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978-1-4244-5118-0/11/$26.00 ©2011 IEEE

A Tunable EBG Absorber for Radio-Frequency Power Imaging

Satoshi Yagitani1, Keigo Katsuda1, Ryo Tanaka1, Masayuki Nojima1,

Yoshiyuki Yoshimura2, and Hirokazu Sugiura2

1Graduate School of Natural Science and Technology, Kanazawa University,

Kakuma-machi, Kanazawa 920-1192, Japan

E-mail: yagitani@reg.is.t.kanazawa-u.ac.jp

2Industrial Research Institute of Ishikawa, 2-1 Kuratsuki, Kanazawa 920-8203, Japan

Abstract

designed to capture 2d radio-frequency (RF) power distributions incident on the absorber surface. The EBG absorber

has lumped resistors interconnecting the mushroom-type surface patches to absorb the incident RF power at the

resonance frequency where the EBG structure exhibits a high-impedance feature. The absorbed RF power distribution

is measured by directly detecting the amounts of RF power consumed by the individual resistors. Varactor diodes are

inserted in parallel with the resistors for tuning the resonance frequency of narrowband absorption. The absorption

characteristics at normal incidence are evaluated in detail based on an equivalent circuit model which exactly explains

the frequency behavior of the surface impedance of the tunable EBG absorber observed in EM simulation. The small

resistance existing in the varactor diode makes it difficult for the surface impedance to be matched with the incident

wave impedance (i.e., for a high absorption to be achieved) over a wide range of resonance frequency. A means to

improve the absorption performance of the tunable EBG absorber is examined.

1. Introduction

A variety of thin electromagnetic absorbers have been designed based on the artificial high-impedance surfaces

such as frequency-selective surfaces and metamaterial surfaces (e.g., [1] and references therein). At the resonance

frequency where these surfaces exhibit the high-impedance feature, an incident wave is absorbed by the additional

resistive components which are matched with the incident wave impedance. Recently it was proposed that a thin

absorber can be used for monitoring 2d radio-frequency (RF) power distributions incident on the absorber surface [2].

A mushroom-type electromagnetic band-gap (EBG) structure is used as the high-impedance surface, where the

absorption is achieved by “lumped resistors” connecting between the adjacent patches on the mushroom layer [3]. With

this configuration the power of an RF wave incident on the mushroom surface is absorbed (or consumed) by the lumped

resistors. By directly measuring the power consumption in each of the lumped resistors arranged in a 2-d matrix, the 2-

d distribution of the RF power incident and absorbed on the mushroom surface is obtained. Such an “RF power

imager” has inherently a narrowband feature around the resonance frequency fixed by the geometrical and

constitutional structure of the EBG surface. To extend the measurable frequency range, the resonance frequency is

made electronically tunable by additional varactor diodes (varactors), as in [4-5]. A 347-mm square EBG absorber was

designed and fabricated to cover the absorbing frequency range from 700 MHz up to 2.7 GHz. Power distributions

were detected at 8 × 8 locations on the absorber, at each of which two RF power detectors with the sensitivity of -70

dBm were placed to measure two orthogonal polarizations. The measured power distributions were transferred to a PC

and displayed as real-time 2-d power images at a rate of 30 images/second. The RF power distributions radiated from a

dipole antenna were measured to be consistent with those expected theoretically, which validated the proposed

technique to measure the RF power distributions. Using such an RF power imager, the power distributions of even

impulsive RF signals and/or noises can be captured and visualized in situ and in real-time, while the electromagnetic

environment is almost undisturbed by the EBG absorber.

In the present study, the absorption characteristics of the tunable EBG absorber designed for RF power

imaging is evaluated in detail based on equivalent circuit analysis and EM simulation.

2. A Tunable EBG Absorber for Detecting RF Power Distribution

Figure 1 shows the geometrical structure of a square unit cell of the tunable EBG absorber designed for RF

Absorption characteristics of a tunable electromagnetic band-gap (EBG) absorber are analyzed, which is

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power imaging, which has lumped resistors and varactors inserted between the adjacent patches on the surface [2]. The

gap g between the adjacent patches is much smaller than the patch size w, and the periodicity of the unit cells, a = w + g,

is set much smaller than the wavelength. For an electromagnetic wave at normal incidence, the surface impedance of

the mushroom structure itself is represented as a parallel connection of the effective inductance and capacitance. The

high-impedance feature is achieved at the LC resonance frequency, where the mushroom layer behaves like an artificial

magnetic conductor. The incident wave power is absorbed by the lumped resistors interconnecting the surface patches;

if we take the value of the resistors as R = 377 Ω matched with the incident wave impedance, the incident wave should

be completely absorbed at the resonance frequency [3]. On the other hand, tunability is achieved by the varactors

inserted in parallel with the resistors, by altering the capacitance component of the EBG structure which specifies the

resonance frequency. As in the same manner designed by [6], the varactors are oriented in opposite directions in each

alternate row as well as in each alternate column of the matrix of mushrooms. Reverse biases are supplied to all the

varactors by alternately biasing half of the cells, and grounding the other half in a checkerboard pattern (see Fig. 3 of

[6]). A separate biasing circuit is placed on the backside of the ground plane. Thus, by applying appropriate bias

voltages to the varactors, we can control the frequency of RF power absorption. The locations of the varactor and the

resistor, as well as their separation distance d, on each side of a patch has an effect on the surface impedance, as

discussed in Sec. 3.

