THE UNIVERSITY OF MICHIGAN
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Technical Report ECOM-00547-1 October 1967
Azimuth and Elevation Direction Finder Techniques
First Quarterly Report
1 July - 30 September 1967
Report No. 1
Contract DAAB07-67-C0547
DA Project 5A6 79191 D902-05-11
Prepared by
J. E. Ferris, B. L. J. Rao and W. E. Zimmerman
The University of Michigan Radiation Laboratory
Department of Electiiceal Engineering
Ann Arbor,' Michigan.
For
United States Army Electronics Cbirii'and,: Fort Monmouth, N. J.
Each transmittal of this document outside the Department of Defense
must have prior approval of CG, U. S. Army Electronics Command,
Fort Monmouth, New Jersey, 07703, ATTN: AMSEL-WL-S.

/i/!?7 THE UNIVERSITY OF MICHIGAN
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ABSTRACT
A block diagram of the proposed DF azimuth - elevation direction finder is
presented and discussed. A simple analysis is presented for a two-dimensional
direction finder and is extended into a three-dimensional system. As for the threedimensional azimuth - elevation direction finder analysis, a number of computer programs have been utilized to determine the accuracy of the system. In general it has
been found that the system accuracy is strongly dependent upon the element pattern
characteristics (i. e., it is important that they have broadband radiation pattern characteristics both as a function of element orientation and frequency). Further, it has
been found that because of the elements being distributed over 27r steradians that the
predicted elevation angles have associated with them a discrepancy from the true angle.
This discrepancy has been found to be predictable and can easily be handled by the
computer to provide the true angle. Discussions have been held with several computer
representatives and it has been determined that it is feasible to employ a small computer to perform the necessary data processing to obtain the required azimuth - elevation data from the hemispherical antenna system.
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THE UNIVERSITY OF MICHIGAN
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FOREWORD
This report was prepared by The University of Michigan Radiation Laboratory
of the Department of Electrical Engineering under United States Army Electronics
Command Contract No. DAAB07-67-C0547. This contract was initiated under United
States Army Project No. 5A6 79191 D902-05-11 "Azimuth and Elevation Direction
Finder Techniques". The work is administered under the direction of the Electronics
Warfare Division, Advanced Techniques Branch at Fort Monmouth, New Jersey.
Mr. S. Stiber is the Project Manager and Mr. E. Ivone is the Contract Monitor.
The authors wish to express their thanks to Messrs. A. Loudon, D. Marble
and E. Bublitz for their efforts in the experimental work that has been performed
during this reporting period, and to Mr. P. Wilcox for preparing the computer program required for the three-dimensional analysis.
The material reported herein represents the results of the preliminary investigation into the study of techniques designing a broadband circularly polarized azimuth
and elevation direction finder antenna.
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TABLE OF CONTENTS
ABSTRACT
FOREWORD iii
LIST OF ILLUSTRATIONS
I INTRODUCTION 1
II A SIMPLE METHOD FOR DIRECTION FINDING 8
2.1 Example of Direction Finding 10
III ANALYTICAL ANALYSIS OF THE AZIMUTH - ELEVATION
DIRECTION FINDER 14
3. 1 Data Requirements for the DF data Processing System 14
3.2 Analytical Results for a Three-Dimensional DF System 19
3. 3 Consideration of Antenna Number and Location 31
IV RIGOROUS METHODS OF DIRECTION FINDING IN THREE
DIMENSIONS USING DATA PROCESSING EQUIPME NT 37
4. 1 Three-Dimensional Radiation Pattern of an Individual Antenna 37
4.2 Vector Addition Method 1 39
4. 3 Vector Addition Method 2 45
4.4 Determination of the Constants, A, B, C and D for a Specific 50
Distribution 50
50
V ELEMENT INVESTIGATION 51
5.1 Spiral Geometry 51
5.2 Spiral Configuration 52
5.3 Balun Considerations 53
VI ELECTROMECHANICAL SWITCH 55
VII COMPUTER REQUIREMENTS 56
VIII CONCLUSIONS 59
REFERENCES 61
DD FORM 1473
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LIST OF ILLUSTRATIONS
1-1 Azimuth - Elevation Direction Finder 2
1-2 Spherical Coordinate System 4
1-3 Azimuth - Elevation Direction Finder Simplified
Computer Flow Design 7
2-1 Vector Geometry 9
2-2 Geometry of a Ring of 8 Antennas 10
2-3 Spiral Antenna Pattern Data for Calculations (Freq. = 1. 8 GHz) 13
3-1 Two-Dimensional Direction Finding with some number "n" of
Equally Spaced Antennas 15
3-2 Co-ordinate System for Azimuth - Elevation Direction
Finding Calculations 21
3-3 Geometry of Azimuth - Elevation Direction Finder with 17
Antennas, Note Antennas Align on Rings in Elevation Plane 22
3-4 Computed Elevation Angle vs. Actual Elevation Angle for
Cosine Antenna Pattern, 17 Antennas 23
3-5 Graph of Various Types of Far-Field Antenna Patterns
Considered in Computer Programs 24
3-6 Computed Elevation Angle vs. Actual Elevation Angle for
Linear 90 Antenna Patterns, 17 Antennas 25
3-7 Computed Elevation Angle vs. Actual Elevation Angle for
Linear 80 Pattern, 17 Antennas 26
3-8 Computed Elevation Angle vs. Actual Elevation Angle for
Linear 70 Antenna Pattern, 17 Antennas 27
3-9 Computed Elevation Angle vs. Actual Elevation Angle for
Cosine Patterns Skewed 100 off Normal, 17 Antennas 29
3-10 Maximum Error in Azimuth vs. the Elevation Angle 0
for Cosine Pattern, 17 Antennas 30
3-11 Maximum Azimuth Error vs. the Elevation Angle for Cosine
Pattern Skeewed 100, 17 Antennas 32
3-12 Spherical Array - X's Mark Elements Utilized for Icosahdron
Direction Finding Calculation 33
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List of Illustrations, Continued
3-13 Maximum Azimuth Error vs. Elevation Angle for Icosahedron
Geometry with Cosine Patterns 34
3-14 Error in Azimuth vs. The Azimuth Angle A for 0 800,
17 Elements with Cosine Patterns 36
4-1 Local Coordinate System Used
4-2 Distribution of Antennas on a Hemisphere
4-3 Illuminated Antennas for all 0 and < < 49
2 - -2
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INTRODUCTION
Below we present a description of the operating characteristics for the azimuth
and elevation direction finder, presently being designed and fabricated by the Radiation Laboratory. A block diagram of the system is shown in Fig. 1-1 consisting of an
antenna, electromechanical switch, receiver (GFE), an Automatic Recognition Signal
Unit (GFE), an A to D converter, computer, and a visual display.
The antenna is conceived to consist of a hemispherical surface to which will be
attached a number of antennas. Each antenna will have associated with it a particular
0 and 0 coordinate of the spherical coordinate system. Direction finding will be accomplished (employing data processing techniques) as a consequence of the relative
amplitudes received by each of the antennas. The total number of antennas has not
yet been specified. It is probable that the minimum number of antennas required will
be 17 and the maximum number 26. The antennas will be interrogated by a rotating
electromechanical switch. Tentatively, the switch will have three rotational rates
(10, 100 and 1000 rpm). The operator will then be able to select the optimum switching rate which will depend upon the types of signals being interrogated by the azimuth
and elevation direction finder. At present the signals which are considered to be of
greatest concern are those from search radars.
To optimize the switching rate of the direction finder, consideration is being
given to typical search radar pulse widths, rates and antenna scanning rates. An additional consideration is the computer cycling rate, which is to be discussed later. Consideration must also be given to signals that have CW, AM and FM modulation. However, it is generally agreed that these signal types will not present a severe problem to
the system.

RPM
100
10 ~-~000
Ref.
Rate
z
Switch
Ant.
I 1PNT
ISwitch
C)
FIG A.. 1 AZIMTH-L O DRCTION FAz.-El.
Rec A S.R.U.Converter Cm.Display
FIG. 1-1: AZIXMUTH-ELEVATION DIRECTION FINDER.

