A Thesis submitted to the Faculty of the DEPARTMENT OF ELECTRICAL ENGINEERING
In Partial Fulfillment of the Requirements For the Degree
MASTER OF SCIENCE In the Graduate Cbllege
THE UNIVERSITY OF ARIZONA
1 9 6 3
STATiShiiNT BY AUTHOR
This thesis has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the library.
Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgement of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in their judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
SIGNED
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below:
SSBfiET' 1." HfioSEi'itR, j] _ Professor of Electrical Engineering
cf/kDate
ACKHOyLEDGMMf
The author wishes to express his appreciation of the advice given by Professor Robert A, Bessemer in the preparation of this thesis»
ABSTRACT
This thesis is an investigation of the possibility of combining two conical frequency independent antenna elements into an array by placing them apex to apex on a common axis to produce an omnidirectional or beacon type pattern. The antenna elements are conical logarithmic spirals that radiate circularly polarized waves. By winding the elements in opposite directions and feeding them in phase their radiated waves should combine to produce an omnidirectional pattern.
An experiment which involves construction and testing of such an array is carried out. The objective of this work is to show that the fields radiated from each element combine to form a beacon type pattern. The results of the experiment indicate that the circularly polarized fields do combine to form a quasi omnidirectional pattern (+ 3 db at 200 me with larger variations up to 1000 me).
It is concluded that such an array could be used to produce a frequency independent beacon type pattern. Many possibilities for further investigation are uncovered and would have to be investigated before this antenna could be considered successful.
This thesis is an investigation of the possibility of combining two conical frequency independent antenna elements into an array by placing them apex to apex on a common axis to produce an omnidirectional or beacon type pattern. The antenna elements are conical logarithmic spirals that radiate circularly polarized waves« By winding the elements in opposite directions and feeding them in phase their radiated waves should combine to produce an omnidirectional pattern.
An experiment which involves construction and testing of such an array is carried out. The objective of this work is to show that the fields radiated from each element combine to form a beacon type pattern. The results of the experiment indicate that the circularly polarized fields do combine to form a quasi omnidirectional pattern (+ 5 db at 200 me with larger variations up to 1000 me).
It is concluded that such an array could be used to produce a frequency independent beacon type pattern. Many possibilities for further investigation are uncovered and would have to be investigated before this antenna could be considered successful.
GHAFEEE 1 IHIBODUCTiOl
% e last decade has witnessed a significant 'breakthrough in the design of frequency independent antennaso This breakthrough is based on the design of antenna shapes by specifying angles alone5 as proposed by ¥0 H„ Bumseyo That is9 if the shape of the antenna were specified entirely by angle s s its response would be independent of frequency „ Such antennas are referred to as "broadband antennasn. The use of the term "broadband" implies radiation characteristics essentially constant over frequency ranges as great as 4-0:1.
One frequency independent antenna receiving attention today is the so-called conical logarithmic spiral * or
2equiangular spiral antenna. Experimental models have been built that exhibit frequency independent operation over a range as great as 20:1. Their radiated field is a circularly polarized, unidirectional lobe off the apex. The beamwidth of the lobe can be adjusted by varying the
1957 IkE Rational Convention Record. Part 1, pp. 114—118.oLogarithmic spiral and equiangular spiral are
• synonymous and are henceforth abbreviated log-spiral.
1
construction parameters of the antenna; however«, it remains a low gain antenna6̂ 9 ^
The gain or directivity of an antenna element can be increased by forming two or more elements into an array9 hence it is reasonable to expect improved gain or directivity with an array of frequency independent elements, provided their frequency independent characteristics are not altered by the arrayo This implies that the array must also be described by angles @ '
Previous work in this field has been done by Be EL, BuBamelo^ Realizing the desirability of designing a broadband antenna with omnidirectional characteristics, DuHamel arranged two planar, trapezoidal tooth, sheet metal structures in a turnstile as shown in Figure lei.
