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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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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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