An antenna integrates a planar structure, wideband compact design, permitg phasability, into a single structure. The antenna design makes it possible to implement the antenna throughout the entire electromagnetic spectrum with little or no need for impedance matching. The antenna comprises a plurality of exponential-spiral shaped antenna arms in which each of the arms has a radially inner and radially outer end and in which the radially inner ends are spaced rotationally about a common axis, and in which the arms are separated circumferentially from each other in proportion to their distance from the common axis. Each of the spiral antenna arms includes an antenna element having a sinuous portion that has amplitude and period characteristics that vary in proportion to their distance from said common axis. The antenna elements are selectively coupled to an antenna feed.

BACKGROUND OF THE INVENTION 
This invention relates generally to antennas and in particular to a 
compact, phasable, multioctave, high efficiency, spiral mode antenna. 
There have always been numerous civilian, scientific and military 
requirements for a generic wideband high efficiency and low profile 
antenna element which can be mounted close to a ground plane. Some, but 
not all, of these requirements have been met with the designs of previous 
antennas. The history of these antenna elements can be traced back to the 
conical log spiral antenna. This antenna consists of two conducting sheets 
on a dielectric cone; the conducting sheets are fed at the cone apex with 
the energy traveling down the cone towards its base. The active 
(radiating) region of the cone is the point at which the phase of the wave 
traveling down the cone changes by approximately 360 degrees around the 
circumference of the cone. In this region a circularly polarized, 
backward-traveling wave is launched (passing the cone apex), having a 
polarization opposite to that of the element winding direction, i.e. if a 
right-hand wave travels down the cone, the radiated wave is left 
circularly polarized. If the element is a self-conjugate antenna, the 
conducting and non-conducting areas are equal and the two areas will be 
precisely interchanged under a physical 90 degree rotation. 
Erickson and Fisher (Reference 1) improved upon the log spiral in a design 
for an element utilized in a decametric-wavelength (15-110 MHZ or 2.7-20 
meters) phased-array radio telescope by replacing the balanced conducting 
sheets (which would present construction and wind-loading difficulties for 
an element designed to operate at meter wavelengths with 3 wires, i.e., 
the edges were defined by wires (2 wires, 1 for each edge), with a third 
wire located along the centerline of each surface. They also realized that 
the element could be operated below its cut-off frequency (the frequency 
at which the circumference at the base of the element was approximately 1 
wavelength), albeit at reduced efficiency, by resistively terminating the 
element windings, at the base of the element, in the characteristic 
impedance of the element. The two wire-defined "surfaces" were fed through 
a balun (balanced-to-unbalanced transformer) from coaxial cable. Another 
opposed pair of winding wires between the two surfaces was electrically 
disconnected. Arrays of 15 elements each could be phased to a desired 
direction simply by electronically switching the balun to the appropriate 
6 out of 8 element windings, thereby changing the phase of each element in 
45-degree increments. Important conclusions they drew from precise and 
exhaustive measurements were: (1) the half-power beamwidth was about 100 
degrees, centered on the zenith; (2) the element efficiency was within 1 
to 3 dB of that of a reference dipole antenna; (3) the element phasing did 
indeed change by 45 degrees per rotation step; (4) cross-polarization 
varied from less than 5% at frequencies below 50 MHZ to 20% at 110 MHZ; 
and (5) the element retained its high efficiency even down to frequencies 
for which the radiating region was close to the ground. Conclusion (5) is 
implicit in their results but is not explicitly stated in their analysis. 
However, it is extremely important in considering how well an active 
region will radiate, and maintain its impedance, when it is located very 
close to a ground plane. The height of their log spiral antenna was 7.2 
meters. 
A broadband but linearly-polarized antenna (Reference 2) constructed with 
wire elements outlining current sheet surfaces also displayed efficient 
operation at frequencies for which the active radiating region was very 
close to a ground plane. However, it had no phasing capability. 
An advance in log spiral antennas was made by Wang and Tripp (References 
3-5) who designed a planar log spiral antenna which could be operated at a 
very small fraction of a wavelength above a ground plane, thereby 
resulting in a low-profile element suitable for a variety of civilian and 
military applications. In commercial literature describing the antenna 
element, they refer to a compact version of the element which, however, 
has only limited bandwidth. 
