Microwave absorbers can effectively reduce the radar cross sections
of aircraft, and so they are commonly used in stealth missions. However,
as radar detection equipment that is developed that can extend to the
near-meter microwave wavelength regime, high-performance absorbers are
required, especially in the ultrahigh-frequency (UHF) band below 2 GHz.
Unfortunately, absorbers are usually thick and have relatively narrow
absorption bandwidth.
Conventional λ/4 Salisbury screen absorbers are widely used for high
frequencies, but absorbers of microwaves with near-meter wavelengths can
be very thick.
1–3
Fortunately, work on metamaterials has shown that a resonant metallic
structure printed on a dielectric substrate acts as a strong resonant
absorber, and such a metamaterial absorber is significantly thinner than
the wavelengths absorbed.
4–6 For example, Costa
et al.
designed an electromagnetic (EM) absorber for a radio frequency
identification device (RFID) system made of a painted patch array; this
absorber had a narrow working bandwidth (865–868 MHz), but its thickness
was only λ/44 of the resonance frequency.
7
Ideal absorbers exhibit broadband performance. Research on active
frequency selective surfaces (AFSSs) shows that a frequency selective
surface (FSS) loaded with lumped elements, such as varactors
8–11 and PIN diodes,
12–15
can exhibit a tunable absorption bandwidth. For instance, an FSS
absorber loaded with PIN diodes has a tunable bandwidth of 5.3–13 GHz
below −10 dB,
8 and using varactors in a three-layer FSS absorber can produce a tunable bandwidth of 1.8–2.4 GHz.
14 Specifically, Kong
et al. presented a tunable FSS absorber loaded with both PIN diodes and varactors for broadband application.
16
These studies show that the resistance of the PIN diode and the
capacitance of the varactor contribute to the input impedance of the
absorber. At different bias voltages, the absorber impedance matches
with free space at different frequencies, and thus the envelope of
reflectivity curves measured at various bias voltages covers a broad
absorption bandwidth. This result suggests that AFSS absorbers are
practical candidates for broadband applications. As such, we believe it
is possible to design an absorber that is both thin and that exhibits a
broad bandwidth for near-meter microwave applications.
In this paper, we present an ultra-thin broadband AFSS absorber with a
stretching transformation (ST) pattern for use in UHF applications.
Using the transmission line (TL) model, we give the resonance frequency
and the real part of the input impedance as functions of loaded and
distributed parameters. The device's ST coefficients of
x =
y
= 1 demonstrate its tunability and strong absorption. Then, to expand
the tunable bandwidth, we apply various ST coefficients to the unit cell
pattern. We also fabricated the proposed ultra-thin absorber, finding
that its measured reflectivity covered a broad bandwidth in the UHF band
below 2 GHz.
A.
Unit cell structure
Figure
1
shows the structure of the proposed absorber. The top layer is FR4 with
a thickness of 0.8 mm, which has a sufficient mechanical strength to
hold up all the units. The next layer is the AFSS loaded with resistors
and capacitors, and the thickness of the copper is 0.04 mm. The third
layer, used as a separation layer, is a 7.0-mm honeycomb with very low
dielectric loss (
ε = 1.07(1 −
i0.0024) and
μ = 1) in the frequency range studied here. The bottom layer is a metallic slab. Figure
1(b) shows the unit cell pattern, which is based on a bow-tie dipole.
11,17 It is composed of a triangle, a semicircle with a radius of
r, and two rectangles each with the dimensions 2
r ×
b.
The width of the bias line is 1 mm. At the center of the pattern, there
is a gap of 1 mm for lumped elements. A varactor with variable
capacitance
Cvariable is connected in parallel to a resistor
R.
Ld and
Cd are the distributed parameters generated by the topological structure of the unit cell pattern.
