UnitedStates Postgraduate School · 2016. 6. 21. · LIBRARY TECHNICALREPORTSECTION NAVALPOSTGRADUATESCHOOL MONTEREY.CALIFORNIA93940 NPS52AB72061A UnitedStates NavalPostgraduateSchool

LIBRARYTECHNICAL REPORT SECTIONNAVAL POSTGRADUATE SCHOOLMONTEREY. CALIFORNIA 93940

NPS 52AB 72061A

United StatesNaval Postgraduate School

GRAPHANT: A FORTRAN PROGRAM FOR THE SOLUTION

AND GRAPHIC DISPLAY OF GAIN AND PATTERNS FOR WIRE

AND LINEAR ANTENNAS IN THE PRESENCE OF LOSSYGROUND

BY

R. W. ADLERAND

C . B. ROBBINS

June 1972

Approved for Public Release; Distribution Unlimited

FEDDOCSD 208.14/2:NPS-52AB72061A

NAVAL POSTGRADUATE SCHOOLMonterey, California

REAR ADMIRAL A. S.

SuperintendentGOODFELLOW M. U. CLAUSER

Provost

ABSTRACT:

An interactive computer graphics antenna gain pattern computationand display program for real-world antenna systems is presented. Theuse of the program as a teaching tool at the Naval Postgraduate Schoolis discussed. Methods for applying the program for the synthesis anddesign of complex antenna systems are indicated. Research applicationsinclude techniques for rapid inspection of gain equations of newlydeveloped antennas. A ship motion model is developed for studying the

effects of electrical geometry variations caused by ship motion in

heavy seas on maritime antenna systems and a dynamic presentation ofpattern variations is made.

- . U

TABLE OF CONTENTS

A. INTRODUCTION

B. BRIEF DESCRIPTION OF PROGRAM

C. DYNAMIC ANALYSIS OF SHIPBOARD ANTENNAS

D. RECOMMENDATIONS

APPENDIX A: DETAILED PROGRAM DESCRIPTION

1. Program Operation

2. Processor Description

3. Processor Functional Description

4. Extension of the Program

APPENDIX B

APPENDIX C

APPENDIX D

APPENDIX E

APPENDIX F

EXAMPLE PATTERN COMPUTATIONS

ANTENNA GEOMETRY AND GAIN AND INPUT RESISTANCE EQUATIONS

PROGRAM LISTING

SHIPBOARD ANTENNA DYNAMIC SIMULATION EQUATIONS

OPERATING INSTRUCTIONS FOR U.S. NAVAL POSGRADUATE SCHOOLGRAPHICS COMPUTER LAB

LIST OF REFERENCES

INITIAL DISTRIBUTION LIST

FORM DD 1473

A. INTRODUCTION

Anyone who has attempted to correlate the actual performance of HFand VHF wire antennas operating in a real-world environment to the "highlysanitary," theoretical radiation patterns and gain which proliferate intext books and handbooks will immediately recognize the need for a simplemethod of predicting antenna performance in the presence of the earth. Thisreport describes the development and use of a computer tool, which enablesanyone with a working knowledge of Fortran and a free-space radiation patternand mutual impedance formulation to analyze and design antenna systems of

arbitrary orientation above a specified lossy plane earth.

It serves as both a teaching aid and a design tool. In instructional use,it provides quick interaction via a graphics display of antenna parametersand radiation patterns plots. In seconds, a student can observe the perfor-mance of several popular HF/VHF antennas in any plane earth configurationhe chooses. Equivalent digital computer/plotter turn-around time is inexcess of 1 hour and manual calculation time on the order of days. Theprogram firmly convinces the student that the antenna system is composed of

the antenna plus its environment.

For the communications system designer, rapid evaluation of antennasystems enables him to choose an antenna type and orientation which willenhance the performance of the total system rather than arbitrarily guessingwhich antenna package might be suitable. When new antenna types are developed,their radiation pattern and impedance equations can readily be added to the

basic calculation package and the full potential of the antenna may be pain-lessly determined, not just for the usual, mystical free space environment,but for the surroundings in which the radiator will be used. Using an HFIonospheric Propagation Prediction program which can return optimum radiationangles for a specified path and time, a systems designer can synthesize anoptimum antenna pattern for the particular situation under investigation.The optimum may be manually entered and each design iteration compared withthe optimum. The pattern Save and Recall options are used to arrive at the

best type antenna and orientation available to him.

Previous work on antenna patterns in the presence of ground is widelyscattered in the literature. Specific antenna types are referenced in the

appendices. The initial incentive for this investigation was to increasethe usefulness of an antenna radiation pattern subroutine for HF antennas,

currently in use as part of a HF Ionospheric Propagation Prediction programwritten by ESSAl. The gain and input resistance equations from this reportwith some modifications and corrections were used. Equations programmed are

included in Appendix C.

The program as presently configured assumes a current distribution on

the antenna. The consequences of this are small errors in terminal impedancewith a corresponding discrepancy in gain value. Radiation patterns areaffected very little by the differences between assumed and actual currents.

To calculate exact current distributions would be prohibitive in both time

and programming effort, considering the limited worth of the more exactgain figures which would result.

1 Ref: ITS 78 Report.

B. BRIEF DESCRIPTION OF PROGRAM

The program consists of two basic parts:

1. The solution of antenna pattern equations for radiators of arbitraryorientation above a flat earth of specified ground constants (conductivityand permitivity) . Gain values are calculated from terminal impedanceexpressions containing self (free space) and mutual (coupling between' theantenna and its image) effects.

2. The graphics display portion which displays program input parametersspecifying antenna type, size, orientation, ground constants and specialfeatures such as recall and storage of patterns. This part of the programalso generates power intensity plots vs. azimuth and elevation angles anddisplays these radiation patterns on the graphics screen. Gain values canbe displayed in conjunction with the patterns.

Subroutines for special functions which are usually found in wire antennapatterns and impedance formulae and numerical quadrature calculations areincluded for the convenience of persons wishing to apply their own specificantenna to the program. The user who wishes to do this must provide patternequations for his antenna for arbitrary orientation. The effect of groundreflections and the selection of observation angles is provided by theprogram itself.

Special features available to the user are:

1. Plotting patterns on a log scale vs. linear.

2. Storage and recall of patterns for comparison purposes.

3. Ability to generate a desired pattern shape (via light pen) whichis stored and recalled for comparison.

4. Simple ship-ocean model for dynamic simulation of shipboard antennasystems

.

When the program is used at USNPGS, the XDS 9300 digital computer core

limitations restrict the calculation and viewing of one pair of cuts in the

3 dimension geometry (i.e. one azimuth rotation at one specified elevationangle and one zenith to horizon elevation cut.) Typical time for a patterncalculation is 15 seconds, with a simple dipole requiring 9 seconds and a

vertical monopole with ground screen up to 2 minutes. Seven common antennasare currently programmed:

1. Arbitrary Tilted Dipole

2. Vertical Monopole

3. Vertical Monopole with Ground Screen

4. Inverted L

5. Sloping Long Wire

6. Rhombic

7. Vertical Half-Rhombic

More complex programs for arrays such as Yagis, Log Periodic Dipolesand Monopoles, and curtains will require fairly long calculation times dueto the extensive mutual impedance calculations.

C. DYNAMIC ANALYSIS OF SHIPBOARD ANTENNAS

The ease of obtaining the effect of the earth on antenna performanceprompted the investigation of the programs potential to display the effectof typical ship motion of shipboard HF antenna radiation. The equations foran arbitrary tilted dipole, sloping long wire and vertical monopole werealready in the form to allow variable tilt angle. By programming a ship-ocean model that reorientates the antenna with ship motion (roll and pitch)

,

it is possible to show slow but dynamic pattern changes with sea surfaceas a function of sea state and ship direction for a chosen type of vessel.This simplified model rocks the antenna in two planes as the ship respondsin roll and pitch to ocean waves but still assumes a plane ocean reflectingsurface. For medium and heavy seas, the results indicate an appreciablere-lobing effect and show that the variation in signal at a particularobservation angle may be as high as 20 db

.

This is an additional factor which should be considered when assigninglocations for antennas in new ship designs. Present efforts at evaluationof these antenna locations do not include sea state perturbations.

The next stage of investigation of ship motion effects will include a

variable geometry for the sea surface to replace the plane shape. At lowHF the effect might be approximated by a partially random "fuzzy" surfacewhile for UHF the distances are large in term of radio wavelengths and the

model could be more nearly that of a rolling surface contour.

