# Patent

## Title
Tunable frequency selective surface

## Abstract

An apparatus and methods for operating a frequency selective surface are disclosed. The apparatus can be tuned to an on/off state or transmit/reflect electromagnetic energy in any frequency. The methods disclosed teach how to tune the frequency selective surface to an on/off state or transmit/reflect electromagnetic energy in any frequency.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This patent application is a divisional application of U.S. application No. 10/903,190 (U.S. Pat. No. 7,173,565), filed on Jul. 30, 2004, which is incorporated herein by reference in its entirety.


FIELD OF THE INVENTION
This technology relates to a frequency selective surface that can be tuned to an on-state, off-state and/or can transmit/reflect electromagnetic energy in any frequency band.
BACKGROUND AND PRIOR ART
Antennas 100 may be hidden behind a radome 110, see FIG. 1, particularly if they are being used in an application where they could be exposed to the environment. The radome protects the antenna from both the natural environment such as rain and snow, and the man-made environment such as jamming signals. Often, the radome is made so that it transmits electromagnetic energy within a narrow band centered around the operating frequency of the antenna, so as to deflect or reflect jamming signals at other frequencies. This is done using a frequency selective surface (FSS), having a grid or lattice of metal patterns or holes in a metal sheet. The design and construction of FSSs is well known to those skilled in the art of radome design and electromagnetic material design.
Two surfaces are commonly used in FSS design, the “Jerusalem cross” structure 200, shown in FIG. 2a, and its “Inverse structure” 300, shown in FIG. 3a. A unit cell equivalent circuit 201 of the Jerusalem cross 200, FSS can be viewed as a lattice of capacitors 210 and inductors 220 in series, shown in FIG. 2b. The capacitors 210 and inductors 220 are oriented in two orthogonal directions so that the surface can affect both polarizations. Near the LC resonance frequency, the series LC circuit has low impedance, and shorts out the incoming electromagnetic wave, thereby deflecting it off the surface. At other frequencies, the LC circuit is primarily transmitting, although it does provide a phase shift for frequencies near the stop band, shown in FIG. 2c. 
The Inverse structure 300, shown in FIG. 3a, has opposite characteristics. A unit cell equivalent circuit 301 of the Inverse structure 300, FSS can be viewed as a lattice of capacitors 310 and inductors 320 in parallel, shown in FIG. 3b. It is transmissive near LC resonance frequency and reflective at other frequencies, shown in FIG. 3c. 
The radome typically transmits RF energy through the radome only at the operating frequency of the antenna, and reflects or deflects at other frequencies. In some applications, it may be desirable to tune the radome, particularly when a tunable antenna is used inside the radome. It may also be desirable to set the radome to an entirely opaque (off) state, so that it is deflective or reflective over a broad range of frequencies. It may also be desirable to program the radome so that different regions have different properties, either transmitting within a frequency band, or opaque as desired. To achieve these requirements the FSS needs to be tunable.
Throughout the years, different techniques have been implemented to achieve the tuning of the FSS. The tuning has been achieved by: varying the resistance, see Chambers, B., Ford, K. L., “Tunable radar absorbers using frequency selective surfaces”, Antennas and Propagation, 2001. Eleventh International Conference on (IEEE Conf. Publ. No. 480), vol. 2, pp. 593-597, 2001; pumping liquids that act as dielectric loading, see Lima, A. C. deC., Parker, E. A., Langley, R. J., “Tunable frequency selective surface using liquid substrates”, Electronics Letters, vol. 30, issue 4, pp. 281-282, 1994; rotating metal elements, see Gianvittorio, J. P., Zendejas, J., Rahmat-Sami, Y., Judy, J., “Reconfigurable MEMS-enabled frequency selective surfaces”, Electronics Letters, vol. 38, issue 25, pp. 1627-1628, 2002; using a ferrite substrate, see Chang, T. K., Langley, R. J., Parker, E. A., “Frequency selective surfaces on biased ferrite substrates”, Electronics Letters, vol. 30, issue 15, pp. 1193-1194, 1994; pressurizing a fluid, see Bushbeck, M. D., Chan, C. H., “A tunable, switchable dielectric grating”, IEEE Microwave and Guided Wave Letters, vol. 3, issue 9, pp. 296-298, 1993; using a varactor tuned grid array that is a kind of quasi-optic oscillator, see Oak, A. C., Weikle, R. M. Jr., “A varactor tuned 16-element MESFET grid oscilator”, Antennas and Propagation Society International Symposium, 1995; using an electro-optic layer, see Rhoads' patent (U.S. Pat. No. 6,028,692); using transistors, see Rhoads' patent (U.S. Pat. No. 5,619,366); using ferroelectrics between an absorptive state and a transmissive state, see Whelan's patent (U.S. Pat. No. 5,600,325).
Although the above-mentioned methods are used to tune the FSS, these methods are not ideal for use with a tunable antenna. Many of the above methods are not practical for rapid tuning because they use moving metal parts, or pumping dielectric liquids. Some of them include switching between discrete states using transistors, which is less useful than a continuous tunable surface. Others include only on and off states, and cannot be tuned in frequency. Others require bulk ferrite, ferroelectric, or electrooptic materials, which can be lossy and expensive. None of the prior art achieves the capabilities of the present technology, even though a need exists for those capabilities.
The present technology 420 is able to transmit electromagnetic energy 450 in a particular frequency band through the radome, and deflect or reflect electromagnetic energy in other frequency bands, shown in FIG. 4. It can also be tuned to an off state where it is deflective or reflective, or an on state where it is absorptive over a broad range of frequencies. Also some regions 440 of the surface can be tuned to different frequencies while other regions 430 of the surface can be set to an opaque state, shown in FIG. 4. Further, it uses rapidly tunable varactor diodes and low cost printed circuit board construction.