TH E -UNIVERSITY OF MICHIGAN
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The switch will consist of either 17 or 26 input ports (each to be
identified with a particular antenna). In addition to the signal input, an identification
signal (Ref. Sig.) must be available from the switch to identify to the computer which
signal port is being interrogated. This identification is conceived to be in the form
of a light beam to be interrupted as the switch output port slews past each of the input
ports. It is anticipated that the switch will interrogate each of the antennas such
that the information will be collected and stored in the computer in a sequential format. An example would be for the first antenna to be associated with 0 - 0~, = 00
(employing the spherical coordinate system of Fig, 1-2); the second antenna would be
at 0 = 45, = 0~; the third at 0 =45, 450, etc., through the last antenna. For
this example, we have assumed a total of 17 antennas, one located at the pole, a ring
of 8 antennas at 0 = 45, and the second ring at 0 = 900. Each of the rings would
consist of 8 antennas placed at 0 increments of 450.
The Ref. Sig. is to be transferred from the switch directly to the computer to
identify the signals being inserted in the computer. The signals themselves would
first be transferred to the RF receiver, where the signals will be amplified and detected. A video amplifier may be required following the receiver to amplify the
detected data to insure proper operation of the computer. In the event more than one
frequency is received that is within the bandwidth of the receiver, an Automatic Signal
Recognition Unit (ASRU) will be required. It is understood that such units are available and have been employed by the military for this purpose. The data from ASRU
is then transferred to the analog-to-digital converter, where it is digitalized in the
proper format for the computer.
In the computer, the data is stored sequentially similar to that discussed above.
For example, the first storage compartment will consist of data for the pole antenna.
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z
E0
Antenna Surface
x
FIG. 1-2: SPHERICAL COORDINATE SYSTEM

THE UNIVERSITY OF MICHIGAN
1084-1-Q
The second storage compartment would have data from the antenna located at 0 = 450,
0 = 0 and the third compartment would have data for 0 - 45, = 450, etc. through
the 17 antennas (in the event a 17 element antenna is employed).
Within the computer a vector addition of the data is performed from which
directional data may be obtained, Figure 1-3 is a simplified flow chart of the computer program to be employed to perform the direction finding analysis. In the first
block, data is stored as noted above. Next, the data that has been collected and
stored will be scanned to determine the maximum signal (A ) such that all of the
remaining data may be normalized with respect to A as noted in Fig. 1-2. After
max
normalization the data for each antenna will be separated into three rectangular components (associatdd with the 0 and 0 coordinates of the particular antenna under consideration) as noted in the third block. The data for the pole antenna would be
separated into the A, A ly and A components as follows:
Alx A1 sin 01 cos 01 (1.1)
Aly A1 sin 01 sin 01 (1.2)
and
Alz A1 cos 01 (1. 3)
A similar set of data will be obtained for each of the K antennas. From this data a
summation of all the sub x, y, and z components would be performed as noted in the
fourth block of the flow chart. From the summation the predicted angles (Op and 0 )
would be determined employing the expressions
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THE UNIVERSITY OF MICHIGAN
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-1 E A (1.4)
B ~tan kV (1.4)
kAx
and
0 =tan-1 Akz (1.5)
Above it has been shown how the p and 0 would be determined by the comp p
puter. Several analytical computer analyses have been made by this laboratory and
have shown that the b0 and 0p differ from the actual angles (~A' 0A). However, it
has been found that each of the Up and 0p angles have a particular error associated
with them such that the error can easily be accounted for by the insertion of a correction factor in the computer. Therefore, the final operation within the computer would
be to correct the p and 0 to obtain the actual (A and 0A) angles of the signal under
interrogation as shown in the sixth block of the simplified flow chart.
After the actual (OA and 0A) angles have been determined by the computer, this
data will then be read into a digital display system which will consist of nixie tubes
to present the angular information in numerical form to the operator. It is felt that
a scope display may not be advantageous since any information that would be
presented on the scope would come from the digital information that provides
the nixie tubes display. For this reason and because of the cost, it is not
felt advisable to incorporate a cathode ray tube display in the present system.
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Storage
A1 (1' 1 )
A2 (,02. 2)
A(., 0
l n
Determine A
max
and
Normalize all to A
max
Alx= A1 sin 01 cos 01
Aly A1 sin 01 sin
A1z =A1 cos 01
ZAkxA1....... Anx
Z ~A~;, =~~~
Akz A
=tan E AhDCAkx
— tan-1 EAkz
00p f(0p)
p p
FIG. 1-3: Azimuth - Elevation Direction Finder Simplified Computer Flow Design

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1084-1-Q
II
A SIMPLE METHOD FOR DIRECTION FINDING
Direction finding may be catalogued into the following four basic techniques:
1) D. F. by using carefully controlled antenna
patterns to produce a null or a pencil beam
(Wullenweber type).
2) D. F. by detecting the direction of arrival
of the phase front (Adcock type).
3) D. F. by Doppler shift where a rapidly rotating
beam produces a Doppler shift of the incoming
signal.
4) D. F. by data processing.
The first three methods (which are classical in nature) require antenna patterns that
are carefully controlled to achieve the required accuracy.
Contract requirements for the azimuth - elevation direction finder call for detection of broadband (5:1 frequency band) circularly polarized signals. These requirements limit the types of antennas that may be utilized in the antenna system. To satisfy the above requirements consideration was initially given to the use of the cavity
backed spirals built for the preceding study [Contract DA 28-043-AMC-01499(E).
The patterns for these antennas are not felt to be suitable for the classical direction
finding techniques, i. e., the first three techniques mentioned above. For example,
patterns skewing off axis as a function of frequency and variations in patterns as a
function of antenna orientation introduce errors that cannot be readily handled by the
classical D. F. methods. Specifications for the subject azimuth - elevation direction
finding system along with the required circular polarization tend to negate the classical direction finding techniques.
One of the interesting classical methods is the Watson-Watt D. F. system employing four antennas with four receivers. The outputs from the four antennas are
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applied to the four electrostatic deflection plates of a cathode ray oscilloscope
(CRO). With the antennas carefully designed (to produce a cosine response) and located on the corners of a square, the system is capable of providing directional information accurate to + 40. Employing this geometry, the coordinate systems of
adjacent antennas are rotated 900 such that one antenna has a cos 0 pattern and the
neighboring antenna has a cos (0 - 90) or sin 0 pattern. Addition of the cos 0 and
sin 0 information, along with the 90~ space orientation of the CRO plates, produces
a resultant trace on the face of the scope along the direction of the incoming signal
as shown in Fig. 2-1 below.
X l s sin 0
cos 0
FIG. 2-1: VECTOR GEOMETRY
Following the above technique (employing a hemispherical array of elements)
consider only an azimuthal ring of antennas (for this simplified discussion) located
at a particular elevation of a spherical surface. These antennas are assumed to be
uniformly spaced on the ring, i. e., separated by a constant angle 0. If each antenna
points outward (normal to the local tangent of the ring), its coordinate system will be
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THE UNIVERSITY OF MICHIGAN
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rotated 0o from its neighbor. An incoming signal arriving at each antenna may be
represented by a magnitude and an angle corresponding to the pointing direction of the
antenna receiving the signal. Vector addition of the signals from all antennas will
result in a first approximation of the angle of arrival of the incident energy. To perform the vector addition a computer will be employed. The computer will compare
voltages resulting from signals received from all the antennas and normalize the signals to the maximum voltage. For the first approximation, this results in assigning
to the antenna with maximum signal, direction information suggesting the signal is
arriving normal to its aperture. A correction is introduced by combining with the
initial predicted information data that would result from a cosine distribution as
demonstrated below.
2. 1 Example of Direction Finding
Consider a signal arriving on a ring of 8 antennas arranged as shown in Fig. 2-2.
46 4\-5
FIG. 2-2: GEOMETRY OF RING OF EIGHT ANTENNAS.
With 8 antennas the angular separation between them becomes p = 450. Let the arrived
signal be 22 to the left of antenna No. 1. For this example, the antenna patterns are
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considered ideal in that they are all similar but not necessarily a cosine distribution.
Further, it is assumed the three dimensional pattern is equivalent to the pattern shown
in Fig. 2-3 when rotated about its axis of symmetry. Table II-1 shows the relative
signal amplitude at the output of the various antennas for a signal arriving from - 220.
TABLE II-1
Antenna 0 With Respect to Signal Level Normalized
Number Antenna Normal From Fig. 2-3(db) Amplitude Amplitude
1 220 -0.9 0.814 1.000
2 670 -8.5 0.141 0. 178
7 680 -8.7 0. 135 0.161
8 23~ -1.0 0.795 0.978
In this example all signal levels more than 900 from the local normal have been rejected due to their low amplitude level. The signals in Table 1I-1 are now added
vectorially in terms of horizontal and vertical components as shown in Table II-2.
TABLE II-2
Vertical Component Horizontal Compontnt
Antenna No. Antenna No.
1 1. 000 x cos 0 - 1. 000 1 1. 000 x sin O0 0. 000'2 0. 178 x cos 45 0. 126 2 0. 178 x sin (+45 ) +0. 126
7 0. 135 x cos 90~ = 0. 000 7 0. 135 x sin (-900) = -0. 135
8 0. 978 x cos 450 0 O. 691 8 0. 978 x sin (-450) = -0. 691
1. 817 -0.700
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TH'E UNIVERSITY OF MICHIGAN
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1 817 -- o o
tan 0 =0 2 6000= -69 90 - 69 = 21 or 1 error from true angle.