The final results of these extensions will be of benefit to the antennalocator, as previously explained, as well as to communications managers.Depending upon the sensitivity of the total communications link to antennalobe structure, communications procedures for a given frequency may be improved

by insight obtained from the investigation of sea state effects.

D. RECOMMENDATIONS

The radiation equations for most of the antennas do not include the

arbitrary geometry factors needed for ship motion effects study and should

be expanded to include them. Gain calculations depend upon input resistancewhich in the case of the sloping long wire and others do not include mutual

effects. Where possible and where warranted, these effects should be included

by deriving coupling terms for input impedance equations. (This will notalter the shape of the radiation patterns and affects only the magnitude of

the fields and hence the gain).

Array antenna equations exist in the literature and should be carefullyverified and adapted for inclusion in the plotting program.

When this program is used for matching patterns produced by HF propagationprediction programs, a convenient data interfacing technique (such as tape)should be developed for use between the graphics system and the lager generalpurpose digital machine used in the prediction calculations.

APPENDIX A

DETAILED PROGRAM DESCRIPTIONAppendix A

Section III contains a description of program operation. The programis divided into processors, program subsections that perform the majorcomputational tasks. Processor operation and interaction are described.

1. PROGRAM OPERATION

The program displays a data and option command input format at thegraphics terminal (see figure A-l) . The program operator enters applicableparameters values for antenna geometry, environment, and option commandsusing text editing techniques. A blank graphics block is then displayed atthe CRT. Trial patterns may be manually entered in this block using graphicsediting techniques. Manually entered patterns will be displayed with allsubsequently computed patterns allowing the operator to compare computedpatterns with trial patterns on the CRT. Exercising the reinitializationoption will erase the trial pattern.

The program computes horizontal and vertical gain patterns and displaysthem at the graphics terminal. The horizontal pattern is computed withzenith constant at the inputed value for 0' and azimuth varied from 1 to 360degrees by one degree increments. The vertical pattern is computed forazimuth constant at the inputed value of $'and zenith varied from 1 to 90degrees by 1 degree increments. Linear and log displays are available. If

a log display is not ordered with the log pattern option command, linearpatterns will be displayed.

Patterns are saved by exercising the save pattern option. Patternvector data is stored in the digital machine in a save array when save is

ordered. Exercising the recall option will cause patterns saved in the savearray to be displayed.

Use of save and recall options allows simultaneous display of saved andcurrent patterns for comparison purposes.

A dynamic simulation of a shipboard antenna mounted on a rolling pitchingship in a stop-action type of presentation is programmed. Entering seastate and direction in the data format causes the simulation to operate. Seamotion is resolved into ship motion and ship motion into antenna parametervariation. Patterns are computed and displayed at 10 degree intervals of

wave period. Sea state must be entered to by-pass the dynamic simulationif it is not desired.

Appendix F is operating instructions for use of the program implementedat the Computer Graphics Laboratory, U. S. Naval Postgraduate School,Monterey, California. Figure A- 16 is a schematic of the graphics computersystem at this facility.

2. PROCESSOR DESCRIPTION

A processor flow chart is presented in figure A-2. Processor operationand interaction is described below.

A. The Parameter Format Processor initializes the display graphics andtext data blocks and displays the text format for parameter and programoptions commands input.

B. The Parameter and Options Input Processor is used to enter problemparameters and program option commands using the format provided by theprevious processor. The parameter and options input processor requiresentry of all parameters each time the program is initialized. All otherutilizations of this processor require changing only individual parametersas desired. If the reinitialization option is selected by the operator,the parameter format processor is branched to from the parameter and optionsinput processor.

C. The Pattern Manual Entry Processor displays a blank graphics datablock. By manually editing this data block, the operator may draw a

pattern that will be displayed with all subsequently computed patterns.Erasing this manually entered pattern must be done by reinitializing inthe parameter and options command processor. If no manual pattern is

desired, this processor may be terminated without entry being made.

D. The Environmental Constants Processor computes the values of

problem constants that are functions of antenna parameters and environmentalconditions and not dependent upon observation angles.

E. The Input Resistance Processor computes a value for input resistanceof the antenna entered in the parameter and options input processor. If

the equations in the gain processor assume a nominal value of input resistance,a value of 1.0 is assigned to input resistance.

F. The Observation Angle Constants Processor computes values of problem

constants that are functions of observation angles for those observationangles for which the antenna gain is to be computed.

G. The Gain Processor computes the gain of the antenna selected in the

parameter and option command input processor at the selected zenith angle

all integer values of azimuth angle from 1-360 degrees, and the selected

azimuth angle and all values of zenith angle from 1-90 degrees. These twogain vectors are the horizontal and vertical gain patterns.

H. The Normalize and Max Gain Processor selects the maximum value of

gain from both horizontal and vertical linear patterns and normalizes bothpatterns with respect to this maximum value. This operation is requiredto scale patterns for graphics display. The absolute value of maximum gainis computed and its log-io taken. This value is displayed in the text dataformat.

I. The Log Gain Processor operates if the operator manually selectsthe log gain option in the parameter and options command input processor.The horizontal and vertical linear patterns are converted to logarithmic,patterns with a 30 db range of (lOlog^gmax gain) to (lOlog-^gmax gain) .

These patterns are renormalized by the log gain processor.

J. The Pattern Display Processor is a two part processor which displaysthe horizontal and vertical patterns at the graphics terminal.

K. The Pattern Save Processor is a two part processor which operatesif the horizontal save and vertical save option are selected by the operatorin the parameter and option command input processor. They may be indepen-dently selected. This processor transfers the pattern currently displayedby the display processor to storage in the digital machine in a save array.Entering a pattern in a save array destroys the pattern previously saved so

care must be exercised to bypass this processor if saving the pattern for

several compute cycles is desired.

L. The Display Saved Patterns Processor operates when the recall optionhas been selected by the operator. The processor recalls the patterns savedin the save array and displays them at the graphics terminal. Operation of

this pattern does not destroy data in the save array.

M. Dynamic Processor . This processor computes and displays a simula-tion of shipboard whip, dipole and sloping longwire antenna patterns.Entry of an integer larger than in ISEA will cause this processor to

operate. The processor computes sinusoidal ocean waves with magnitude de-pendent upon sea state. Ship roll and pitch which are functions of shiptype, sea state and relative direction of the seas are computed. Parametervariations caused by ship motion are computed and the normal compute loopentered with the modified values of antenna parameters. The patterns arecomputed and displayed and the gain at the ' and <J>' inputed in the parameterinput processor is displayed under SIGL in the text data format. The oceanmodel is re-entered. The ship roll and pitch cycles are divided into 36

discrete steps and a pattern computed and displayed for each step. Thedisplay will be a stop-action type display of antenna pattern vs. time.

Entry of 0000 under ISEA will cause this processor to be bypassed.

3. PROCESSOR FUNCTIONAL DESCRIPTION

Figures A- 3 thru A-15 are functional flow diagrams of processors.Equations for the ocean model, gain, and input resistance used in the gainand input resistance processors are included in Appendix E. The sourcesfor gain and input resistance equations are ESSA Technical Report ESSA-ERL-110-ITS 78, A.F. Barghausen, J. W. Finney, L. L. Proctor, L. D. Schultz,

May 1969 and ESSA Technical Report ESSA-ERL-104-ITS 74, M.T. Ma, L.C.

Walters, April 1969. A listing of the Fortran Program used to implementthe program is Appendix D.

4. EXTENSION OF THE PROGRAM

The program may be extended to compute patterns for other types of

antennas. Adding antennas may be accomplished by inserting an inputresistance branch in the input resistance processor and a gain branch in

the gain processor. If additional parameters are required, the parameterformat must be changed to accept them. Multi-element antennas such as

Yagi or Log Periodic will have a mutual impedance matrix; the terms of this

matrix may be evaluated using the mutual impedance equations in the dipole

branch. Specific changes required to add antennas to the USNPGS implemen-tation are as follows:

1. Statements 134 and 135 may be changed to new parameter names.

2. After statement 162, add DECODE statements for new parameters.

3. New constants statements, if any, should be inserted betweenstatements 198 and 218.

4. After statement 229 in the input resistance processor, insertIF(ANTN.EQ.9) GO TO 1900.

5. After statement 771 in the input resistance processor, add 1900INPUT RESISTANCE BRANCH STATEMENTS

GO TO 2000

6. In the gain processor after statement 272, insert IF(ANTN.EQ.9)GO TO 900.

7. In the gain processor after statement 771, insert 900 ANTENNAGAIN STATEMENTS

GO TO 42

The dynamic simulation is available for whip, sloping longwire andvertical whip antennas. Simulation of other antennas aboard ship may be madeby rewriting gain equations to allow arbitrary orientation of theantenna. Orientation variations are available in the ocean model and the

dynamic simulation can then be made.