BRIEF DESCRIPTION OF THE FIGURES AND THE DRAWINGS
FIG. 1 depicts an arrangement of the antenna and radome;
FIG. 2a depicts a top view of the Jerusalem cross FSS;
FIG. 2b depicts a unit cell equivalent circuit of the Jerusalem cross FSS;
FIG. 2c depicts a transmission spectrum of the Jerusalem cross FSS;
FIG. 3a depicts a top view of the Inverse structure of the Jerusalem cross FSS;
FIG. 3b depicts a unit cell equivalent circuit of the Inverse structure of the Jerusalem cross FSS;
FIG. 3c depicts a transmission spectrum of the Inverse structure of the Jerusalem cross FSS;
FIG. 4 depicts an arrangement of the steerable antenna and tunable radome where the radome has an opaque region and a transparent region, and the antenna sending a microwave beam through the transparent region;
FIG. 5a depicts an inappropriate series LC unit cell equivalent circuit;
FIG. 5b depicts an appropriate parallel LC unit cell equivalent circuit;
FIG. 5c depicts an example of an appropriate TFSS unit cells;
FIG. 5d depicts an example of an appropriate TFSS unit cells;
FIG. 6a depicts a surface view of a circuit board containing conductors and varactors on both sides;
FIGS. 6b-c depict the front view of each surface of the circuit board in FIG. 6a; 
FIG. 6d depicts a transparent view of the first surface of the circuit board in FIG. 6a over the second surface of the circuit board in FIG. 6a; 
FIG. 6e depicts the results of modeling the circuit board in FIG. 6a on the Ansoft HFSS software;
FIG. 6f depicts tuning both sides of the circuit board in FIG. 6a to a resonance frequency;
FIG. 6g depicts tuning the first surface of the circuit board in FIG. 6a to three different resonance frequencies;
FIG. 6h depicts tuning the second surface of the circuit board in FIG. 6a to three different frequencies;
FIG. 6i depicts a transparent view of the first surface over the second surface and the propagation of different resonance frequencies through the circuit board in FIG. 6a; 
FIG. 6j depicts setting the circuit board in FIG. 6a to an opaque state;
FIG. 6k depicts tuning a region of the first surface to one frequency and setting the remaining region of the first surface in opaque mode;
FIG. 6l depicts tuning a region of the second surface to one frequency and setting the remaining region of the second surface in opaque mode;
FIG. 6m depicts a transparent view of the first surface over the second surface and the propagation of frequency and opaque mode through the circuit board in FIG. 6a; 
FIG. 7a depicts a surface view of a circuit board containing conductors and varactor on both sides;
FIGS. 7b-c depict the front view of each surface of the circuit board in FIG. 7a; 
FIG. 7d depicts a transparent view of the first surface of the circuit board in FIG. 7a over the second surface of the circuit board in FIG. 7a; 
FIG. 7e depicts the results of modeling the circuit board in FIG. 7a on the Ansoft HFSS software;
FIG. 7f depicts tuning both sides of the circuit board in FIG. 7a to a resonance frequency;
FIG. 7g depicts setting the circuit board in FIG. 7a to an opaque state;
FIG. 8a depicts a surface view of a circuit board containing conductors and varactor on the first surface, conductors on the second surface and vias connecting first and second surface;
FIGS. 8b-c depict the front view of each surface of the circuit board in FIG. 8a; 
FIG. 8d depicts a transparent view of the first surface of the circuit board in FIG. 8a over the second surface of the circuit board in FIG. 8a; 
FIG. 8e depicts the results of modeling the circuit board in FIG. 8a on the Ansoft HFSS software;
FIG. 8f depicts tuning both sides of the circuit board in FIG. 8a to a resonance frequency;
FIG. 8g depicts setting the circuit board in FIG. 8a to an opaque state;
FIG. 9a depicts a surface view of a circuit board containing conductors on the first surface, conductors and varactor on the second surface and vias connecting the first and the second surface;
FIGS. 9b-c depict the front view of each surface of the circuit board in FIG. 9a; 
FIG. 9d depicts a transparent view of the first surface of the circuit board in FIG. 9a over the second surface of the circuit board in FIG. 9a; 
FIG. 10a depicts a surface view of a circuit board containing varactors on the first layer, conductors on the second and third layers and vias connecting all the layers;
FIGS. 10b-d depict the front view of each layer of the circuit board in FIG. 10a; 
FIG. 10e depicts a transparent view of the first layer of the circuit board in FIG. 10a over the second layer of the circuit board in FIG. 10a over the third layer of the circuit board in FIG. 10a; 
FIG. 11a depicts a surface view of a circuit board containing conductors and varactors on the first surface, conductors on the second surface and vias connecting first surface and second surface;
FIGS. 11b-c depict the front view of each surface of the circuit board in FIG. 11a; 
FIG. 11d depicts a transparent view of the first surface of the circuit board in FIG. 11a over the second surface of the circuit board in FIG. 11a; 
FIG. 11e depicts the results of modeling circuit board in FIG. 11a on the Ansoft HFSS software;
FIG. 11f depicts tuning the circuit board in FIG. 11a to a resonance frequency;
FIG. 11g depicts setting the circuit board in FIG. 11a to an opaque state;
FIG. 11h depicts tuning the circuit board in FIG. 6a to three different frequencies and an opaque state;
FIG. 12a depicts a surface view of a circuit board containing conductors on the first surface, conductors and varactors on the second surface and vias connecting the first surface and second surface.
FIGS. 12b-c depict the front view of each surface of the circuit board in FIG. 11a; 
FIG. 12d depicts a transparent view of the first surface of the circuit board in FIG. 12a over the second surface of the circuit board in FIG. 12a; 
FIG. 13a depicts a surface view of a circuit board containing varactors on the first layer, conductors on the second and third layers and vias connecting all the layers.
FIGS. 13b-d depict the front view of each layer of the circuit board in FIG. 13a; 
FIG. 13e depicts a transparent view of the first layer of the circuit board in FIG. 13a over the second layer of the circuit board in FIG. 13a over the third layer of the circuit board in FIG. 13a; 



DETAILED DESCRIPTION
Of the two surfaces that are commonly used in FSS design, the Inverse structure 300 is the most appropriate in designing a TFSS. The series LC circuit 510, shown in FIG. 5a, used by the Jerusalem cross 200 is difficult to use because it lacks a continuous metal path throughout the surface, so it is difficult to provide DC bias to the internal cells. Whereas, the parallel LC circuit 511, shown in FIG. 5b, used by Inverse structure 300, does not have this limitation.
The parallel circuit 512, which is an equivalent circuit for LC circuit 511, can be constructed as a varactor diode 530 in parallel with a narrow metal wire 540, which acts as an inductor, and in parallel with a DC blocking capacitor 550, as shown in FIG. 5c. 
The parallel circuit 513, which is another equivalent circuit for LC circuit 511, can also be constructed as two varactor diodes 560 and 561 in parallel with a narrow metal wire 570, which acts as an inductor, as shown in FIG. 5d. 