THE UNIVERSI' Y OF MICHIGAN
1084-1-Q
FIG. 2-3: SPIRAL ANTENNA PATTERN DATA FOR CALCULATIONS
(Frequency = 1.8 GHz).
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III
ANALYTICAL ANALYSIS OF THE AZIMUTH - ELEVATION DIRECTION FINDER
It has been decided that vector addition data processing is to be employed to
effect azimuth - elevation direction finding. During this interim we have been concerned with several parameters that may affect the system accuracy. Typically the
parameters considered were as follows:
1) antenna pattern,
2) number of receiving antennas,
3) antenna location, and
4) the measurement errors particular to the system.
Below we will discuss computer programs that have dealt with the first three
variables. More work is necessary on measurement error, this problem will be
discussed in a future report.
3. 1 Data Requirements for the DF Data Processing System
As noted above, the probability of employing the three-dimensional vector addition for direction finding originated from the standard two-dimensional DF systems
(utilizing 4 antennas oriented 900 with respect to each other). Analytical studies that
have been conducted for the three-dimensional system have shown that its accuracy is
strongly dependent upon the antenna pattern characteristics and is less dependent on the
geometrical location of the antennas. Further, there are inherent limitations associated
with the three-dimensional system that are not found in the conventional two-dimensional system, (Watson-Watt DF system employing 4 antennas), (Jasik, 1961).
To gain familiarity with the vector addition concept we consider an example
which employs a ring of n antennas; separated by equal angles of 9 as
shown in Fig. 3-1, the antennas are not orthogonal to one another as is the
case in the Watson-Watt system.
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THE UNIVERSITY OF MICH'IGA.N
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Incoming Signal
\
2 Q
0\
FIG. 3-1: TWO-DIMENSIONAL DIRECTION FINDING WITH
SOME NUMBER "N" OF EQUALLY SPACED ANTENNAS.
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THE UNIVERSITY OF MICHIGAN
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To assist in the analytical analysis, Table 3-1 lists the expressions from
which the relative amplitude levels (at each antenna) may be calculated (assuming the
direction of the unknown signal is arriving from an angle 0).
TABLE 3-1
Antenna Responses
1) cos (0- 2/)
2) cos (0-3)
3) cos 0
4) cos (0+3)
5) cos (O + 23)
To illustrate the limitation of this system, we will assume that the unknown signal is
arriving at an arbitrary angle 0 and that only three antennas receive data. Further,
it is assumed that the three antennas are located at = 0 and + 45. We have
chosen these specific angular locations to simplify the math. However, if one were
to employ a more general analysis it would have similar results to those obtained
from this simplified analysis. Further, we will show that unless one considers all
antennas over a 3 = 1800 sector, there will be an inherent discrepancy in the calculation of the predicted angle of arrival of the unknown signal. Table 3-2 is the expression
for the vertical and horizontal components of the three antennas noted above. The
horizontal and vertical components may then be combined in a ratio to attain tan 0
as shown in equation (3. 1).
tan 0 hor. comp. cos (o - ) sin - - cos (O + ) sin (3.1)
vert. comp. cos (0 - /) cos + cos 0 + cos (0 + /) cos3
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TABLE 3-2
Vertical Component
2) cos (O -P) cosf3
3) cos (0)cos 00
4) cos(O + ) cos3
Horizontal Component
2) cos (0-) sinj
3) cos 0 sin 00
4) - cos ( 0+ 3) sinf3
Expanding the sum and difference trigometric expressions, equation (3. 2) is obtained,
which reduces to a more simple form involving tan 0 multiplied by a trigometric
ratio which is dependent on the angular position of the antennas. It is the multiplication
factor which causes the discrepancy between the calculated and actual angle of arrival
(0).
(cos 0 cos + sin 0 sinin in - [cos 0 cosI - s in sin] sin B
[cos 0 cos 3+ sin 0 sin I] cos + cos 0 + jcos 0 cos - sin 0 sin l] cos
sin0 2 sin2 i,2
2 sin tan 0 2sin 2 (3. 2)
cos 0 1+ 2 cos 1+ 2 cos 3
Let us now consider using all of the antennas that are within a = 1800 sector
(+ 900 with respect to the angular position of the unknown signal. For the purposes of
this analysis we will assume five antennas (however, one need not be limited to
five). Table 3-3 lists the expression for the vertical and horizontal component that
would be associated with each of the five antennas.
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TABLE 3-3
Vertical Component,
1) cos (0 - 23) cos 2P
2) cos (0 - ) cos/3
3) cos 0 cos 0~
4) cos (0 +) cosf3
5) does not receive signal as 0 + 2/ > 900
Horizontal Component
1) cos (0-2 2) sin 2/
2) cos (0-) sin/3
3) cos 0 sin 00
4) cos (0+/)sin3
5) does not receive signal as 0 + 2/3 > 900
Through the use of equation (3. 3), tan 0 for the unknown signal is obtained employing
all antennas within the 1800 sector.
tan 0 = opp - vertical comp
adj horizontal comp
cos (0 - 2/) cos 2/+ cos (0 - 3) cos3+ cos 0+ cos (0+/3) cos3
(3. 3)
cos (0 - 21) sin 20 + cos (0 - P) sin P - cos (0 + P) sin P
Equation 3. 4) is the trigometric expansion of this and equation (3. 5) has been simplified
to a form which gives a trigometric ratio times the tangent of 0. It may be shown that
the trigometric ratio is equivalent to unity for the case of five antennas that are equally
spaced ( - 45 ). However, had there been more antennas and again equally spaced
the trigometric ratio would have been more complex, but it can be shown that it would
be equivalent to unity as in the case for five antennas. Therefore, the predicted angle
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of arrival is equal to the actual angle of arrival only when all of the sampling antennas
are located within a 1800 sector and these outputs are employed in the data processing.
Intuitively, one might reason that this is to be expected since for the purposes of this
simplified analysis, we have assumed that the radiation patterns of each of the antennas
fits a cosine distribution in the range of 3 = + 900.
(cos 0 cos 23 + sin 0 sin 23) cos 213 + (cos 0 cos + sin 0 sin 1) cos 13 + cos 0
(cos 0 cos 23 + sin 0 sin 23) sin 23 + (cos 0 cos ( + sin 0 sin (3) sin 3
+ cos 0 cos, - sin 0 sin 3 cos )
(3. 4)
- cos 0 cos 3 - sin 0 sin(
note 3 45~ and cos 2 =0 sin 2 =- 1
cos + 2 cos os + cos 0 cos 0 1+ 2 cos (35)
~~2 ~~~~~~~~2 (3.5)
sin 0 + 2 sin 0 sin sin 0 1+ 2 cos 2
for 3 = 45 cos sin:3
From the above analysis (for the two-dimensional system) we have attempted to
show that if antennas are not located over a 1800 sector, there will be inherent deviations in the calculation of the angular location of the unknown signals. It must
be noted that this deviation is predictable and therefore can be corrected if needed.
Below we will discuss several analytical results that have been obtained for the threedimensional system that will illustrate this point more explicitly.
3. 2 Analytical Results for a Three-Dimensional DF System
Several computer programs have been prepared and employed during this interim
employing a three-dimensional DF system with antennas located on a hemispherical
surface. Data from these programs have shown that there will be a discrepancy in the
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predicted angle in both elevation and azimuth. The discrepancy in elevation has
been greater because of the non-symmetry of the antennas (antennas are located on a
hemisphere of 2r steradians) which was expected from the above discussion for the
simple two-dimensional system. However, the azimuth errors were found to be
minimal provided the element patterns were well behaved. We might elaborate a
little on the elevation deviations and note again that the discrepancy in elevation results because the spherical area illuminated is less than the desired 2ir
steradians. Data from the computer program bear this out; in the case of
0 - 0 only (see Fig. 3.2) will antennas be excited over 27 steradians.
The first set of data calculated assumed 17 antennas equally spaced over 27
steradians (at 0 and 0 increments of 450, as shown in Fig. 3-3) of the hemisphere and
that each antenna had a cosine pattern that was symmetrical about the axns of
the antenna. Typical elevation data is shown in Fig. 3-4 which illustrates the deviation of the predicted angle from the actual angle. It will be noted there are two sets
of data points which represent the maximum and minimum deviation of the predicted
elevation angle as a function of the azimuth angle. The large variations in this predicted angle may be corrected for, within the computer, prior to reading out the information to the display system (see Fig. 1-1).
Because of the discrepancy between the predicted and the actual angular data
noted above, we have investigated the effects of element pattern variations and the
number of antennas to be employed to effect the necessary direction finding information.
Here we will discuss the variations of cosine versus linear patterns as shown
in Fig. 3-5. We will refer to these patterns as the cosine, linear 900, 800, and
70 which are self explanatory from Fig. 3-5. Figures 3-6, 3-7, and 3-8 are respectively the predicted angles for linear 900, 800 and 700 patterns. It is interesting
to note there is a very little difference between the data for the cosine pattern (Fig. 3-4)
and the linear 900 pattern (Fig. 3-6). However, the deviation for the linear 700 and
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0=0, 0 = 00
E
= 900 0=900
FIG. 3-2: COORDINATE SYSTEM FOR AZIMUTH-ELEVATION
DIRECTION FINDING CALCULATIONS.

