PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27–30, 2012
314
Ultra Thin Metamaterial Absorbers Using Electric Field Driven LC
(ELC) Resonator Structure
Somak Bhattacharyya and Kumar Vaibhav Srivastava
Department of Electrical Engineering, Indian Institute of Technology, Kanpur, India
Abstract— The aim of this paper is to construct ultra thin absorbers using metamaterials in
C-band. An Electric Field Driven LC (ELC) structure has been proposed and its equivalent LC
circuit combination has been shown. The simulation of the proposed structure using Ansoft HFSS
shows that absorption occurs at 6.46 GHz with absorbance of 98.24% with S11 of −17.55 dB. The
frequency where absorption occurs is reduced significantly as compared to previously reported
structure. The proposed structure can be further reduced in area to provide a more compact
structure which reduces the extra metallic strip in the outer side. The capacitor value can
be changed by incorporating changes in the proposed structure which shows the absorbance of
99.2% at 6.70 GHz. Thus, the size reduction of the ELC element is possible with slight increase
of frequency where the absorption occurs.
1. INTRODUCTION
Microwave absorbers play a crucial role in stealth technology [1], where reduction of Radar CrossSection [2] is one of the major challenges. To make thin absorber at microwave frequencies, metamaterials [3] have been used where the thickness as well as size can be reduced significantly. SRR-based
metamaterials are first used as absorbers [4], but the wave has to travel all along the length of the
elements. Later, by using periodic metallic wires and SRRs, Landy et al. [5] proposed a structure where the wave has to travel much shorter distance. Li et al. [6] has suggested metamaterial
absorbers using the Electric Field Driven LC (ELC) resonator structure, which is explained in [7].
In this paper, an ELC driven metamateral absorber structure has been proposed, where the
capacitance value has been increased and hence the resonance frequency reduces to 6.46 GHz from
9.92 GHz [6]. This structure suffers from fabrication point of view, where more area is needed;
but the difficulty can be overcome if one uses the modified structure as discussed in this paper.
The modification leads to the absorbance of 99.2% at 6.70 GHz. Thus, the frequency at which
absorbance occurs is increasing slightly at the cost of compactness.
2. DESIGN OF THE STRUCTURE
The front view of the basic unit cell structure of the proposed structure is shown in Fig. 1(a). The
direction of electric field, magnetic field and wave propagation in the structure is also shown. The
absorbance can be found out as shown in Equation (1) [5], where A(ω), |S11 (ω)|2 and |S21 (ω)|2 are
the absorbance, reflected power and transmitted power respectively at an angular frequency ω.
A(ω) = 1 − |S11 |2 − |S21 |2
(1)
The structure consists of two layers [6], with the upper layer consisting of an array of ELC
resonators [7] which are responsible for electric resonance and the back layer made up of copper
sheet. These two layers are separated by a dielectric substrate FR-4 (relative permittivity of 4.4
and dielectric loss tangent of 0.02) with thickness of 1 mm. The metal used in this structure is
copper with conductivity of 5.8 × 107 S/m. The dimension of the cell is a = 5 mm, d = 3.6 mm,
l = 1.5 mm, w = 0.4 mm, and g = 0.2 mm with the thickness of the copper film of 0.035 mm. Since
the structure is backed by copper sheet, |S21 | = 0 and thus A(ω) = 1 − |S11 |2 . Thus, by reducing
the reflection from the structure, absorbance can be maximized.
The equivalent L-C circuit of the proposed structure is shown in Fig. 1(b). In the equivalent
structure, there are two identical capacitances C are in parallel with each other and hence the
net capacitance value increases as compared to the ELC resonator structure as discussed in [7].
However, at the same time the effective inductance value slightly comes down than [7]. So, this
leads to the reduction in the frequency at which absorption occurs.
The simulation of the structure is carried out in the FEM-based solver Ansoft HFSS software
where proper boundary conditions are given. The top and bottom side of the structure in Fig. 1(a)
have been assigned as PEC boundary while the right and left side of the structure have been
Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27–30, 2012 315
(a)
(b)
Figure 1: (a) Proposed ELC resonator structure. (b) Equivalent L-C circuit.