Using varactor diodes has the advantage in that the opaque state is easy to achieve by simply forward-biasing the varactors, so that they are conductive. Although other kinds of varactors or equivalent devices could be presently used, such as MEMS varactors or ferroelectric varactors, for clarity's sake, this discussion will concentrate on implementing this technology using varactor diodes.
In one embodiment, the TFSS includes a circuit board 600, with an array of conductors 640a-c, 650a-c and varactors 630 on a major surface 610 and an array of conductors 670a-c, 680a-c and varactors 660 on a major surface 620, as shown in FIG. 6a. FIG. 6a shows the side view of the substrate 600.
FIG. 6b shows a schematic of a circuit on the major surface 610. The major surface 610 has varactors 630 organized in rows where the orientation of the varactors in one row is a mirror image of the varactors in the neighboring row, as shown in FIG. 6b. Conductors 640a-c and 650a-c run across the major surface 610 between the rows of varactors 630.
FIG. 6c shows a schematic of a circuit on the major surface 620. The surface 620 has varactors 660 organized in columns where the orientation of the varactors in one column is a mirror image of the varactors in the neighboring column, as shown in FIG. 6c. Conductors 670a-c and 680a-c run across the major surface 620 between the columns of varactors 660.
Although the conductors in FIGS. 6b and 6c are represented as straight lines, it shall be understood that the conductors can have different shapes, including but not limited to straight lines, crenulated lines and/or wavy lines, for this technology to work.
Although the conductors in FIGS. 6b and 6c are represented as parallel lines, it is to be understood that the conductors do not have to be perfectly parallel for this technology to work. The distance between the conductors may vary throughout the length of the conductors.
Structure 690 in FIG. 6d shows an overlay of the circuit on the major surface 610 and the circuit on the major surface 620. Varactors and conductors on major surface 610 are oriented at an angle to the varactors and conductors on the major surface 620. Although the varactors and conductors on the major surface 610 are depicted at a 90° angle to the varactors and conductors on the major surface 620 as shown in structure 690 in FIG. 6d, it needs to be appreciated that the angle can be varied.
The lattice period of structure 690 is represented by distance 1B and 1C as shown in FIGS. 6b-d. For this technology to work the distances 1B and 1C can range from 1/15 of the wavelength to 1⁄2 of the wavelength. It needs to be appreciated that the distances 1B and 1C do not have to be equal for this technology to work.
The thickness 1A of the circuit board 600, shown in FIG. 6a, is sufficiently small to produce capacitive coupling between the conductors on major surface 610 and the conductors on major surface 620. Since capacitive coupling between conductors depends on the distance between the conductors and the width of the conductors, in this embodiment the width of all the conductors and thickness 1A are matched so as to produce capacitive coupling between the conductors on major surface 610 and the conductors on major surface 620.
Structure 690 was modeled using Ansoft HFSS software. See FIG. 6e. In the first simulation the lattice period was modeled at 1B=1C=1 cm, the conductors were modeled at 1 mm width, and substrate was modeled at 1A=1 mm thickness. The varactors were modeled as a cube of dielectric material whose dielectric constant was tuned from 1 to 64 by factors of 2. Increasing the dielectric constant from 1 to 64 tuned the resonance frequency of the surface from 8 Ghz down to about 2 Ghz. In the second simulation, the lattice period was modeled at 1B=1C=1 cm, the conductors were modeled at 1 mm width, and the substrate was modeled at 1A=7 mm thickness. The varactors were modeled as a cube of dielectric material whose dielectric constant was 8. Due to reduced capacitive coupling between conductors on the major surface 610 and the conductors on the major surface 620, the transmission level in the pass-band was reduced by about 50%, and the pass-band shifted in frequency.
Applying voltages to conductors on each major surface of the substrate controls the propagation of different frequencies through the TFSS. Depending on the voltages applied, the capacitance of the varactors is tuned and the resonance frequency of the TFSS is adjusted. Setting bias wires 640a-c and 670a-c to 0 volts and setting bias wires 650a-c and 680a-c to +10 volts, as shown in FIG. 6f, will cause all of the varactors to be reverse biased and this will allow a certain resonance frequency to pass through the entire TFSS. The voltage numbers are just provided as an example; a person familiar with this technology would know that the voltage numbers could be varied to achieve desired resonance frequency.
In this embodiment different regions of the TFSS can be tuned to propagate different resonance frequencies along the length of the conductors on each major surface of the circuit board 600. The propagation of the resonance frequency with horizontal polarization through the TFSS can be controlled by applying appropriate voltages to the conductors on major surface 610 as shown in FIG. 6h. Setting conductors 640a-c to 0 volts and setting conductor 650a to +10 volts will cause varactors in region R1 to be reverse biased and this will allow only a resonance frequency with horizontal polarization HF1 to propagate through the R1 region of TFSS between the conductors 640a and 640b, as shown in FIG. 6g. Setting conductor 650b to +15 volts will cause varactors in region R2 to be reverse biased and this will allow only a resonance frequency with horizontal polarization HF2 to propagate through the R2 region of TFSS between the conductors 640b and 640c, as shown in FIG. 6g. Setting conductor 650c to +20 volts will cause varactors in region R3 to be reverse biased and this will allow only a resonance frequency with horizontal polarization HF3 to propagate through the R3 region of TFSS between the conductors 640c and 650c, as shown in FIG. 6g. The voltage numbers are just provided as an example; the voltage numbers could be varied to achieve desired resonance frequency.
The propagation of the resonance frequency with vertical polarization through the TFSS can be controlled by applying appropriate voltages to the conductors on major surface 620 as shown in FIG. 6h. Setting conductors 670a-c to 0 volts and setting conductor 680a to +10 volts will cause varactors in region R4 to be reverse biased and this will allow only a resonance frequency with vertical polarization VF1 to propagate through the R4 region of TFSS between the conductors 670a and 670b, as shown in FIG. 6h. Setting conductor 680b to +15 volts will cause varactors in region R5 to be reverse biased and this will allow only a resonance frequency with vertical polarization VF2 to propagate through the R5 region of TFSS between the conductors 670b and 670c, as shown in FIG. 6h. Setting conductor 680c to +20 volts will cause varactors in region R6 to be reverse biased and this will allow only a resonance frequency with vertical polarization VF3 to propagate through the R6 region of TFSS between the conductors 670c and 670c, as shown in FIG. 6h. The voltage numbers are just provided as an example; the voltage numbers could be varied to achieve desired resonance frequency.
