[6] P. J. Wood,“Spherical wavesin antenna problems”, Marconi frequencymaynotbetheoptimumatanotherfrequency.

Rev., vol. 34, no. 182, pp. 149-172,1971. Theantennadesignermaynothavecompletefreedom in

[7] S. von Hoerner, “The design of correcting secondary reflectors,” selectinglocationandfrequency.However,knowledgeasto
IEEE Trans. Antennas Propagat., vol.AP-24,pp. 336-340, May
1976. how the efficiency varies with frequency and location can help
in the selectionof the best allowable optimum.
In order to select the optimum location and frequency, one
could compute and plot a family of curvesof efficiency versus
position versus frequency. Presented here is a technique which
shouldinvolveconsiderably less computation,andalso give
Small Antenna Location Synthesis Using Characteristic Modes more physical insight. The technique involves the computation
of thecharacteristicmodesofthesupportstructure.The
E. H. NEWMAN theory of characteristic modes has been presented by Garbacz
[ 1 ] and by Harrington and Mautz [ 21. Numerically efficient
Abstr.oct-It is shown that the efficiency of a small antenna can be techniques,usingthemethod of moments,forcomputing
substantially increased by properly locating it on its support structure. characteristic modes have also been presented by Harrington
Characteristic modes are used to determine the optimum location and and Mautz [ 31 and are applied in this work.
frequency. The characteristic modes are real currents on the surface of
a conducting body. Denoting J n as a characteristic mode, the
I. DISCUSSION choice J , as a basis set for the current diagonalizes the imped-
ance matrix or operator of the conducting body. The charac-
Animportantproblem in antennadesign is thedevelop- teristicmodeshaveorthogonalityoftheradiated fields.
mentofrelativelyefficientelectricallysmallradiating ele- Associated with each characteristic mode J , is a real charac-
ments. The antenna efficiency can be defined as teristic value or eigenvalueA,.
The eigenvalues are important because they tell how well a
particularmoderadiates.Thosemodeswithsmall 11, 1 are
goodoreffectiveradiators,whilethosewithlarge Ih, I are
poor or ineffective radiators. In order to improve substantially
where R , is the radiation resistance and R I is the loss resist-
the efficiency of a small antenna mounted on a support struc-
ance.Smallantennasaregenerallyveryinefficientbecause
ture, it is necessary to excite modes which are effective radia-
their radiation resistance is low. The radiation resistance of a
tors, i.e., those with small Ih, l. Associated with each eigen-
smalldipolevariesaswhilethat of asmallloopvariesas
value is a characteristic angle defined by
(Z/x)*, where I is the maximum extent of the antenna and1 is
t h e wavelength.Therearetwoconventionalapproachesto
improvingtheefficiencyofsmallantennas.Thefirst is to
01,= 180° - tan-l (A,). (2)
reduce the loss resistance, letus say by using thick highly con- Modes with characteristic angles near 1 80° are effective radia-
ducting wires to construct the antenna, or by using low loss tors, while those with characteristic angles near 90” or 270’
components in the tuning or matching networks. The second are ineffective radiators.
is t o increase the radiation resistance, let us say by top-loading A source or probe, with impressed field E’, excites the nth
a short dipole or ferrite-loading a small loop. A third technique characteristic mode with strength
for increasing the radiation resistance is described below.
Small antennas are usually designed on test beds resembling
either free space or an infinite ground plane. However, in use V, = //Jn E’ds (3)
they are often mounted on support structure such as a ship, a s
tank, a man, or an airplane. The basic idea here is to think of where the integral extends over the surface of the body. Equa-
the small antenna not as the primary radiator, but rather as a tion (3) shows that in order to excite J , as strongly as pes-
probe to excite currents on the support structure. Since the sible, the probe should be placed at or near the maximum Of
support structure is often not electrically small, it can be an J,. Further, the probe should be orientedso that E’ and J,, are
effective radiator. Thus the radiation resistance and efficiency parallel. Thus, t o improve the efficiency of a small antenna,we
of a small antenna can be increased by properly locating it on wish t o locate it on its support structure where a characteristic
its support structure. mode, with characteristic angle near 180°, is maximum. The
One problem is where to locate the small antenna. Some design example below will illustrate this procedure for a small
locations may result in substantial improvements in efficiency, loop on a crossed wire.
while others may result in little or no improvement. A second
and related problem is the selection of an operating frequency 11. DESIGN EXAMPLE
which optimizes the efficiency. The optimum location at one A design example will now be presented to illustrate theuse
of characteristic modes to select the operating frequency and
Manuscriptreceived October 24, 1978; revised April 30, 1979. location for a small loop on a crossed wire.The crossed wire is
This work was supported in part by the Department of the Navy and shownintheinsertinFig.1andcouldrepresentacrude
in part by the Ohio State UniversityResearch Foundation under model for an airplane shape. As adesignrestrictionwe Will
Contract N00014-78C-0049. assume that the loop must be located on the longer vertical
The author is with the ElectroScience Laboratory, Ohio State
University, Columbus,OH 43212. wire of length L.