This antenna was omnidirectional within +, 2,1 dbe A three armed structure was also tested and was found to be omnidirectional within _+ 3 dbe DuHamel concludes that the more arms a structure has the more omnidirectional it will
Do Dyson, "The Unidirectional Equiangular Spiral A n t e n n a I R E Trans„ on Antennas and Propagation, 7ol» AP-7, ppo 329-53z$rrOct., 1935.
Do Dyson and P e E.e Mayes, "Hew Circularly- Polarized Frequency-Independent Antennas with Conical Beam or Omnidirectional Patterns," IRE Trans, on Antennas and Propagation. Vol. AP-9, pp« 33^-34-2 ; July, 1961«
^R. H® DuHamel and P. R. Ore, Logarithmically Periodic Antenna Designs, Collins Radio Company, CTR-198, March, 1958.
% speZoi^2
°°thSlip,
beo Since an axial cross section of the conical log-spiral antenna used "by Dyson closely resembles the planar? trapezoidal tooth antenna used by BuHamel? it is possible to visualize the conical log-spiral substituted for the multi- armed structure=
In this thesis a new antenna array? using two conical log-spiral elements placed apex to apex on a common axis? is constructed and tested= Such a structure is described entirely by angles? thus retaining the essential characteristic of frequency independence? and it should retain the omnidirectional characteristics observed by DuHamel= The author believes an investigation of this type antenna has not been reported in the literaturec
\
CHAPTiSR 2 CONSTRUCTION
2.1 The Conical Lok-s iiral ElementsThe antenna elements used to form the array are
projections of a planer logarithmic spiral on a conical surface. The planer logarithmic spiral is defined by the equation
that determines the starting point of the spiral• The planer antenna is made from this curve by producing a conductor whose edges are defined by the curves
Thus the edges of the conductor are similar curves with
conductor is defined by a similar set of equations except that the angle 0 is increased by pi radians. A two arm symmetric planer antenna is thus produced.
pendicular to the plane of the spirals at the point of their origin and the spirals are projected orthogonally onto the conical surface, a conical log-spiral results. The equation describing the projected curve is
(2.1)are polar coordinates and p is a constantwhere
(2.2) (2.j)
one curve rotated through the fixed anglef. A second
If a conical surface is placed with its axis per-
r (2.4)5
6where r and rQ are the projections of ̂ and ^ on the conical surface. The constant b is determined by 9Q, the angle describing the conical surface, and by ̂ , the angle between the radius vector and a tangent to the log-spiral curve at the point of intersection (Pig. 2.1). The following relationships are true:
where r^ and rg determine the first arm and r^ and r^ determine the second arm. These tapered arms are difficult to construct on a scale necessary for this thesis. Ityson
^J. D. I%rson, July 61, op. cit., p.
al Lo
introduces the modification of making the arm width constant7rather than tapered.' This allows the arms to be con
structed of wire and eliminates two of the defining equations.
By limiting the values of r, a finite structure is described. Two values of r must be selected. They are completely independent of each other. Their selection determines a right circular truncated cone upon which the conducting arms are wound. Of course this truncated antenna is no longer completely independent of frequency since a dimension, that of the arm length, has been introduced. The upper and lower frequency limits of the antenna are determined by the diameters of the truncated cone. Pyson has found that the highest frequency is determined when the small diameter
(2.11)and the lowest frequency is determined when the large diameter
Dg - .8 (2.12)2.2 The Conical Log-Spiral Array
The antenna array is constructed by mounting two conical log-spiral elements on a common axis. The elements are identical in construction, except that the conducting
D. Byson, Oct. 59, op. cit., p. 335*8Ibid.. p. 331.
arms of one element are wound in the opposite sensee 5fhuss when placed on a common axis, one element becomes the geometric image of the other»
!3?he array is fed by coaxical cable o The cable is placed along the axis of one element* entering from the large truncated end and terminating at the apex (Fig® 2®2)« Electrical connections were made in the following manner= Each conducting arm of one element was soldered to the corresponding arm of the opposite element in such a manner that the geometric images were electrically connected= The coaxial cable was then soldered to the arms at the apex(ligo 2o5)o2*3 Construction Details
The conical surface which supports the conducting arms was made from plywood discs, % inch wooden dowels, and
Note: Corresponding arms areconnected to the coaxial feed line with d, = d phase delay is i!