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= 45o
0 = 9O
FIG. 3-3: GEOMETRY OF AZIMUTH-ELEVATION DIRECTKIN FINDER
WITH SEVENTEEN ANTENNAS. NOTE ANTENNAS ALIGN ON
RINGS IN ELEVATION PLANE.
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70
60
- 50
bZ
~0 40
4)
to — 30
0
0 20
V -
10 20 30 40 50 60 70 80 90
Actual Elevation Angle (degrees)
FIG.3-4: COMPUTED ELEVATION ANGLE VERSUS ACTUAL ELEVATION
ANGLE FOR COSINE ANTENNA PATTERN; SEVENTEEN ANTENNAS,.
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1.0
Cosine
0.
0.8
0.6- \X\ Linear 90
I I I. I I Iinear 80
o Linear 70,-24
0.310 20 30 40 50 60 70 80 90
Angle from Antenna Normal (degrees)
FIG. 3-5' VARIOUS TYPES OF FAR FIELD ANTENNA PATTERNS
CONSIDERED IN COMPUTER PROGRAMS.
Z4

THE UNIVERSITY OF MICHIGAN
1084 -1 -Q
70/
-60
-50
-Z40
to.P.40D
30
-20
Begin Deviation
10
l3 10.0 30 40 50 60 70 80 9
True Elevation Angle
FIG.3-6: COMPUTED ELEVATION ANGLE VERSUS ACTUAL ELEVATION
ANGLE FOR LINEAR 90 ANTENNA PATTERN, SEVENTEEN
ANTENNAS. 25

THE UNIVERSITY OF MICHIGAN
1084-1 -Q
70
-60
50
f.O
0 — 40
0 4
-40
O)
30
20
10
10 20 30 40 50 60 70 80 90.1I. I I I, I I I I I
True Elevation Angle
FIG. 3-7: COMPUTED ELEVATION ANGLE VERSUS ACTUAL ELEVATION
ANGLE FOR LINEAR 80 PATTERN, SEVENTEEN ANTENNAS.
26

THE UNIVERSITY OF MICHIGAN
1084-1 -Q
80
70
60.4Q)
X - 40
0
30
20
10 20 30 40 50 60 70 80 90
True Elevation Angle
FIG.3-8:COMPUTED ELEVATION ANGLE VERSUS ACTUAL ELEVATION
ANGLE FOR LINEAR 70 ANTENNA PATTERN, SEVENTEEN
ANTENNAS. 27

THE UNIVERSITY OF MICHIGAN
1084-1-Q
800 (with respect to the cosine data) are appreciably larger. Typical far-field radiation patterns that have been measured for spiral antennas have shown that they exhibit
patterns that may be closely approximated by an analytical expression similar to
that for the linear 900 distribution.
We have noted many spiral patterns whose maximums are skewed from the
axis of the antenna surface. In an attempt to determine the effects of a skewed
pattern on the variations that may result between the predicted versus the actual
angle of arrival, a computer program was employed assuming the main beam was
skewed 100 off axis for a linear 900 pattern. An attempt was made to randomly orient
the skewed pattern over the hemispherical surface such that the skewing would not all
point in the same direction. Figure 3-9 is a plot of the predicted elevation angles as
a function of the actual angle employing the skewed patterns. It is interesting to note
that the variation in the predicted angle was a random variation which would be difficult
to correct for to obtain the actual angle of arrival, As a consequence, it is felt that
the patterns (of the individual element) must be well behaved (have a minimum of
skewing < < 100) both as a function of antenna orientation as well as a function of
frequency, i. e., the main lobe must be symmetrical about the axis of the antenna as
a function of antenna orientation and frequency.
Above, consideration has been given to discrepancies that are probable in the
elevation plane. Here we will discuss azimuthal discrepancies. We will show that
because of the lack of antennas below 0 = 900, there will be discrepancies in the
azimuthal angular predictions as a part of the direction finding analysis. Figure 3-10
is a graph of the maximum azimuthal error as a function of the elevation angle (assuming the element patterns satisfy a cosine distribution). It is interesting to note that
from 0 = 0~ to 45, there is no azimuthal discrepancy. However, from 0 = 450 to 90~
there is an azimuthal discrepancy which is a periodic function with the maximum
occurring at & = 80~, Since the discrepancy is periodic it is amenable to correction
within the computer as has been discussed above.
28

THE UNIVERSITY OF MICHIGAN
1084-1-Q
70
60
50
40
0
30
20
10
1o 2_ 3) 40 50 60 70 80 90
Actual Elevation Angle
FIG. 3-9: COMPUTED ELEVATION ANGLE VERSUS ACTUAL ELEVATION
ANGLE FOR COSINE PATTERNS SKEWED 10~ OFF NORMAL,
SEVENTEEN ANTENNAS.
29

Error in Degrees Error in Degrees
0-I I I I
CD CD
CD
(D
CD
CD CD
FIG. 3-10: MAXIMUM ERROR IN AZIMUTH VERSUS ELEVATION ANGLE 0 FOR
COSINE PATTERNS SEVENTEEN ANTENNAS.
co C] C1)~~~~~~~~~~~~~~~~~~~~~~~~J
COSINE PATTERN, SEVENTEEN ANTENNAS.

THE UNIVERSITY OF MICHIGAN
1084-1-Q
In the discussion of the elevation angles, consideration was given to the use
of antennas whose patterns may be skewed. As a part of the azimuth study, consideration was again given to the use of skewed patterns. An attempt was made to randomly orient the skewed patterns on the hemisphere. Figure 3-11 is a plot of the
predicted angle in azimuth as a function of the elevation angle. It is interesting to
note that the deviation in the predicted azimuthal angle from the actual angle is greatest near 0= 0 (top of the hemisphere), where it approaches 10 or more. However,
when data is collected near the horizon, the discrepancy decreases to approximately
30. Although the discrepancy has decreased, it is larger than is acceptable. It may
be conculded that the disadvantage of employing elements with skewed patterns for the
azimuth - elevation direction finder would be the large discrepancies incurred both
in azimuth and — elevation and the difficulty in correcting for this discrepancy, since the
discrepancy is not analytically expressable.
3. 3 Consideration of Antenna Number and Location
Above we have assumed that 17 antennas are employed and are equally distributed over the surface of the hemisphere. A second distribution consisted of antennas located on an icosahedron as shown in Fig. 3-12 and discussed by
Sengupta, et al, (1966). The icosahedron distribution has the advantage of achieving
a uniform coverage of antennas over the surface of the hemisphere. Early data from
a 26 element icosahedron distribution showed there was no advantage to employing it
over the 17 element design discussed above. Figure 3-13 is a plot of the maximum
azimuth discrepancy as a function of the elevation angle for the icosahedron distribution. The data shown in Fig. 3-13 was calculated in increments of 50 for the azimuth
angle. A later set of data was collected at 10 increments and the data compared with
the 17 element system also showed that there was insufficient advantage to employing
the icosahedron 26 element distribution. Therefore, we have chosen to employ the
17 element system for the azimuth - elevation direction finder.
31

THE UNIVERSITY OF MICHIGAN
1084-1-Q
10
9
8
7
6 —
o5
r2
1I 21 31~1 o 501, 6? 710 8p o q
Elevation Angle
FIG. 3-11: MAXIMUM AZIMUTH ERROR VERSUS ELEVATION ANGLE FOR COSINE
PATTERN SKEWED 100, SEVENTEEN ANTENNAS.
32

THE UNIVERSITY OF MICHIGAN
1084-I-Q
x
x~~~~ x
/X
X
x~~
x
(~~~~~~~
FIG. 3-12: SPHERICAL ARRAY. X's MARK ELEMENTS UTILIZED
FOR ICOSAHEDRON DIRECTION FINDING CALCULATIONS
33

.7.6
5 Z
-.4 C,
_.3
5 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
E I X I I I,. I I I I. I I1 I I I I I I I
FIG. 3-13: MAXIMUM AZIMUTH ERROR VERSUS ELEVATION ANGLE FOR ICOSAHEDRON
GEOMETRY WITH COSINE PATTERNS.