Figure 2: Proposed modified ELC structure.
assigned as PMC boundary. This enables the simulation of array structure of the unit cell. The
waveports are suitably defined in the structure at the front and back side respectively to evaluate
the reflected power from the structure. Due to the metal backing, |S21 | = 0.
The value of capacitance in Fig. 1(a) can be modified where the extra metallic patches are
removed and hence the structure size is becoming compact in nature as shown in Fig. 2. The other
dimensions remain constant while l = 0.95 mm is taken. This leads to decrease of the effective area
of the metal patch and hence the decrease of capacitance value. But, this also leads to a slight
increase of the resonance frequency as compared to the structure defined in Fig. 1(a). The same
boundary condition is used to simulate the new structure in HFSS.
3. SIMULATED RESULTS
The simulation of the first proposed structure shows a dip in the plot of S11 to −17.56 dB at
6.46 GHz as shown in Fig. 3(a). This corresponds to absorbance value A(ω) of 98.24% at 6.46 GHz
as shown in Fig. 3(b) as calculated from Equation (1). Thus, the structure will behave as absorber
at frequency of 6.46 GHz.
The simulation in the modified structure shows that the minima of S11 and maxima of A(ω) take
place at 6.70 GHz, where these values are −19.6 dB and 99.2% respectively as shown in Fig. 4(a)
and Fig. 4(b) respectively.
The normalized input impedance z of the structure is given as [8] in Equation (2a). Since
|S21 | = 0, this equation is reduced to the form as shown in Equation (2b). So, the real part of
the normalized impedance should be unity and the imaginary part of the impedance should be
null at the frequency where the absorption takes place. The plot in Fig. 5 shows that the real and
imaginary parts are unity and null respectively at 6.70 GHz to ensure absorption at this frequency.
s
2
(1 + S11 )2 − S21
z =
(2a)
2
(1 − S11 )2 − S21
1 + S11
z =
(2b)
1 − S11
The size of the unit cell is scaled to change the frequency of absorption varying in C-band. The
dimensions of the metallic patches of the unit cell can be scaled by a factor k so that the frequency
of absorption can vary from the obtained one. A scaling factor k of 0.8 and 1.2 respectively yields
absorption at 7.9 GHz and 5.74 GHz respectively with absorbance of 85.64% and 95.34% respectively
as shown in Fig. 6.
PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27–30, 2012
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Absorbance (%)
S11 (dB)
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Frequency (GHz)
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Frequency (GHz)
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Absorbance (%)
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Figure 3: (a) S11 plot and (b) absorbance plot for the proposed structure shown in Fig. 1(a).
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0
4
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Frequency (GHz)
(a)
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Frequency (GHz)
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(b)
Figure 4: (a) S11 plot and (b) absorbance plot for the modified ELC Structure shown in Fig. 2.
Figure 5: Impedance plot of the modified structure.
Figure 6: Absorbance as a function of frequency for different scale factors k.
Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27–30, 2012 317
4. CONCLUSIONS
The simulation result shows that microwave absorber can be made at C-band with ELC resonating
structures, where the incident electromagnetic wave has to travel across the thickness of the FR-4
substrate; thus making advantage of using such structures instead of conventional metamaterials
structure. The resonating frequency comes down to 6.46 GHz and 6.70 GHz respectively as compared to 9.92 GHz as mentioned in [6]. Also, the absorption criterion is supported by calculating
input impedance which shows the matching of impedances at 6.70 GHz. The scaling of the unit
cell leads to a shift of frequency where absorption occurs. Experiments should be carried out to
validate the result obtained by using the simulations.
The structure can be used as a multiband absorber provided different scale factors of the dimensions of the metallic patches of the unit cell can be used in array. If a 3 × 3 array is used with
dimensions scaled as 1.2, 1 and 0.8 respectively, the structure will resonate at 5.74 GHz, 6.7 GHz
and 7.9 GHz respectively. So, in the C-band, the structure can be used as multiband absorber. If
the resonant frequencies can be made closer to each other, then there will be broadband absorption
by using the modified structure.
ACKNOWLEDGMENT
The authors want to acknowledge all the staffs of Microwave Circuit Laboratories for their continuous support and IIT Kanpur institute for the financial support.
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