Recovering Suppressed Resonance Frequency by Bias Lines in Reconfigurable FSS

Abstract

In reconfigurable frequency selective surface, FSS, bias lines can suppress a resonant frequency. This is a disadvantage, as it reduces a FSS potential application. In this paper, a procedure to recover the suppressed resonant frequency is described. A FSS based on four arms star geometry is considered and its reconfigurability is achieved by the use of varactors, for which bias lines suppress the x polarization resonance. So, dipoles are added to the unit cell geometry recovering this resonance. In order to validate the proposed procedure, a reconfigurable FSS using the varactor SMV1231 (0. 466 pF ≤ C_v < 2. 35 pF) was fabricated and characterized. Numerical and measured results shown a good agreement, confirming that the FSS reconfigurability is preserved and the suppressed resonance recovered.

Index Terms
Four arms star; reconfigurable FSS; suppressed resonance; varactor

I. Introduction

Frequency selective surfaces, FSS, have attracted the attention of several research groups, both for simplicity of manufacture and for the diversity of applications [ ¹ ]—[ ³ ]. Dual band antennas systems [ ⁴ ], [ ⁵ ], radomes [ ⁶ ], [ ⁷ ], electromagnetically smart buildings [ ⁸ ]—[ ¹⁰ ] and reconfigurable antennas [ ³ ], [ ¹¹ ]—[ ¹³ ] are examples of FSS applications. Basically, a FSS is composed by a periodic array of unit cells, usually engraved on a dielectric substrate, designed to be transparent in some frequency bands, while reflecting or absorbing the others. The FSS frequency response depends on the type of unit cell (patch or aperture), its geometry and periodicity, as well as substrate properties (e.g. thickness and permittivity) and polarization of the incident wave [ ⁴ ], [ ¹⁴ ]. Although FSS may be three-dimensional, in this paper only planar FSS are considered, that is, when the thickness of the metallization layer is much less than the wavelength at the resonant frequency [ ¹⁵ ], [ ¹⁶ ]. FSS can also present a variable frequency response, when they can be nominated reconfigurable FSS.

Reconfigurable FSS are especially attractive to smart antennas applications [ ³ ], [ ¹¹ ]–[ ¹³ ].

In order to obtain the FSS reconfigurability mechanical and electronic tuning have been exploited. Commonly, electronic tuning is achieved by adding active elements, such as PIN diodes, MEMS switches and varactors to FSS unit cell, [ ³ ], [ ¹⁴ ], [ ¹⁹ ]–[ ²¹ ]. Mechanical tuning is especially attractive when no power supply is desired and, in this case, mechanical modifications (e.g., rotate, stretching, sliding, and folding) are utilized, [ ³ ], [ ⁹ ], [ ¹⁷ ], [ ¹⁸ ]. Both electronic and mechanical tuning can be discrete or continuous, depending on the adopted technique. In the discrete electronic tuning, when a limited number of the FSS frequency responses is required, normally PIN diodes or MEMS switches are used. For electronic tuning still, if a continuous variation of the FSS frequency response is desired, usually varactors are used.

In the reconfigurable FSS, in addition to the insertion of the active component, it is also necessary to include the bias lines, as depicted in Fig. 1 , for the four arms star geometry [ ¹⁴ ]. A problem that arises is that the resonance for the polarization χ is practically suppressed, as can be seen in Fig. 2 . However, considering present requirements of the telecommunication systems, operating in different frequencies, retrieving this resonance may be useful, especially considering that it takes advantage of a structure that is already available, increasing its functionality.

Fig. 1
Four arms star geometry [ ¹⁴ ].

Fig. 2
FSS frequency response with and without bias lines.