The propagation of the resonance frequency with horizontal and vertical polarization is achieved through structure 690 in FIG. 6i. When structure 690 is set up as shown in FIGS. 6i there will be overlapping regions that will allow both a vertical and horizontal polarization of a single resonance frequency to propagate through the TFSS. Region R7, as shown in FIG. 6i, allows the propagation of both HF1 and VF1 through the TFSS. Region R8, as shown in FIG. 6i, allows the propagation of both BF2 and VF2 through the TFSS. Region R9, as shown in FIG. 6i, allows the propagation of both HF3 and VF3 through the TFSS. The size and shape of the regions that allow both vertical and horizontal polarization resonance frequencies to propagate through TFSS shown here are just provided as an example. The size and shape of these regions can be adjusted by applying appropriate voltages to the appropriate conductors.
When structure 690 is set up as shown in FIGS. 6i, there will also be overlapping regions that will allow both a vertical and horizontal polarization of different resonance frequencies to propagate through the TFSS. Region R10, as shown in FIG. 6i, allows the propagation of BF1 and VF2 through the TFSS. Region R11, as shown in FIG. 6i, allows the propagation of HF1 and VF3 through the TFSS. Region R12, as shown in FIG. 6i, allows the propagation of HF2 and VF1 through the TFSS. Region R13, as shown in FIG. 6i, allows the propagation of HF3 and VF1 through the TFSS. Region R14, as shown in FIG. 6i, allows the propagation of HF3 and VF2 through the TFSS. Region R15, as shown in FIG. 6i, allows the propagation of HF2 and VF3 through the TFSS.
In this embodiment, the TFSS can also be set to an opaque (off) state. The opaque state is achieved by forward biasing the varactors, as shown in FIG. 6j, which shorts across the continuously conductive loop. Setting conductors 640a-c and 670a-c to 0 volts and setting conductors 650a-c and 680a-c to −1 volts, as shown in FIG. 6j, will cause all of the varactors to be forward biased thereby blocking all the resonance frequencies from propagating though the TFSS. The voltage numbers are just provided as an example; the voltage numbers could be varied and still cause all of the varactors to be forward biased.
In this embodiment, the region of the TFSS can be set to an opaque state while the remaining region is set to propagate a certain resonance frequency. The propagation of a particular resonance frequency with horizontal polarization through a region of the TFSS and blocking the remaining resonance frequencies with horizontal polarization through the rest of the TFSS can be controlled by applying appropriate voltages to the conductors on major surface 610 as shown in FIG. 6k. Setting conductors 640a-c to 0 volts and setting conductors 650a and 650c to −1 volts will cause varactors in regions R16 and R18 to be forward biased and this will block any resonance frequency with horizontal polarization from propagating through the R16 and R18 regions of TFSS, as shown in FIG. 6k Setting conductors 650b to +15 volts will cause varactors in region R17 to be reverse biased and this will allow a resonance frequency with horizontal polarization HF2 to propagate through the R17 region of TFSS, as shown in FIG. 6k. The voltage numbers are just provided as an example. The voltage numbers could be varied to achieve desired resonance frequency or an opaque state.
The propagation of a particular resonance frequency with vertical polarization through a region of the TFSS and blocking the remaining resonance frequencies with vertical polarization through the rest of the TFSS can be controlled by applying appropriate voltages to the conductors on major surface 620 as shown in FIG. 6l. Setting conductors 670a-c to 0 volts and setting conductors 680a and 680c to −1 volts will cause varactors in the regions R19 and R21 to be forward biased and this will block any resonance frequency with vertical polarization from propagating through the R19 and R21 regions of TFSS, as shown in FIG. 6l. Setting conductor 680b to +15 volts will cause varactors in the region R20 to be reverse biased and this will allow a resonance frequency with vertical polarization VF2 to pass through the R20 region of TFSS, as shown in FIG. 6l. The voltage numbers are just provided as an example, the voltage numbers could be varied to achieve desired resonance frequency or an opaque state.
The propagation of a particular resonance frequency with horizontal and vertical polarization through a region of the TFSS and blocking of the remaining resonance frequencies through the rest of the TFSS is achieved through the structure 690 in FIG. 6m. When structure 690 is set up as shown in FIG. 6m there will be a region propagating a particular resonance frequency, regions with horizontal and vertical polarization, regions blocking all the frequencies, regions propagating only horizontal polarization of the particular frequency and regions propagating only vertical polarization of the particular resonance frequency. Region R30, as shown in FIG. 6m, allows the propagation of HF2 and VH2 through the TFSS. Regions R22, R29, R27 and R25 as shown in FIG. 6m, block all the vertical and horizontal polarizations of all the resonance frequencies from propagating through the TFSS. Regions R26 and R23 allow propagation of only VF2 through the TFSS. Regions R28 and R24 allow propagation of only HF2 through the TFSS. The size and shape of the region that allows both vertical and horizontal polarization resonance frequencies to pass through TFSS shown here are just provided as an example. The size and shape of these regions can be adjusted by applying an appropriate voltage to the appropriate conductors. The size and shape of the opaque regions shown here are also just provided as an example. The size and shape of these opaque regions can be adjusted by applying an appropriate voltage to the appropriate conductors.
In another embodiment, the TFSS includes a circuit board 700, with an array of conductors 740a-d, 730a-d and varactors 750 on the major surface 710, an array of conductors 160a-c, 770a-c and varactors 780 on the major surface 720 and vias 795 and 796 connecting major surfaces 710 and 720 as shown in FIG. 7a-c. FIG. 7a shows the side view of the substrate 700.
FIG. 7b shows a schematic of a circuit on the major surface 710. The major surface 710 has a plurality of oppositely oriented varactors 750 connected in series and organized in rows where the orientation of the varactors in one row is a mirror image of the varactors in the neighboring row, as shown in FIG. 7b. Conductors 740a-d run along the length of the major surface 710 between the rows of varactors 750. Conductors 730a-d run along the width of the major surface 710 between the varactors 750 connecting the conductors 740a-d, as shown. in FIG. 7b. 
FIG. 7c shows a schematic of a circuit on the major surface 720. The major surface 720 has a plurality of oppositely oriented varactors 780 connected in series and organized in columns where the orientation of the varactors in one column is a mirror image of the varactors in the neighboring column, as shown in FIG. 7c. Conductors 760a-c run along the width of the major surface 720 between the columns of varactors 780. Conductors 770a-c run along the length of the major surface 720 between the varactors 780 connecting the conductors 760a-c, as shown in FIG. 7c. 
Although the conductors in FIGS. 7b and 7c are represented as straight lines, it is to be understood that the conductors can have different shapes, including but not limited to straight lines, crenulated lines and/or wavy lines, for this technology to work.
