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RADIATION EFFICIENCY OPTIMIZATION FOR PRINTEDCIRCUIT ANTENNAS USING MAGNETIC SUPERSTRATESN. G. Alexopoulos a & D. R. Jackson aa Electrical Engineering Department, University of California, Los Angeles, CA, 90024Version of record first published: 27 Feb 2007.
To cite this article: N. G. Alexopoulos & D. R. Jackson (1983): RADIATION EFFICIENCY OPTIMIZATION FOR PRINTED CIRCUITANTENNAS USING MAGNETIC SUPERSTRATES, Electromagnetics, 3:3-4, 255-269
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RADIATION EFFICIENCY OPTIMIZATION FOR PRINTED CIRCUIT ANTENNAS USING MAGNETIC SUPERSTRATES
N. G. Alexopoulos and D. R . Jackson, Electrica1,Engineering Department, University of California, Los Angeles, C A 90024
ABSTRACT
The radiation efficiency of printed circuit antennas due to
surface-wave effects is optimized to 100% for lossless materials.
This is attained with a magnetic superstrate layer on a dielectric
substrate. A combination of substrate-superstrate thickness and
material parameters results in the elimination of surface wave
modes and, therefore, radiation efficiency optimization. when
antennas are printed on a grounded substrate with moderate values
of dielectric constant, elimination of surface wave modes aiid,
therefore, 100% radiation efficiency due to material effects can
be obtained only with the addition of a magnetic superstrate
layer if radiation resistance is to be kept at a useful
level.
I. INTRODUCTION
The total radiation efficiency of
- 'rad et - - 'in
antennas is defined as [I].
(1)
where Pradisthe total power radiated into free space and Pin the
total power input in the antenna terminals. The radiation
Electromagnetics 3:255-269. 1983 Copyright O 1983 by Hemisphere Publishing Corporation
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256 N. G. ALEXOPOULOS AND D. R. JACKSON
efficiency of printed circuit antennas can also be written as
where ec is the efficiency factor due to ohmic losses in the
antenna conducting structure. The factor esd is defined here as
the overall layer efficiency and is given as
where Pd is the power loss in the printed antenna layer material.
If there are no ohmic ,losses in the layer material, the power loss
'is due to unattenuated surface waves which propagate radially out
from the antenna. If the layer is lossy, the surface waves
attenuate as they propagate'and the losses may be considered to be
ohmic in nature only. If the material is only slightly lossy,
the total power which is dissipated throughout the materia1,is
essentially that which is initially launched into the surface waves,
and treating the problem as completely lossless will give a good
approximation to esd. That is,
where Psew;=power in surface waves for the lossless case. This
factor es may prove to be the most critical one in lowering the
overall radiation efficiency of printed circuit antennas, depend-
ing on substrate thickness and permittivity/permeability pro-
perties. The purpose of this,paper is to determine particular
geometry and material combinations for substrates with a magnetic
superstrate (cover) layer such that es = 100% for antennas printed
on practical dielectric substrates..
The importance of substrate effects on printed circuit
antenna radiation efficiency was first noted by Uzunoglu
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RADIATION EFFICIENCY OPTIMIZATION
&. [2]. Subsequently, Katehi and Alexopoulos [ 3 ] , [4],
Alexopoulos g g. [ S ] , and Pozar [ 6 ] presented a more thorough
investigation of the radiation efficiency component es. These
investigations proved the significance of es, especially in
applications where thicker substrates or materials with high
relative permittivity are necessary. It was shown, e.g., that
for a typical substrate used in integrated circuits, such as
GaAs, es < 28% when the substrate is thick enough to achieve
a significant radiation resistance. This leads to the question of
whether it is possible to achieve es = loo%, i.e., to eliminate
all surface wave modes in the structure. The typical microstrip
geometry (Fig. la) supports a fundamental TM surface wave mode
with zero cut-off; therefore, for this geometry es < 100%.
On the other hand, asymmetric layers (Fig. lb) exhibit a k - B
diagram indicating a fundamental mode with nonzero cut-off [7],
allowing thereby the possibility of es = 100%. The half-space
efficiency for this configuration is, however, less than loo%,
since radiation is directed into both half spaces.
A method which utilizes the concept of a superstrate layer and
yields es = 100% has been developed recently (Fig. lcI[81.
