Finite Frequency Selective Surface Modelling
R. 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.
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.
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, submillimetre 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
This work was funded by UK Centre for EO Instrumentation (CEOI)
Fig. 1. MWS single aperture frequency plan
Parameter
Transmission Bands
Transmission Insertion Loss
Reflection Bands
Reflection Insertion Loss
Incident Angle
Physical diameter
Table 1. FSS specification
Requirement
23.66 – 23.94 GHz
31.4 – 31.49 GHz
< 0.3 dB
50.21 – 57.67 GHz
87 - 91 GHz
164 - 167 GHz
175.3 – 191.3 GHz
228 – 230 GHz
< 0.3 dB
45°
250 mm
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.
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.
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.
(a)
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
(b)
Fig. 4. (a) Convergence of linear array with pass number, (b) tetrahedral mesh
produced at final pass
(a)
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˚.
(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
ACKNOWLEDGEMENTS
Measurements at 23 – 30 GHz were carried out by Dr Manju
Henry at STFC Rutherford Appleton Laboratory, Oxford.
REFERENCES
[1]
[2]
(a)
[3]
[4]
[5]
[6]
(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 quasioptical 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 depointing of the beams can be detected.
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.
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.
Ben A. Munk, “Finite Antenna Arrays and FSS, Wiley Interscience,
2003.
High frequency structural simulator (HFSS) is a commercially available
finite element method solver used for antenna design.
http://www.ansys.com/Products/Simulation+Technology/Electromagneti
cs/High-Performance+Electronic+Design/ANSYS+HFSS
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. 19851994, 2009.
Computer Simulation Technology CST, www.cst.com
/Products/CSTMWS