Varactordiode

Via

wg

Resistor (R)

d

x

y

R

CS

LS

CDLDRD

M

LV’

LR’R

CS

LS

CDLDRD

LV

LR

η0= 377 Ω

(a) (b)

k

ZZ

η0= 377 Ω

Fig. 1: Structure of a unit cell of the EBG absorber Fig. 2: Equivalent circuit model

On the EBG absorber in Fig. 1, the incident wave power is absorbed and dissipated in the surface resistors,

when there are no losses in the varactors and in the substrate. The amount of power absorbed by each resistor depends

on the incident polarization; the resistors connecting the adjacent patches in the x- and y-directions absorb the amounts

of RF power with the electric field polarized in the x- and y-directions, respectively [2]. In either case, the power

absorbed by each resistor is considered to be the Poynting flux of the incident wave multiplied by the area of a unit cell.

By detecting directly the amounts of power consumed in the 2-d matrix of surface resistors, the 2-d power distribution

of the RF wave illuminating the EBG surface is measured with polarization discrimination. Power detectors are put on

the backside of the EBG absorber, to detect the amounts of power consumed by the individual surface resistors [2].

3. Equivalent Circuit Analysis

Here the characteristics of the tunable EBG absorber shown in Fig. 1 are evaluated. The geometrical and

constitutional parameters are similar to those of the EBG absorber designed in [2], which had 33 × 33 square unit cells

formed on an FR-4 substrate of 347 mm square and 1.6 mm thick. The size of a patch is w = 10 mm and the gap

between the adjacent patches is g = 0.5 mm, so that the cell periodicity is a = 10.5 mm. The via diameter is 0.6 mm.

The relative permittivity of the FR-4 substrate is taken as 4.56 with no loss (tanδ = 0). The varactor is modeled as a

series RLC circuit; the series resistance RD = 1 Ω, the parasitic inductance LD = 1.8 nH and the capacitance CD is

variable from 0.67 to 12 pF (which makes the abosorber tunable from 700 MHz to 2.7 GHz). It is noted that the resistor

was chosen here as R = 845 Ω instead of 377 Ω, to have maximum absorption at 2 GHz (see the discussion in the next

paragraph). Using these parameters, the absorption characteristics of the EBG absorber were computed by an EM

simulator (CST Microwave Studio). A linearly polarized plane wave was incident normally on the EBG surface. A

square area containing four unit cells of the absorber was modeled by defining the periodic boundary condition, which

corresponds to simulating infinitely extending periodic unit cells.

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shown in Fig.2 (a). The effective capacitance and inductance of the mushroom structure are CS = 0.628 pF and LS =

1.86 nH, respectively. The effects of the surface currents on a patch flowing toward the varactor (CD , LD and RD) and

the resistor (R) are represented by a transformer, LV and LR coupled with the coefficient k, which are dependent of the

geometrical configuration of the varactor and the resistor on each side of the patch (i.e., their locations as well as their

separation distance d). The parameters of the transformer can be replaced with LV’, LR’ and their mutual inductance M

as in Fig. 2 (b); for the case of d = 1 mm, LV’ = 0.371 nH, LR’ = 0.41 nH and M = 0.235 nH. From this circuit, two

resonance frequencies are derived by solving Eq. (1) for ω .

111

10

ω

ω ωωωω

The surface impedance Z of the EBG absorber becomes purely resistive RP at each resonance frequency, and the

reflection coefficient is given as Γ = (RP −η0) / (RP +η0), where η0 = 377 Ω is the incident wave impedance. When the

capacitance of the varactor CD is varied, the resonance frequencies are changed accordingly. The value of the resistance

RP at the resonance frequency ω r is calculated as

=−

+−

where // means the parallel connection of the impedance. The typical frequency variation of the surface impedance

under the circuit parameters mentioned above is shown in Fig. 3. The absolute value of surface impedance |Z| is shown

by the solid line for the case of CD = 1.35 pF. In this case the first and second resonance frequencies appear at 2.0 GHz

and 6.7 GHz, respectively, which are observed as the two peaks on |Z|. When CD is varied from 12 pF down to 0.67 pF,

the first resonance frequency is changed from 700 MHz up to 2.7 GHz, whereas the second one is from 6.23 GHz up to

6.85 GHz. Over each resonance frequency range, the value of the resistance moves on the broken curve specified by Eq.

(2). From the viewpoint of achieving frequency tunability, the first resonance should be taken, as the variable range of

the second resonance frequency is unpractically narrow. To achieve a high absorption at each resonance frequency, the

resistance should be as close as possible to the incident wave impedance, η0 = 377 Ω (the dotted line). From Eq. (2), RP

becomes equal to R at ω r = ω S , and RP ~ (ZS

becomes smaller as the resonance frequency becomes lower. Thus the existence of the small resistance RD in the

varactor has a considerable effect on the frequency behavior of the surface impedance [4]. Here ω S /2π = 4.66 GHz and

ZS

becomes larger and smaller than 377 Ω, respectively, leading to impedance mismatch in either case.

