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高阻抗表面的设计与测量

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The design process of High Impedance Surface (HIS) is a challenge in realizing low-profile antenna. To carry out properly this process, a 3D-electromagnetic simulator is required. This paper shows an overview of the different numerical techniques which can be applied to simulate the behaviour of an HIS

using CST Microwave Studio (CST MWS). The considered HIS is composed of a metallic square patches array printed on the top of a metal backed substrate. To demonstrate the validity of the different solvers used, some measurements of the dedicated structure have been performed in a waveguide simulator.

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Design and Measurement of High Impedance

Surface

F. Linot^∗†, R. Cousin^‡, X. Begaud^∗, M. Soiron^†

Institut Telecom - Telecom ParisTech - LTCI - CNRS - UMR 5141

∗

46 Rue Barrault, 75634 Paris, France

‡

CST AG

Bad Nauheimer Str. 19, D - 64289 Darmstadt, Germany

†

THALES Airborne Systems

78852 Elancourt Cedex France

Abstract—The design process of High Impedance Surface

(HIS) is a challenge in realizing low-proﬁle antenna. To carry out

properly this process, a 3D-electromagnetic simulator is required.

This paper shows an overview of the different numerical tech-

niques which can be applied to simulate the behaviour of an HIS

using CST Microwave Studio ꢀ (CST MWS). The considered

HIS is composed of a metallic square patches array printed on

the top of a metal backed substrate. To demonstrate the validity

of the different solvers used, some measurements of the dedicated

structure have been performed in a waveguide simulator.

I. INTRODUCTION

(a)

This research is in the framework of collaboration between

Telecom ParisTech and Thales Airborne Systems to design

low-proﬁle antenna considering high impedance surface (HIS).

To develop tools to simulate HIS, a partnership with CST

AG ꢀ has been done. These surfaces can exhibit surface

wave band gaps where the propagation of electromagnetic

waves is prohibited [1]. High impedance surfaces can exhibit

frequency band where the propogation of electromagnetic

wave is prohibited. Moreover these structures can imitate

the interesting phase behaviour of a hypothetically perfect

magnetic conductor (PMC) at resonance: the high-impedance

surface reﬂects all of the power just like a perfect electric

conductor (PEC), but it reﬂects in-phase, rather than out-of-

phase, allowing the radiating element to be directly adjacent

to the surface. High impedance surface consists on a periodic

(b)

Fig. 1. (a) Part view of the inﬁnite HIS analyzed, (b) View of the lattice

considered

metallic arrangement printed on a metal-backed substrate. To this paper the Finite Integration Technique (FIT) is used as

design HIS easily and quickly, several analytical models based a generalization of the FDTD approach. The FIT approach

on an equivalent transmission line model have been proposed which has been developed at CST is using the Perfect Bound-

[2]. However all the geometry’s dimensions must be smaller ary Approximation (PBA) as a better geometry discretization

than the wavelength in order to consider a quasi-static model without increasing the memory consumption. As the previous

[3], and a Computational Electromagnetic (CEM) simulation methods mentioned, the accuracy of the results depends on the

is required to demonstrate the validity of designing complex volume mesh computed. To demonstrate the validity of this

3D-HIS structures. Several ”full-wave” methods namely the computational code in the high impedance surfaces domain,

Finite Difference Time Domain method (FDTD) [4], and a HIS consisting of a metallic square patches array printed

the Finite Element Method (FEM) [5], are widely used to on the top of a metal backed substrate is studied. The goal

plot the reﬂection coefﬁcient of the artiﬁcial structure. These of this paper is to describe several approaches to validate

numerical methods consist on a volume discretization to solve the reﬂection coefﬁcient of an HIS using CST MICROWAVE

the Maxwell’s equations using different mesh techniques. In STUDIO ꢀ (CST MWS) in order to predict the behaviour of

such devices. In this paper, only the phase relection property hexahedral mesh discretization. This technique reveals to be a

is considered but all these approaches can be used to predict highly efﬁcient method as it combines easy-to-use cartesian

the absorption coefﬁcient [6]. All the results are compared and grids without any approximation of the structure geometry

validated to measurement done in a waveguide simulator [7]. [8]. The PBA can improve the geometry description without

increasing the memory. As illustrated in Fig. 2, the hexahedral

mesh grid is applied to the structure with a denser mesh near

II. OVERVIEW OF THE DIFFERENT APPROACHES

The reﬂection property of high impedance surfaces is gen-

erally described by the reﬂection coefﬁcient which is the ratio

of the reﬂected ﬁeld on the incident ﬁeld at the top of the

structure.