10

FIGURE A-l

ANTN

LENG

HGHT

PHIP

THEP

FREQ

EPSL

SGMA

PHI

THET

PARM

ISTH

ISTV

IRCL

HGTT

ALPH

GAIN

ISEA

ICRS

SIGL

11

PARAMETERFORMAT PROCESSOR

PARAMETER ANDOPTION INPUTPROCESSOR

PATTERN MANUALENTRY

PROCESSOR

TEST \ GTSEA STATE

^

ENVIRONMENTALCONSTANTSPROCESSOR

OCEAN/SHIPMODEL

(DYNAMIC DISPLAY)

INPUT RESISTANCEPROCESSOR

INDEXN = I, 2

INDEXJ = 1.560

HOR PATTERN

YES

YES INDEX1= I, 90

VERT PATTERN

1 JZ

CONSERVATION ANGLECONSTANTSPROCESSOR

GAIN PROCESSOR

INORMALIZE AND

MAX GAINPROCESSOR

JJJ<37

DYNAMIC GAINDISPLAY

(DYNAMIC PROCESSOR)

DYNAMICPATTERN DISPLAY

(DYNAMIC PROCESSOR)

Figure A-2Processor Flow Chart

DISPLAY SAVEDPATTERNSPROCESSOR

12

INPUT TEXT FORMAT DATA

INITIALIZE TEXTDATA BLOCKS

iASSIGN FORMATS TOTEXT DATA BLOCKS

iENCODE TEXT DATABLOCK VARIABLES

INITIALIZE MANUAL

ENTRY PATTERN, VERTICALAND HORIZONTAL SAVE VECTORS

IDISPLAY PARAMETER FORMAT

USING TEXT DISPLAY SUBROUTINE

Figure A.

3

Parameta Format Processor

13

ENTER PARAMETERS ANDOPTION COMMANDS USING

TEXT EDIT AND TEXT INPUTSUBROUTINES

DECODE PARAMETERTEXT BLOCKS

Figure A. 4

Parameter and Option Input Processor

14

NITIALIZE GRAPHICSDATA BLOCKS

ASSIGN DATA FORPATTERN AXES

ENCODE MANUAL PATTERNARRAY TO GRAPHICS

DATA BLOCK

DISPLAY MANUAL PATTERNGRAPHICS BLOCK

ENTER PATTERN BYEDITING GRAPHICS BLOCK

TRANSFER MANUAL PATTERNTO MANUAL PATTERN ARRAY

TFigure A. 5

Pattern Manual Entry Processor

15

compute <£', Q\ a\ ac ,

A , K, K^ R ^ , Rv

A

Figure A. 6

Environmental Constants Processor

16

TESTANTN=DIPOLE

NO

TESTANTN = VERT.

WHIP

NO

TESTANTN = WHIPW/G SCREEN,

NO

TESTANTN= INV L

NO

TESTANTN = SLOPELONG WIRE

NO

YES

YES

YES

YES

COMPUTE RINFOR ARBITRARILYTILTED DIPOLE

COMPUTE RIN

FOR VERTICALWHIP

COMPUTE RINFOR VERTICAL WHIPWITH GROUND SCREEN

COMPUTE RINFOR INVERTED

L

YES COMPUTE RINFOR SLOPINGLONG WIRE

TESTANTN = SLANT

YESRIN = 10

NO

TESTANTN = RHOMBIC

YESRIN

NO

TESTANTNHALF

= VERTHOMBIC

YESRIN = 1.0

Figure A 7

Input Resistance Processor

17

COMPUTE R, R u ,

V

V ^

Figure A. 8

Observation Angle Constants

Processor

18

TESTANTN = WHIP W

•GROUND SCREEN-

NO

NO

NO

NO

NO

YES

YES

YES

YES

YES

YES

YES

COMPUTE COMPUTE

COMPUTEVERT

WHIP GAIN

COMPUTEE„ . E8 4>

FOR NO GROUND SCREEN

COMPUTEEFFECT OF

GROUND SCREEN

COMPUTEGAIN FOR VERT

WHIP WGROUND SCREEN

COMPUTEE0,

'">

COMPUTEINV L GAIN

COMPUTE

COMPUTEE ,E<A 82 2

COMPUTEGAIN FOR

SLOPE LONG WIRE

COMPUTEE ,E

COMPUTE

<A' 8

2 2

COMPUTE GAINFOR SLANT

VEE

COMPUTE GAINFOR

RHOMBIC

COMPUTE

COMPUTE

V E*V2 2

COMPUTEGAIN FOR

VERT HALFRHOMBIC

COMPUTEGAIN FOR

TILTED DIPOLE

CT>o

<l 0)o

 cli. D

e>

19

INDEXI= 1,360

YES

2

YESINDEXI = 1,90

N =I

NORMALIZINGFACTOR (N)a

FAC (N) =

GAIN

N = N + I

NORM = 0.0

INDEXN = 1,450

NORM = MAX (NORM,FAC (N)

Figure A. 10

Normalize and Max Gain Processor

20

LOWERLIMIT = 10

BLIM

r3

INDEXI =

1 , 90

TEMP = G(I,I)/

NORM

G(l,I) = ALOG|0

(TEMP.)

+ 30

INDEX1 = 1,360

TEMP =

G(2,I)/N0RM

G(2,I) =

ALOG|Q

TEMP) +3

NORM = 3.0

TEMP =

NORM/RIN

TEMP =

ALOG|Q(TEMP)

DISPLAY TEMP IN

TEXT DATA FORMAT

GAIN = 10* GAIN

T

YES

YES

-»]

temp="bl

< TEMP = BLIM

Figure A. II

Low Gain Processor

21

CONVERT GAIN TO GRAPHICSBLOCK DATA (X, Y COORD)

ENCODE PATTERN DATA INTOGRAPHICS DATA BLOCKS

DISPLAY PATTERNS USINGGRAPHICS EDITING SUBROUTINES

MANUALLY TERMINATEPROCESSOR OPERATION(DISPLAY CONTINUES)

Figure A. 12

Pattern Display Processor

22

DECODE GRAPHICSPATTERN DATA

ASSIGN GRAPHICS PATTERNDATA TO SAVE ARRAY

Figure A. 13

Pattern Save Processor

23

ENCODE INTO GRAPHICS DATABLOCKS PATTERS IN SAVE

PATTERN ARRAY

DISPLAY SAVED PATTERNSUSING GRAPHICS EDIT

SUBROUTINE

MANUALLY TERMINATEPROCESSOR OPERATION

Figure A. 14

Saved Pattern Display Processor

24

FM TEST SEA STATE

FM DYNAMICDISPLAY

COMPUTEOCEAN WAVEPOSITION

COMPUTEAB'\, A9'2,

DIPOLE ^^ TEST \ WHIP~^>n. ANTN ^/>~

COMPUTE

h, A8',e'

TO ENVIRONMENTALA CONSTANT PROCESSOR

COMPUTE

%

irCOMPUTE

irCOMPUTE

1 1

9 d

A TO ENVIRONMENTAL CONSTANT PROCESSOR\

FM NEUTRALIZE AND MAX GAIN PROCESS

COMPUTEGAIN AT

OBSERVATION POINT

DISPLAYIN DATAFORMAT

TO DISPLAY PROCESSOR

Figure A. 15

Dynamic ProcessorCONVERT GAINTO GRAPHICS

DATA

ENCODE INTOGRAPHICSDATA BLOCKS

DISPLAYGRAPHICSDATA BLOCKS

TO OCEAN MODEL

XDS 9300

1

L

1

1 t

ADAGE10

A

Operator

It ADAGE10

CRT CRT^

W

Figure AI6

Naval Postgraduate School

Computer Graphics Laboratory

26

APPENDIX B

EXAMPLE PATTERN COMPUTATIONS

Example pattern calculations for the seven antennas programmed arepresented in this section. Patterns were computed for typical parametervalues for each antenna. Computation of effects of parameter and environ-ment variations as well as the use of program control options are demons-trated. The text input required to compute each pattern is presented witha CRT photograph of the pattern computed. The USNPGS user may use thetext input in conjunction with the user instructions of Appendix F to

learn program use.