Although the conductors in FIGS. 7b and 7c are represented as parallel lines, it is to be understood that the conductors do not have to be perfectly parallel for this technology to work. The distance between the conductors may vary throughout the length of the conductors.
Although conductors 730a-d appear to be perpendicular to conductors 740a-d in FIG. 7b, it is to be understood that these conductors do not have to be perfectly perpendicular for this technology to work. The angle between the intersecting conductors may vary.
Although conductors 760a-c appear to be perpendicular to conductors 770a-c in FIG. 7c it is to be understood that these conductors do not have to be perfectly perpendicular for this technology to work. The angle between the intersecting conductors may vary.
Structure 790 in FIG. 7d shows an overlay of the circuit on the major surface 710 and the circuit on the major surface 720. Varactors and conductors on major surface 710 are oriented at an angle to the varactors and conductors on the major surface 720. Although the varactors and conductors on the major surface 710 are depicted at a 90° angle to the varactors and conductors on the major surface 720 as shown in structure 790 in FIG. 7d, it needs to be appreciated that the angle can be varied.
Vias 796 connect the varactors 780 on the major surface 720 to conductors 730a-d on the major surface 710, shown in FIG. 7d. Vias 795 connect the varactors 750 on the major surface 710 to conductors 770a-c on the major surface 720, shown in FIG. 7d. 
The lattice period of structure 790 is represented by distance 2B and 2C as shown in FIG. 7d. For this technology to work, the distances 2B and 2C can range from 1/15 of the wavelength to 1⁄2 of the wavelength. The distances 2B and 2C do not have to be equal for this technology to work.
The thickness 2A of the circuit board 700, shown in FIG. 7a, is less important than the thickness 1A of the circuit board 600 described above. Vias 796 and 795 make the circuit board 700 less susceptible to the variations in the thickness 2A.
Structure 790 was modeled using Ansoft HFSS software. See FIG. 7e. In the first simulation the lattice period was modeled at 2B=2C=1 cm, the conductors were modeled at 1 mm width, and the substrate was modeled at 2A=1 mm thickness. The varactors were modeled as a cube of dielectric material whose dielectric constant was tuned from 1 to 64 by factors of 2. Increasing the dielectric constant from 1 to 64 tuned the resonance frequency of the surface from 8 Ghz down to about 2 Ghz. In the second simulation the lattice period was modeled at 2B=2C=1 cm, the conductors were modeled at 1 mm width, and the substrate was modeled at 2A=7 mm thickness. The varactors were modeled as a cube of dielectric material whose dielectric constant was 8. As can be seen by the results, shown in FIG. 7e, this design is more resistant to variations in the substrate thickness. The transmission level in the pass-band was reduced by about 20%. This design is less concerned with maintaining capacitive coupling and is more resistant to variations in the thickness 2A.
Applying voltages to conductors on each major surface of the substrate controls the propagation of different frequencies through the TFSS. Depending on the voltages applied, the capacitance of the varactors is tuned and the resonance frequency of the TFSS is adjusted. Setting conductors on the major surface 710 to 0 volts and setting conductors on the major surface 720 to +10 volts, as shown in FIG. 7f, will cause all of the varactors to be reverse biased and this will allow a certain resonance frequency to pass through the entire TFSS. The voltage numbers are just provided as an example; the voltage numbers could be varied to achieve desired resonance frequency.
In this embodiment, the TFSS can also be set into an opaque (off) state. The opaque state is achieved by forward biasing the varactors, as shown in FIG. 7g, which shorts across the continuously conductive loop. Setting conductors on major surface 710 to 0 volts and setting conductors on major surface 720 to −1 volts, as shown in FIG. 7g, will cause all of the varactors to be forward biased, thereby blocking all the resonance frequencies from propagating through the TFSS. The voltage numbers are just provided as an example; the voltage numbers could be varied and still cause all of the varactors to be forward biased.
In another embodiment, the TFSS includes a circuit board 800, with an array of conductors 840a-d, 830a-d and varactors 880 on the major surface 810, an array of conductors 860a-c, 870a-c on the major surface 820 and vias 895 connecting major surfaces 810 and 820 as shown in FIG. 8a-c. FIG. 8a shows the side view of the substrate 800.
FIG. 8b shows a schematic of a circuit on the major surface 810. The major surface 810 has a plurality of oppositely oriented, interconnected varactors 880 organized in rows where the orientation of the varactors in one row is a mirror image of the varactors in the neighboring row, as shown in FIG. 8b. Conductors 840a-d run along the length of the major surface 810 between the rows of varactors 880. Conductors 830a-d run along the width of the major surface 810 between the varactors 880 connecting the conductors 840a-d, as shown in FIG. 8b. 
FIG. 8c shows a schematic of a circuit on the major surface 820. The major surface 820 has conductors 860a-c running along the width of the major surface 820 and conductors 870a-c running along the length of the major surface 820 connecting the conductors 860a-c, as shown in FIG. 8c. 
Although the conductors in FIGS. 8b and 8c are represented as straight lines, it is to be understood that the conductors can have different shapes, including but not limited to straight lines, crenulated lines and/or wavy lines, for this technology to work.
Although the conductors in FIGS. 8b and 8c are represented as parallel lines, it is to be understood that the conductors do not have to be perfectly parallel for this technology to work. The distance between the conductors may vary throughout the length of the conductors.
Although conductors 830a-d appear to be perpendicular to conductors 840a-d in FIG. 8b, it is to be understood that these conductors do not have to be perfectly perpendicular for this technology to work. The angle between the intersecting conductors may vary.
Although conductors 860a-c appear to be perpendicular to conductors 870a-c in FIG. 8c, it is to be understood that these conductors do not have to be perfectly perpendicular for this technology to work. The angle between the intersecting conductors may vary. Structure 890 in FIG. 8d shows an overlay of the circuit on the major surface 810 and the circuit on the major surface 820. Conductors on major surface 810 are oriented at an angle to the conductors on the major surface 820. Although the conductors on the major surface 810 are depicted at a 90° angle to the conductors on the major surface 820 as shown in structure 890 in FIG. 8d, it needs to be appreciated that the angle can be varied.
Vias 895 connect the varactors 880 on the major surface 810 to the point of intersection of conductors 870a-c and 860a-c on the major surface 820, shown in FIG. 8d. 
The lattice period of structure 890 is represented by distance 3B and 3C as shown in FIG. 8d. For this technology to work, the distances 3B and 3C can range from 1/15 of the wavelength to 1⁄2 of the wavelength. The distances 3B and 3C do not have to be equal for this technology to work.
