetic modelling technique to investigate edge illumination effects on finite size FSS performance. The work extends the commonly used unit cell approach and models the FSS as a linear array with Gaussian beam excitation. Bistatic scattering from the FSS is calculated at 23.8 GHz for a 45˚ incident beam. The results presented relate the beam size, edge illumination and scattering performance.

Index Terms—atmospheric science instrumentation, frequency selective surface, FSS, microwave, radiometers

I. INTRODUCTION Spaceborne radiometer instruments enable the retrieval of a wide range of geophysical parameters on a global scale. Radiometers operate by detecting thermal emissions from the Earth’s surface and atmosphere at microwave, millimetre, sub-millimetre and THz wavelengths. Detection of emissions in the microwave range enables the discrimination of temperature and humidity profile components. FSS (Frequency Selective Surface) demultiplexing is a critical technology for radiometer instruments. The filters are used to spectrally separate the thermal emissions that are collected by a single reflector antenna.

FSS design is generally carried out using the unit cell infinite array approach. However this numerical technique does not allow investigations into the effects of edge illumination, nor predictions of the radiation pattern. These details are particularly important in multichannel radiometers such as the MicroWave Sounder MWS [1] which is currently being developed for the European Space Agency. Within this instrument there are four FSS located in the quasi-optical (QO) network beam path. Generally if the edge illumination levels are below -35 dB, beam truncation effects can be ignored. However as part of the QO network design many trade-off’s are carried out on component size and placement within the available instrument volume. This can impact on the beam size requiring edge illumination effects to be quantified by additional FSS modelling. The MWS instrument has 24 frequency channels over seven frequency bands in the range 23 GHz – 230 GHz. Four FSS are employed to demultiplex the

incoming signal to five receiver locations within the instrument. The first FSS in the network separates the transmission bands centered at 23.8 and 31.4 GHz, from the five reflection bands as shown in Fig. 1. In this paper the modeling of this FSS is extended from the unit cell method [2] to include edge illumination effects, using the linear array approach. The FSS has a wide operating band 23 – 230 GHz, and is illuminated by the 23 GHz horn which is the largest in the QO network. Therefore, it is particularly important to extend the FSS modelling to consider the effects of edge illumination due to the large incident beam at this frequency. Table 1 summarises the FSS specification requirements.

Fig. 1. MWS single aperture frequency plan

Parameter Requirement

Transmission Bands23.66 – 23.94 GHz31.4 – 31.49 GHz

Transmission Insertion Loss < 0.3 dB

Reflection Bands

50.21 – 57.67 GHz87 - 91 GHz

164 - 167 GHz175.3 – 191.3 GHz

228 – 230 GHzReflection Insertion Loss < 0.3 dB

Incident Angle 45°Physical diameter 250 mm

Table 1. FSS specification

This work was funded by UK Centre for EO Instrumentation (CEOI)

II. FSS MODEL SETUP AND SPECTRAL RESPONSE COMPARISONS

When Floquet’s Theorem is used in both periodicities to solve FSS scattering the induced currents are uniform across the array, when excited with a plane wave. In modelling software this can be implemented using a unit cell approach as shown in Fig. 2 below. For this case the energy is always in the near field, and the far field radiation patterns cannot be calculated.

Fig. 2. Model of FSS using Floquet Theorem, unit cell approach

The finite FSS setup proposed using a linear array [3], differs from the infinite FSS model, because the array size is finite in two axes. This allows far field calculations to be made in the finite planes which feature the angle of incident vector, as shown in Fig. 3.

Fig.3. Finite FSS linear array model setup, TE 45 incidence illumination

In the orthogonal z-axis the array is infinite and uses periodic boundary conditions to apply Floquets theorem. This approach keeps the volume of the model to a manageable level, while allowing an investigation into scattering effects caused by the FSS edges. The linear array consisted of ~200 resonant elements to give an array length of 250 mm. The model was solved using a commercial FEM (Finite Element Method) solver, HFSS [4]. In a previous study using unit cell FSS modelling the spectral response was computed to

accuracy better than 0.5% using the FEM method [5]. Solving using the FD (Frequency Domain) has benefits in terms of accuracy and robust convergence of the resonant structure, compared to time domain solvers [6], but requires more memory.

To solve the problem all of the workstations 80 GB of available memory was required to adaptively mesh the problem which used 3.4 million tetrahedral mesh cells. Fig. 4(a) shows good monotonic convergence for the linear array with pass number. The final pass converged solution provides a well developed mesh around the critical features of the resonant structure, Fig. 4(b). Poynting vector calculations were made over surfaces defined above and below the FSS, close to the radiation boundaries. The results depicted in Fig. 5 show excellent agreement at 23.8 GHz, with the unit cell predictions using CST, and spectral measurements reported previously [2]. Note that while the unit cell simulation yields usable transmission data along the main angle of incidence, Fig. 5, the transmission spatial energy distribution is not forthcoming hence the bistatic pattern needs to be calculated using the finite array strategy.