0 1979 IEEE
0018-926X/79/0700-0530$00.75
TRANSACTIONS
IEEE ON ANTENNAS
PROPAGATION,
AND VOL. AP-21, NO. 4, JULY 1919 53 1

0 170
150
L = 1.5m
lost 1 i 7 R A D I A T I O N RESISTANCE OF P
SMALL LOOP O N A CROSSED
WIRE AT L / X = 0.75
o =0.001m
I30 -
110-
90 I I I
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
‘/x
Fig. 1. Characteristic angles for crossedwire.

d ( METERS)
Fig. 3. Radiation resistance of small loop on crossedwire.Although
shown in plane of cross, loop is actually in plane perpendicular to
cross.
properlylocatingit on itssupportstructure.Characteristic
C H A R . MODES @ L/i= 0.75 modes are shown to be a useful tool for determining the opti-
Fig. 2. Characteristicmode currents for crossed wire. mum location and operating frequency. For two reasons, the
technique is bestapplicabletosupportstructureswhichare
The design is begun by computing the characteristic modes not electrically large. First, the size of the moment method
and characteristic angles of the crossed wire versus frequency. impedance matrix, necessary for the computation of the char-
Fig. 1 shows a plot of the characteristic angles of the first few acteristicmodes,canbecomeimpractically large. Second, as
modes versus L f i . The optimum frequencies are those where the electrical size of the support structure increases, more and
the various modes are resonant, i.e., (Y = 180°. Fig. 2 shows a more characteristic modes are effective radiators. In this case,
plot of the characteristic modes atL f i = 0.75 where modeC is the exact antenna location and operating frequency is likely
nearlyresonant. In thisfigurethesolidlinerepresentsthe to be far less critical.
current on the vertical wire of length L , while the dotted line
REFERENCES
represents the current on the horizontal wire of length 2L/3.
[ l ] R. J. GarbaczandR. H. Turpin, “A generalized expansion for
The arrows indicate the direction of current flow. The char- radiatedand scattered fields,” IEEE Trans. Antennas Propagat.,
acteristic angles of the modes are also shown. Note that modes vol. AP-19, pp. 348-358, May 1971.
A and D haveanglesnear 90’ and 270°, respectively.Thus [2] R. F. Harringtonand J. R. Mautz, “Theory of characteristic
they are poor or ineffective radiators, and we have no interest modes for conducting bodies,” IEEE Trans. Antennas Propagat.,
vol. AP-19, pp. 622-628, Sept. 1971.
in exciting them. Mode B , with (Y = 148O, is a reasonably good [3] -, “Computation of characteristic modes for conducting bodies,”
radiator, but it has zero current on the vertical wire where the IEEE Trans. Antennas Propagat., vol. AP-19, pp. 629-639, Sept.
small antenna must be located. Thus we will not be able to 1971.
excite mode B with substantial strength. Finally, mode C is an
excellent radiator with (Y = 178’. It has maximum current just
above the wire junction, and thus this is the optimum location
of the small loop. A Nonrectangular Patch Modelfor Scattering from Surfaces
Fig. 3 shows a plot of the radiation resistance of a small
loop,normalizedtoitsvalueinfreespace,versustheloop JITENDRA SINGH, MEMBER IEEE, AND
position o n t h e crossed wire at Llh = 0.75. The ratio RJR,,, A. T. ADAMS, SENIOR MEMBER, IEEE
where R , , is the radiation resistance of the loop in free space Abstract-A model is derived for treatment of surfaces using non-
and R, is the radiation resistance of the loop on the crossed rectangular patches. Tests show good agreement, where comparison is
wire, is equal to the increase in efficiency due to the crossed possible, with results published elsewhere. The results are shown to be
wire, provided the efficiency is low. Note, that as predicted
above, the radiation resistance increases substantially when it
Manuscriptreceived February 2,1978; revised September 27,
is located just above the junction, and that orders of magni- 1978.
tude improvement in the efficiency are possible. J. Singh was with Syracuse University, Syracuse, NY 13110. He is
nowwith the Department ofElectricalEngineering,WorcesterPoly-
111. SUMMARY technic Institute, Worcester, MA 01609.
It has been demonstrated that the radiation resistance and A. T. Adams is with the Department of Electricaland Computer
efficiency of a small antenna can be substantially increased by Engineering, Syracuse University, Syracuse,NY 13210.

0018-926X/79/0700-0531$00.75O 1979 IEEE