Figure B-21 is a film strip of the 36 images that comprize thedynamic simulation of a shipboard vertical whip antenna in a state 5

sea from 045 degrees relative to ship's bow. Figure B-22 is a dynamicsimulation of a horizontal dipole in the same sea conditions. The imagesof the dynamic simulation are computed at 10 degree intervals of the ship'sroll and pitch period. Figures B-21 and B-22 should be scanned down columnsand from bottom of left column to top of right columns.

VERTICAL WHIP DIPOLE

1.0m150.0 mhze r

= 80

6 = 5.0= 75°

4>=

h s 6m

2. Sm

f = 30.0 mhz

I.= 80

6 = 5.00= 045

* - 060

27

FIGURE B.l

ANTN

0001

LENG

01.0

HGHT

01.0

PHIP

0000

THEP

0090

FREQ

150.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

FARM

0000

_STH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGL

Comments: Manually entered A/2

Vertical dipole pattern; height A/2

28

FIGURE B.2

ANTN

0001

LENG

01.0

HGHT

01.0

PHIP

0000

THEP

0090

FREQ

150.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGL

Comments

:

a/2 dipole; A/2 height; good ground; *= 0. 9'=90,

f=150 mhz, £=1.0 h=1.0; overlay manually entered pattern;

Observation angles $=0, = 80

29

FIGURE B.3

ANTN

0001

LENG

01.0

HGHT

01.0

PHIP

0000

THEP

0090

FREQ

150.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0001

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGL

Comments : Erase manual trial pattern

no pattern computed

30

FIGURE B.A

ANTN

0001

LENG

01.0

HGHT

02.0

PHIP

0000

THEP

0090

FREQ

150.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

1STH

0001

ISTV

0001

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRA

0000

SIGL

Comments A/2 dipole; X height; good ground; ^'=0, 0'=90,

f= 150 mhz, 1= 1.0, h=2.0; Observation angles<t>=0

,

0=80; save patterns

31

FIGURE B.5

ANTN

0001

LENG

01.0

HGHT

02.0

PHIP

0000

THEP

0090

FREQ

225.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0001

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGLComments 2 A/3 dipole; A A/3 height, good ground, <J>'=0, 0'-90,

f=225 mhz, £=1.0, h=2.0; observation angles, 4>=0 ,0=80.

The effects of changing frequency are shown here.

32

FIGURE B.6

ANTN

0001

LENG

01.0

HGHT

02.0

PHIP

0000

THEP

0090

f req

225.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0001

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGLComments Recall pattern 4 and overlay on pattern 5. The use of save

and recall options are shown in this example. The options

are used to compare the A dipole (inside and 2 lobe pattern)

with 4/3X dipole (outside and 3 lobe pattern).

FIGURE B.7

ANTN

0001

LENG

01.0

HGHT

02.0

PHIP

0000

THEP

0090

FREQ

225.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0002

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGLComments: Two thirds wave length dipole; Four thirds wave length

height; good ground ,4> ' =0 ,0 '=90 , f=225 mhz, £ = 1.0, h=20;observation angles 4>=0 0=80 ;Log patterns 30 db scale.Log pattern option is used to study side lobe structure.

34

FIGURE B.8

ANTN

0001

LENG

01.0

HGHT

02.0

PHIP

0000

THEP

0045

FREQ

225.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGL

Comments: Two thirds wavelength dipole; four thirds wave length height,good ground, <j>'=0, 0'*45° (tiltangle), f=225 mhz, £=1.0h=2.0, observation angles $=Q 0=80; Tilted dirole. Theeffect of tilt on dipole radiation patterns is demonstrated here,

35

FIGURE B.9

ANTN

0002

LENG

02.5

HGHT

00.0

PHIP

0000

THEP

0000

FREQ

30.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGLComments: Quarter wavelength whip; good ground, f=30 mhz, £=25

observation angles (J)=0 , 0=80

36

'1GI RE 3. 10

ANTN

0001

LENG

02.5

HGHT

00.0

PHIP

0000

THEP

0000

FREQ

030.

EPSL

04.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

01.0

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGL

Comments: Quarter wavelength whip; poor ground, f=30 mhz, £= 2.5,observation angles *=0 , 0=80. The effects of changes in

reflecting "round are shown in this example. The ground

change from good ground to poor ground causes a decrease in

gain of 2db and a slight increase in of max .radiation.

T7

FIGURE B.ll

ANTN

0003

LENG

02 .5

HGHT

05.0

PHIP

0000

THEP

0000

FREQ

030.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGL

Comments : A/4 vertical whip with

half wave length ground radial screen

38

FIGURE B.12

ANTN

0003

LENG

02.5

HGHT

10.0

PHIP

0000

THEP

0000

FREQ

030.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGL

Comments : A/4 vertical whip with wave lengthground screen. Increasing screen narrows anddepresses vertical pattern.

39

FIGURE B.13

ANTN

0004

LENG

20.0

HGHT

10.0

PH1P

0000

THEP

0000

FREQ

30.

EPSL

10.0

SGMA

0.01

PHI

0060

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

S1GL

.'••n»«l M...-.--iii»i(iw(m«ii«i""" "folilllllM ^

' •• •..

;

... ....

Ifl-

•i r

1 f ' f" \l/

/

Ml V; /fltf

HI

it f

SVM /TV\1 ll

ttsr

t»cr

IIU

6/\ifftl

MmmiKTVlilt

PCllll

>«TT

tilt

till

f^^

t

s

SEA

tit

t III

*4l»,.—>; r--- •»•-.-

Comments: Inverted L, horizontal run two wavelengths, vertical runone wavelength; good ground; h=10.0, £=20.0, f=30 mhz;observation angles $=60, 0=80.

40

FIGURE B.14

ANTN

0004

LENG

20.0

HGHT

05.0

PHIP

0000

THEP

0000

FREQ

030.

EPSL

10.0

SGMA

0.01

PHI

0090

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGL

Jfl-

•I f

III! \ /naa ^y %ptu /^^\m. / /*v \if i 1/ XJ0Ut II

wIM1mmtill

»tsmi sS^~)KM y^ /mi / /no. / s'mi { ^s^«TTmiVJ".

mi3*:1

:

&

:»>uii:•.«

:nrV.l

Comments Inverted L, horizontal run two wavelengths, vertical run

one-half wave lenth; good ground; h=5.0, £=20.0, f=30 mhz;

observation angles 0=90, 0=80. The effects of change in

vertical run length are shown here.

41

FIGURE B.15

ANTN

0005

LENG

20.0

HGHT

00.0

PHIP

0000

THEP

0045

FREQ

030.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

0000

SIGLComments: Sloping Long wire; two wavelengths; good ground; 4>=0

,

0'=45°, £=20, f = 30 mhz, observation angles <f>=0 , 0=80,

42

FIGURE B. 16

ANTN

0005

LENG

20.0

HGHT

00.0

PHIP

0000

THEP

0060

FREQ

30.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0000

GAIN

ISEA

0000

ICRS

SIGLComments: Sloping Longwire; two wavelengths; good ground; $'=0,0' =60,

£=20.0, f=30 mhz; observation angles $=0 , 0=80. This set of

two examples demonstrates the effect of variation of tilt

angle on radiation patterns.

43

FIGURE B.17

ANTN

0007

LENG

30.0

HGHT

10.0

PHIP

0000

THEP

0000

FREQ

030.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0030

GAIN

I SEA

0000

ICRS

0000

SIGLComments: Horizontal rhombic; three wavelength sides; good ground;

one wavelength height; £=30.0, h=10.0, a=30° , f=30 mhz;

observation angles $=0, 0=80.

44

FIGURE B.18

ANTN0007LENG30.0HGHT10.0PHIP0000THEP0000FREQ

030.EPSL10.0SGMA0.01PHI

0000THET0080PARM0000ISTH

0000ISTV

0000IRCL

0000HGTT0000ALPH0045GAIN

ISEA0000ICRS

0000SIGL

Comments: Horizontal rhombic, three wavelength sides; good ground,

one wavelength height; £=30.0, h=10.0 a=45°, f=30mhz;observation angles $=0, 0=80. These last two computationsshow clearly how the program may be used to synthesizeantenna systems. A non-optimum a is compared to the optimumfor a given h ,£ etc. Since this antenna is fairly difficultto build, the use of the program to synthesize the optimumis well justified.