the edges of the PEC sheet for a better ElectroMagnetic (EM)

ﬁeld discretization. In CST MWS, several methods can be used

to simulate the reﬂection phase in normal incidence. Firstly

the analytical expression (1) can be computed in a Visual

Basic language for Application (VBA) which requires three

simulations in that case: one for extracting the incident ﬁeld

components without any parasitic reﬂection in the calculation

domain, the second one to take into account the modiﬁed E-

ﬁeld components reﬂected at an equivalent PEC reference and

the last one to deduce the phase shift created by the real case.

An Electric Probe is required to record the time signals for all

the three simulations. This method can be used to simulate

the reﬂection phase diagram of ﬁnite structure. However,

this method requires few minutes to simulate the reﬂection

coefﬁcient of the real structure [9]. Another method is used,

consisting in deﬁning the appropriate boundary conditions to

introduce a crossed-E and H-ﬁeld such that a TEM wave is

applied similar to a plane wave considering one single element

as inﬁnitely periodic in the x and y directions. The reﬂection

phase diagram is then computed for normal incidence of the

ElectroMagnetic (EM) ﬁeld propagation. The phase reference

Z_s− Z₀

Γ =

(1)

Z_s+ Z₀

Where Z_sand Z₀are respectively the surface impedance

of the structure and the free space impedance. For a perfect

electric ground plane, the reﬂected E-ﬁeld and the incident E-

ﬁeld have opposite signs, resulting in a coefﬁcient reﬂection

equal to -1. In the case of a hypothetically PMC surface,

the reﬂection phase is null corresponding to a coefﬁcient

reﬂection equal to +1. However, HIS reveals that they can

realize the PMC condition in a certain frequency band. At very

low frequency, the HIS behaves like a PEC. At the resonant

frequency, the impedance of the structure tends to inﬁnity,

resulting in a zero reﬂection phase. To calculate the reﬂection

phase of an high impedance surface, a plane wave illuminating

the structure where a PEC surface is set as a reference leads

to a normalization of the reﬂected phase of the HIS (Φ^HIS

from the PEC surface (Φ^{P EC}):

)

Φ = Φ^HIS− Φ^{P EC}+ π

(2)

A surface impedance is comprised of metallic square

patches printed on the top of a metal backed dielectric sub-

strate without vias (see Fig.1a). According to Fig. 1a, the

parameters of the high impedance surface analyzed are: P =

4mm, g = 0.4mm, h = 1mm and ꢀ_r= 10.2. Where P is the

periodicity of the patch array, g is the gap between adjacent

patches, h the height of the dielectric substrate and ꢀ_rthe

relative permittivity of the host medium. As the HIS is a

periodic structure, only one lattice is needed to discribe the

behaviour of the whole structure. With the periodic boundary

conditions used, the structure can be modelled as an inﬁnite

surface (see Fig. 1b).

(a)

A. The Time Domain

All time domain ”Full-Wave” methods such as FIT, FDTD

and TLM techniques use a conformal cartesian grid. Whereas

the FDTD approach uses the hexahedral mesh grid, this dis-

cretization has some limitations when complex 3D-structures

have to be simulated at higher frequency range for which the

level of accuracy has to be enhanced. For a better geometry

discretization, mainly thin structures, rounded solids and shell

objects, the PBA was implemented in connection with the FIT

to reduce the global number of mesh cells of an equivalent

FDTD simulation for a considerable enhanced level of ac-

curacy. For instance, that means that a mesh cell can take

(b)

Fig. 2. Hexahedral discretization of the lattice: (a) Front view, (b) Perspective

into account two different material properties in the global view

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