The equivalent circuit which exactly reproduces the absorption characteristics obtained in the simulation is

4

2

2

S

2

D

2

S

2

D

2

C

ω

−+++ =

, where

1/2

−

1/2

−

1/2

−

(),(),()

SSSDDVDCSD

L CLL M C L C

ωωω

′

==++=

. (1)

()

2

2

2

S

2

r

2

S

1

/

//

11/

S

r

P

DSr

S

Z

R

RR

M L

ω

ω

ω

ω

ωω

−

, where

1/2

)(/

SSS

ZLC

=

, (2)

2

/RD) (ω r /ω S)2 // [R / (1+M /LS)2] for ω r << ω S ; the surface resistance

2

/RD = 2.96 kΩ, and R was chosen as 845 Ω so that RP becomes 377 Ω at 2.0 GHz. Above and below 2.0 GHz, RP

1

10

100

1000

Z0

10000

0.11 10

Impedance |Z| [Ω]

Frequency [GHz]

RP(adjusted)

RP

|Z|

(CD= 1.35 pF)

1st resonance

2nd resonance

η0

-50

-40

-30

-20

-10

0

10

0.51 1.5

Frequency [GHz]

2 2.53

S11Magnitude [dB]

simulation

eq. circuit

CD= 5.81 pF

2.51 pF

1.35 pF

0.81 pF

Fig. 3: Surface impedance of the EBG absorber Fig. 4: Reflection magnitude of the EBG absorber

analysis and the simulation, which are plotted by gray and dotted lines, respectively. In each case four representative

profiles are plotted for the varactor capacitances fixed as CD = 5.81 pF, 2.51 pF, 1.35 pF and 0.81 pF, which correspond

to the resonance frequencies of 1.0 GHz, 1.5 GHz, 2.0 GHz and 2.5 GHz, respectively. For each of the capacitance

values, the reflection profile calculated by the equivalent circuit analysis agrees well to that observed in the simulation,

Figure 4 shows the reflection magnitude profiles for the first resonance obtained by the equivalent circuit

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which validates the accuracy of the equivalent circuit in Fig. 2. Also for the second resonance, though not shown here,

a good agreement was observed between the reflection profiles obtained by the equivalent circuit analysis and in the

simulation. On each curve, the reflection becomes minimum (the absorption becomes maximum) at the resonance

frequency determined by the value of CD. As discussed above, the amount of absorption becomes highest (S11 ~ −45

dB) at the resonance frequency of 2.0 GHz for the case of CD = 1.35 pF, where the surface impedance of the EBG

absorber RS becomes 377 Ω. When the resonance frequency goes above or below 2.0 GHz, the maximum absorption is

degraded due to the increase in mismatch between RS and 377 Ω.

As discussed above, Eq. (2) is approximated as RP ~ (ZS

frequencies ω r << ω S . If the three conditions, (ZS

Ω so that a high absorption would be achieved over a certain range of resonance frequency. Since the first condition is

rewritten as ω r

The other is to increase the effective inductance LS by increasing the thickness of the substrate. The gray line in Fig. 3

shows the surface resistance profile expected for the case of RD = 0.5 Ω, R = 377 Ω, LS = 3.72 nH (corresponding to the

substrate thickness of 3.2 mm) and M = 0 nH (which is achievable by adjusting the distance d between the resistor and

the varactor). In this case RP ~ 377 Ω is achieved over a wide range of resonance frequency above 1 GHz.

4. Conclusion

Absorption characteristics of the tunable EBG absorber used for imaging the RF power distributions were

evaluated by the equivalent circuit analysis and the simulation. A realistic equivalent circuit model was derived which

exactly explains the frequency behavior of the surface impedance of the EBG absorber for normal incidence observed in

the simulation. It was shown that the small resistance existing in the varactor diode makes it difficult for the surface

impedance to be matched with the incident wave impedance over a wide range of resonance frequency. A means to

improve the absorption performance of the tunable EBG absorber was examined. Evaluation for oblique incidence will

be the future work.

Acknowledgments

The authors would like to thank Dr. M. Ozaki for his valuable suggestions and discussions. This study was

supported by KAKENHI (21560444).

References

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by an EBG Absorber,” IEICE Trans. Commun., 2011, submitted.

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2

/RD) (ω r /ω S)2 // [R / (1+M /LS)2] at first resonance

/RD) (ω r /ω S)2 >> R, R = 377 Ω and M << LS , are satisfied, RP ~ 377

2

2 LS

2 / RD >> R, one way to make it so is to use the varactor with the resistance RD as small as possible.