THE UNIVERSITY OF MICHIGAN
1084 -1 -Q
The maximum discrepancy for the 17 element system with cosine
pattern distribution occurs at 0=800 and midway between elements in the p-plane.
A plot of the discrepancy as a function of 0 for 80800 is shown in Fig. 3-14. The
maximum discrepancy here is 0.860. It may be shown that the discrepancy can
either be increased or decreased by respectively decreasing or increasing the
number of elements. However, in view of the contractual requirements, it is
felt that using a smaller number of elements will decrease the system accuracy
and sensitivity. Increasing the number of elements would improve both the accuracy and sensitivity but would further complicate the data processing requirement (computer and associated hardware) thus increasing the costs. In view
of these and many other factors involved, it is recommended that the 17 element
system be employed for the present feasibility model.
35

Error in Degrees
0o 0 o 0 o9 o b o *b I MARX 4 m
co -- m
CO
FIG. 3-14: ERROR IN AZIMUTH VERSUS AZIMUTH ANGLE ~ FOR 0=80~
SEVENTEEN ELEMENTS WITH COSINE PATTERNS.
ft9 d~~~~~~~~~

THE UNIVERSITY OF MICHIGAN
1084-1-Q
IV
RIGOROUS METHODS OF DIRECTION FINDING IN THREE
DIMENSIONS USING DATA PROCESSING EQUIPMENT
Two methods of direction finding in three dimensions are discussed using data
processing equipment, vector addition, and assuming cosine radiation patterns for
the elements. In the first method, the signals induced in all the antennas, which
are distributed on a hemisphere, are added vectorially to determine the direction
of arrival of the signal. In the second method, the signals induced in a selected
number of antennas are added vectorially. Then techniques to find the direction of
arrival by proper data processing is discussed. The errors involved in the first
method and the difficulties encountered in correcting them are also discussed. Theoretically, the second method gives correct direction of arrival of the signal.
4.1 Three Dimensional -Radiation Pattern of an Individual Antenna
Before we discuss the methods used for direction finding, it is necessary to
express the radiation patterns of the individual antennas, which are disposed on a
hemisphere, in terms of spherical coordinates with the center of the hemisphere as
the origin.
The individual antennas are assumed to be distributed on a hemisphere in such
a way that the maximum radiation is directed radially outward and have a cosine radiation pattern which is rotationally symmetric about the radial line passing through the
antenna and the center of the hemisphere as shown in Fig. 4-1.
In Fig. 4-1, x, y, and z represent the rectangular coordinate system referred
to the center of the hemisphere. xt, y', and z' are the rectangular coordinates
referred to the center of the Antenna A, which is located on the hemisphere. 0 and
j are the polar coordinates of the antenna A referred to the unprimed coordinate
system. In the primed coordinate system, the antenna pattern is assumed to be cos 0'.
Using the appropriate coordinate transformation, it can be shown (Sengupta,
et al, 1965), that
37

THE UNIVERSITY OF MICHIGAN
1084-1-Q
ZI
~~z~~~~~'
Radiation Pattern
A i Given by cos 0'
Direction
of Signal
0o
x
FIG. 4-1: LOCAL COORDINATE SYSTEM USED.
38

THE UNIVERSITY OF MICHIGAN
1084-1-Q
cos O' = sin a sin 0 cos (A - ) )+ cos a cos 0 (4.1)
The right hand side of the equation (4. 1) represents the radiation pattern referred
to the unprimed coordinate system. In general, if ac and:n represents the position coordinates of any antenna on the hemisphere, the antenna pattern referred to
unprimed coordinates is given by
F (0, )= sin a sin a cos (i - /) + cos a cos 0 (4. 2)
n n n
Except for a proportionality constant, the signal induced E due to a plane wave
n
arriving from the direction given by (0, ~) is equal to F (0, 1). Hence,
n
E sin a sin 0 cos (A - )+cos a cos 0 (4. 3)
n n n n
Given the position of the antenna (a,,) and the direction of the incident signal
(0, A), it is straight-forward to find the signal induced in that antenna using equation
(4. 3).
4. 2 Vector Addition Method 1
In this method and the second method to follow, the individual antennas are
assumed to be distributed uniformly around the circles of constant elevation angles
as shown in Fig. 4-2.
Even though the following discussion applies to any number of elements distributed
uniformly on circles of constant elevation angles, the final expressions are specialized
for 17 antenna elements distributed as shown in Fig. 4-2.
In this method, the signals induced in different antennas will be added vectorially
in three dimensions, To do this each signal will be resolved into the components along
39

THE UNIVERSITY OF MICHIGAN
1084- 1-Q
AX~x
x
X X
X
x
x, x X
X Xx x
x 1
Top View
x a
X I X X
x. x x _ x x
Side View
FIG. 4-2: DISTRIBUTION OF ANTENNAS ON A HEMISPHERE.
40

THE UNIVERSITY OF MICHIGAN
1084-1-Q
the cartisian coordinates and then the components are added vectorially. If E is
resolved into x, y, and z components, we obtain
E = E sine cos P (4.4)
nx n n n
E =E sin a sin n (4.5)
ny n n n
E = E cos c (4.6)
nz n n
If there are N antennas, the total x, y, and z components are given by
N
E Z Ensina cosI3 (4.7)
n= 1
N
Ey = E sin asin3n (4.8)
Y n 1n n
N
E - E E cosa (4.9)
z n n
where E is given by equation (4. 3).
The direction of the resultant vector is given by
tan -1 (4.10)
a E
and
0 =cos E.E+ (4.11)
x y

THE UNIVERSITY OF MICHIGAN
1084-1-Q
The vector addition method 1 assumes that O and 0 will represent the direction
of the incident signal which is assumed to be 0 and 0. Later on we will consider a
specific example to study the error involved in this method and how to correct it (if
possible).
Equations (4.7) through (4. 11) can be used for any type of distribution of antennas
on the hemisphere. If the antennas are uniformly distributed on circles of constant
elevation angles a and if / is the angle between any two antennas on a circle, then
P m = M/2 +1
x m M Lsin sin 0 cos ( - m) + cos cos 0 sin a cos m/ (4. 12)
p 1 mI 1M/2
P M/2+ 1 n sinm (4.13)
p=l m=-M/2
P M/2 + 1
E = E Lsin a sin 0 cos (m3) + Cosa Cos0c os a +cos0 (4.14)
p = 1 m = -M/2
where P is the number of circles of constant elevation, and M is the number of
elements on each circle minus two.
In using equations (4. 7), (4. 8), (4. 9), or (4. 12), (4. 13) and (4. 14), one should
note that only the contributions of the antennas which are illuminated by the incident
signal should be taken into consideration. In general, the number of antennas which
are illuminated depends both on 0 and 0. Hence, it is not possible to simplify the above
42