The substrate, under this scheme, serves the function of
a supporting layer with the antennasprinted at the interface
of the substrate and superstrate with ~~u~ > ~ ~ u ~ . (In this nota-
tion E. ui(i = 1.2) represent the relative permittivity and 1'
permeability of the corresponding layer, while co and u are 0
the total values for free space). A disadvantage of this approach
for nonmagnetic layers is the fact that for substrate materials
with only moderately high E~ values 2 2.0) the maximum
allowable substrate thickness is quite small, regardless of the
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258 N. G. ALEXOPOULOS AND D. R. JACKSON
c2 value used, if es = 100% is to be achieved. For example, 'I,
if c1 = 2.1, then 5 Bmax/Ao % .010 (Ao is the free space wave-
length). Furthermore, as c2 becomes large, the maximum substrate
thickness decreases, so it would be necessary to use E~ values
very close to 1.0 to achieve significant substrate thickness.
For example, with a GaAs top layer (c2 % 12.5), it is necessary
that E~ ( 1.10 in order to achieve 5 Bmax/Xo 2 -05 [El. For
thin substrates, the radiation resistance is very low due to ground
plane image effects and this may lead to an impractical design for
achieving es = 100%.
These undesirable properties of low radiation resistance or
impractically low c1 values may be eliminated by using a magnetic
superstrate layer. It is then possible to achieve es = 100% with
reasonable radiLtion resistance and a moderate variety of
values. However, for high c1 values, this scheme requires low
loss magnetic superstrates with high u2 values, which tends to
make this scheme impractical.
11. SURFACE WAVE EFFECTS ON RADIATION EFFICIENCY FACTOR
It will be assumed henceforth that the geometry of Figure lc ..
is under consideration and that the antenna is an x directed
elementary dipole printed at the interface. The efficiency
factor due to surface wave effects, es, is computed by finding
the radiated power by reciprocity and then finding the surface
wave power from the surface wave fields obtained in each region
by solving the boundary value protilem and using the residue
theorem [ 81 . A
The TE and TM mode surface waves (TE or TM to the z direction)
are characterized by a radial propagation constant B=ATE, ATM
where 'TE,TM is the corresponding root of the TE mode
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RADIATION EFFICIENCY OPTIMIZATION
characteristic function De(A) or the TM mode characteristic
function Dm(X) given by
and
2 2 Dm(A) = -sinh[u2(H-B) 1 {u E p + u1c2 uultan(ulB)) - 2 1 1
2 2 4 2 2 4 In the above expressions, we have u = (A - ko) , u1 =(A -kl) , 2
u2 = (A - k:)' with ko = W- and kl,2 = k0nln2 where
n = 7 and n2 = . The values u,u 1 YlE1 at the roots ATE,TM
A
determine the field variation in the z direction for the surface
wave modes in the different regions.
As for the case of a substrate without cover, the dominant
surface wave mode is a TM surface wave with zero cut-off frequency
[ a ] . Since the lowest order mode has zero cut-off, there exists
the implication that in general there will always be power coupled
into surface waves and, therefore, es < 100%. However, it can be
shown [ a ] that all surface wave modes can be eliminated provided
that the superstrate thickness obtains the critical value tc
given by
and the substrate thickness satisfies the condition B ( Bmax
where Bmax is determined by the solution of the relation
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N. G. ALEXOPOULOS AND D. R. JACKSON
When the condition stipulated by equation ( 7 ) is satisfied,
the dominant TM mode is not excited, although it has zero cut-off.
This is the case because under these conditions u = 0. 1TM
Since the magnetic field components of the surface wave field vary
as cosh(ulTMz) for the z dependence in the substrate, the electric
field component Ex vanishes in the substrate for this TM mode.
Therefore, by reciprocity, the basic TM mode is not excited,
which means es = 100% as long as no other modes exist (B ( Bmax).
111. MAGNETIC SUPERSTRATE LAYERS '
omp put at ions for the geometry which provides es = 100% with
the antenna printed o n a dielectric substrate with a magnetic super-
strate layer are considered in this section.
A variety of substrate materials have been considered and
some results are shown in Figure 2 where n2tc/Ao is graphed vs.
p 2 for es = 100%. Figure 3 shows nlBmax/Ao for these cases.