that no2 so that i ntreduced •
Method of Feeding
Figure 2.3HH
12$he cone angle of 22)6 degrees was _ selected "based on
observations made by DuHamel=^ It was noted that increasing the cone angle increased the beamwidth in the sheet metal structiares = It was decided that an angle of 22)6 degrees was the desirable angle for the conical structureo
The valne of b in equation 2«,4 was based on a cone angle 90 of 22)6 degrees and three different values of1/'*The values of '■h selected were» first 45 degrees, then 65 degrees, and f inally 73 degrees * The selection of three values of f' resulted in three different antennas being constructed* They are individually discussed at greater length in Chapter 4*
To place the conducting arms on the cone it was necessary to solve for the various values of r using equations 2*4 and changing values of 0 by 45 degrees increments * Values of r were computed at every point where the arm was to cross a slat * A small groove at the angle */' was then cut in the slat* The conducting arms, of number eleven copper wire, were then laid snugly in the grooves and held in place with masking tape* The wire was laid so that it approximated the smooth conical shape between slats*
Both cones were then mounted on a )6 inch wooden dowel axis seven feet Iqng* The dowel was rigid enough to support the upper element as shown in figure 2*2* A small
B* DuHamel, op* cit*, p* 11*
wooden shim was added at the apex to keep the two elements the proper distance apart«
CHAPTER 3 EXPERIMENTAL TECHNIQUES
3®1 Equipment SetupField measurements were taken using the array as a
receiving antenna and a horizontal dipole as the source. Approximately 13 meters separated the two antennas. This provided at least 10 wavelengths separation at the lowest frequency (200 me).
The dipole was driven by General Radio Company unit oscillators, types 1209-B and 1218-A. General Radio Company unit power supply type 1203-B and unit oscillator (1000 cps modulator) type 1214— A were also utilized. The oscillators were calibrated using a General Radio Company slotted line, type 874--LBA. Miscellaneous line pads and stubs completed the source equipment.
The coaxial cable from the array was terminated approximately four feet from the base of the array in a General Radio Company type 874— D50 adjustable stub and type 874— VR crystal detector. Amphenol RG-122/U coaxial cable carried the 1000 cps demodulated signal to a Meinschel Engineering Go. Antenna Pattern Analyzer, Model BA-7® See Figure 3=1®
Since absolute gain measurements were not the subject of this thesis no reference signal -was provided. Only the
lo The proper frequency was set on the generator and the circuit tuned® Due to the non linear power output of the generators it was also necessary to adjust modulation percentage for each new frequency® A minimum of a 10 db line pad and/or a low pass filter was used to isolate the generator®
2® The 50 cm stub at the end of the array was adjusted for maximum signal on the pattern analyzer® The 'analyzer was then adjusted to some convenient reference level®
3® Measurements were taken by rotating the antenna through 4-5® increments and noting the changes in level on the analyzer® See Figure 3®2®
Measurements of variations in 9 were accomplished by supporting the antenna in a horizontal position® The dipole was then rotated 90® to the vertical so that the relative position of dipole and array remained unchanged® The above steps were then repeated® See Figure
Z Receiving Array
Dipole Source (Horizontal)
FiberboardPedestal
Movable PlatformMeasurements in 9 = 90 degree Plane
Figure 3*2
Y
Dipole Source (Vertical)
Z
WoodenSupports
i— 0 ---------------------------------- C 7 -
Movable PlatformMeasurements in 0 = 0 degree Plane
Figureoo
CHAPTER 4 EXPERIMENTAL RESULTS
4.1 IntroductionThree arrays using different angles for ̂ were con