45

FIGURE B.19

ANTN

0008

LENG

30.0

H.GHT

10.0

PHIP

0000

THEP

0000

FREQ

050.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

ISTV

0000

IRCL

0000

HGTT

0000

ALPH

0030

GAIN

ISEA

0000

ICRS

0000

SIGL

<( r

i i

mi••«o* .

Illln^j \/1Ml i™ '^HePi- P>1 1

i

mt f i

»ii

tini»cr

mi

till

ISPi

miis:/ i

lilt1

/-:«. L >mi l/ê^

Sf

tutJ*:-

.;*

»

:>«,

Comments: Vertical half rhombic, three wavelength sides, good ground,

£=30.0, a=30°, f=30mhz; observation angles $=0, 9=80. This

antenna has a major lobe at approximately 40° elevation and

may be suited for propagation conditions requiring high

elevation lobes.

FIGURE B.20

ANTN

0008

LENG

30.0

HGHT

10.0

PHIP

0000

THEP

0000

FREQ

030.

EPSL

10.0

SGMA

0.01

PHI

0000

THET

0080

PARM

0000

ISTH

0000

1STV

0000

IRCL

0000

HGTT

0000

ALPH

0045

GAIN

ISEA

0000

ICRS

0000

SIGLComments: Vertical half rhombic, three wavelength aides, good ground,

£,=30.0, a=45° , f = 30 mhz; observation angles (j)=0 , 0=80.

Increasing a splits the energy into a high and low lobe and

decreases gain from the previous case.

47

Vertical Whip PatternSmall ShipSea State 5 from 045°R

Figure B-21

48

Figure B-21

49

Figure B-21

50

Vertical WhipHorizontal Pattern

Figure B-21

51

Figure B-21

52

Figure B-21

53

Half Wave DipoleVertical Pattern

Small ShipSea State 5 from 0A5°R

Figure B-22

54

Figure B-22

55

Figure B-22

56

Figure B-22

56

Half Wave DipoleHorizontal Pattern

Figure B-22

57

Figure B-22

58

Figure B-22

59

APPENDIX C

ANTENNA GEOMETRY AND GAIN AND INPUT RESISTANCE EQUATIONS

This appendix details the antenna geometry of the programmed antennasand the equations used in the gain processor and input resistance processor.The sources of equations and geometry are ESSA Technical Report ESSA-ERL-110-ITS 78 and ESSA Technical Report ESSA-ERL-104-ITS 74. The sphericalcoordinate system used ro describe antenna patterns is the IEEE standardand is shown in figure C-l Antenna geometry for the antennas programmedis shown in figures C-2 thru C-9

.

The definitions of the terms used in antenna equations are as follows:

I = length of a unit radiator in meters

h = height of antenna feed point above ground plane

0"" Tilt angle of the antenna axis measured from the zenith

A "= Tilt angle of the antenna axis measured from the horizontal

= Observation zenith angle

A = Observation elevation angle

a = Apex half angle

a^- Complement of apex half angle

<|> = Observation azimuth angle

£r= Dielectric constant of ground plane

o = Conductivity of ground plane

R, = Complex ground reflection factor for a horizontally polarized waveh

CH = Magnitude of horizontal reflection factor

4V-= Phase of horizontal reflection factor

R = Complex ground reflection factor for a vertically polarized wave

CV= Magnitude of vertical reflection factor

T = Phase of vertical reflection factorv

R ,,= Complex horizontal reflection factor evaluated for normal incidenceh

R ^= Complex vertical reflection factor evaluated for normal incidencev

-"

f = Frequency in mhz

60

A = wave length in meters

a = radius of ground screen

c radius of ground screen wire

Equations for quantities that are common to all antennas programmedare as follows:

X ,= 3.0 x 108

k = 2II/A

k2» 1 I

r = cose - k

*2

L - j 1.8 x 104g j

*

[-ft-)7cose + k fi -A siNe \ |

k2 L v

k2 ) J

r^ = cose - k2

|"i -/k siNe \2

|

1/2

cose + k [i -/k sino V 11/2

ITL

\^2 /J

Rv'

= k2

- k V = k - k2

k2+ k k + k

2

51 = COS (ik - 2Kh SINA )n

52 = SIN (V, - 2Kh SINA )h

53 = COS (Y - 2Kh SINA )v

54 = SIN (T - 2Kh SINA )v

61

C- 1 ARBITRARILY TILTED DIPOLE

The equations presented are for a thin, single element, center feddipole arbitrarily oriented above a flat ground plane.

GI = COS ( l/2k«, (SINA SINA' + COSA COSA ' SIN 4> ) - COS (l/2k&)

1.0 - (SINA SINA' + COSA COSA' SIN<£)2

DI = COS (l/2k& (COSA COSA' SIN <j> - SINA SINA' )- COS (l/2kfc )

1.0 - (COSA COSA' SIN<j>- SINA SINA' )

2

E^ = (COSA' SIN 4> SINA - SINA' COSA ) -GI

- (COSA' SIN<J>SINA + SINA' COSA )-DI-CV'S3

E^. = COSA' COS <}> (GI + DI-CH-S1)

E = (COSA' SIN $ SINA + SINA' COSA )-DI'CV»S4J2

El = COSA' COS

(f>•DI-CH'S2

*2

Gain = 120- (E2+ E

2+ E

2+ E

2) /Rin

S • 2h

S = S SING' COS d)1

x

S - S SING' SIN d>'

y

S - S COSQz

p.[ S2

+ (Y + S )

2 1/2x o y J

Y =2 COSA ' ho —

A \ for mutual impedance

Z - 2 SINA' h

I

for self impedance

Y - /Hx 103

• n/Xo

Z = .0o

r =[p2 + (Z + S) 2

]1/2

I o z J

r = p2+ (Z + S + 1/2* )

2 1/21 L o z J

r, = p2+ (Z + S - 1/2* )

2J

1/2Z ^ o z J

62

SR = 1/r SIN (2nr)

SRI = l/r1

SIN (2nr1

)

SR2 = l/r2

SIN (2nr2)

FACR = 2*SR COS (IU)

CR = 1/r COS (2IIr)

CR1 = l/r1

COS (2nr1

)

CR2 = l/r2

COS (2nr2)

FACX = 2«CR«COS (IU)

Z. . = (R. . + j X. . )iJ ij ij

h,-»fl ' 2

l\l( SR1.(S + Z + £)+ SR. (S + Z - £ )z °T 2z o y '

- FACR-(S + Z ) )'(S :

Z O / X

rsiN2n(£ - Isl ) 12 dS

L s J

r ll1 (r /X. .= -30

1 k CRWv

]2+YS + S 2) + S (FACR - SRI - SR2)o y y z }'

- A ) - FACR (S + Z ) )•

2:')

](S2 + YS + S 2) I + S «(FACX - CR1-CR2)x o y y z

!

SIN2II (£ - |S )

]

dS

Z.., = self impedance

Z = mutual impedance

R. = Rin 11

+ Real Z21

(Rh'

C0SA ' + J R ' SINA? ) (COSA' - j SINA"]

63

C.2 VERTICAL MONOPOLE

Vertical whip antenna equations are for a base loaded vertical whipabove a flat ground plane.

S3 = COS (4> )

s4 - sin (y )v

A = COS (k£ SINA) - COS (k£)

B = SIN (kl SINA) - SINA SIN (k£)

Gain = ) [ a» (1+CV-S3) + B-CV'S4]2

-I- [ A-CV S4 + B« (1-CV*S3) ]2

'

R. COS Ain

R - 15 <[2 + 2 COS (2k£)J»[en (2kft) + Y - Ci (2k£)] -

COS (2kA)-[jln (4k£) + Y- Ci (4kfc) ]-

2 SIN (2k£)'Ptf + Si (2kA) 1 + SIN (2k£)«U_+ Si (4k£) I

I2

J I1 J)

Y = .577

Ci(x) = - costdt

Si(x) = - SINtdt

'x

64

C.3 VERTICAL WHIP WITH GROUND SCREEN

The vertical whip with ground screen is a single monopole above a flatground with a radial conductor ground system consisting of N equally spacedradial conductors. A value of 120 is used for N and 1 cw wire is assumed.

