A Tunable, Band-Pass, Miniaturized-Element Frequency Selective surface: Design and Measurement

Farhad Bayatpur * and Kamal Sarabandi

Department of Electrical Engineering and Computer Science University of Michigan, Ann Arbor, MI, 48109-2122

{farhadbp, saraband}@eecs.umich.edu

Introduction

Frequency selective surface (FSS) structures, with resonant unit cells whose dimensions are comparable to half of a wavelength, have been studied for a variety of applications like radar and satellite communications. As a result, their behavior is well understood [1]-[2]. FSSs are usually 2D planar, periodic structures consisting of one or more metallic patterns, each backed by a dielectric substrate. The frequency response of an FSS is entirely described by the geometry of the structure in one period called a unit cell. In traditional FSS design, the frequency selective properties result from mutual interactions of the periodic FSS elements. Therefore, to observe a desired frequency selective behavior, a large number of unit cells must be present. Consequently, the FSS screen size is large. On the other hand, for some applications where a low sensitivity with respect to the incidence angle of the exciting wave is required or in cases where a uniform phase front is difficult to be established, the FSS panel size needs to be small. To address this problem, a new class of FSSs called miniaturized-element FSSs (MEFSS) with unit cell dimensions much smaller than a wavelength (<λ0/5) has shown to be promising [3]. In addition to the specific area of investigation discussed above, growing efforts are being devoted to realization of FSSs with electronically tunable frequency response. The focus of the recent efforts, however, has been mostly on the band-stop characteristics produced by FSSs, [4]-[5], and structures with band-pass characteristics have been rarely studied. A simple, tunable, band-pass MEFSS architecture, with elements that are as small as λ0/12, is presented in this article. The unit cell of this structure is composed of a metallic loop and a metallic grid on either side of a thin substrate. By appropriately incorporating tuning varactors into the MEFSS screen, a high-order, band-pass response, which can be tuned over almost an octave, is obtained from only a single-substrate FSS. The flexibility of the structure response is demonstrated through extensive numerical simulations using a commercial FEM- (finite element method) solver. To verify the simulations, a prototype sample of the MEFSS at X-band is fabricated using fixed lumped capacitors. The reflection and transmission parameters of the fabricated design are measured using a standard waveguide measurement setup.

Band-Pass MEFSS: Design and Operation Mechanism

The unit cell geometry of the proposed miniaturized-element FSS (MEFSS) is shown in Fig. 1. The structure has two layers: a 2D, periodic array of metallic square loop and a wire grid. As shown in [3], the wire grid alone is an inductive surface. The square loop array, on the other hand, is expected to behave like a series LC circuit. In this array, the gap between the loops acts as a capacitor, and the sides of the loops that are parallel with the electric field of the incident wave behave as an inductor. Thus the surface containing the loops is modeled as notch filter (series LC). In addition to the layers, the substrate choice is another important issue of the design, as a very thin substrate is needed in order for the layers to be highly coupled: The magnetic field excited by the current flowing in

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the wire grid circles the strips of the wire grid itself and a portion of that couple through the square loops on the other layer, hence inducing some electric current on the loops’ traces. Conversely, the current on the loops produces a magnetic field that couples to the wire grid. This coupling becomes stronger as the substrate thickness decreases. The crossing area between the strips of the wire grid and the square loops, on the other hand, form a capacitive junction. Existence of this series capacitance is somewhat counter-intuitive considering the fact that the excitation field has no longitudinal component. At resonance where there are significant electric current in the loops and the wire grid, considerable displacement current flows between the two layers through this capacitor. Finally, the tunability of the MEFSS response is achieved by interconnecting the loops via variable capacitors. The static design parameters, as shown in Fig. 2, are the loop trace width δ, the loop spacing s, the strip width w, the substrate thickness t, and Dx and Dy as the unit cell dimensions.

Band-Pass MEFSS: Modeling and Simulation Based on the qualitative description provided in the previous section, an equivalent circuit model for the MEFSS is presented. The model, see Fig. 3, includes two parallel branches, each representing a layer of the MEFSS. The right branch is purely inductive which models the wire grid. The left branch in the circuit model represents the array of loop that is modeled as a series combination of a capacitor and an inductor (notch filter). The total capacitance placed on the circuit model is composed of the loops’ gap capacitance, Cg, and the lumped capacitance of the tuning varactor, Cv, mounted in parallel with Cg in the gap between two successive loops. Fig. 4 shows the results of the simulations of the circuit model, using a circuit simulator, and the MEFSS structure, using an FEM solver. As shown, the model response not only predicts the FEM result, but it also tracks the MEFSS response changes as the lumped capacitance is tuned. The parameters’ values for a band-pass MEFSS design are shown in Table. 1. Using these fixed design values, FEM simulations are performed. The results for different values of the lumped capacitance, Cs, are shown in Fig. 5. As can be seen, a frequency range from 6.4GHz to 9.7GHz can be swept by altering the varactor capacitance from 0.3pF to 0.1pF. The simulations predict a very wide tuning range with nearly no degradation in the MEFSS performance.