The thickness 3A of the circuit board 800, shown in FIG. 8a, is less important than the thickness 1A of the circuit board 600 described above. Vias 895 make the circuit board 800 less susceptible to the variations in the thickness 3A.
Structure 890 was modeled using Ansoft HFSS software. See FIG. 8e. In the first simulation, the lattice period was modeled at 3B=3C=1 cm, the conductors were modeled at 1 mm width, and the substrate was modeled at 3A=1 mm thickness. The varactors were modeled as a cube of dielectric material whose dielectric constant was tuned from 1 to 64 by factors of 2. Increasing the dielectric constant from 1 to 64 tuned the resonance frequency of the surface from 8 Ghz down to about 2 Ghz. In the second simulation, the lattice period was modeled at 3B=3C=1 cm thickness, the conductors were modeled at 1 mm width, and the substrate was modeled at 3A=7 mm thickness. The varactors were modeled as a cube of dielectric material whose dielectric constant was tuned from 1 to 64 by factors of 2. As can be seen by the results, shown in FIG. 8e, this design is more resistant to variations in the substrate thickness and requires less varactors which offers simpler construction.
Applying voltages to conductors on each major surface of the substrate controls the propagation of different frequencies through the TFSS. Depending on the voltages applied, the capacitance of the varactors is tuned and the resonance frequency of the TFSS is adjusted. Setting conductors on the major surface 810 to 0 volts and setting conductors on the major surface 820 to +10 volts, as shown in FIG. 8f, will cause all of the varactors to be reverse biased and this will allow a certain resonance frequency to pass through the entire TFSS. The voltage numbers are just provided as an example; the voltage numbers could be varied to achieve desired resonance frequency.
In this embodiment, the TFSS can be set into an opaque (off) state. The opaque state is achieved by forward biasing the varactors, as shown in FIG. 8g, which shorts across the continuously conductive loop. Setting conductors on major surface 810 to 0 volts and setting conductors on major surface 820 to −1 volts, as shown in FIG. 8g, will cause all of the varactors to be forward biased thereby blocking all the resonance frequencies from propagating though the TFSS. The voltage numbers are just provided as an example; the voltage numbers could be varied and still cause all of the varactors to be forward biased.
It should be apparent that this embodiment could be implemented in other ways.
For example, the TFSS includes a circuit board 900, with an array of conductors 940a-d, 930a-d on the major surface 910, an array of conductors 960a-c, 970a-c, varactors 980 on the major surface 920 and vias 995 connecting major sides 910 and 920 as shown in FIG. 9a-c. FIG. 9a shows the side view of the substrate 900.
FIG. 9b shows a schematic of a circuit on the major surface 910. The major surface 910 has conductors 930a-d running along the width of the major surface 910 and conductors 940a-d running along the length of the major surface 910 connecting the conductors 930a-d, as shown in FIG. 9b. 
FIG. 9c shows a schematic of a circuit on the major surface 920. The major surface 920 has a plurality of oppositely oriented, interconnected varactors 980 organized in rows where the orientation of the varactors in one row is a mirror image of the varactors in the neighboring row, as shown in FIG. 9c. Conductors 970a-c run along the length of the major surface 920 between the rows of varactors 980. Conductors 960a-c run along the width of the major surface 920 between the varactors 980 connecting the conductors 970a-c, as shown in FIG. 9c. 
Although the conductors in FIGS. 9b and 9c are represented as straight lines, it is to be understood that the conductors can have different shapes, including but not limited to straight lines, crenulated lines and/or wavy lines, for this technology to work.
Although the conductors in FIGS. 9b and 9c are represented as parallel lines, it is to be understood that the conductors do not have to be perfectly parallel for this technology to work. The distance between the conductors may vary throughout the length of the conductors.
Although conductors 930a-d appear to be perpendicular to conductors 940a-d in FIG. 9b it is to be understood that these conductors do not have to be perfectly perpendicular for this technology to work. The angle between the intersecting conductors may vary.
Although conductors 960a-c appear to be perpendicular to conductors 970a-c in FIG. 9c it is to be understood that these conductors do not have to be perfectly perpendicular for this technology to work. The angle between the intersecting conductors may vary.
Structure 990 in FIG. 9d shows an overlay of the circuit on the major surface 910 and the circuit on the major surface 920. Conductors on major surface 910 are oriented at an angle to the conductors on the major surface 920. Although the conductors on the major surface 910 are depicted at a 90° angle to the conductors on the major surface 920 as shown in structure 990 in FIG. 9d, it needs to be appreciated that the angle can be varied.
Vias 995 connect the varactors 980 on the major surface 920 to the point of intersection of conductors 930a-d and 940a-d on the major surface 910, shown in FIG. 9d. 
In another example, the TFSS includes a circuit board 1000, with an array of conductors 1040a-d, 1030a-d on the major surface 1010, an array of conductors 1060a-c, 1070a-c on the major surface 1020, varactors 1080 on the major surface 1025 and vias 1095 and 1096 connecting major sides 1010, 1025 and 1020 as shown in FIG. 10a-d. FIG. 10a shows the side view of the substrate 1000.
FIG. 10b shows a schematic of a circuit on the major surface 1010. The major surface 1010 has conductors 1030a-d running along the width of the major surface 1010 and conductors 1040a-d running along the length of the major surface 1010 connecting the conductors 1030a-d, as shown in FIG. 10b. 
FIG. 10c shows a schematic of a circuit on the major surface 1020. The major surface 1020 has conductors 1070a-c running along the length of the major surface 1020 and conductors 1060a-c running along the width of the major surface 1020 connecting the conductors 1070a-c, as shown in FIG. 10c. 
FIG. 10d shows a schematic of a circuit on the major surface 1025. The major surface 1025 has a plurality of oppositely oriented, interconnected varactors 1080, as shown in FIG. 10d. 
Vias 1095 connect the varactors 1080 on the major surface 1025 to the point of intersection of conductors 1030a-d and 1040a-d on the major surface 1010, shown in FIG. 10e. 
Vias 1096 connect the varactors 1080 on the major surface 1025 to the point of intersection of conductors 1070a-c and 1060a-c on the major surface 1020, shown in FIG. 10e. 
Although the conductors in FIGS. 10b and 10c are represented as straight lines, it is to be understood that the conductors can have different shapes, including but not limited to straight lines, crenulated lines and/or wavy lines, for this technology to work.