SUMMARY OF THE INVENTION 
The invention integrates a planar structure, wideband compact design, that 
permits phasability, into a single antenna structure. The antenna design 
makes it possible to implement the antenna throughout the entire 
electromagnetic spectrum with little or no need for impedance matching. 
The antenna comprises a plurality of exponential-spiral shaped antenna 
arms in which each of the arms has a radially inner and radially outer end 
and in which the radially inner ends are spaced rotationally about a 
common axis, and in which the arms are separated circumferentially from 
each other in proportion to their distance from the common axis. Each of 
the spiral antenna arms includes an antenna element having a sinuous 
portion that has amplitude and period characteristics that vary in 
proportion to their distance from said common axis. An antenna feed is 
selectively coupled to the antenna elements. 
OBJECTS OF THE INVENTION 
It is an object of the invention to provide an improved antenna. 
Another object of the invention is to provide an antenna whose design is 
frequency independent. 
Another object of the invention is to provide an antenna that is 
dimensionally compact. 
Yet another object of the invention is to provide an antenna that is 
wide-band. 
Another object of the invention is to provide an antenna that permits ease 
of phase changing. 
Yet another object of the invention is to provide an antenna structure that 
permits ease of feed mode changing. 
Still yet another object of the invention is to provide an antenna that 
requires a minimum of impedance tuning.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring to FIG. 1, an antenna according to a preferred embodiment of the 
invention begins with the paths of eight spiral shaped antenna arms 10, 
each one of which follows an exponential spiral described by equation (1) 
as follows: 
EQU r(.PHI.)=r1.multidot.exp (.beta..multidot..PHI.), eq. (1) 
where .PHI. is the polar angle in units of rotation, r is the radius from 
the origin or spiral axis 11, r1 is a chosen constant and .beta. is a 
radial scale factor, i.e., each arm rotation increases its radius by exp 
(.beta.). FIG. 1 illustrates the path of the eight spiral arms in which 
the radially inner ends of the arms (indicated by reference numbers 0-7) 
are spaced rotationally about common origin/axis 11, each arm 45 degrees 
from a previous arm. According to this embodiment, arms 10 separate 
circumferentially from each other in proportion to their distance from 
origin/axis 11, so that the further the arms from origin/axis 11, the 
greater the arms separate from each other. 
According to the invention, the spiral arms are refined according to the 
imposition of a sinuous variation on the spiral windings. Referring to 
FIG. 2A, conductive antenna elements 12 are designed to follow the path of 
sinuously varied spiral arms 10, shown in FIG. 1, and can be fabricated of 
planar wires such as printed circuit board traces on a dielectric 
substrate for microwave frequencies or can be heavy gage wire at lower 
frequencies. The sinuous variation increases the path length for each 
element winding rotation so that the circumference through which the phase 
increases by 360 degrees is correspondingly decreased. The path deviation 
of the sinuous variation from that of the spiral may be written as: 
EQU y(.PHI.)=a1.multidot.r(.PHI.).multidot.sin 
(2.multidot.pi.multidot.N.multidot..PHI.), eq. (2) 
where a1 is the amplitude of the sinuous variation as a function of radius 
and N is the number of sinuous cycles per rotation of .PHI., these 
characteristics being illustrated further in FIG. 2B. 
Thus the sinuous deviation is proportional to the spiral arm radius. As the 
active region of the antenna element will always be at a radius which is 
proportional to wavelength, the sinuous amplitude itself is proportional 
to wavelength. Further, the spatial period of the sinuous term is a 
constant fraction (1/N) of the circumference, so all parameters scale in 
proportion to wavelength--the active region physical parameters, 
normalized by wavelength, are a constant, which is an important 
consideration for a wideband antenna. Further, as the design parameters of 
the invention are proportional to the antenna's operating wavelength, the 
impedance of the antenna will remain close to constant, minimiing the need 
for impedance tuning. When N is an integer multiple of 8, it is known that 
the sinuously varied elements will not physically interfere. 