53 = COS ^v

54 = SIN i|j

A = COS (k£SINA) - COS (k£) B = SIN (k£SINA) - SINASIN (kl)

Gain =

2 2

[A-(l + CV»S3) + B-CV-S4]2+ [A-CV-S4 + B- (1-CV-S3)

]

2Â3+ B

3j

R.in

A3+JB 3-

n =

rka 2 2 2.1/21 - nSINS [ e

nX } - eJXC0S(k£)] J

1(xSIN9)dx

120n SIN(k£) [COSCkJICOSe) - C0S(k£)]

1/2f j^ 1o + j a) e

J

R, = R. of vertical whip (C.2)1 in

« -

4ns IN Qui)

12kA -J2WW 4e^Êi ["J 2k ( r + £ ) ] + e Ei [-J 2k ( r " £) ^

+ 2C0S (k£) Ei[-j2ka] + 4 C0S(k£) Ei [-jkr^

- 4C0S(k£)eJkS,

EI C0S(k£)ejk£

E:

AZ, n[s-J

L [-JkC^ - H)l - 4

r/ 2 2

1 ^ 2

I -jk(p + «, 1 _e"jkp C0S(k£)l

i r-jk(r1+£)J |

2IIp SIN Qui)

dp

Ei (+ jx) = Ci(x) + j Si(x)

, 2^fl2,l/2

r = (a +1 )o

rx

= a + (a2+£

2)

1/2

CT+]W£j

n fj240n2pUn^ \

'e \ NA / VNc /

R. = R, + Real (AZ, + AZ.)in 1 12

65

C. 4 INVERTED L

The inverted L antenna equations are for a long wire antenna that isbase loaded and arranged in an inverted L configuration.

A - COS(k£) COS (khSINA) - SINA SIN Qui) SIN CkhSINA)

- COS (k (h+fc))

B = SINA SIN (k£) COS (kh SINA) + COS (k£) SIN (kh SINA)

- SINA SIN (k (h+O )

GI = SIN (kS. COSA SIN <}) - COSA COS $ SIN Qui)

GR = COS (k£ COSA SIN<J)

- COS Qui)

- S3) + GI-CV-S4)g

[

SIN 4> SINA LgR(1,

1.0 - C0S2A SIN

2<j>

[

A (1.0 + CV« COS i + B CV.SINi^_v vCOSA ]

S INj SINA (GI (1.0 - CV'S3) - GR'CV»S4

1.0 - C0S2A SIN

2ij>

B (1.0 - CV'COS Jb ) + A'CV'SIN ^

COSA

'cos 4

1 - cos2a COS 4>

]

,|lGR(l. + CH» SI) - GI-CH-S2

]

+ [GI ( 1.0 + CH-S1) + GR-CH-S2 ]

Gain = 30-0 [|e/+ |e/]

)

RinSi(x) = I

xdx

Rin = 60 L.41 + In I 21 \ + SIN (2kg, )

\ X / 2k£ J

(Jin (2kh) + 1.270 - Ci (4kh)

In (2kh) + 0.577 - Ci (2kh))

1/2 Si (4kh) - Si (4k£) I

+ 30.0 I- 1/2 COS (2kh)|Un (2kh) + 1.270 - Ci (4kh)

+ (1.0 + COS (2kh))| ^n (2kh) + 0.577 - Ci (2kh))

- SIN (2kh) 1/2 Si (4kh) - Si (4k£)

66

C.5 SLOPING LONG WIRE

The equations for this antenna are for a base loaded longwire antennaarranged in a sloping configuration; the antenna zenith angle may be assignedvalues of thru 90 degrees.

t i

CIG = COS [k£ (SINA SINA + COSA COSA COS*)] - COS (ki )

i i o

1.0 - (SINA SINA + COSA COSA COS *)

i »

SIG = SIN [kg. (SINA SINA + COSA COSA COS *) ] -(SINASINA '+COSAC0SA 'COS*) SIN(k&'i i

21.0 - (SINA SINA + COSA COSA COS*)

CIGP = COS [kfc) ( COSA COSA COS*- SINA SINA )]- COS Qui)i i 2

1.0 - (COSA COSA COS*- SINA SINA )

1

21-0 - (COSA COSA COS*- S-INA SINA )

f i

+ (SINA SINA - COSA COSA COS *) SIN (ki)

rSIGP = SIN['k&) ( COSA COSA COS*- SINA SINA )]

L LO - (COSA COSA COS * - J

]

1E - -COSA SIN *

J

CIG + CH '(CIGP COS * - SIGP "SIN it )

E = - COSA SIN* SIG + CH (CIGF'SIN* SIGP COS*)

! I »

E = CIG (COSA COS * SINA - SINA SINA) + CV (COSA COS * SINA1

+ SINA COSA)*I

CIGP -COS tL - SIGP* SIN $ 1

F ' ' * '

2= SIG (COSA COS * SINA - SINA COSA) - CV (COSA COS * SINA+ SINA COSA)

IciGP'SIN* + SIGP'COS *

Gain = 30 |E.2

+ E ,

2+ E

2+ E

21/ Rin

L *1 *2 *i *2 J

Rin = 30 { 1/2 [an (ki) + .577 + Ci (4k£)|

+ 0,693 + COS (kO [COS k£ Qln (k£) +.577

- 2.0 Ci (2k£) + Ci (4k£)) - SIN (k£) (Si (4kjO

- 2.0 Si (2kH) I (

/oo J)

x^- dt

"J! 2?katSi(x) =

67

C. 6 TERMINATED SLOPING VEE

The terminated sloping vee equations are for two sloping longwireantennas arranged in a vee configuration. The feed point is the apex of the

vee. The elements are fed 180 degrees out of phase. The elements of the vee

are terminated in 370 ohm non inductive resistors.

COS t|)

COS \\i

COS i-

COS i<

cos i

cos i

cos i

cos i

SINA SINA

SINA SINA

-SINA SINA

-SINA SINA

COSA SINA

COSA SINA

-COSA SINA

-COSA SINA

+ COSA COSA

+ COSA COSA

+ COSA COSA

+ COSA COSA

+ SINA COSA

+ SINA COSA

+ SINA COSA

+ SINA COSA

COS

COS

COS

COS

COS

COS

COS

COS

4»-

<*

)

<()+ a )

<J>

- a )

4>+ o )

t»- a)

cf + or )

+ -a)

U = k£ (1.0 - COS ij, Ji i

i = 1, 2, 3, 4

A = COS ^ _ (COS (U ) - 1.0) - COS i . (COS (U ) - 1)

+ cv

.

COS i S3(C0S (U4

) - 1-0) S4 + SIN (U^)

- COS ip (COS (U3

) - 1-0) S3 + SIN (IL) S4]

B = COS ty SIN (IL) - C0Si|; SIN C^)

+ CVJ

COS i> c I SIN (U3

) S3 - (COS (U3

) - 1.0) S4 j

(

+ COS i , I (COS (U,) - 1.0) S4 - SIN (U) S3oi4 4)

+ C0Si|<, ( (COS (IL) - 1.0) S4 - SIN (U) S36 V 4 4

x U

68

C = SIN U + a) (COS (U2

) - 1.0) - SIN ( cj> - a ) CCOS Cljj) - 1.0 )

,

A) - 1.0) - SIN C4> -a) (COS CU

3)+ CH

J

SI ("siN (<fc+a) (COS 0}

( L ^

-S2[siN (<|>-a) SIN (U )- SIN ( <fr

+ a ) SIN (1^)1

U.,

1.0) j

D = SIN U-a)SIN (U ) - SIN U+a) SIN QJ )

+ CH |~SIN ( 4> - a ) SIN (U ) - SIN (<}> + a) SIN (U )|. sl}

+ SIN ( $ + a

D'3 4

) (COS (U ) -10) - SIN (<(>-a) (COS (U3

) - 1.0 ) S2

Gain = 0.05o 9 ' 7 2

A + B + COSZA (C + D )

69

C. 7 HORIZONTAL RHOMBIC

The horizontal rhombic antenna equations were developed under theassumption of uniform current distribution of the effective value of current,

The antenna is loaded at the apex and terminated in dissipation lines at theopposite corner.

u\ = 1 .0 - COSA CSIN a COS<J>+ COS a SIN cj> )

1 c c

U„ = 1 ;0 - COSA (SIN a COS $ - COS a SIN <j> )2 c c

Gain = 2 .16 COS a SIN (1/2 kAUjSIN (1/2 k£U.)c

;1_ 2

U1U2

(COS <j>- SIN o COS )

2(CH

2+ 1 .0 + 2 .0 -CH- SI) +

SIN2A SIN

24> (CV

2+ 1.0-2.0 -CV- S3)

J

70

C. 8 VERTICAL HALF RHOMBIC

The vertical half rhombic are for a base loaded longwire arranged in thevertical half rhombic configuration and terminated in a 40Q-50Q ohm non-induc-tive resistor.