(a)

(b)

Fig. 4. (a) Convergence of linear array with pass number, (b) tetrahedral mesh produced at final pass

Fig.5. Comparison of measured transmission data and CST [2, 6] unit cell predictions with the developed linear array illuminated by a Gaussian beam, adaptively solved at 23.8 GHz

III. BISTATIC SCATTERING

The bistatic scattering from the 250 mm long linear FSS was calculated for various Gaussian beam radii, including 44 mm, 80 mm and 112 mm. The beam radius (o) is defined as the distance from the beam axis where the energy intensity drops to ≈13.5% of its maximum intensity. Due to the 45˚ incident illumination, the beam is spread by a factor of 2 across the linear array. The beam intensity can be calculated at any axial radius, and taking into account the spreading of the beam, intensity levels fall to -35dB (o = 2 44 mm), -10 dB (o = 2 80mm), -5dB (o = 2 112mm) at the edge of the FSS.The corresponding electric field and Poynting vector power flow are shown in Fig. 6(a) – 8(a), for the three different sized beams.

Fig. 6(b) shows the bistatic scattering radiation pattern for the -35 dB illumination case. The main lobe points at 45º and the power directed back in the direction of incidence is below -32 dB. The -12.7 dB signal which is reflected from the FSS at - 45º is due to a small mismatch at this frequency. The pattern shows the main beam with side lobes below -20 dB and well suppressed smaller diffraction clutter.

When the incident beam radius is increased to 80 mm, or -10 dB edge illumination, the power directed back to the source increases to -24 dB, as shown in Fig. 7(b). The main beam side lobes increase to -10.3 dB, compared to the below -20 dB for the -35 dB illumination case. For 112 mm illumination the main beam side lobe levels increase significantly to -8.1 dB, as shown in Fig. 8(b). Overall for the wider beams the main beam narrows which is attributed to higher array efficiency. Both show increasing levels of the pattern clutter, which starts to obscure the main lobe at 45˚.

(a)

(b)Fig.6. 45 TE incidence Gaussian beam 44 mm radius, (a) electric field and

power flow (b) bistatic scattering radiation pattern

(a)

(b)

Fig.7. 45 TE incidence Gaussian beam 80 mm radius, (a) electric field and power flow (b) bistatic scattering radiation pattern

(a)

(b)

Fig.8. 45 TE incidence Gaussian beam 112 mm radius, (a) electric field and power flow (b) bistatic scattering radiation pattern

IV. CONCLUSIONS

Electromagnetic modelling of a finite FSS structure has been demonstrated at 23.8 GHz. The method uses the linear array approach and provides radiation pattern scattering related to the edge illumination levels. The model demonstrated that higher edge illumination and corresponding diffraction combine to increase energy levels away from the main beam direction. Containing the energy to the main beam is desirable as radiation outside this direction reduces instrument efficiency and may cause interference in the other channels.

The computer model developed allows the radiometer instrument designer to relate beam size, edge illumination and radiation patterns. The results can be incorporated into quasi-optical network models to give improved system performance, and provides a means to investigate spillover effects and spurious lobes. Features such as the FSS mounting brackets and absorbing materials at the FSS edges can now be included in the simulations. In addition, the radiation pattern provides the directions of the transmitted and reflected beams, any de-pointing of the beams can be detected.

ACKNOWLEDGEMENTS

Measurements at 23 – 30 GHz were carried out by Dr Manju Henry at STFC Rutherford Appleton Laboratory, Oxford.

REFERENCES

[1] V. Kangas, S. D’Addio, M. Betto, H. Barre and G. Mason, “MetOp second generation microwave radiometers”, Microwave Radiometry and Remote Sensing of the Environment (MicroRad), ESA, The Netherlands, pp. 1-4, March 2012.

[2] Dickie R, Cahill R, Huggard P, Henry M, Kangas V and de Maagt P: ‘Development of a 23-230 GHz FSS for the MetOp Second Generation Microwave Sounder Instrument’, Proc 7th European Conference on Antennas and Propagation, EUCAP 2013, Gothenburg, Sweden, April 2013.

[3] Ben A. Munk, “Finite Antenna Arrays and FSS, Wiley Interscience, 2003.

[4] High frequency structural simulator (HFSS) is a commercially available finite element method solver used for antenna design. http://www.ansys.com/Products/Simulation+Technology/Electromagnetics/High-Performance+Electronic+Design/ANSYS+HFSS

[5] R. Dickie, R. Cahill, H. Gamble, V. Fusco, M. Henry, M. Oldfield, P. Huggard, N. Grant, Y. Munro, and P. de Maagt, “Submillimeter Wave Frequency Selective Surface With Polarisation Independent Spectral Responses”, Proc. IEEE Antennas and Propagation, vol. 57, pp. 1985-1994, 2009.

[6] Computer Simulation Technology CST, www.cst.com /Products/CSTMWS