The ratio of the path length along the sinuous element windings to an 
undeviated winding is given by the following equation (3) integral: 
##EQU1## 
Where .xi.=local angle (in radians) governing the sinuous variation so 
that as .xi. advances from 0 to 2.pi., a complete sinuous cycle will be 
traced out. The inverse of the ratio given by equation (3) is the velocity 
factor, so-called because it is the ratio of the sinuous circumferential 
propagation velocity to the undeviated propagation velocity, which is 
approximately the speed of light. 
In FIG. 2A, an example of an element with a slow-wave velocity factor of 2, 
or velocity factor of 0.5, is shown. The following further numerical 
description and calculations can be used for the specific sinuously varied 
spiral configuration shown in FIG. 2A: 
EQU sf=3; vel fac=0.5; rot=1; Nwind=8; Nfac=8; N=Nwind.multidot.Nfac 
EQU r1=1; .beta.:=1n(sf); frq rat=exp[.beta. (rot-1)]; frq rat=3; 
##EQU2## 
ti dfac=16.362; a1(dfac)=0.041 
EQU r(.PHI.)=r1.multidot.exp(.beta..multidot..PHI.); 
y(.PHI.):=r(.PHI.).multidot.(1+a1(dfac).multidot.sin(2.multidot..pi..multi 
dot.N.multidot..PHI.)) 
In which: 
"sf"=a scaling factor equaling the ratio of spiral arm radius after n turns 
to radius after n-1 turns (sf=3 equates with a spiral radius that 
increases by a factor of 3 after each complete spiral turn) 
"ve1 fac"=ratio of the phase velocity through the sinuous winding to the 
phase velocity through the undeviated spiral winding 
"rot"=number of turns of each spiral arm winding 
"Nwind"=number of spiral arm windings 
"Nfac"=number of sinuous cycles, start of one spiral arm winding to the 
start of the next 
"N=Nwind.multidot.Nfac"=number of sinuous cycles per spiral arm turn 
r1=a constant 
.beta.=the radial scale factor previously described 
frq rat=ratio of highest frequency to lowest=ratio of outer circumference 
to inner 
a1=amplitude of sinuous variation as a fraction of the radius as described 
previously 
.xi.=local angle governing sinuous variation--as .xi. advances from 0 to 
2.pi., a complete sinuous cycle is traced out 
dfac=the value of "x" for a given velocity factor 
.PHI. is the spiral angle measured in units of rotation 
r(.PHI.)=r1.multidot.exp (.beta..multidot..PHI.)=equation of spiral trace 
r(.PHI.)=distance from spiral arm origin/axis to spiral trace 
y(.PHI.):=r(.PHI.).multidot.(1+a1(dfac).multidot.sin(2.multidot..pi..multid 
ot.N.multidot..PHI.))=equation of sinuous trace 
y(.PHI.)=distance from spiral arm origin/axis to sinuous trace 
FIG. 2C is an enlarged view of the innermost half turn of each of the 8 
element windings of FIG. 2A. In this example of the invention, the element 
is fed electrically from one side, A, of a balanced transmission line by 
connecting 3 adjacent element windings together, e.g., element windings 0, 
1, and 2 are connected, leaving the next element disconnected (floating), 
i.e., element winding 3 (shown dashed), then connecting to the other side, 
B, of the balanced transmission line the next 3 element windings together, 
i.e., 4, 5, and 6, and leaving the next element winding 
disconnected/floating, i.e., element winding 7 (shown dashed). 
For the purpose of phasing two or more antennas together for directional 
beam control, the particular grouping of antenna element windings can be 
changed. For example, a linear array of antennas can be phased with a 
45-degree phase gradient from one antenna to the next. Assuming that 
antenna element winding number 0 for each antenna is always at a reference 
direction, e.g., north, then the gradient would result if, for the first 
antenna, the element windings are connected as described above, and for 
the second antenna, element windings 1, 2 and 3 were connected to side A 
of the transmission line, while 5, 6, and 7 are connected to side B. For 
the third antenna, element windings 2, 3, and 4 would be connected to A 
and 6, 7, and 0 would be connected to B, elements 0 and 4 being left 
disconnected, etc. 