With High-Frequency Structure Simulator (HFSS) electromagnetic
simulation software, one can accurately simulate and optimize absorption
performance. Figure
2
shows our model built in HFSS. The Floquet port is assigned to the top
boundary along the k direction, and the bottom boundary is grounded by a
plate made of a perfect electric conductor. The periodical boundary
condition (master-slave boundary) is adopted in the air layer. The
incident wave is modeled as a normal incident wave with the electric
field polarized along the E axis. Finally, the resistor and varactor are
simulated using a lumped LRC model.
To meet the needs of applications in the UHF band below 2 GHz, we
consider both the resonance frequency as well as the absorption
bandwidth. Setting
Cvariable = 1 pF, we optimize the dimensions of the unit cell pattern by using a genetic algorithm.
18 In this optimization, the resonance frequency
f0 must be smaller than 2 GHz and ideally as low as possible. (2 −
f0) is the deviation of
f0 from 2 GHz. The relative bandwidth is written as
BW/
f0, where
BW is the bandwidth with the reflectivity below −10 dB. Overall, the goal function is
(1)
where
m and
n
are the weighting factors of relative bandwidth and resonance
frequency. Such a treatment is helpful in achieving better absorption at
lower frequency. The optimized parameters of the unit cell are
r = 20 mm and
b = 2 mm.
B.
Transmission line model of the absorber
Absorptivity can be described by
A(ω) = 1 −
R(ω)−
T(ω), where
R(ω) is the power reflection coefficient and
T(ω) is the power transmission coefficient. When the reflection coefficient and transmission coefficient are calculated by
R(ω) = s11
2 and
T(ω) = s21
2, the absorptivity is described as
A(ω) = 1 − s11
2 − s21
2. For an absorber grounded with metal slab, the transmission coefficient
T(ω)
equals zero. To minimize reflection of the incident wave, the intrinsic
impedance of the material must be matched to that of free space. In
effective medium theory, effective permittivity (
ε = ε′ + iε′′) and effective permeability (
μ = μ′ + iμ′′) are generally used to analyze absorptivity, because the characteristic impedance of a material can be defined as
. In previous work on metamaterials and ferrite-based absorbers,
19–22
the effective permittivity and effective permeability are easily
measured or calculated. However, in some cases, the EM parameters cannot
be obtained. In such a case, the TL model is a powerful tool to
characterize and interpret this novel structure.
The unit cell of the proposed AFSS absorber is recognized as a
microstrip line resonator loaded with a varactor and a resistor in the
center. The electromagnetic wave is perpendicularly incident to the
AFSS, with the electric field polarized along the E axis and the
magnetic field polarized along the H axis. When the unit cell resonates,
it exhibits pure resistance, and its total input reactance is zero. If
the resonator is modeled by a capacitor
Cs cascaded with an inductor
Ls, the resonance frequency of the absorber will be
. Figure
3(a) gives a rough equivalent circuit model of the absorber.
Cvariable
is the capacitance of the varactor. As the bias voltage decreases, the
capacitance of varactor increases, thus shifting the resonant point to a
lower frequency. The simulated results in Figures
3(b) and
3(d) agree well with the rough equivalent circuit model. As shown in Figure
3(d), the value of the resistor
R is not equal to
Rs.
R is the resistance of the lumped resistor while
Rs is the equivalent resistance of the distributed and lumped resistance. Figure
3(c) shows the electric field distribution for the AFSS absorber, with
R = 700 Ω and
Cvariable = 1 pF, revealing that the resonance state exists and may be important for deep absorption.
To numerically study the absorption performance, we establish an accurate model for the AFSS absorber. Figure
4(a) gives the equivalent circuit model of our absorber based on TL theory.
23–25 By separating the imaginary and real parts, the impedance of the AFSS layer can be described as
(2)
which is equivalent to a resistor connected with a capacitor. The real part of
ZAFSS is a resistor
Requ, and the imaginary part of
ZAFSS is a capacitor
Cequ. ω is the angular frequency of the electromagnetic wave.
Requ and
Cequ are described by
(3)
(4)
The equivalent impedance of the honeycomb along with a metallic slab is described as an inductor with an inductance
Lequ
(5)
where
β is the propagation constant and
d is the thickness of the honeycomb.