TABLE I BAND-PASS MEFSS STATIC DESIGN PARAMETERS AT X-BAND

s δ w t εr Dx×Dy

0.15 mm 0.15 mm 0.5 mm 0.125 mm 2.2 2.5 × 2.5 mm2

Band-Pass MEFSS: Fabrication and Measurement

To demonstrate the validity of the simulations, a prototype sample of the MEFSS is fabricated and tested using a rectangular waveguide at X-band frequencies. Using image theory, a finite sample of the MEFSS in a rectangular waveguide supporting TE10 mode can be shown to behave as an infinite structure illuminated at oblique incidence. Although the response of the MEFSS in the waveguide is different than a normal incident plane wave, the main features of the frequency response are preserved, and comparison between the measurements and simulations validates the analyses presented. For these

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measurements, instead of a varactor, we used a fixed capacitor as biasing the varactors inside an enclosed metallic structure is very complicated. The circuit board is fabricated using a low-loss duroid substrate through a standard printed circuit board etching process. The capacitors used are thin-film chip capacitors with a very small package size (0201 standard size). To allow for longitudinal conduction current on the waveguide walls, via holes are fabricated on the perimeter of the prototype MEFSS where the waveguide flanges meet. Lack of good metallic contact and disruption of the longitudinal currents give rise to spurious response. In order to compare the numerical and experimental results, a set of new simulations in a waveguide environment supporting TE10 mode is performed. Fig. 6 compares the simulation and experimental results. As can be seen, there is a good agreement between the results. The measured results, however, show an insertion loss of 1.5dB at the center frequency, which is higher than that predicted by the simulation. This increased loss is primarily related to the lack of a perfect electric connection between the waveguide flanges through the via holes at the MEFSS edges. In our experiment, it was observed that the existence of an air gap between the waveguide flanges and the MEFSS metallic edges can significantly affect the response, causing unwanted resonances and increased insertion loss.

Conclusion In this paper, a new, miniaturized-element frequency selective surface (MEFSS) is presented. A single substrate is used to generate a high-order, band-pass response that can be electronically tuned using varactors mounted on one side of the substrate. The unit cell size of this design can be as small as λ0/12, which is a factor of 6 reduction in size compared to a typical traditional FSS. The salient feature of MEFSS structures is that their property is localized and thus suitable for moderate size antennas at low frequencies. To give insight into the new MEFSS behavior, an accurate circuit model is developed. The accuracy of the model is verified using a full-wave approach. The frequency tuning capability of the response is demonstrated through numerical simulations. A wide tuning range with a negligible loss of performance is observed. To show the validity of the simulations, a prototype sample of the MEFSS is fabricated. A good agreement between the simulation and experimental results is observed.

References: [1] J.C. Vardaxoglou, “Frequency-selective surfaces: Analysis and design,” Research

Studies Press, Ltd., Taunton, UK, 1997. [2] T.K. Wu, “Frequency-selective surface and grid array,” Wiley, New York, 1995. [3] Sarabandi, K., and N. Behdad “A Frequency Selective Surface with Miniaturized

Elements" IEEE Transactions on Antennas and Propagation, submitted for publication (March 2006).

[4] J. P. Gianvittorio, J. Zendejas, Y. Rahmat-Samii, and J. Judy, “Reconfigurable MEMS-enabled frequency selective surfaces,” IEE Electron.Lett., vol. 38, no. 25, pp. 1627–1628, Dec. 2002.

[5] C. Mias, “Frequency selective surfaces loaded with surface-mount reactive components,” IEE Electron. Lett., vol. 39, no. 9, May 2003.

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(a) (b)

Fig. 1: One period (unite cell) of the proposed MEFSS composed of square loops on one side and a wire grid on the other side of a thin substrate. (a)-Front view, (b)-Back view

Fig. 2: The physical parameters of the loop and wire grid structure that affect the frequency response of the MESS.

Fig. 3: An equivalent circuit model for the coupled wire grid and loop array surfaces of the proposed MEFSS.

Fig. 5: Full-wave simulations of the MEFSS frequency response (return loss and transmission). The results show that a wide tuning range can be obtained using a typical varactor at X-band.

Fig. 4: Circuit model simulations are compared with FEM results for different values of the lumped capacitor.

Fig. 6: Experimental and simulation results

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