Miniaturized wide- and dual-band multilayer electromagnetic bandgap for antenna isolation and on-package/PCB noise suppression

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Miniaturized Wide- and Dual-Band Multilayer
Electromagnetic Bandgap For Antenna Isolation and
on-Package/PCB Noise Suppression
Petros Bantavis, Marc Le Roy, Member, IEEE, André Perennec, Raafat Lababidi, Member, IEEE, Denis Le jeune
Lab-STICC UMR CNRS 6285,
Université de Brest (UBO)-ENSTA-Bretagne, Brest, France
Marc.LeRoy@univ-brest.fr
Abstract— This work presents a new design approach of
wideband multilayer Electromagnetic Band Gaps (EBGs)
suitable for both on package antenna isolation and switching
noise suppression in high speed digital circuits. Depending on the
target applications, the design principle is implemented from two
conventional types of EBGs in order to improve their initial
performance. By stacking multiple dielectric layers with
integrated vias in both types of EBGs, it’s possible to achieve
dual band performance, to enhance the relative bandwidth of the
first band gap and to miniaturize the unit cell. The dispersion
diagrams of the multilayer EBGs are proposed and full-wave
simulations are performed to validate the antenna isolation and
noise suppression bandwidths of the final structures.
Keywords— Antenna isolation; wide bandwidth; multi-layer
stack; EBG; artificial-impedance surface; signal integrity;
simultaneous switching noise; System-on-Package
I. INTRODUCTION
Electronics markets witness a continuous increasing need
for highly integrated advanced devices which emphasizes the
density of integration of different functional blocks in System-
in-Package (SiP) or System-on-Package (SoP). Multiple
technologies are combined in a same package, so that antennas
and RF circuits have to coexist with analog and digital circuits
with multiple interconnections and power distribution
networks. Moreover, the associated signal integrity issues
become more critical with increasing clock speeds and
decreasing supply voltages. Several spurious couplings or
noises may then occur both on the chip and in the package or
PCB substrates. A generic technique is investigated here to
overcome two of these issues.
First, at the antenna level in the RF front end, surface-
wave leakage is one of the main sources of unwanted coupling
between antennas. Electromagnetic Band Gaps (EBGs) are
one of the best candidates to reduce this mutual coupling by
eliminating the surface waves that are excited in the common
dielectric substrate of the two antennas. Traditionally, such
EBGs are suitable to isolate RX and TX antennas [1] but also
to get high isolation between MIMO antennas [2] or to highly
isolate RX and TX antennas in Full-Duplex (FD) systems [3].
Nevertheless, achieving a wideband isolation is still
challenging.
On the other hand, SiP and SoP advanced technologies
also require the suppression of noise coupling due to
Simultaneous Switching Noise (SSN, also named
power/ground noise). EBG structures that act as bandstop
filters are also able to strongly reduce the noise likely to
propagate in the Parallel-Plate Waveguide (PPW) formed by
the power/ground planes. Thus, the design of compact
wideband SSN canceller in power distribution network [4] is
currently a major concern in mixed signal circuit design.
In this work, multilayer stacked EBGs are studied and it
will be demonstrated that by increasing the number of
dielectric layers, the unit-cell size becomes drastically smaller
with respect to the bandgap wavelength. Moreover, the
relative bandwidth of the bandgap increases and a second
bandgap is produced at higher frequencies. Depending on the
target applications, i.e. antenna isolation or SSN suppression,
two types of EBGs will be implemented. An equivalent
lumped model is proposed and extended to both
configurations and validated by comparing the theoretical
results to electromagnetic simulations and dispersion
diagrams.
II. GENERALIZED MULTILAYER EBG DESIGN AND
MODELLING
A. Multilayer model for wideband microwave applications
In planar antennas (e.g. microtrip antennas), surface wave
modes are excited in the dielectric substrate at the antenna
edges. Several topologies of EBGs with vias have been
investigated to suppress the TM and TE surface-wave modes
that are able to propagate in such a grounded dielectric slab.
Here, a square lattice was selected due to its wider bandwidth
[5]. In single-dielectric-layer mushroom EBG as illustrated in
Fig. 1a, the unit cell (Fig.1.b) and the surface impedance are
usually modelled by an LC resonant circuit to express the
centre angular frequency