SI = SIN (K (1.0 - COS i ))

CI = COS (K (1.0 - COS t|< ))

S2 = SIN (K (1.0 - COS ty ))

C2 = COS (K (1.0 - COS i|; ))

COS i = COSA COSA COS <j>- SINA SINA

COS Tj; = COSA COSA COS <j> + SINA SINA

Rl = 1 - CI II = SI

l.o - cos i> i.o - cos ^

R2 = CI (1.0 - C2) + S1-S2 12 = C1-S2 - SI (1 .0 - C2 )

i.o - cos i 1.0 - cos i

R3 = (1.0 - CI) COS (2k 2, SINA SINA) + SI SIN (2k£ SINA SINA)

i t

13 = SI COS (2k£ SINA SINA ) - Q- .0 - CI) SIN ( 4IU SINA SINA)

Fl = I3-C1 - R3-S11.0 - COS \\)

F2 = R3-C1 + I3-S1

F3 = 1.0 - C2

1.0 - COS ty2

F4 = S21 - COS 4'

71

RB = Rl + R2 - CV [(F2 + F3) S3 - (Fl + F4) S4 ]

Bl = II + 12 - CV [(F2 + F3) S4 + (Fl + F4) S3 ]

RC - R2 - Rl + CV [(F2 - F3) S3 - (Fl - F4) S4 ]

CC = 12 - II + CV [(F2 - F3) S4 + (Fl - F4) S3 ]

RA = Rl + R2 + CH [(F2 + F3) SI - (Fl + F4) S2 ]

Al = II + 12 + CH [(F2 + F3) S2 + (Fl + F4) Si]

r ' *2Gain = 0.1 (RB COSA COS <£ SINA + RC SINA COSA)

'' 2

+ (Bl COSA COS $ SINA + CC SINA COSA)

+ (RA COSA SIN <j> )

2+ (AI COSA SIN $ )

2

72

Figure C-l

Spherical Coordinate System

73

L

H

9

ength of dipole

height measured al center

of dipole

Tilt angle (measured in zenith)

Tilt angle (measured in elevation

above horizontal)

<f>Train angle (measured in azimuth)

Figure C -2

Arbitrarily Tilted Dipole Geometry

74

'

L Length

•

Figure C-3

Vertical Whip Geometry

75

L length of whip

H radius of ground screen radial elements

Figure C - 4

Vertical Whip with Ground Screen Geometry

76

X

H - Height of vertical run

L - Length of horizontal run

Figure C-5

Inverted L Geometry

77

L — Length of Long wire

9 — Tilt angle (measured in zenith)

a — Elevation angle

Figure C-6

Sloping Long -Wire Geometry

78

370 X2

L

a

9

H

Length of sloping element

Half element separation

Slope angle (measured from zenith)

Height of load point

Figure C-7Terminated Sloping Vee Geometry

79

L - Length of side

H - Height

a - Half separation angle q^ load point

a -c

Complement of a

Figure C-8

Rhombic Geometry

80

z

A

tH

k >x

L -

H -

8'-

a -

Length of side

Height

Tilt angle of side (measured from zenith)

Half separation angle of rhombus at load

point

Figure C-9

Vertical Half- Rhombic Geometry

81

APPENDIX D

PROGRAM LISTING

This appendix is a listing of the Fortran implementation of the antennapattern graphics program. The listing is preceded by a partial listing of

definitions of the computer variables used. Variables used in graphicsdisplay processors only were not included in the below list.

ANTN

L

H

PHIPR

THEPR

F

EPSLN

SIGMA

M

KAY

PAR

ISTRH

ISTRV

ALPH

ALP CM

DLPRI

LMDA

K

C2

RHPRI

RVPRI

S

Antenna Type

length

height

?

f in mhz

er

a

in degrees (observation zenith)

<f>in degrees (observation azimuth)

Reinitialize and Log Gain option command

Save horizontal pattern option command

Save vertical pattern option command

a<

A'

A

k

k2

VR

,v

82

sx SX

SY S

y

SZ sz

YO Yo

ZO Zo

ROW P

R r

Rl rl

R2 r2

PI n

RIN R.m

THETA

PHI *

KCOS COS (0)

RV RV

RH \SIGHV KSIGHH HDELTA A

COSDL COS ( A )

SINDL SIN ( A )

SINDP SIN (a')

COSDP COS (a')

SINPI SIN (<}> )

COSPI COS (* )

83

ETHT1 \ETHT2 \EPHI1 E

hEPHI2 \)

G Gain (relative pattern)

GAIN Max Gain

NORM Max value of linear gain

EPHI |E*

,2

ETHET |E

*I

2

KOS1 COSi

KOS2 COS *2

KOS3 COS *3

KOS4 COS i\>

KOS5 COS ^5

KOS6 cos i6

KOS7 COS t\>

7

KOS8 COS \\>

COSU1 COS (Ul)

COSU2 COS (U2)

COSU3 COS (U3)

COSU4 cos (U4)

SINU1 SIN (Ul)

SINU2 SIN (U2)

SINU3 SIN (U3)

84

SINU4

SINAC

COSAC

IRCAL

ISEA

ICRS

SIGL

ADA

DPHIP

WAVE

DLTI

DLT2

DLT3

SIND3

SINA

COSA

VAR

Z

RGRAL

XGRAL

CEE

SRFAC

DLTZ1

DLTZ2

CV

CH

SIN (U4)

SIN (a )c

COS Co)c

Recall saved pattern option command

Sea State

Sea direction

Log1Q

(G CM, KAY) )

n

A <j>

wave

Aei

A0.

SIN (A03)

SIN CA<J>)

COS (Ac)))

U)t I[wave)

z

Ri -iK1 J

Xij

C

CA3+ JB3)

AZ.

AZ2

Rv|

Rhl

85

Computer variablesv that are identical to the terms in Appendix C theyrepresent, are not listed here.

The following sub-programs are included in the program:

1. SUBROUTINE SINUS (X, SC)

COMPUTER Si (x) = - SIN t/SINdt

2. SUBROUTINE KOSINUS (X, CC)/oo

COS tx - dt

3. FUNCTION CINC (x)

COMPUTER COS xx

4. FUNCTION SINC (x)

COMPUTER SIN Xx

5. FUNCTION AKEX (x)

COMPUTER Ei (±.jx)

6. FUNCTION ADAE (x)

COMPUTER ne

7. FUNCTION ZGRAL (x)

COMPUTER integrand for AZ2

= ( ) dr

8. FUNCTION RESIST (s)

COMPUTER INTEGRAND for Rij = I ( ) ds

9. FUNCTION REACT (s)

COMPUTER INTEGRAND for Xij = ( ) ds

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118

APPENDIX E

SHIPBOARD ANTENNA DYNAMIC SIMULATION EQUATIONS

This appendix presents the development of ship motion equations as

functions of sea state and relative direction of the sea. Ship motion is

resolved into parameter variation. The values for time varying parametersare used in the compute loop for the dynamic simulation.

The ship-ocean combination is modeled as follows:

1. The ship will roll sinusoidally 8 degrees per sea state if the seais on the beam, ie . from 090 R or 270 R.

2. The ship will pitch sinusoidally 2.4 degrees per sea state if the sun is on

the bow or stern, ie. from 000 R or 180 R. (This represents a small navalcombatant ship)

3. Sea state and direction is resolved into ship motion:

Vertical Whip or Sloping Long Wire

AA = 2«L* SIN (AG1/2)

BB = 2-L- SIN (A91/2)

CC = AA2+ BB

2

DD = L2

- (CC/2)2

|A

|= 2. tan

_1( CC/2 )

3 DD

A - |A|

o3

e3 ^

o' (t) = e' (0) - A (TILT)°3

SIN A = SIN AG SIN Ae3

o3

2 1/2COS AG = (1 - SIN AG)

I A $ (

= tan"1 SIN A

fycOS A $ (azimuth change)

119

Wave

ROU : A0I

Pitch A02

= 8-SEA-SIN (wt)

= Wave • SIN (CRS. ^q)= 0.3- wave- cos (CRS. %<,)

Pitch

DipoleB\t) = 9

l

(0) - l9z (tilt)

H (r) =H (O)-cos (A0l)-cos (A0 1 ) (height)

120

if: A > and AQ

> Q A $ = |A$|

1 2

A < Q and AQ

> A'$=-|Acf|1 2

AQ

> and A < A $ = (II- | A |)

* (t) =<J>' CO) - A i

Definition of terms :

A - ship roll*ei

A - ship pitchS2

A - tilt of whip or long wire caused by ship motion (whip)G3

wave - sinusoidal wave

to - wave radar frequency

(t)- antenna tilt (Dipole)

h (t)- antenna height (Dipole)

A 4> - variation in antenna train caused by ship motion (whip)

<(> (t) - antenna train (whip)

CRS - Direction of sea relative to ship's bow

121

APPENDIX F

OPERATING INSTRUCTIONS FOR U.S. NAVAL POSTGRADUATE SCHOOL GRAPHICS COMPUTER LAB

This appendix gives step by step operating instructions required to usethe antenna patterns graphics program at the Naval Postgraduate School. Useof the graphics library program "GATED" and computer light-off procedures arecovered in the operators manual and laboratory memoranda and are not includedin this appendix.