THE UNIVERSITY OF MICHIGAN
1084-1-Q
equations for all 0 and 0. At this point we consider a specific distiribution of
elements with P =t 2, Mt =_
elements with P = 2, M = 6, al = and a2 = 2 With this distribution g =.
1 4 It it2 4
From Fig. 2, it is clear that if 0 < - all the antennas on the circle with a1 - 4
are illuminated along with the antenna on the horizon and 4 antennas on the circle
if
with a2 = -. For this case the equations (4. 12), (4.13), and (4. 14) could be
simplified and are given below.
E = sin snr sin 0 cos (-m4) + cos os 0 sin cos m
2 _,r
+ Z 2 4 2 2 4!
+ E sin sin 0 cos (~ - m )+ cos cos 0 sin cos tm 4, 45)
This will be simplified to
E = 4 sin 0 cos (4. 16)
x
Similarly one can easily show that
E = 4 sin0sin (4..17)
y
and
E =5 cos 0 (4.18)
z
From equations (4.16), (4.17) and (4. 18), the apparent azimuth angle and
elevation angle are given by
= =an -1 tan () = (4.19)
-1 E -V 5 cos _
0 =COs 2o z s (c4.20)
x + E + E 16 sin 0 + 25 cos2 o
43

THE UNIVERSITY OF MICHIGAN
1084-1-Q
From (4. 19) it is evident that the correct azimuth angle is obtained by
the method used here. However, from equation (4.20) it is clear that the
elevation angle, even though independent of 0, is in error. Fortunately, it
is not difficult to obtain correct elevation angles by a simple modification
of vector addition as outlined below.
Let
5
E' - E =5 sin 0 cos 0 (4.21)
x 4 x
E' = E 5 sin 0 sin 0 (4.22)
y 4 y
Then define
-1 E
0 = cos (4.23)
a 2 2 2
Et + ET +E
x y z
Substituting E', Et, and E in equation (4.23), it can easily be verified
that
o =0 (4.24)
a
From the above discussion it is clear that by simple modification of
vector addition, one could predict the correct elevation and azimuth angles,
provided 0 <K r/4. Even though the specific example given above assumes 8
antennas on each circle of constant elevation, the same procedure could be used,
provided the number of antennas on each circle are 4 J (J an integer) and the
44

THE UNIVERSITY OF MICHIGAN
1084- 1-Q
correct elevation and azimuth angles could be predicted (for 0 = < r/4)
The above type of simplication is not possible if 5 > 7. The reason for this is
that the number of antennas illuminated by the incident signal vary with 0 and ~.
Consequently no single analytical expression could represent the resultant vector.
Even though the vector addition method 1 is straight-forward using a computer, the
results will in general be in error and there is no simple modification which can be
used for 0 > - to predict the correct elevation and azimuth angles as was demonstrated for 0 <
We have computed 0a and Oa using a computer for the distribution given in
Fig. 4-2 for different values of 0 and i. Our results agree with the results obtained
here analytically for 0 < 4. For 0 >4 our results show that there is only a weak
dependence of 0a on 0 and Oa on 0. So there is a possibility to use some correcting
factors to predict the correct values of 0 and P. Even after using the correcting
factors there will be some errors in the final values. If there is no alternate method
of predicting the correct elevation and azimuth, vector addition method 1 may be
satisfactory. An alternate method will be given below which will predict the correct
elevation and azimuth in the whole range of interest.
4. 3 Vector Addition Method 2
In this method, instead of adding vectorially the contributions of all the antennas
which are illuminated, as was done in method 1, only the contributions of the maximum
number of antennas which are illuminated for all 0 and A will be added vectorially.
The advantage of this approach is that the number of antennas contributing to vector
addition remains unchanged and results in a single expression for Ex, Ey, and Ez
as a function of 0 and a. By proper data processing, one could predict the correct
0 and p.
45

THE UNIVERSITY OF MICHIGAN
1084-1-Q
For this method it is assumed that the number of elements on each circle of
constant elevation are in multiples of 4. In the beginning our discussion applies to
any number of circles of constant elevation angle and any number of elements on
each circle with the previously mentioned assumption.
Let the antennas at A = 0 have the maximum signal compared to other antennas
on each circle. Then choose M + 1 antennas on each circle which are illuminated
for all 0, and -, where 3 is the angle between any two antennas on a circle.
Let P be the number of circles. If M is the total number of elements in any circle,
it is not difficult to show that M1 (M - 4)/2. The sector in which the antennas are
illuminated are shown in Fig. 4-3. We now consider the contributions of antennas
within the sector shown in Fig. 4-3. From equation (4.12), we can write that
P = M1/2
E = ) [sin a sin 0 cos ( M-m )+cos a c os 0 sin a cos m
x L..../ p p p
p=l m=-M1/2
m = M1/2
p = 1 m = -M1/2
On rewriting, we have
E A sin O cos + B cos 0 (4. 26)
where
P M /2
A-L E 1sin2 a cos m3
p- 1 m=-M1/2 P
46

THE UNIVERSITY OF MICHIGAN
1084-1-Q
and
P M1/2
B= s_B- L j cos ca sina cos mf
p=l m = -M1/2
From equation (4.13) we can write that
P M1/2
Ey Lsin a sin 0 cos (-m) + cosa cosl 0 sina sin mo
y p p p
p M1/2 2 2
p=1 m=-M1/2
on rewriting we have
E =CsinOsin (4.28)
y
where
P M 12
C= / " sin2 a sin m
p 1 m = -Ml12 P
From equation (4.14), we can write
P M1/2
E = cos 0 + sin i sini 0 o cos(-m)+cos a cos olcos a
p=l m=-M1/2
47

THE UNIVERSITY OF MICHIGAN
1084-1-Q
P M1/2 P M1/2
=os + sin acos cos sin cos cos m sincos+ cos cos
p = 1 m =-M1/2 p 1 m -M1/2
(4.29)
on rewriting we have
E =D cos 0 + G sin 0 cos p (4.30)
z
where
P M1/2
D 1+, cos aC.
p= 1 m=-M1/2 P
and
P M1/2
G = ~~,sin a cos a cos mf
p = 1m=-M1/2
Note that G is also equal to B.
Now we plan to find 0 and 0 from equations (4. 26), (4. 28), and (4. 30) using the
following data processing. From equations (4. 26), and (4. 30), we note that
DE -BE =(DA - BG) sin 0 cos B (4.31)
X z
and
(AE -GE )=(DA - BG) cos 0 (4. 32)
z x
Now we define
DE - BE
X z
E't. C (4.33)
x DA - BG
and
AE - GE
E' =....... C (4.34)
z DA - BG
48

THE UNIVERSITY OF MICHIGAN
1084- 1-Q
0=9o6'x
/ x
x -x x 0
FIG. 4-3: ILLUMINATED ANTENNAS FOR ALL 0 AND < <.
49

THE UNIVERSITY OF MICHI'G AN
1084-1-Q
It is easy to show that
E C sin 0 cos ~ (4. 35)
x
E? C cos 0
z
We already have
El = C sin 0 sin (4. 37)
y
From equations (4, 35), (4. 36), and (4. 37), it is straight-forward to find the correct
0 and. and are given by
E
a =tank Y = (4. 38)
x
and
0 = lCos v 0 (4. 39)
I summary, the induaced signals in individual antennas in a sector are used to
find Ex, E a and E. Then knowing the constants A, B, C, and D (which depends only
on the distribution of antennas on the hemisphere); E' and El are determined using
x z
equations (4. 33) and (4. 34), Finally 0 and 0 are determined from (4. 38) and (4. 39).
4.4 Determinatin f the Constants A B C and D for a pecific Distribution
The specific distribution is shown in Fig. 4-2 for which M - 8, P = 2 with,1 4
and2 and. Substituting these values in the expressions for A, B, C and D,
we obtain
M= 2
A=3, B=0.5+ j, C=1,5, D =2. 5, and G=B,

THE UNIVERSITY OF MICHIGAN
1084-1-Q
V
ELEMENT INVESTIGATION
As a result of recent analytical studies with the direction finder, we have
found that it is extremely important that the electrical characteristics of the antenna
elements be well behaved such that the radiation characteristics do not vary both as a
function of angular orientation of a particular antennas as well as the frequency of
operation. To ensure that the antennas will have the required consistency in radiation characteristics, both as a function of angular orientation and the frequency of
operation, consideration is now being given to the employment of conical spirals
having a quadrafilar element being fed by a stripline balun configuration.
The Naval Ordnance Test Station (NOTS), China Lake, California was
contacted and the feasibility of employing spiral antennas as the basic elements
for the DF antenna system was discussed. During our discussions three areas
were covered that were felt to be of interest to this contract: 1) spiral geometry,
2) spiral configuration, and 3) balun consideration.
5. 1 Spiral Geometry
During our discussions of spiral geometry it was noted that several unsuccessful attempts have been made to employ cavity backed spirals for broadband applications.
Broadbandwidths are generally considered to be much greater than the 2:1, e. g., 10:1
are typical. A typical requirement is for the pattern characteristics to remain
relatively constant over both the frequency range of interest, and as a function of spiral
orientation. It should be noted that NOTS is interested in employing one spiral to
operate in both the sum and difference modes which is considered to be a very severe
restriction. The sum mode is defined as having a main lobe on axis, while the difference mode has a null on axis ( a split beam ). An additional requirement is for
the gain to remain relatively constant in the frequency range of interest.
51