Although the conductors in FIGS. 10b and 10c are represented as parallel lines, it is to be understood that the conductors do not have to be perfectly parallel for this technology to work. The distance between the conductors may vary throughout the length of the conductors.
Although conductors 1030a-d appear to be perpendicular to conductors 1040a-d in FIG. 10b it is to be understood that these conductors do not have to be perfectly perpendicular for this technology to work. The angle between the intersecting conductors may vary.
Although conductors 1060a-c appear to be perpendicular to conductors 1070a-c in FIG. 10c it is to be understood that these conductors do not have to be perfectly perpendicular for this technology to work. The angle between the intersecting conductors may vary.
Structure 1090 in FIG. 10e shows an overlay of the circuit on the major surface 1010, the circuit on the major surface 1025 and the circuit on the major surface 1020. Conductors on major surface 1010 are oriented at an angle to the conductors on the major surface 1020. Although the conductors on the major surface 1010 are depicted at a 90° angle to the conductors on the major surface 1020 as shown in structure 1090 in FIG. 10e, it needs to be appreciated that the angle can be varied.
These are just some of the examples of implementing this embodiment; there are other implementations available although not specifically listed here.
In another embodiment, the TFSS includes a circuit board 1100, with an array of conductors 1130a-h and varactors 1150 on the major surface 1110, an array of conductors 1140a-h on the major surface 1120 and vias 1160 connecting major sides 1110 and 1120 as shown as shown in FIG. 1a-c. FIG. 11a shows the side view of the substrate 1100.
FIG. 11b shows a schematic of a circuit on the major surface 1110. The major surface 1110 has a plurality of oppositely oriented, interconnected varactors 1150 organized in columns where the orientation of the varactors in one column is a mirror image of the varactors in the neighboring column, as shown in FIG. 11b. Conductors 1130a-h run along the width of the major surface 1110 between the columns of varactors 1150, as shown in FIG. 11b. 
FIG. 11c shows a schematic of a circuit on the major surface 1120. The surface 1120 has conductors 1140a-h running across the length surface 1120, as shown in FIG. 11c. 
Although the conductors in FIGS. 11b and 11c are represented as straight lines, it is to be understood that the conductors can have different shapes, including but not limited to straight lines, crenulated lines and/or wavy lines, for this technology to work.
Although the conductors in FIGS. 11b and 11c are represented as parallel lines, it is to be understood that the conductors do not have to be perfectly parallel for this technology to work. The distance between the conductors may vary throughout the length of the conductors.
Structure 1170 in FIG. 11d shows an overlay of the circuit on the major surface 1110 and the circuit on the major surface 1120. Conductors on major surface 1110 are oriented at an angle to the conductors on the major surface 1120. Although the conductors on the major surface 1110 are depicted at a 90° angle to the conductors on the major surface 1120 as shown in structure 1170 in FIG. 11d, it needs to be appreciated that the angle can be varied.
Vias 1160 connect the varactors 1150 on the major surface 1110 to conductors on the major surface 1120, shown in FIG. 11d. 
The lattice period of structure 1170 is represented by distance 6B and 6C as shown in FIG. 11d. For this technology to work, the distances 6B and 6C can range from 1/15 of the wavelength to 1⁄2 of the wavelength. It needs to be appreciated that the distances 6B and 6C do not have to be equal for this technology to work.
The thickness 6A of the circuit board 1100, shown in FIG. 11a, is sufficiently small to produce capacitive coupling between the conductors on major surface 1110 and the conductors on major surface 1120. The capacitive coupling between conductors depends on the distance between the conductors and the width of the conductors. In this embodiment, the width of all the conductors and thickness 6A are matched so as to produce capacitive coupling between the conductors on major surface 1110 and the conductors on major surface 1120.
Structure 1170 was modeled using Ansoft HFSS software. See FIG. 11e. In the first simulation, the lattice period was set at 6B=6C=1 cm, the conductors were modeled at 1 mm width, and the substrate was modeled at 6A=1 mm thickness. The varactors were modeled as a cube of dielectric material whose dielectric constant was tuned from 1 to 64 by factors of 2. Increasing the dielectric constant from 1 to 64 tuned the resonance frequency of the surface from 8 Ghz down to about 2 Ghz. In the second simulation, the lattice period was modeled at 6B=6C=1 cm, the conductors were modeled at 1 mm width, and the substrate was modeled at 6A=7 mm thickness. The varactors were modeled as a cube of dielectric material whose dielectric constant was 8. As can be seen by the results, shown in FIG. 11e, this design is more resistant to variations in the substrate thickness. There was only minor degradation of transmission magnitude as the substrate thickness was increased.
Applying voltages to conductors on each major surface of the substrate controls the propagation of different frequencies through the TFSS. Depending on the voltages applied, the capacitance of the varactors is tuned and the resonance frequency of the TFSS is adjusted. Setting bias wires 1130a-h to 0 volts and setting bias wires 1140a-h to +10 volts, as shown in FIG. 11f, will cause all of the varactors to be reverse biased and this will allow a certain resonance frequency to pass through the entire TFSS. The voltage numbers are just provided as an example; the voltage numbers could be varied to achieve desired resonance frequency.
In this embodiment the TFSS can be set into an opaque (off) state. The opaque state is achieved by forward biasing the varactors, as shown in FIG. 11g, which shorts across the continuously conductive loop. Setting conductors 1130a-h to 0 volts and setting conductors 650a-c and 680a-c to −1 volts, as shown in FIG. 11g, will cause all of the varactors to be forward biased, thereby blocking all the resonance frequencies from propagating though the TFSS. The voltage numbers are just provided as an example; the voltage numbers could be varied and still cause all of the varactors to be forward biased.
In this embodiment, different regions of the TFSS can also be tuned to propagate different resonance frequencies and be set to an opaque state. Setting conductors 1130d-e to 0 volts and setting conductors 1140d-e to +10 volts will cause varactors in region R39 to be reverse biased and this will allow a resonance frequency with horizontal and vertical polarization HVF4 to propagate through the R39 region of TFSS, as shown in FIG. 11g. Setting conductors 1130a-c and 1130f-h to +5.5 volts and conductors 1140a-c and 1140f-h to 4.5 volts will cause varactors in region R31, R33, R35 and R37 to be forward biased, thereby blocking the propagation of all horizontal and vertical resonance frequencies through the R31, R33, R35 and R37 regions of TFSS, as shown in FIG. 6g. As a by-product, varactors in the regions R32 and R36 are also reverse biased and this will allow a resonance frequency with horizontal and vertical polarization HVF5 to propagate through the R32 and R36 region of TFSS, as shown in FIG. 11g. Varactors in the regions R38 and R34 are also reverse biased and this will allow a resonance frequency with horizontal and vertical polarization HVF6 to propagate through the R38 and R34 region of TFSS, as shown in FIG. 11g. The voltage numbers are just provided as an example. A person familiar with this technology would know that the voltage numbers could be varied to achieve any desired resonance frequency. The size and shape of the regions that allow the resonance frequencies to propagate or not propagate through TFSS shown here are just provided as an example. The size and shape of these regions can be adjusted by applying appropriate voltages to the appropriate conductors.