structed and tested. The first array, with * 45 degrees, was unsatisfactory. Array number two was constructed based on experience gained from number one. A ^ of 65 degrees was utilized. Again the results were unsatisfactory; however, a marked improvement was noted. The results indicated a still larger Y was needed. Array number three was constructed with j// = 75 degrees. Field measurements compared favorably with those taken by other observers with different antenna structures. Array number three can therefore be considered successful.4.2 Array Number One
The first array was assembled with a ^ of 45 degrees•This selection was based on data from a single conical log-spiral element, as reported by Dyson.^ He notes that the pattern beamwidth is related to the rate of spiral and varies from around 70 degrees for a ^ of 74- degrees, to approximately 180 degrees for a ^ of 45 degrees. Using a ^ of 45 degrees I)yson is able to come within 6 db of a circularly
D. Dyson, Oct. 1959, op. cit., p. 533•
19
20polarized isotropic source in one hemisphere.11 It was felt that the 180 degree beamwidth of the individual elements was best suited to combine in the array to produce an omnidirectional pattern. It should be noted that Ityson’s measurements are based on an antenna with tapered arms. He points out that in the modified version, where the arms are made of wire, multilobing of the main beamand radiation of the base of the cone begin to occur as ^
12approaches 45 degrees.Figure 4.1 shows the data taken for this array.
The electric field was measured in the 6 ■ 90 degree plane. Instead of an omnidirectional pattern a figure eight pattern appeared. The field followed DuHamel1s figure eights but with greater variations (_+ 10 db). The results were definitely unsatisfactory. It is difficult to determine exactly what caused such an irregular pattern. It was certainly due in part to the multilobing observed by Hysonfor a ̂ near 45 degrees•
\ The wire arms of this array spiraled very loosely. That is, the arm made only one 560 degree turn through 0, from its start at the apex to its termination at the base. If one of the arms is assumed to start at the apex, at 0 = 0 degrees, and end at the base, at 0 = 560 degrees, it
11Ibld.J . D. Dyson, July 1961, 0£. cit.. p. 335»
21is possible to visualize that part of the arm between 0 * 0 degrees and 0 * 180 degrees t and that part between 0 * 180 degrees and 0 = 560 degrees. The part between 0 and 180 degrees lies on the smaller portion of the cone and is much shorter than the other part of the arm which lies on the large, base portion of the cone. Therefore, as the array was rotated for test purposes, the profile presented by each arm changed drastically and is believed to be partially responsible for the variations in the field. The obvious corrective action is tighten the rate of spiral by increasing the angle V-'•
It is interesting to note that the figure eight pattern rotates in the 9 * 90 degree plane as the frequencyis increased. Careful examination of the maximum andminimum points in Figure 4.1 clearly shows a definite rotation through 0 as frequency increases. This rotation can be explained. Using the wavelength as the basic unit of length, equation 2.1 can be written as
^ - e 0( V - ^ A >) (4.1)
or p'= ea{4-^)
where 6" - ^ A .A change in wavelength or frequency changes the angle and causes the pattern to rotate. The same rotation is noted in the conical log-spiral antenna but it is not detected
Notes: 1. Frequencies in megacycles2. Zeroes indicate maximum power points. All other values are in
decibels below zero db,3 , +db indicates maximum variation for each frequency.
Data for Array Number OneFigure 4,1
23easily due to the pattern symmetry#*^ Since the pattern symmetry deteriorates in the array it would be reasonable to expect some evidence of pattern rotation.4.3 Array Number Two
Based upon the experience gained from array number one, it was decided to construct array number two with a ̂ of 63 degrees. This allowed the arms to make three complete turns. No data could be found describing the exact beam- width of the individual elements with this particular ̂ 5 however, by interpolation, it had to be somewhat less than 180 degrees. It was felt that a beacon type pattern would still result.