THE UNIVERSITY OF MICHIGAN
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The Navy has found for broadband operation (greater than 2:1), one should consider the use of the conical spiral in lieu of a cavity backed spiral. When employing
a cavity backed spiral, the cavity is designed to be V4 deep at the center frequency
of the frequency band, and at frequencies other than this the cavity deviates from A/4.
Because of this variation in electrical cavity depth the performance of the antenna
deteroirates when operated over bandwidths greater than 2:1. This has been observed
by this laboratory in work with spiral antennas both of our own design and other
organizations' designs.
5.2 Spiral Configuration
The spiral configuration that would best suit the requirements of the DF system,
i.e., to achieve broadband pattern characteristics and the required gain, was also
discussed. First, the disadvantages of the bifilar spiral configuration were noted.
From a simple analysis of the bifilar spiral and the current distribution along the elements of the spiral, we find that higher order current bands are formed when the spiral
electrical circumference is equal to (m + n)k (where m is equivalent to 1 for the E
mode and 2 for the A mode and n is equivalent to the number of filaments) e.g. 1, 3,
5,...,. Further, it should be noted that the above exists for the Zmode when the
two elements are to be fed 1800 out of phase. For a multifilar element, it can be seen
from the above expression, that the radiating current bands become more randomly
distributed as the number of filaments increases. A quadrafilar spiral whose four
terminals are fed, 0, 90, 180 and 2700 will have a radiating band when the electrical
circumference is one wavelength in diameter and the next higher order radiating band
occurs when the spiral is five wavelengths in diameter. Therefore, it would appear
desirable to employ a multifilar spiral to minimize the number of radiating bands.
52

THE UNIVERSITY OF MICHIGAN
1084-1-Q
It is recommended that we consider as a minimum, a quadrafilar
spiral for the DF antenna to ensure good pattern characteristics for the 5:1 frequency
band.
5. 3 Balun Considerations
We also discussed the problems associated with the construction of a broadband
balun. One of the difficulties associated with the present bifilar spiral antenna is the
construction of a balun that has good phase and amplitude characteristics over the
frequency range of interest (in our case a 5:1 frequency band). Previous work with
broadband antenna configurations has employed the balun configuration described by
Duncan and Minerva (1960). This balun, although simple to construct) has been found
to have unsatisfactory phase and amplitude characteristics over broadbandwidths.
NOTS has given consideration to other techniques by which an unbalanced line may be
converted to a balanced line (the construction of a better broadband balun). From
efforts they have funded at Radiation Systems, Inc., they found that a stripline 3db
coupler and a stripline 90 phase shifter could be constructed to operate over large
frequency bands ( > 10:1) to effect a broadband balun. This work has been documented
by Shelton and Mosko, (1966). From this investigation, they found that it was possible
to broadband such elements. However, one cannot expect to have a constant 3db power
split nor a uniform 90 phase shift over the frequency range of interest. However, one
may place a ripple factor on both the amplitude and the phase characteristics and build
a broadband (greater than 2:1) 3db directional coupler that has equal power split and
90~ phase shift within the ripple factor limits. Mosko showed data for a typical 3db
coupler that has uniform power split with a very small ripple and a constant phase shift
of 90~ again with small ripple for a 14: 1 frequency band. Similarly, an investigation was conducted to determine how one might broadband a phase shifter. They found
(using a technique originally conceived by Shiffman, 1958) that a broadband phase shifter
53

THE UNIVERSITY OF MICHIGAN
1084-1-Q
could be built having a small ripple in the phase as a function of frequency. Both of
these components have been developed and a number of them have been fabricated and
tested, and appear to be within the state-of-the art at this time.
By properly arranging power spliters and phase shifters, one can design the
required phasing to build a balun for either a conventional bifilar or multifilar spiral.
For example, to feed a quadrafilar spiral, one must use three 3db directional
couplers and one 900 phase shifter, all of which must be broadband over the frequency
range of interest. Each of these can be evaluated and analyzed prior to their construction and after the units have been constructed they may be evaluated such that the
experimental data may be compared with the analytical data.
54

THE UNIVERSITY OF MICHIGAN
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VI
ELECTROMECHANICAL SWVITCH
Several laboratory models of the electromechanical switch required for the
azimuth - elevation direction finder have been assembled and tested. Preliminary
test results have shown that a single pole (n) throw switch can be built to have a
VSWR of less than 1. 5:1 with respect to 50 Q. In addition, the isolation between
adjacent ports has been found to be greater than 20db. The above data has been
collected at several frequencies in the 5:1 frequency band (600 - 3000 MHz).
During the preliminary study of the switch, consideration has been given to
the design of both the switching ports and the rotary joint to be required for the
switch. The switching ports will be of a non-contacting capacitively coupled configuration. Likewise the rotary joint will be non-contacting and capacitively coupled.
We have discussed with shop personnel the feasibility of fabricating a switch that
can rotate at rates up to 1000 rpm. From these discussions it is felt to be within
the present state-of-the-art to fabricate such a device.
The results of this study have indicated that a switch can be fabricated that
will fit within a cylindrical volume 6" in diameter and 5 or 6 inches high.
55

THE UNIVERSITY OF MICHIGAN
1084-1-Q
VII
COMPUTER REQUIREMENTS
We have discussed the requirements of the computer for the azimuth - elevation direction finder with several computer representatives. During these discussions
we have learned the most difficult problem is that of sampling the antenna data to be
read into the analog-to-digital (A to D) converter. It is important to the proper operation of the azimuth - elevation direction finder, to ensure that all data received during
the on mode of each antenna (this is referred to the switch aperture) is read into the
A to D converter. Many commerically available computers (suitable to the azimuth -
elevation DF system) sample incoming data at a 60kc rate. Presently it is assumed
that the sampling switch (of the DF system) will consist of 17 inputs each having on
time (switch aperture) of 1.17 milliseconds for the 1000 rpm switching rate. A conventional 60 kc sampler would then sample each switch aperture three times during a
particular DF scan cycle. In the event the DF data in the switch aperture are from a
radar having a high prf rate, there is a possibility that the sampling would occur during
a no-signal interval. Therefore, it has been concluded that we must either increase
the sampling rate or employ an alternate technique.
Before discussing the above further, we should note another complication (which
has been discussed previously) which requires we have some knowledge of the rise time
of the receiver so that the pulses will be interrogated properly. In the event the receiver has a poor rise time there will be a leading and trailing edge associated with
each pulse and sampling during the rise time would lead to erroneous data. A third
problem that must be considered is the possibility of very low prf radars such that only
a small portion of a pulse may be intercepted by the antenna during the switch aperture
interval. This would give a very narrow pulse for the analog-to-digital converter to
sample during the total aperture interval.
56

THE UNIVERSITY OF MICHIGAN
1084-1-Q
To overcome these problems noted above, it is possible to increase the probability of detection of the maximum signal for both low and high prf's by considering
much faster sampling rates in the analog-to-digital converter (e. g., 500kc).
However, at a minimum, there are two undesirable features associated with this
choice, iLe..,, the cost of the unit increases along with a reduction in accuracy of the
overall DF system. As for the cost, a 60kc sampler costs $4500. 00 while the cost of
a 500 kc sampler would range between $8000. 00 and $9000. 00. Inaccuracies may occur
since data would be sampled at a very high rate and it is conceivable that portions of
the data would be sampled during the rise and trailing time of pulse signals thus providing erroneous data for the computer. This would then require an additional operation to be performed by the computer to average the data which in turn increases the
complexity of the computer program. Further, we would be requiring the computer to
store a considerable amount of non-functional data employing the 500 kc sampling rate.
During discussions with personnel of the University of Michigan Computer
Center, they confirmed that the most difficult problem for the computer in so far as the
DF system is concerned was sampling the signal during the time interval of the switch
aperture as noted above. They expressed concern with regards to employing a 500 kc
sampling rate since they felt it was close to the limiting response time of the computer
and that it may not be a state-of-the-art item at this time. They suggested an alternate
method which would perform the sampling by integrating the voltage within the switch
aperture. However, this was discarded because of the erroneous signal which would
result particularly for radars having very low prf's. As was noted earlier, there is
a high probability that such signals may be present in the switch aperture for a small
part of the pulse. The average of this data, when integrated over the entire switch
aperture period, would be very low providing erroneous data to the computer. As a
consequence, it was recommended that we consider a more complex interface (that
would preceed the computer) to determine the maximum signal voltage.
57