It is interesting that the value of n2tc/Ao found from Eq. ( 7 )
does not depend on the substrate thickness. The only restriction
is that B - < Bmax. As can be seen from Fig. 3, magnetic superstrates
allow for fairly thick substrates in achieving es = 100% for most
substrate materials. In most cases, nlBmax/Ao 2 0.25 can be
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RADIATION EFFICIENCY OPTIMIZATION
Geometry of (a) Microstrlp .(b)Asymmetrlc Layers and
(c) Mlcrostrlp wilh a Superstrata.
n 2 t c / ~ 0 vs. ~2 for eS-1oo% (PI - 1,c2-1)
Figure 2
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262 N. G. ALEXOPOULOS AND D. R. JACKSON
achieved by using large enough u2 values. It may not be desirable
to have nlBmax/Ao much larger than this, however, since this is
roughly where radiation power P is maximized. corresponding rad
to the curve values in Fig. 3 are the substrate thicknesses
- shown in Fig. 4 which maximize radiation resistance. Rro - (Rro' max.
The radiation resistance of the infinitesimal dipole is defined
from
where I is the (constant) current assumed in the dipole. The
2 values of Rro are normalized by a factor of 3011 ( L / X ~ ) ~ where
L is the length of the dipole (L << Xo). The values of (Rro)max
are shown in Fig. 5.
Figure 6 shows plots of efficiency es, directive gain, and
radiation resistance for the case of a quartz substrate (cl = 4.01
with a magnetic superstrate layer (c2 = 1.0, u2 = 8.0). The
directive gain is in the direction normal to the interface,
referred to an isotropic radiator, and is expressed in dB. The
gain and radiation resistance show large, broad peaking behavior due to a
kind of transmission line resonance behavior discussed in [a].
?he values of n2t/Xo which maximize radiation resistance do not
in general agree with the n2tc/Xo values for es = 100%. Thus,
with magnetic superstrates, it is fairly easy to achieve e, = 100%
for moderate c1 values, though radiation resistance will not be
optimized simultaneously. This is in contrast to the behavior
with nonmagnetic layers, where efficiency and radiation resistance
are usually optimized simultaneously for a certain optimum super-
strate thickness [ a ] , but es = 100% is difficult to obtain with
moderate values. As Fig. 3 indicates, substrates with large
values such as GaAs (cl = 12.5) require fairly high u2 values
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RADIATION EFFICIENCY OPTIMIZATION
0 -
to 20 30 PI
Figure 3 "Anax/& .vs. p2 .tor el-loo% (PI -1,
12 Rmax vs. p, for el-10
(7
Rmax 70
(Rrad)max a
I
7
6
4
3
2
7
0 . . . . . . . . . . . . . . . . 0 40 20 50 P.
F l ~ u r e 4 vs. pl
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N. G. ALEXOPOULOS AND D. R . JACKSON
€1 - 4.00 0 A 9. p,- 1.00 - 0 '9. 0 Dlpole Is at the Interlace
D
Y O 2 2- w - 0 - - ij 3 .
Flgure 6a Elllclency vs. n,tlAo
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RADIATION EFFICIENCY OPTIMIZATION
Dlpols Is at the Interface
Flgure 6b GAIN vs. n,tlX,
Dlpole Is at the Interface
Flgure 6c Normallzed Radlatlon(Rrad)Reslstance vs. n,tlX,
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N. G. ALEXOPOULOS AND D. R. JACKSON
- Flgure 8 d E-Plane Pattern
( ~ , - 4 , p , - l . , € ~ - I , p ~ - 8 , n,Bl&-0 .2 . nZl lAo-0.10,
Oaln-0.764 dB, (Rrad) - 0.775. Dlpole at the Interface )
- Flaure Be H-Plane Paltern
( € - 4 . P 1 - 1 , 6 , -1. P z - 8 . n,BIA,-0.2. n,tlA,-0.18.
Qaln-8.764dB . (Rrad) -0.776 . Dlpole at the Interface
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RADIATION EFFICIENCY OPTIMIZATION
to achieve es = 100%. However, high permeability and low loss
magnetic materials are difficult to make. It is suggested that
the upper achievable limit is u 2 6 10.0 [9] which implies that
typically used substrates such as GaAs or Si cannot be used in
conjunction with a magnetic superstrate layer to produce es = 100%.