0, the bandwidth BW, and the
impedance surface Z. The inductance value LT is related to the
substrate thickness and permeability while the gap capacitance
C is related to the mushroom and gap dimensions and substrate
permittivity. Approximate closed-form equations and the
design procedure are given in [5]. Several approaches, such as
mushroom with overlapping plates [6] or unidimensional [7]
were proposed to reduce the dimension of the cell by
increasing the capacitance value but at the expense of the
relative bandwidth. Indeed, reducing the cell size while
simultaneously widening the bandwidth requires higher
capacitance and inductance per unit cell values.
978-1-5386-2299-5/18/$31.00 ©2018 IEEE

g
b)
substrate
ground plane
c)
C
LT
a)
h
w
gw
via
LT
C
+-
Fig. 1. (a) Top-view of a classical single layer EBG. (b) Side-view and
behaviour of a unit cell. (c) Equivalent lumped model of a unit-cell.
0
1
T
L C

 (1)
0
0 0
/
/
T
L C
BW


 

  (2)
2
1
T
T
L
Z j
L C


 (3)
Here, a multilayer EBG (M-EBG) structure is proposed in
two configurations (Fig. 2a and 2b). This structure allows
increasing simultaneously the inductance and capacitance
values to reduce the cell size while keeping a wide surface-
wave stop-band bandwidth suitable for both intended
applications.
As a first approximation, the capacitances C between
adjacent mushrooms are considered equal regardless of the
layer position (top and intermediate layers). The inductance LT
(defined from the single layer configuration) is subdivided into
three parts (Fig. 2.a) that correspond to the vias and ground
contributions, LV and LG, respectively; i.e. LT =LG+2LV. Thus, a
multilayer lumped equivalent model of the surface impedance
can be expressed as detailed in Fig. 2.a. Starting from the
single layer admittance Y1 = jB1 with the initial conditions
BG = -1/(

LG), the 2-layer admittance Y2 can be deduced as a
function of B1 and so on and so forth, as explained in Fig. 2a.
For an n layer-stack, the surface impedance Zn or admittance
Yn=jBn is purely reactive which is expressed by (4). As in the
case of a single layer EBG, this multilayer lumped
representation only estimates the central frequency of the first
bandgap as well as the impedance surface.
 
1
1
21
1
2....
....
1
2
iterations
n
V
V
V G
B C
L
C
L
L L
n





 
 

 
 

(4)
This stack-model can be applied to design a wideband
surface-wave isolation between wideband planar circuits,
typically microstrip antenna array, i.e. where the top guiding
structure is initially a grounded dielectric slab.
B. Multilayer EBG model for wideband SSN suppression
Simultaneous Switching Noise (SSN) occurs between two
reference planes due to high speed voltage and current
switching in digital sections of PCB and packages (SiP/SoP).
In this case, high speed switching excites modes in a Parallel-
Plate Waveguide (PPW) formed by the power distribution
network. The structure understudy (Fig. 2b) consists of a PPW
where the bottom metallic plate is replaced by the n-layer
stacked EBG studied in the previous section. Our objective
here is to estimate the bandgap and its central frequency by
extending the model of EBG-grounded dielectric slab studied
in the previous section to this PPW configuration by using the
transverse resonance method (TRM) [8]-[9]. TRM was initially
developed to study waveguides with inhomogeneous
transverse-section waveguide. The multilayer structure (PM-
EBG) is investigated by using the TRM to model the continuity
of electric and magnetic fields in the transverse directions by
an equivalent resonant circuit with transmission lines. As
shown in Fig. 2c, a cross section of the whole structure can be
modelled by the surface impedance Z-x=Zn=-j/Bn when looking
into the n-layer EBG direction (x<0); and by a transmission
line with a characteristic impedance Zw when (x>0).
C
LVLV
LG
1 layer
LVLV
2 layers
C
LVLV
LG
C
n layers
C
LVLV
C
LVLV
n layers C
LG
short-circuit
Zw ,

x , h
a)
M-EBG
PM
-
EBG
b)
Zn
x=0
x=h
h
h
n
n
j
Z
B
 
1 1
1
2V G
Y j C jB
L L
 
 
  
 
 
 
2 2
1
1
1
2V
Y j C jB
LB


 
 
 
  
 
 
 
 
1
1
( )
1
2
n n
V
n
Y j C jB
LB



  
 
x>0
x<0
c)
PM
-
EBG TRM model
h
h
Fig. 2. (a) Multilayer EBG (M-EBG) and the corresponding lumped-modelling. (b) Power-plane Multilayer EBG (PM-EBG) side view, with its equivalent TRM
transmission line model (c).