Figure 4.2 is the data taken for this array. The field is still in the form of figure eight; however, the variations are not as sharp as those of array number one.In the worst case (800 me) a variation of only + 8 db is noted. The lower frequencies are especially encouraging.It appears that by increasing the angle f' the field pattern improves•4.4 Array Number Three
It was decided that array number three would be constructed with a JA' of 73 degrees. This would permit the arms to make five turns from apex to base. It would certainly eliminate the multilobing that occurred for smaller values of yz. The results were most gratifying.
2e Zeroes indicate maximum power pointse All other values are in decibels below zero db„
3 e +db indicates maximum variation for each frequency»Bata for Array Humber Two
Figure 4,2
25Figure 4-„5 is the data taken for this array. The
lower frequencies are again the closest to being omnidirectional with + 5 db variation at 200 me. This is the same variation obtained by DuHamel with his trapezoidal tooth structures (Figure 1,1)
The figure eight patterns are no longer identifiable and in the higher frequency range the pattern resembles a cardioid. The presence of the notch cannot be -explained at this time, It was thought'the coaxial cable feed might be responsible. There is no doubt that it has some effectf especially at the higher frequencies; however4 the notch in the cardioid rotates in the 6 = 90 degree plane just as the figure eight did in the previous antenna. Since the coaxial cable was within one half inch of being concentric with the axis of the array, it is doubtful that it could have caused the notch.
The chapter on construction points out that care was taken to insure that the four conducting arms of the array were of equal length (Fig. 2.3). Since the signal must travel from the feed point along the arms to the active region, any variations in arm length would cause a phase delay which would upset the pattern. Other phase delays could be caused by irregularities in construction including the curvature of the arm between slats, slight rotation of .
2o Zeroes indicate maximum power pointse All other values are in decibels below zero db«
3o ±db indicates maximum variation for each frequency.Data for Array Humber Three (0 variations)
Figure 4»5
one element with respect to another in the 0 direction, and slight bending of the axis» Measures were taken to minimize such irregularities, but it is certain that they did affect the operation.
2o Zeroes indicate maximum power points® All other values are in decibels below zero db.
Data for Array Number Three (0 variations)Figure 4e4
ro00
29they had been reported by DuHa melhowever, a study of his papers does not lead one to expect lobes at 9 = 0 and 180 degrees= At this point no explanation can be offered for the lobes along the z axis„ It should be noted that the lobes on the z axis are conical and point up and down, while the other lobes are cross sections of a torroid or donut about the middle of the antenna,, The majority of the power lies in the torroid, not in the vertical lobes® 4-0$ Summary
An investigation of the antenna array formed by mounting two frequency independent elements on a common axis has shown that it is possible to obtain an omnidirectional pattern® Investigation of published articles indicated such an antenna was possible® Other investigations using variations on planar log-spiral antennas had proved successful® Ho references to this particular array could be found in the literatures so it was decided to build and test one® '
The first array was based on data already available for the antenna elements® The results were unsuccessful but pointed the direction for the second array® By increasing the angle the wire arm makes with the radius vector it was possible to tighten the rate of spiral® This placed more wire on the antenna and reduced the multilobing®
15Ibid
30The second array was a definite improvement over
the first "but left something to be desired in its fieldo It was decided to increase the angle ^ again in hopes that more improvements would result«
Array number three compared favorably with results obtained by other observers« The field pattern was quasi omnidirectional but not beacon type* Two lobes appeared along the Z axis that were not expected and could not be explainedo With the exception of the two axial lobes the pattern was beacon type* Only a small portion of the radiated power was contained in the axial lobese
The lack of a professional antenna range greatly hindered this investigation. This became especially obvious when the array was oriented horizontally to measure variations in 9. The eardioid patterns located when the antenna was vertical had disappeared.