In order to recover the suppressed resonance, this paper describes the inclusion of dipoles along the χ direction, obtaining the respective resonance, without altering the reconfigurable behavior in the y polarization. A first dipole is added between the bias lines, aligned with the switch point. Aiming to reinforce the χ polarization resonance, a second dipole is inserted between the four arms stars. Besides, this second dipole is dislocated to avoid a coupling with the bias lines. After this Introduction, four arms star and dipole geometry are described in Section II, which also included the varactor model. The proposed procedure to recover the suppressed resonance is detailed in Section III, including numerical and measured results. In Section IV, results and conclusions are summarized.

II. Four arms star and dipole geometries and varactor model

In this Section the dipole and the four arms star geometries are described, including adopted initial design equations. Furthermore, the considered varactor model is presented.

A. Dipole

Dipole is one of the simplest geometries, for which the first resonant frequency occurs when its length is approximately half wavelength, considering that the electric field and the dipole have the same direction [ ⁴ ].

Fig. 3
Dipole geometry.

The dipole resonant frequency, f_res–dip, can be approximately determined by ( 1 ), [ ⁴ ], [ ²² ],

(1) $$f_{res-dip}(GHz)=\frac{0.3}{2L_{dip}\sqrt{{\epsilon }_{ref}-dip}},$$

in which ε_ref–dip is given by ( 2 ), [ ²² ],

(2) $${\mathcal{E}}_{ref-dip}=\frac{{\epsilon }_{ref-MS}+{\epsilon }_{ref-CPW}}{2}.$$

Where

ε_ref-MS is the effective dielectric constant for a microstrip, considering the microstrip width equals the dipole width, W_dip , and a dielectric thickness h .

ε_ref–CPW is the effective dielectric constant for a coplanar waveguide without ground plane, for which the distance between the center strip and the ground planes, s , is 10 × h and the center strip width is equal to the dipole width, w_dip, [ ²³ ].

ε_ref-MS and ε_ref-CPW can be easily calculated using available software [ ²⁴ ], [ ²⁵ ].

B. Four arms star geometry

Four arms star geometry was introduced in [ ²⁶ ], with very interesting characteristics, such as miniaturization and switching. In Fig. 4 , the four arms star geometry is depicted and the procedure to obtain it is detailed in [ ¹⁹ ], [ ²¹ ].

Fig. 4
Four arms star geometry.

Without the gap, Fig. 4(a) , the FSS resonant frequency can be estimated by ( 3 ), [ ¹⁴ ], [ ¹⁹ ], [ ²¹ ],

(3) $$\frac{0.3}{2(Lx+Ly)}\le f_{res}(GHz)\le \frac{0.3}{2\left(\sqrt{L{x}^2+L{y}^2}\right)\sqrt{{\epsilon }_{ref-CPW}}},$$

where, similar to dipole, ε _ref-CPW is defined as the effective dielectric constant for a coplanar waveguide without ground plane, for which the distance between the center strip and the ground planes, s , is 10 × h and the center strip width is equal to 0.5( dx + dy ).

With the gap and the bias lines, roughly speaking, the resonant frequency, f_res-gb , can be estimated by ( 4 ).

(4) $$1.5f_{res}\le f_{res-gb}\le 2.0f_{res},$$

Despite the resonant frequencies obtained by ( 1 )—( 4 ) are not exact, these equations are useful as a first step for a numerical optimization.

C. Varactor model

The varactor is a PN junction diode that is specially designed to operate in the reverse-bias electrical condition. It takes advantage of the junction capacitance, that is increased as much as possible in the manufacturing process, and can be controlled by the reverse bias voltage [ ²⁷ ]. A more accurate varactor model includes, besides the variable capacitance, inductances and resistances [ ²⁸ ], Fig. 5 . However, in many applications a simplified model, considering only the variable capacitance, can be adopted. A detailed modeling of the resonant behavior of a continuously reconfigurable FSS based on four arms star geometry, using the varactor as active component, is reported in [ ¹⁴ ].

Fig. 5
Varactor models.

In this paper the varactor SMV1231-079LF was used and its capacitance versus reverse voltage curve is presented in Fig. 6 , [ ²⁹ ].