Zw corresponds to the wave impedance of the type of modes,
i.e. TEM, TMn and TEn in a PPW. The transmission line is
loaded by a short circuit which represents the metal plate at
x=h. Such a short-circuited stub of length h along x presents
input impedances Z+x associated to the transverse wave
number

x:
tanh( )
TM x
x x
Z j h



 
(5a)
0
tanh( )
TE
x x
x
Z j h




(5b)
Where
2 2 2
x
k
 
 
, with 2 2
0 0
r
k
   
, and

x is purely
imaginary for TE modes in (5b) and real in (5a) for TM modes.
The first mode is a TEM mode which starts from DC and then
becomes TM0 up to the bandgap which corresponds to (5a),
whereas (5b) is for the second mode, i.e. TE1 that propagates
after the resonance. The resonance condition of the TRM
requires that the impedance seen when looking in one
transverse direction (e.g. x<0) at the interface is the opposite of
the impedance seen in the other direction (x>0):
0
x x
Z Z

 
(6)
Inserting (4), (5a) or (5b), into (6) provides after simplification
the dispersion relations for the power-plane EBG waveguide:
For TM0:
2 2
0 0 2 2
0 0
0
1
tanh( . ) 0
r
r
n r
h
B
         
 

   
(7a)
For TE1:
2 2
0
0 0
2 2
0 0
1
tan( . ) 0
r
nr
h
B

    
    
   
 (7b)
Dispersion diagrams can be obtained by solving these
transcendental equations for a different number of layers. The
cutoff frequencies of the TE1 modes can be directly obtained
by solving (7b) for

= 0. In the next section, a validation of
both the surface impedance lumped-model for the M-EBG
structure and of the TRM modelling for the PM-EBG one is
carried out by comparison to corresponding dispersion
diagrams from a commercial eigenmode solver and full-wave
electromagnetic (EM) simulations of a practical case.
III. VALIDATION OF MULTILAYER-LUMPED AND TRM MODELS
BY COMPARISON TO EM SIMULATIONS
A. M-EBG lumped-model simulation results and validation
Fig. 3 shows the dispersion diagram (the triangle ,
corresponds to the irreducible Brillouin zone) calculated by
using the eigenmode solver of CST Studio for the unit cell
made up of 1 and 3 layers of Fig. 2a.
Fig. 3. M-EBG dispersion diagrams for 1 and 3 layers. Cell size: w=2.25 mm,
g =0.3 mm,