Zc is the characteristic impedance of free space. The FR4 layer is thin enough to be ignored, simplifying the analysis. Figure
4(b) shows the simplified equivalent circuit model. The resonance frequency
fresonance of the simplified circuit is described as
(6)
The real part of the input impedance at the resonance frequency is described as
(7)
where
Requ,
Cequ, and
Lequ all are functions of
R,
Cvariable,
Ld, and
Cd.
ST is applied to the unit cell pattern. The size of the unit cell is (
x ×
a) × (
y ×
a), where
a is the basic size before ST and
x and
y
are the ST coefficients on each side. The topological structure of the
AFSS pattern significantly affects the resonant point of the absorber.
For example, consider the dipole antenna: if resonance happens, the
dipole length must be an integer multiple of λ/2, where λ is the
wavelength of the resonance frequency. Thus, a larger unit cell will
have a lower resonance frequency.
Ld and
Cd
represent the distributed parameters, including inductance and
capacitance. On one hand, they are determined by the pattern of the unit
cell and on the other,
Ld and
Cd
can also be adjusted by applying the ST to the chosen pattern. To
obtain the parameters ideal for broadband absorption, we applied various
ST coefficients to the unit cell pattern. Based on Wen
et al.
26 extraction of distributed parameters by applying the ABCD matrix method to an electric split-ring resonator,
4 we calculated
Ld and
Cd by simulating the AFSS layer. Figure
5 shows the S parameters calculated by using the TL model (short dashed lines), with
R = 700 Ω,
Cvariable = 1 pF, and
x = 1,
y
= 1. For comparison, the results of HFSS simulations (solid lines) are
also shown. These results agree well with each other over the whole
frequency range studied. This agreement shows that the equivalent
circuit model and the extracted parameters are reliable. The calculated
distributed parameters are
Ld = 3.76 nH and
Cd = 0.63 pF.
If the input impedance of the absorber matches with that of free
space, the real part will be 377 Ω and the imaginary part will be 0.
According to Eqs.
(6) and
(7), the resonance frequency
fresonance and real part at resonance
Zre,resonance are functions of
Cd,
Ld,
Cvariable, and
R. With
x =
y = 1, the calculated distributed parameters are
Ld = 3.76 nH and
Cd = 0.63 pF. In this case,
fresonance and
Zre,resonance depends only on the lumped elements
Cvariable and
R.
Figure
6 shows how
fresonance varies with the capacitance of the varactor
Cvariable, when compared with the simulated results calculated by the HFSS. The
fresonance–
Cvariable curve shown in Figure
6(a) was calculated according to Eq.
(6), which indicates that the resonant point is a descending function of
Cvariable. Figure
6(b) shows the simulated results with various
Cvariable,
which agree well with the calculated curve. However, there is still a
small discrepancy between these two results. For instance, the simulated
resonance frequency is ∼1.19 GHz at
Cvariable
= 1 pF, while the calculated resonance frequency is ∼1.21 GHz. This
difference is mainly caused by the simplification of the TL model.
While
fresonance is a descending function of
Cvariable, the resistance of the lumped resistor contributes little to
fresonance. The relationship between
R and
fresonance is described in Figure
7(a), where we set
Cvariable = 1 pF. When
R varies from 400 to 2000 Ω,
fresonance remains unchanged. Figure
7(b) shows the simulated results for various
R. The simulated results and calculated curve indicate that changing
R affects
fresonance only slightly.
Figure
8 shows the relationship between
Zre,resonance and the lumped elements at various
Cvariable. At each
Cvariable,
Zre,resonance increases with increasing
R, and there is a clearly ideal
R for impedance matching, named
R0. As
Cvariable varies from 1 to 10 pF,
R0 varies slightly from 750 to 800 Ω. As such, an
R0 calculated for one
Cvariable is close to ideal for all other
Cvariable, and
Zre,resonance will not change much with changes in
Cvariable.