It is best to incorporate these materials as superstrates having
an optimum thickness dependent on the substrate used (81.
Finally, Figures 6d and 6e show a typical radiation pattern
for one of the substrate thicknesses.
IV. CONCLUSION
The effect of a magnetic superstrate layer on antennas
printed on a dielectric substrate has been investigated. It has
been shown that by choosing the proper thicknesses for given
materials, all surface wave modes can be eliminated. Elimination
of surface waves is significant since this leads to:
a) Raising the radiation efficiency due to substrate-
superstrate effects to es = loo%, and
b) Reducing the mutual impedance effect in the design
of microstrip arrays.
It has been seen that magnetic superstrates can,be used to
achieve es = 100% for substrates with moderate izl values (cl 6.01.
For large this is impractical, since low loss magnetic materials
with high values are difficult to obtain. When materials with 2
high € values are used, they may be incorporated as superstrates
over appropriate substrates to optimize efficiency [ a ] .
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N. G. ALEXOPOULOS AND D. R. JACKSON
REFERENCES
C. A. B a l a n i s , Antenna Theory, A n a l y s i s and Design, Harper and Row, 1982, N e w York.
N. I<. Uzunoglu, N. G. Alexopoulos, and J. G. F i k i o r i s , " R a d i a t i o n P r o p e r t i e s o f M i c r o s t r i p Dipoles , ' ' IEEE Trans . Antennas and Propagat . , Vol. AP-27, pp. 853-858, Nov., 1979.
P. B. Ka teh i and N. G. Alexopoulos, "On t h e E f f e c t o f S u b s t r a t e Thickness and P e r m i t t i v i t y on P r i n t e d C i r c u i t Antennas ," IEEE Trans . on Antennas and P ropaga t . , Vol. 31, pp. 34-39, J anua ry , 1983.
P. B. K a t e h i and N . G . Alexopoulos, "On t h e Theory o f P r i n t e d C i r c u i t Antennas f o r M i l l i m e t e r Waves," i n S i x t h I n t . Conf. I n f r a r e d and, M i l l i m e t e r Waves Dig. , December, 1981, pp. F. 2.9-F.2.10.
N. G . Alexopoulos, P. B. Ka teh i , and D. B. Ru t l edge , " S u b s t r a t e O p t i m i z a t i o n f o r I n t e g r a t e d C i r c u i t Antennas ," IEEE Trans . . on Microwave Theory and .Techn iques , Vol. MTT-31, pp. 550-557, J u l y , 1983.
D. Poza r , " C o n s i d e r a t i o n s f o r M i l l i m e t e r Wave P r i n t e d Antennas ," IEEE Trans . on Antennas and P r o p a g a t . , Vol. AP-31, pp. 740-747, September, 1983.
H. Kogeln ik , "Theory o f D i e l e c t r i c Waveguides," i n I n t e g r a t e d O p t i c s , T. Tamir, Ed. N e w York: Sp r inge r -Ver l ag , 1975.
N. G. Alexopoulos and D. R. Jackson, "Fundamental S u p e r s t r a t e (Cover) E f f e c t s o n P r i n t e d C i r c u i t Antennas ," UCLA Repor t No. ENG-83-50, Oc tobe r , 1983. Accepted f o r p u b l i c a t i o n , IEEE Trans . on Antennas and P ropaga t ion .
P e r s o n a l Communication w i t h P r o f e s s o r R . M. Walser , E l e c t r i c a l Eng inee r ing Department , U n i v e r s i t y of Texas , A u s t i n , Texas 78712
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RADIATION EFFICIENCY OPTIMIZATION
ACKNOWLEDGEMENTS
T h i s r e s e a r c h was performed under :
Nor throp No. 82-110-1006 and U . S . Army Research C o n t r a c t DAAG 29-83-K-0067
The a u t h o r s a l s o wish t o thank D r s . P. B a r g e l i o t e s and J. F. Cashen o f Nor throp C o r p o r a t i o n f o r encourag ing i n i t i a t i o n o f t h i s r e s e a r c h . Also a p p r e c i a . t i o n i s due t o M s . I . Andreadis f o r t y p i n g t h e ' m a n u s c r i p t and t o M r . K . Abolhassani f o r drawing t h e f i g u r e s .
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