Fig. 6
Varactor SMV1231-079LF, Capacitance (pF) × Reverse voltage (V) curve [ ²⁹ ].

In the next Section, in order to recover the suppressed resonance, the use of previously described geometries and the varactor model are detailed, including numerical and measured results.

III. Recovering the suppressed resonance

In order to verify the proposed design procedure, numerical and measured results were obtained. Numerical results were achieved using the commercial software ANSYS HFSS, and, unless specified, the incidence is considered normal to the FSS. Measured results were acquired at the GTEMA/IFPB microwave measurements laboratory using an Agilent E5071C two ports network analyzer, two double ridge horn antennas and a measurement window as shown in Fig. 7 . A low-cost fiber-glass substrate (FR-4, ε_r = 4.4, loss tangent 0.02, thickness 1.0 mm) was employed.

Fig. 7
Measurement setup.

As a first step, a FSS based on the four arms star geometry, Fig. 4(a) , was designed with the following unit cell dimensions: Wx = Wy = 32 mm, Lx = Ly = 26 mm, Sx = Sy = 4 mm, dx = dy = 3 mm, msx = msy = 1 mm . It was numerically characterized and its frequency response is shown in Fig. 8 . As expected, the frequency responses are the same for x and y polarizations. The first resonant frequency is f_res = 3.40 GHz , in accordance with ( 3 ), 2.88 GHz ≤ f_res ≤ 3.52 GHz .

Fig. 8
FSS frequency response - Four arms star geometry.

In the next step, the gap and the bias lines were introduced ( g = 1 mm, wb = 1.5 mm ), Fig. 4(c) , and the obtained frequency response is presented in Fig. 9 . The FSS became polarization dependent, with band pass and band stop characteristics, for x and y polarizations, respectively. For the y polarization, the resonant frequency is f_res-gb = 5.75 GHz , in consonance with ( 4 ), 5.10 GHz ≤ f_res-gb ≤ 6.80 GHz . For X polarization the band stop resonance was practically suppressed.

Fig. 9
FSS frequency response - Four arms star geometry with gap and bias lines.

In the dipole specification, initially it is considered a single dipole, Fig. 10(a) , with L_dip = 20 mm and w_dip = 2 mm . Then, a second dipole is placed in the unit cell, Fig. 10(b) , Fig. 10(c) . Note that this new dipole is placed in parallel with the existing dipole, but displaced. Fig. 11 shows the frequency response for the single dipole and with the second dipole. As for the y polarization no resonant frequency is observed, results are presented for the x polarization only. For the single dipole, the resonant frequency determined using ( 1 ) is 4.86 GHz , a good result when compared to the numerical result, 5.20 GHz . With the second dipole, the resonant frequency, obtained numerically, is 5.75 GHz . Observe that the dipole resonant frequency can be easily adjusted, which is interesting in the FSS design.

Fig. 10
FSS unit cell with dipoles.

Fig. 11
FSS frequency response - Dipoles, x polarization only.

Then, four arms star and dipole geometries are superposed. In this case, a FSS prototype was fabricated with the previously described unit cell dimensions. The whole FSS has 6 × 6 unit cells, arranged in 6 lines, with 192 mm × 192 mm, Fig. 12 . Despite the cell lines could be individually controlled, in this work they were connected and controlled all together. The FSS dimensions are summarized in Table I . The frequency responses for the FSS prototype, without the insertion of the varactor, polarizations x and y are shown in Fig. 13 and Fig. 14 , respectively, verifying a good agreement between numerical and measured results.

Fig. 12
FSS prototype.

TABLE I
FSS DIMENSIONS

Wx = Wy	Sx = Sy = 4 mm	wb
Lx = Ly	msx = msy =	Ldip =
dx = dy = 3 mm	g = 1 mm	wdip

Fig. 13
FSS frequency response, without varactor insertion - x polarization.