Overall, the resonance frequency
fresonance is mainly related to
Cvariable, while the real part of the resonance frequency
Zre,resonance mainly depends on
R.
AFSS loaded with a resistor and varactor is practical as a design of a
broadband tunable absorber. Adopting the varactor, which supplies a
variable
Cvariable at varying bias voltages, produces the device's tunability.
R0
reliably produces strong absorption at the resonance frequency, which
is realized by using a lumped resistor with constant resistance.
The resonance peaks combine the effects of interference and absorption. Figure
9 shows the volume loss density distribution of the designed AFSS absorber, where
C = 1 pF and the resonance frequency is 1.19 GHz. Figure
9
also shows that both interference and absorption on the AFSS exist and
contribute to the total energy loss. The loss on the AFSS is mainly
produced by absorption from the resistive elements. Resonance happens at
1.19 GHz, where the equivalent circuit yields a strong electric field.
The varactor guides the generated current through the narrow band-gap
between the triangle and the semicircle. Then, with the help of a
resistor, electric-field energy gets converted into thermal energy. The
loss between the AFSS and the metal slab is mainly produced by
destructive interference of the wave reflected from the surface and from
the back.
27–29
In this case, destructive interference exists but contributes little to
the total energy loss. Most of the energy losses comes from absorption
of the lumped resistive element.
Based on our qualitative analysis of tunability, it is appealing to
expand the tunable bandwidth of our proposed absorber. Aside from the
lumped impedances of the loaded elements, the distributed parameters
will also contribute to the absorption performance. Thus, we apply
various ST coefficients to the unit cell pattern to obtain the available
parameters to expand the tunable bandwidth.
Figure
10(a) shows the results of the HFSS simulations, showing the resonance frequency
fresonance varying with the ST coefficients
x and
y, where
Cvariable = 1 pF,
R = 700 Ω, and
d = 7 mm. The resonance frequency moves regularly from 0.8 to 1.64 GHz, with ST coefficients from 1.5 to 0.5 for
x, and 0.5 to 1.5 for
y. Figure
10(b) shows the tunable bandwidth varying with
x and
y, where the bandwidth is calculated with
Cvariable varying from 1 to 14 pF. The tunable bandwidth moves regularly from 0.53 to 1.10 GHz, with ST coefficients from 1.5 to 0.5 for
x and 0.5 to 1.5 for
y. This result suggests that a pattern with a small ST coefficient ratio
x/
y leads to a high resonance frequency and also produces a wider tunable bandwidth.
To gain insight into the mechanism of the ST coefficients affecting resonance frequency
fresonance and the tunable bandwidth, we now focus on the three patterns in Figure
11. These patterns are conversions of the pattern shown in Fig.
1(b). The ST coefficients are
x = 0.7,
y = 1 for Pattern (1);
x = 1,
y = 1 for Pattern (2); and
x = 1.3,
y = 1 for Pattern (3). Table
I shows the calculations for the distributed parameters by using the discussed TL model. Figure
11 plots
fresonance–Cvariable curves for the three patterns. These curves agree well with the simulated results in Figure
10. When
Cvariable = 1 pF, the curve for Pattern (1) with a smaller
x/
y has a higher resonant point at 1.55 GHz, while Pattern (3) with a greater
x/
y has a lower resonant point at 1.05 GHz. With
Cvariable varying from 1 to 14 pF, the tunable bandwidth for Pattern (1) is 1.15 GHz, while that for Pattern (3) is 0.65 GHz.
Providing more numerical calculations, Figure
12 shows the distributed capacitance
Cd varying with the ST coefficient ratio
x/
y. Generally, a pattern with greater
x/
y has a larger distributed capacitance
Cd, while
x/
y more weakly affects the distributed inductance
Ld. According to the TL model described in Figure
4(a), where two
Cd are connected in parallel to
Cvariable, the distributed capacitance
Cd affects
fresonance the same as
Cvariable. In this case, a small (
Cvariable +
Cd) leads to high-frequency resonance, while a high (
Cvariable +
Cd) leads to low-frequency resonance. When
Cvariable = 0.5 pF, the decrease in
Cd greatly affects (
Cvariable +
Cd), increasing the resonance frequency. When
Cvariable = 14 pF, the decrease in
Cd slightly affects (
Cvariable +
Cd),
leaving the resonance frequency unchanged. Thus, the tunable bandwidth
is markedly wider for Pattern (1) than for Patterns (2) and (3). This
result shows that the ST coefficients greatly affect the design of a
broadband tunable absorber. A pattern with a small ST coefficient ratio
x/
y will effectively expand the tunable bandwidth.