1. Light-off SDS digital computer in accordance with operating instruc-tions .

2. Light off ADAGE graphics computer in accordance with operatinginstructions and load library program "Gated".

3. Load the program in the XDS-9300 computer. If an overlayed versionof the program is used, the entire program may he loaded. If an overlayedversion of the program is not used, computer memory limitations allow loadingonly two antennas at a time. The input resistance branches, gain branches,and required subroutines for the antennas desired should be loaded alongwith the main program. A missing lables warning will result but the programmay be operated if only antennas loaded are called.

4. When the input light on the teletype is lighted type IDEV = 1* if

ADAGE 1 is to be used or IDEV = 2* if ADAGE 2 is to be used. Pushing the

carriage return will cause the data input format to be displayed at the graphicsterminal.

5. Enter parameters and option commands using "Gated" text editingtechniques. Inputs should be as follows:

a. Under ANTN enter one of the following to specify antenna type:

0001 Tilted Dipole0002 Vertical Whip0003 Vertical Whip with Ground Screen0004 Inverted L

0005 Sloping Longwire0006 Sloping Vee0007 Horizontal Rhombic0008 Vertical Half Rhombic

b. Under LENG enter length in format F4.1

c. Under HGHT enter height in format F4.1

d. Under PHIP enter 4> in format 14

e. Under THEP enter in format F4.Q

f. Under FREQ enter f in format F4.0

g. Under EPSL enter e in format F4.1& r

122

h. Under SGMA enter a in format F4 .

2

i. Under PHI enter the observation azimuth angle for the verticalpattern using format 14.

j .Under THET enter the observation zeniuth angle for the horizon-

tal pattern using format 14.

k. Under PARM enter 0000. If reinitialization is desired toerase a manually entered pattern, enter Q001. If Log Gain patterns aredesired, enter 0002.

1. Under ISTH and ISTV enter 0000. If saving the pattern thatwill be computed in the current compute cycle is desired, enter 0001. Ifit is desired to keep the pattern in the save array, these option commandsmust be set to 0000 in the succeeding compute cycle.

m. Under IRCL enter 0000. If displaying saved patterns is desired,enter 0001.

n. Under HGTT enter 0000. Entering 01.0 will multiply the valueof sigma by .1. Entering 02.0 will multiply the value of sigma by .01.

o. Under ALPH enter a in format 14.

There are two unused data blocks which no operation edits must be madeto finish the data input processor.

6. Axes and a blank graphics data block will now be displayed on theterminal screen. A pattern desired for comparison purposes may be enteredin this block using manual graphics editing techniques. To terminate thisprocessor operation, push the end edit button on the function switch panel.This processor may be terminated without entry if desired.

7. The antenna patterns selected will be computed and the horizontalpattern displayed on the upper axis. Pushing the end edit button will causethe vertical pattern to be displayed on the lower axis.

8. If the display saved patterns option has been selected, pushingthe end edit button two additional times will cause the vertical andhorizontal patterns to be superimposed on the current vertical and horizontalpatterns. The program will, then, return to the enter parameters and optioncommands processor. If recall has not been selected, the program will returnto the enter parameters processor from terminating the vertical patterndisplay processor termination (end edit)

.

The compute cycle is now repeated. Ending the program must be done in

accordance with laboratory operating instructions. Figures 4.1 thru 4.20are the entries for the examples of section 4.

p. Under ISEA enter sea state in 14, if a dynamic display is desiredfor dipole, whip or longwire antennas. If dynamic display is not desired,

enter 0000.

q. Under ICRS enter relative direction of seas if dynamic displayis desired.

123

LIST OF REFERENCES

1. U. S. Department of Commerce/ Environmental Science Service AdministrationReport ERL 110-1TS 78, Predicting Long Term Operational Parameters ofHigh Frequency Sky Wave Telecommunication Systems , A. F. Barghausen,J. W. Finney, L. L. Proctor, L. D. Scholty, May 1969.

2. Jordan, E. C, and Balmain, K. G. Electromagnetic Waves and RadiatingSystems , Prentice Hall, 1968.

3. U. S. Department of Commerce/Environmental Science Service Administra-tion Report ERL 104-ITS 74, Power Gain for Antennas Over Lossy PlaneGround , M. T. Ma, L. C. Walters, April 1969.

4. Baker, H. C, Lagrone A. H., Digital Computation of the Mutual Impedancebetween Thin Dipoles, Proc. IRE Trans. AP-10, No. 2, P. 172-178.

5. Wait J. R. , Pope W. A., Characteristics of a Vertical Antenna with a

Radial Conductor Ground System , Appl . Sci. Res B, Vol. 4, P. 177-195.

124

DISTRIBUTION LIST

Defense Documentation Center 2

Cameron StationAlexandria, VA 22314

Attention: IRS (20 copies)

LibraryNaval Postgraduate SchoolMonterey, CA 93940 (2 copies)

Commanding OfficerNaval Ships Engineering CenterNavy DepartmentWashington, D. C. 20350

Commanding OfficerNaval Electronic Laboratory CenterSan Diego, CA 92152

Research Administration OfficeNaval Postgraduate SchoolMonterey, CA 93940

Professor G. A. RaheDepartment of Electrical EngineeringNaval Postgraduate SchoolMonterey, CA 93940

Professor R. W. AdlerDepartment of Electrical EngineeringNaval Postgraduate SchoolMonterey, CA 93940 (10 copies)

LT C. B. Robbins371 B. Bergin DriveMonterey, CA 93940

125

UnclassifiedSecurity Classification

DOCUMENT CONTROL DATA -R&D{Security classification of title, body of abstract and indexing annotation must be entered when the overall report Is classified)

I originating ACTIVITY (Corporate author)

Naval Postgraduate SchoolMonterey, CA 93940

2«. REPORT SECURITY CLASSIFICATION

Unclassified26. GROUP

3 REPORT TITLE

GRAPHANT: A Fortran Program for Solution and Graphic Display of Gain and Patternsfor Wire and Linear Antennas in the Presence of Lossy Ground

4 DESCRIPTIVE NOTES (Type of report and.inclusive dates)

Technical Report 19725 authORISI (First name, middle initial, last name)

Adler, R. W.

Robbins, C. B.

6 REPOR T D A TE 7a. TOTAL NO. OF PAGES

1 June 1972 95

7b. NO. OF REFS

8a. CONTRACT OR GRANT NO.

b. PROJEC T NO.

9a. ORIGINATOR'S REPORT NUMBERIS)

NPS-52AB 72061A

9b. OTHER REPORT NOI5I (Any other numbers that may be assignedthis report)

10 DISTRIBUTION STATEMENT

Approved for Public Release; Distribution Unlimited

II. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

U. S. Naval Postgraduate School

13. ABSTR AC T

An interactive computer graphics antenna gain pattern computation and displayprogram for real-world antenna systems is presented. The use of the program as

a teaching tool at the Naval Postgraduate School is discussed. Methods for

applying the program for the synthesis and design of complex antenna systems are

indicated. Research applications include techniques for rapid inspection of

gain equations of newly developed antennas. A ship motion model is developed for

studying the effects of electrical geometry variations caused by ship motion in

heavy seas on maritime antenna systems and a dynamic presentation of pattern

variations is made.

DD F0R" 1473i NOV es I "T I WS/N 0101 -807-681

1

(PAGE 1)Unclassified

126Security Classification

A- 31400

Security Classification

KEY WO ROS

AntennasAntenna GainAntenna PatternsComputer ProgramInteractive Computer SolutionGraphics Display

DD ,

F°?.,1473 <«*« UnclassifiedS/N 01 01 -807-68? T

127 Security Classification

UU7735

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