The effect of the rotation in the figure eight and cordioid patterns was accounted for. The variations that did appear in the field were due, to a great extent, to the phase distortions introduced by dimensional variations.
This investigation was by no means exhaustive. It uncovered some of the basic facts about a particular antenna, but also raised many new and interesting questions.
CHAPTER 5 COHCLUSIOHS
The idea of designing an antenna shape "by specifying angles alone is relatively new5 but it is a fundamental concept., ,The exploitation of this concept and engineering application of such antenna shapes has opened a vast and important area of research and development. This thesis has presented another step in man’s efforts to broaden the diversity of form of frequency independent antennas =
It has been shown that two frequency independent elements can be formed into an array to produce an omnidirectional pattern. This was done using two conical log- spiral antennas as the independent elements. The unidirectional % circularly-polarized pattern of each element combined to produce a pattern that was within + 3 db of "being omnidirectional at 200 me9 with greater variations as the frequency was raised to 1000 me. These results compared favorably to those obtained by other workers using various other types of frequency independent structures.
The experiment showed that while it was possible to approximate.the tapered metal arms with wire, it was also necessary to carefully control their rate of spiral.If the rate of spiral was too loose near 45 degrees) multilobing occured in the elements and disrupted the pattern
5i
52of the arrayc It is concluded that ^ is the major controlling factor in the design of this antenna0
The rotation of the field with changes in frequencywas noted and explainedo The effect tends to "become less obvious as the pattern becomes more omnidirectional0 It is concluded that this effect is not harmful„
The appearance of the two lobes along the z axiscould not be explained= It is concluded that their presence does not detract from the omnidirectivity of the pattern- (in the 0 direction) since they are symmetric about the z axis 0
The placement of the coaxial feed line presents a problem* The cable is an unbalanced line and should be placed where it can effect the field the least* Investigation of balanced feed lines would also be worthwhile*
During the course of this investigation the author noted that the field of the array was very sensitive to slight rotations of one of the elements with respect to another* This introduced the possibility of improving the field pattern by rotating one element through some fixed angle and feeding the two elements out of phase*
It should be obvious that the number of variationsis unlimited and that efforts to understand and improve
*frequency independent antennas will continue for some time*
55
BIBLIOGRAPHY
Hyson, Je D,, "The Equiangular Spiral Antenna," IHE Transo on Antennas and Propagation* Vol. AP-7. Ho. 1 ipH T, ig ^ T F p : isirrsT": —
2.0 Hyson, J. D,, "The Unidirectional Equiangular Spiral Antenna," IBS Trans, on Antenna and Propagation, Vol. AP-7* Ho* ZTToEtober,"T95^7ip7 329-33%: ---
3. Hyson, J. D* and P. E= Mayes, "Hew Circularly-Polarised Frequency-Independent Antennas with Conical Beam or omnidirectional Patterns," IRE Trans, on Antenna and Propagation, Vol. AP-9, Ho. 4, Huly, 1961. pp. 334—34-2.
4. BuEamel, E. H. and B. G. Berry, "Logarithmically Periodic Antenna Arrays," Collins Radio Technical Report Ho. 206, September, 1958.
3. DuHainel, E. H. and F. R. Ore, "LogarithmicallyPeriodic Antenna Designs," Collins Radio Technical Report Ho. 198. March, 1958.
6. Elliot, R. S., "A View of Frequency Independent Antennas," The Microwave Journal, December, 1962,pp. 61-68.
7. Bessemer, R. A., "Backward-Wave Radiation from an Equiangular Spiral Antenna," IRE Transactions on Antennas and Propagation, Vol. AP-9, Ho. 6 , Hovember,iggIT" - - ---
8. Mayes, P. E., "Broadband Backward-W^ve Antennas,"The Microwave Journal, January, 1963, pp. 61-71=
9. Rumsey, V. H., "Frequency Independent Antennas,"1957 IRE Rational Convention Record* Part 1, pp„ 114- H B t