Based on our analyses, we designed and fabricated a broadband AFSS
absorber with an ST pattern for use in UHF applications. Figure
13(a)
shows the fabricated sample, which had overall dimensions of
500 × 500 × 7.8 mm. The AFSS was fabricated on a printed circuit board,
and the resistors and varactors (BB131, NXP) were soldered between each
of the two AFSS units. The AFSS substrate is FR4 with a thickness of
0.8 mm (
ε = 4.4(1 −
i0.02) and
μ = 1). Figure
13(b) shows the topological structure of the unit cell, where the ST coefficients are
x = 0.7,
y = 1. All the varactors worked in reverse bias. Figure
13(c)
shows a schematic representation of the power issue. The bias lines
with the same polarity are connected together. All the devices are in
parallel and biased at the same voltage. The reflectivity calculated by
HFSS, shown in Figure
13(d),
agrees well with the discussed theory. As capacitance increases, the
resonant point moves to a lower frequency, covering a band below −10 dB
from 0.7 to 2 GHz.
The reflectivity was measured with a free space setup,
30 as shown in Figure
14.
The measurement setup comprised a vector network analyzer (Agilent
8753ES), a double-ridged horn antenna (measurement range of 0.4–2 GHz), a
power source, a pyramidal absorber, and a 500 × 500 mm metal slab. The
frequency range measured was 0.4–2 GHz. To eliminate multiple scattering
between the sample and the horns, time-domain gating was applied.
Figure
15
shows the experimental results. As we varied the bias voltage from 10
to 48 V with the power control system, the resonant point moved to a
higher frequency and covered a frequency band of 0.7–1.9 GHz below
−10 dB. The total specific mass of the sample was 0.189 g/cm
2.
The total thickness was only ∼λ/54 of the lower limit frequency, ∼λ/29
of the center frequency, and ∼λ/20 of the higher limit frequency. As the
bias voltage changed from 10 V to 48 V, the power consumption of each
unit varied from 0.07 W to 1.65 W.
The measured reflectivity does not perfectly agree with the simulated
result: there are small discrepancies such as the depth of the peak and
the bandwidth of each absorption beam. There are likely three reasons
for these differences. First, the resistor and varactor have distributed
impendence so, they are not exactly ideal. Second, the fabricated
absorber is finite, while the device modeled in HFSS is infinite.
Finally, there is a tolerated error for both the HFSS and the
measurement system. Despite these discrepancies, both the measurements
and simulated results indicate that our AFSS absorber with an ST pattern
can be thin and achieve broad bandwidth simultaneously.
We proposed and fabricated an ultra-thin broadband AFSS absorber with
an ST pattern for UHF applications. Based on the TL model, the
resonance frequency and real part of input impedance are given as
functions of loaded and distributed parameters. With ST coefficients of
x =
y
= 1, the tunability and strong absorption are concisely demonstrated.
The calculated results suggest that the varactor modulates the imaginary
part of the input impendence, producing the tunability, while the
resistor mainly adjusts real part, producing the strong absorption.
Applying various ST coefficients to the unit cell pattern, we found that
a small
x/
y
effectively expands the tunable bandwidth. The measured reflectivity of
the proposed absorber covers a broad band of 0.7–1.9 GHz below −10 dB,
and the total thickness 7.8 mm is only ∼λ/29 of the center frequency. As
radar detection equipment continues to improve, our thin absorbers with
broad bandwidth and working in the UHF band will be widely useful.