THE UNIVERSITY OF MICHIGAN
1084-1-Q
Let us note that the technique employed for reading data into the computer will
have an influence on the amount of time allocated for the computer to determine the
desired 0 and 0 coordinates of the unknown signal. A second complication would
occur if one employs a high sampling rate to read data directly into the computer during the period of the switch aperture; the computer memory will be burdened with
absorbing a large amount of non-functional information as noted above.
Therefore, to overcome these undesirable features, it was recommended that
we employ a direct access technique allowing the computer to determine the signal
maximum during the off time of the switch. However, a more complicated interface
would be required which would determine the signal maximum during the period of the
switch aperture and that at the end of the aperture, read this information into the
computer. Simultaneously the computer would reduce the data obtained during the
preceeding switch aperture into its respective rectangular components and continuously
add them as each switch aperture provides its information to the computer. Having
the computer collect, reduce and sum the data simultaneously as the individual switch
apertures interrogate the antennas it would be necessary for the computer to perform
one calculation to obtain the direction of arrival ( 0 and 0 coordinates) of the incoming
signal. It is probable that the computer would be capable of calculating the new direction of arrival during every rotation of the switch.
From these discussions, consideration is now being given to two computers for
use with the azimuth - elevation direction finder. The computers are the Data Machines,
Incorporated, 620I and the Hewlett-Packard, 2115A.
58

THE UNIVERSITY OF MICHIGAN
1084-1-Q
VIII
CONCLUSIONS
During this interim considerable effort has been of an analytical nature in addition to a small experimental effort associated with the design of the electromechanical
switch. A number of laboratory models for the switch have been built and evaluated,
and presently an engineering model is being assembled. The analytical work has
shown that it is extremely important for the antenna elements to be electrically well
behaved (patterns and impedance) over the range of frequencies of interest (600 MHz
to 3 GHz). Discussions with computer representatives have assured us that the computer requirements of the azimuth - elevation direction finder are well within the
present state-of-the-art of computer techniques.
At this time it would appear that the most difficult problem is in the design and
development of the feasibility model of the azimuth - elevation direction finder is the
development of antenna elements. We are presently investigating the use of multifilar
conical spirals. Since there is little in the open literature with respect to multifilar
spiral elements, we have discussed them with several investigators. It is generally
felt that the element pattern requirements for the azimuth - elevation direction finder
will be difficult to achieve. However, there is evidence that broadband (5:1) circularly
polarized elements can be developed to satisfy the azimuth - elevation direction finder
requirements. Therefore, an effort is being expended on the development of elements
to be employed with the subject DF system.
From discussions with computer representatives, it is apparent that the cost of
the computer (for the azimuth - elevation direction finder) will be in the neighborhood
of 030, 000. A present consideration is to determine the optimum method of reading
antenna information into the computer. The principal type of data that will be difficult
to read into the computer is radar pulse information. We are also giving further consideration to this problem before we make arrangements to purchase a computer.
59

THE UNIVERSITY OF MICHIGAN
1084-1-Q
Although the analytical studies have shown that azimuth - elevation direction
finding can be accomplished employing techniques that have been described in this
report, there are many problems that will be associated with the hardware. Emphasis
must be placed on the problems that will be associated with the design and development
of the antenna elements. As the program progresses, we are sure there will be additional problems associated with the system and it is suggested that there be a close
liaison maintained between the University and Ft. Monmouth as the program progresses.
60

THE UNIVERSITY OF MICHIGAN
1084-1-Q
REFERENCES
Jasik, H. Antenna Engineering Handbook, McGraw Hill Book Company, New York
p. 28-24, 1961.
Sengupta, D. L.., J. E. Ferris, R. W. Larson and T. M. Smith (1965), "Azimuth and
Elevation Direction Finder Study", Quarterly Report No. 1, ECOM-01499-1,
The University of Michigan Radiation Laboratory Report 7577-1-Q.
Sengupta, D.L., J.E. Ferris, R.W. Larson, G. Hok and T.M.Smith (1966), Azimuth
and Elevation Direction Finder Study", Final Report,EC OM-01499-4, The
University of Michigan Radiation Laboratory Report 7577-1-F.
Shiffman, B. M., "A New Class of Broad-Band Microwave 90 Degree Phase Shifters",
IRE Trans. on Microwave Theory and Techniaues, Vol. MTT-6, No. 2,
April, 1958, pp. 232-237.
Duncan, J.W. and V.P. Minerva (1960), "100:1 Bandwidth Balun Transformer,"
Proc. IRE Vol. 8, pp. 156-164.
Shelton, J..P. and J.A. Mosko (1966), "Synthesis and Design of Wide Band
Equal-Ripple TEM Directional Couplers and Fixed Plane Shift,"
IEEE. Trans. MTT-14, No. 10, pp. 462-473.
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UNCLASSIFIED
Security Classification
DOCUMENT CONTROL DATA. R & D
(Security classification of title, body of abstract 1,*d ttlc xintg ainnotation nlist be enitered when the overall report i. clasaifed)
1. ORIGINATING ACTIVITY (Corporaute author) 2a. REPORT SECURITY CLASSIFICATION
The University of Michigan Radiation Laboratory, Dept. of UNCLASSIFIED
Electrical Engineering, 201 Catherine Street, 2b. GROUP
Ann Arbor, Michigan 48108
3. REPORT TITLE
AZIMUTH AND ELEVATION DIRECTION FINDER TECHNIQUES
4. DESCRIPTIVE NOTES (7'ype of report and inclusive dates)
First Quarterly Report 1 July - 30 September 1967
5. AU THOR(S) (First name, middle initial, last name)
Joseph E. Ferris, Boppana L. J. Rao, and Wiley E. Zimmerman
6. REPORT DATE 7I,. TOTAL NO. OF PAGES 7b. NO. OF REFS
October 1967 61 6
8a. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S)
DAAB07-67-C0547
1084- 1-Q
b. PROJECT NO.
5A6 79191 D902-05-11
C. "'h. OTHER REPORT NO(S) (Any other numbers thoat may be assigned
this report)
ECOM-00547- 1
10. DISTRIBUTION STATEMENT
Each transmittal of this document outside the Department of Defense must have prior approval
of CG, U. S. Army Electronics Comnmand, Fort Monmouth, New Jersey, 07703, ATTN:
AMSEL-WL-S.
1I. SUPPLEMENTARY NOTES 112. SPONSORING MILITARY ACTIVITY
U. S. Army Electronics Command
AMSEL-WL-S
Ft. Monmouth, NJ 07703
13. ABSTRACT.
A block diagram of the proposed DF azimuth-elevation direction finder is
presented and discussed. A simple analysis is presented for a two-dimensional
direction finder and is extended into a three-dimensional system. As for the threedimensional azimuth-elevation direction finder analysis, a number of computer
programs have been utilized to determine the accuracy of the system. In general
it has been found that the system accuracy is strongly dependent upon the element
pattern characteristics (i.e. it is important that they have broadband radiation
pattern characteristics both as a function of element orientation and frequency).
Further, it has been found that because of the elements being distributed over 2T|
steradians that the predicted elevation angles have associated with them a discrepancy has been found to be predictable and can easily be handled by the computer to provide the true angle. Discussions have been held with several computer
representatives and it has been determined that it is feasible to employ a small
computer to perform the necessary data processing to obtain the required
azimuth-elevation data from the hemisphere antenna system.
1 NO4V 6 7 3 UNCLASSIFED
S. e uri t (.'ts sit i t i(ult

NCLASSIFIED
Security Classification
14 KEY WORDS LINK A LINK B LINK C
ROLE WT ROLE WT R0 OLE W T
Azimuth Elevation Direction Finder
Circular Polarization
Conical Spiral
Multifilar Spiral
Broadband Directional Cduipler
Broadband Phase Shifter
Data Processing
Electromechanical Switch
TU CIZ SSI FI ED
S,? c.' rri (' I.l,.sS i fi,:, t x(i:,f

UNIVERSITY OF MICHIGAN
3 9015 02826 7154