via = 200 m, h=1.6 mm, metal thickness t=35 m,

r=2.2.
The single layer EBG produces a unique bandgap from 11
to 20 GHz with a relative bandwidth of 58%. For three layers,
a dual-band performance is achieved where the first band gap
ranges from 5 to 10 GHz with a relative bandwidth of 66.6%.
Thus, this behavior corresponds to a minimization of the unit
cell size since the band gap appears at a lower frequency band,
with an enhanced relative bandwidth. Additionally, a second
band gap is produced in the 12-14 GHz band. The results
obtained by following the same procedure for 3 up to 10 layers
are summarized for clarity in Table I. Indeed, adding multiple
stacked layers confirms that the resonance frequency for both
band gaps is decreased and the relative bandwidth for the first
one is slightly increased. Full ElectroMagnetic (EM)
simulations were also carried out in a practical case (a
finite 5x5 EBG structure from 1 to 10 layers with a coplanar
line excitation) and the results fit accurately the dispersion
diagrams while showing a high isolation level in the band gap.
Table I sums up the bandgap frequencies and bandwidths
versus the number of stacked layers. In order to verify the
proposed lumped model, LT, LV, LG, and C are first estimated
from classical closed-form equations [5], [10]-[11]. For the
structure and cell dimensions specified in Fig. 3, the following
component values are extracted: LT = 2.01 nH, LV = 658 pH,
LG = 693 pH, C = 56.1 fF. Then, the resonance frequencies of
the equivalent lumped model (dot curves in Fig. 5) are
extracted from (4) and found to be consistent with the bandgap
central-frequencies from eigenmode solver/EM simulations.
B. PM- EBG TRM model and dispersion diagrams
The same approach to calculate using CST the resonant
frequencies of eigenmodes along the Brillouin zone is applied
to the PM-EBG structure (Fig. 2b) with identical dimensions
and substrate layers to get the dispersion diagrams from 1 to
10 layers.
TABLE I: Bandwidths (BW) and bandgaps obtained from dispersion diagrams for one to ten layers for M-EBG and PM-EBG.
M-EBG
Number of layers 1 2 3 4 5 6 7 8 9 10
1
st
Bandgap (GHz) 11-20 6.7-13.2 5-10 3.6-8 3.3-6.5 2.5-6.4 2.4-4.9 2.1-4.5 2-4.5 1.8-3.8
2
nd
Bandgap (GHz) -
-
12-14
10-12.2
9-10.5
8.1-9.5
7.5-9.6
7.1-8.2
6.5-7.2
5-5.7
BW (%) 58 65.3 66.6 75.8 65 67.4 68.4 72.7 76.9 71.4
PM-EBG
1
st
Bandgap (GHz) 8-23 5.9-17.4 4.7-14 3.9-12.2 3.4-10 3-9.2 2.6-8.2 2.4-7.3 1.9-5.9 1.8-5.6
2
nd
Bandgap (GHz) - - 17.2-19 15.1-17.5 13-16 11.4-14.4 10-13 9-11.2 8.2-9.5 6.5-8.1
BW (%) 96.7 98.7 99.4 103.1 98.5 101.6 103.7 101 102.5 102.7

Fig. 4. PM-EBG Dispersion diagrams for 1 and 6 layers.
Fig. 5. Comparison of central frequencies and bandwidths for M-EBG and
PM-EBG from equivalent models and dispersion diagrams.
Identical global trends as in section III-A are evidenced in
Fig. 4 (only dispersion diagrams for n = 1 and 6 layers are
plotted for clarity) and in table I, i.e. a wide relative bandwidth
that slightly increases versus n with a strong shift to lower
frequencies of these stopbands. A 2nd bandgap is also created
and follows identical behaviors. By using (7a) and (7b) with
the aforementioned lumped components values, the dispersion
bandgaps are calculated following the TRM principle. Fig. 5
illustrates the obtained results in comparison with eigenmode
solver ones (hatched areas for the bandwidth and scatters for
the central frequencies). The bandgap lower edge is estimated
from TRM with (7a) for TM0 mode which is actually the lower
resonance frequency of Zn; whereas the cutoff frequency of TE1
defines the bandgap upper bound. The TRM center frequencies
are consistent with those from CST whereas the relative
bandwidths follow the same global trend with a slight increase.
But nevertheless, the bandwidths from TRM method are under
evaluated as in [8]. A part of the discrepancies in bandgap
bound estimation comes from the approximate values of the
lumped components. Moreover, the EBG in TRM is considered
as an equivalent uniform surface defined by Zn which implies
that this approximation provides better results when the
wavelength is big compared to the cell size, which is confirmed
for n = 10 in Fig. 5.
IV. CONCLUSION
In this paper, a generalized design of multilayer stacked
EBGs for wideband applications is presented and then
dedicated respectively to mitigate the coupling between on
package/PCB RF circuits such as Tx/Rx antennas and also to
reduce the SSN between power planes in high-speed digital
systems in SiP/SoP technologies. Both multilayer
implementations proved that increasing the number of stacked
dielectric layers with integrated vias results in a dual band
performance, minimizes the unit cell size and enhances the
relative bandwidth of the first band gap. Moreover, an
equivalent lumped model of the multi-layer EBG structure is
proposed in this paper and extended by TRM to the power-
plane configuration. Furthermore, the two models are validated
by a comparison to dispersion diagrams. This approach can be
applied to any EBG to gain in compactness and bandwidths.
This allows the implementation of miniaturized, high-level and
wideband isolation structure between planar MIMO antennas
or in Full-Duplex transceivers, as well as wideband SSN
canceller in multi-layers and -packages digital/mixed systems.
Such multilayer EBGs have then the ability to limit the surface
wave propagation over a wide bandwidth in order to reduce the
unwanted coupling between antennas or to provide artificial
impedance surfaces to improve antenna design [5].
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