The connections as described above give rise to a so-called Mode 1 antenna 
pattern characterized by a maximum response in the direction perpendicular 
to the plane of the antenna array. However, the access to the individual 
element windings of the invention also makes it easy to excite other 
modes. 
To eliminate reflections and extend the usable low frequency response of 
the antenna, the element windings should be terminated with a resistive 
load, not shown. For a self-conjugate antenna, the theoretical feed-point 
impedance is 189 ohms so that for 3 element windings in parallel, the 
theoretical impedance of each is approximately 570 ohms. Thus the outer 
end of each element winding requires a termination of 570 ohms. 
It should be noted that the radiation resistance of the compact spiral mode 
antenna will be significantly less than the theoretical 189 ohms, 
depending on the slow-wave velocity factor. However, this reduction in 
impedance could even be a design parameter by itself in the sense that an 
antenna engineer may wish to attain a desired element impedance by 
intentionally "tuning" the amplitude of the sinuous variation. 
Typically the connection of the element windings to the transmission line 
would be done through electronic switches for control of the antenna feed. 
In Reference (6) there is an example of such a switching scheme 
implemented using diode switches. However, for high-power transmitting 
applications, where diode switches would not be suitable, 
electromechanical relays can be used. 
In comparison with prior art antenna elements, this element integrates a 
planar structure, wideband compact design, and phasability into a single 
physical structure. In addition, because of access to the windings, the 
feed mode can be easily changed. The design is generic and 
frequency-independent in the sense that the same design equations can be 
used, whether the element is to be used at 10 MHZ or 10 GHz. Only the 
physical size and implementation i.e., element windings, will change. 
There are numerous parametric combinations of .beta., a1, and N possible 
for specific design requirements. The effects of these combinations will 
be understood through numeric-theoretic studies (using NEC, for example, 
the Numerical Electromagnetic Code) and appropriate measurements of 
feed-point impedance, pattern, polarization purity (i.e., degree of 
circularity), and efficiency as a function of frequency. Other equations 
could be used to describe the sinuous component. For example, instead of 
using a sine wave, it might be easier for either computational or physical 
construction reasons to use a triangular wave. The object is to 
superimpose a deviation in the spiral winding to decrease the phase 
velocity around the circumference and thereby correspondingly decrease the 
diameter required to radiate efficiently at a specified minimum frequency. 
The following is a list of references cited herein: 
Reference (1) "A New Wideband, Fully Steerable, Decametric Array at Clark 
Lake," W. C. Erickson and J. R. Fisher, Radio Science, vol. 9, no. 3, pp 
387-401, March 1974; 
Reference (2) "Broad-Band Antenna Array with Application to Radio 
Astronomy," IEEE Trans. Antennas Propagat., C. L. Rufenach, W. M. Cronyn 
and K. L. Neal, vol. AP-21, no. 5, pp 697-700, September 1973; 
Reference (3) "Design of Multioctave Spiral-Mode Microstrip Antennas," J. 
J. H. Wang and V. K. Tripp, IEEE Trans. Antennas Propagat., vol. 39, pp 
332-335, March 1991; 
Reference (4) "Spiral Microstrip Antenna Suits EW/ECM Systems," J. J. H. 
Wang and V. K. Tripp, Microwaves and RF, vol. 32, no. 12; 
References (5) U.S. Pat. No. 5,313,216 issued to Johnson J. H. Wang and 
Victor K. Tripp titled "Multioctave Microstrip Antenna" developed at the 
Georgia Institute of Technology by research funded through 
Wright-Patterson Air Force Base; and 
Reference (6) DESIGN TESTS OF THE FULLY STEERABLE, WIDEBAND, DECAMETRIC 
ARRAY AT THE CLARK LAKE RATIO OBSERVATORY, J. R. Fisher, Ph.D. 
Dissertation (University of Maryland, Astronomy Program, Department of 
Physics and Astronomy), 1972. 
Obviously, many modifications and variations of the invention are possible 
in light of the above teachings. It is therefore to be understood that 
within the scope of the appended claims the invention may be practiced 
otherwise than as has been specifically described.