Fig. 14
FSS frequency response, without varactor insertion - y polarization.

For x polarization the measured resonant frequency is 6.00 GHz , not so different from the numerical value, 5.70 GHz . This resonant frequency is practically the same for the dipoles (5.75 GHz) , recovering the resonance for the x polarization. Furthermore, the resonant frequency can be adjusted according to the dipole length and the resonance around 7.0 GHz can be removed.

For y polarization the measured resonant frequency is 6.13 GHz , a difference of 7.5 %, when compared to the numerical value, 5.75 GHz . Two main factors can be related to the observed differences between measured and numerical values: fabrications process limits and dielectric constant value, assumed as 4.4, which can vary from a FR-4 sheet to other.

With the varactor insertion, an additional variable capacitance is introduced. The capacitance value can be estimated from the curve shown in Fig. 6 , and the resonant behavior modeling is detailed in [ ¹⁴ ]. For three different varactor capacitance values, frequency responses are presented in Fig. 15 and in Fig. 16 , x and y polarizations, respectively.

Fig. 15
FSS frequency response, with varactor insertion - x polarization.

Fig. 16
FSS frequency response, with varactor insertion - y polarization.

For x polarization, Fig. 15 , numerical results are independent of the varactor capacitance value, then only one result is shown. A good agreement between numerical and measured results is verified, confirming that x polarization resonant frequency is recovered.

In Fig. 16 , for y polarization, it is observed the variation of the frequency response with the varactor capacitance. Therefore, the added dipoles did not affect the FSS reconfigurable behavior.

In Fig. 17 it is shown the resonant frequency as a function of the varactor reverse voltage, with a good agreement between numerical and measured results. For x polarization, the recovered resonance remains practically constant. For y polarization a resonance variation from 3.30 GHz to 4.46 GHz , and bandwidth of 1.16 GHz was achieved. These are interesting values for antennas applications.

Fig. 17
Resonant frequency (GHz) × Reverse voltage (V).

IV. Conclusions

As bias lines in reconfigurable FSS can suppress a resonant frequency, a procedure to recover this suppressed resonance was described in this paper. Considering the four arms star geometry, basically, dipoles are added to the original reconfigurable FSS unit cell. Initial design equations for four arms star and dipole geometries were presented, as well as the varactor model. Each geometry was numerically characterized and the results obtained indicated the validity of the initial design equations. A reconfigurable FSS prototype was fabricated with the composed geometry (four arms star and dipoles), and, without the varactor insertion, numerical and measured results confirmed that the respective geometry resonances are maintained.

The SMV1231 varactor (0.466 pF ≤ C_v < 2.35 pF) was implemented and it was verified that the FSS reconfigurability was not affected by the dipoles, achieving, for y polarization, a variation from 3.30 GHz to 4.46 GHz , a bandwidth of 1.16 GHz , an interesting value for many telecommunication applications. Furthermore, for x polarization, the recovered resonant frequency remains practically unchanged (5.75 GHz numerical/6.00 GHz measured). In this way, the proposed FSS shown two distinct frequency response: a reconfigurable, y polarization, and the other fixed, x polarization. It must be highlighted that the x polarization resonant frequency can be adjusted according the dipole length, a flexible design variable. Finally, it is possible to say that the objectives have been achieved, and a procedure has been described to recover the resonance suppressed by the bias lines.

ACKNOWLEDGMENT

The authors would like to thank to Leanne Vincent, from Skyworks, by the provided varactors. This work was supported in part by the CNPq (Project 407028/2016-1) and CAPES, Brazilian Federal Agencies, and by the IFPB, Federal Institute of Paraíba (PPGEE, PRPIPG 01/2019).

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Publication Dates

• Publication in this collection
  29 Sept 2021
• Date of issue
  Sept 2021

History

• Received
  04 Feb 2021
• Reviewed
  10 Feb 2021
• Accepted
  18 May 2021