It should be apparent that this embodiment could be implemented in other ways.
For example, the TFSS includes a circuit board 1200, with an array of conductors 1230a-h on the major surface 1210, an array of conductors 1240a-h and varactors 980 on the major surface 1220, and vias 1260 connecting major sides 1210 and 1220 as shown in FIG. 12a-c. FIG. 12a shows the side view of the substrate 1200.
FIG. 12b shows a schematic of a circuit on the major surface 1210. The major surface 1210 has conductors 1230a-h running along the width of the major surface 1210, as shown in FIG. 9b. 
FIG. 12c shows a schematic of a circuit on the major surface 1220. The major surface 1220 has a plurality of oppositely oriented, interconnected varactors 1250 organized in rows where the orientation of the varactors in one row is a mirror image of the varactors in the neighboring row, as shown in FIG. 12c. Conductors 1240a-h run along the length of the major surface 1220 between the rows of varactors 1250, as shown in FIG. 12c. 
Although the conductors in FIGS. 12b and 12c are represented as straight lines, it is to be understood that the conductors can have different shapes, including but not limited to straight lines, crenulated lines and/or wavy lines, for this technology to work.
Although the conductors in FIGS. 12b and 12c are represented as parallel lines, it is to be understood that the conductors do not have to be perfectly parallel for this technology to work. The distance between the conductors may vary throughout the length of the conductors.
Structure 1270 in FIG. 12d shows an overlay of the circuit on the major surface 1210 and the circuit on the major surface 1220. Conductors on major surface 1210 are oriented at an angle to the conductors on the major surface 1220. Although the conductors on the major surface 1210 are depicted at a 90° angle to the conductors on the major surface 1220, as shown in structure 1270 in FIG. 12d, it needs to be appreciated that the angle can be varied.
Vias 1260 connect the varactors 1250 on the major surface 1220 to conductors on the major surface 1210, shown in FIG. 12d. 
In another example, the TFSS includes a circuit board 1300, with an array of conductors 1330a-h on the major surface 1310, an array of conductors 1340a-h on the major surface 1320, varactors 1350 on the major surface 1325, and vias 1360 and 1365 connecting major sides 1310, 1325 and 1320 as shown in FIG. 13a-d. FIG. 13a shows the side view of the substrate 1000.
FIG. 13b shows a schematic of a circuit on the major surface 1310. The major surface 1310 has conductors 1330a-h running along the width of the major surface 1310, as shown in FIG. 13b. 
FIG. 13c shows a schematic of a circuit on the major surface 1320. The major surface 1320 has conductors 1340a-h running along the length of the major surface 1320, as shown in FIG. 13c. 
FIG. 13d shows a schematic of a circuit on the major surface 1325. The major surface 1325 has a plurality of oppositely oriented, interconnected varactors 1350, as shown in FIG. 13d. 
Vias 1360 connect the varactors 1350 on the major surface 1025 to the conductors 1330a-h on the major surface 1310, shown in FIG. 13e. 
Vias 1365 connect the varactors 1500 on the major surface 1025 to the conductors 1340a-h on the major surface 1320, shown in FIG. 13e. 
Although the conductors in FIGS. 13b and 13c are represented as straight lines, it is to be understood that the conductors can have different shapes, including but not limited to straight lines, crenulated lines and/or wavy lines, for this technology to work.
Although the conductors in FIGS. 13b and 13c are represented as parallel lines, it is to be understood that the conductors do not have to be perfectly parallel for this technology to work. The distance between the conductors may vary throughout the length of the conductors.
Structure 1370 in FIG. 13d shows an overlay of the circuit on the major surface 1310, the circuit on the major surface 1325, and the circuit on the major surface 1320. Conductors on major surface 1310 are oriented at an angle to the conductors on the major surface 1320. Although the conductors on the major surface 1310 are depicted at a 90° angle to the conductors on the major surface 1320, as shown in structure 1370, in FIG. 13d, it needs to be appreciated that the angle can be varied.
These are just some of the examples of implementing this embodiment; there are other implementations available although not specifically listed here.
While several illustrative embodiments of the invention have been shown and described, numerous variations and alternative embodiments will occur to those skilled in the art. Such variations and alternative embodiments are contemplated, and can be made without departing from the scope of the invention as defined in the appended claims.

## Claims

1. A method of tuning at least a region of a tunable frequency selective surface, the method comprising:
applying a first voltage to alternating conductors disposed along a length of a first major surface of the tunable frequency selective surface and alternating conductors disposed along a width of a second major surface of the tunable frequency selective surface;
applying a second voltage to remaining conductors disposed along the length of the first major surface of the tunable frequency selective surface so as to cause a plurality of varactors coupling the conductors on the first major surface to be reverse biased and tuned to a resonance frequency; and
applying the second voltage to remaining conductors disposed along the width of the second major surface of the tunable frequency selective surface so as to cause the plurality of varactors coupling the conductors on the second major surface to be reverse biased and tuned to the resonance frequency.

2. A method of tuning at least a region of a tunable frequency selective surface, the method comprising:
applying a plurality of voltages to conductors disposed on a first major surface and on a second major surface of the tunable frequency selective surface so as to cause a plurality of varactors coupling the conductors to be reverse biased and to cause the at least a region of the tunable frequency selective surface to be tuned to a frequency, wherein applying the plurality of voltages comprises:
applying a first voltage to alternating conductors disposed along a length of the first major surface and alternating conductors disposed along a width of the second major surface;
applying a second voltage to remaining conductors disposed along the length of the first major surface so as to cause the plurality of varactors coupling the conductors on the first major surface to be reverse biased and tuned to a resonance frequency; and
applying the second voltage to remaining conductors disposed along the width of the second major surface so as to cause the plurality of varactors coupling the conductors on the second major surface to be reverse biased and tuned to the resonance frequency.