Theses and Dissertations Thesis Collection - core.ac.uk · Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 1987 The use of coaxial transmission line

Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1987

The use of coaxial transmission line elements in

log-periodic dipole arrays.

Tarleton, Robert E. Jr.

http://hdl.handle.net/10945/22570

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NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESISTHE USE OF COAXIAL TRANSMISSION LINE

ELEMENTSIN LOG-PERIODIC DIPOLE ARRAYS

by

Robert E. Tarleton, Jr.

June 1987

Thesis Advisor Richard W. Adler

Approved for public release; distribution is unlimited.

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1987 JuneIS PAGE COoNT

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Log-periodic dipole array, k-beta diagram,Snyder dipole, Numerical Electromagnetics Code

A8S r RAC T (Continue on >t,eit if ntctmry tnd identity by bloxk numb+r)

This thesis examines the feasibility of designing a log-periodiclipole array (LPDA) with ccaxial transmission line elements andromparing the resulting operational bandwidth with that of a

Jpnventional LPDA. Using the Numerical Electromagnetics Code (NEC), a

paxial dipole was modeled to optimize the bandwidth and zhen used aslie element in a variety of uniform arrays. Different types o£ element:onnections were examined including switched series, switched parallel,.nd unswitched parallel. The results of NEC for each of the arrays are>lotted as k-P diagrams to compare to the standard arrays.

The results of the investigation show that the Snyder dipole>rovides more operational bandwidth than a standard dipole, but when?laced in a uniform array there is no more bandwidth than that of a:onventional uniform array.

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UNCLASSIFIED•.AVE OF RESPONVRlE ND-viOUALRichard W. Adler

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Approved for public release; distribution is unlimited.

The Use of Coaxial Transmission Line Elementsin Log-periodic Dipole Arrays

by

Robert E. Tarleton, Jr.

Electronic Engineer. Department of DefenseB.S.E., Arizona State University, 1980

Submitted in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOLJune 1987

ABSTRACT

This thesis examines the feasibility of designing a log-periodic dipole array

(LPDA) with coaxial transmission line elements and comparing the resulting

operational bandwidth with that of a conventional LPDA. Using the Numerical

Electromagnetics Code (NEC), a coaxial dipole was modeled to optimize the

bandwidth and then used as the element in a variety of uniform arrays. Different types

of element connections were examined including switched series, switched parallel, and

unswitched parallel. The results of NEC for each of the arrays are plotted as k-P

diagrams to compare to the standard arrays.

The results of the investigation show that the Snyder dipole provides more

operational bandwidth than a standard dipole, but when placed in a uniform array

there is no more bandwidth than that of a conventional uniform array.

/

TABLE OF CONTENTS

I. INTRODUCTION 8

A. THE LOG-PERIODIC ANTENNA 8

B. THE LOG-PERIODIC DIPOLE ARRAY 9

C. CHARACTERISTICS OF SUCCESSFUL LOG-PERIODIC ANTENNAS 11

D. THE LPDA WITH COAXIAL ELEiMENTS 11

II. DEVELOPMENT OF THE SNYDER DIPOLE 13

A. THE NUMERICAL ELECTROMAGNETICS CODE 13

B. PROCEDURE FOR OBTAINING OPTIMUM SNYDERDIPOLE 13

III. K-BETA DIAGRAMS 17

A. K-BETA DIAGRAM DESCRIPTION 17

B. OBTAINING THE K-BETA DIAGRAM DATA USINGNEC 18

IV. EXPERIMENTAL PROCEDURES AND RESULTS 20

A. CHARACTERISTICS OF UNTAPERED ARRAYS 20

B. DEVELOPMENT OF THE SNYDER LPDA 20

C. EXPERIMENTAL RESULTS 21

1. Switched Series Array 21

2. Switched Parallel Array 23

3. Unswitched Parallel Array 32

D. COMPARISON OF SNYDER ARRAY TOCONVENTIONAL ARRAY 32

V. CONCLUSIONS AND RECOMMENDATIONS 44

APPENDIX A: NEC DATA SETS 46

APPENDIX B: NEAR-MAGNETIC FIELD PLOTS FOR SNYDERSWITCHED SERIES ARRAYS 48

APPENDIX C: NEAR-MAGNETIC FIELD PLOTS FOR SNYDERSWITCHED PARALLEL ARRAYS 87

APPENDIX D: NEAR-MAGNETIC FIELD PLOTS FOR SNYDERUNSWITCHED PARALLEL ARRAY 132

APPENDIX E: NEAR-MAGNETIC FIELD PLOTS FOR STANDARDELEMENT ARRAYS 147

LIST OF REFERENCES 162

INITIAL DISTRIBUTION LIST 163

LIST OF FIGURES

1.1 Log-periodic Toothed Planar Antenna (from Ref. 2) 9

1.2 Log-periodic Dipole Array (from Ref. 2) 10

1.3 Connection of LPDA Elements (from Ref. 3) 10

1.4 The Snyder Dipole (from Ref. 5) 12

2.1 Dipole and Transmission Line Susceptances 15

2.2 Standard Dipole and Snyder Dipole Bandwidths 16

3.1 k-p Diagram (from Ref. 8) 17

4.

1

Types of Voltage Feed 22

4.2 k-P Diagram for a Snyder Switched Series Array. Element Spacing =

1/8 Wavelength 24

4.3 Attenuation of a Snyder Switched Series Array. Element Spacing =

1/8 Wavelength 25


1/4 Wavelength 26


1/4 Wavelength 27


3/8 Wavelength 28


3/8 Wavelength 29

4.8 k-p Diagram for a Snyder Switched Parallel Array. Element Spacing

= 1/8 Wavelength 30

4.9 Attenuation of a Snyder Switched Parallel Array. Element Spacing =

1/8 Wavelength 31

4.10 k-P Diagram for a Snyder Switched Parallel Array. Element Spacing

= 14 Wavelength 33


1/4 Wavelength 34

4.12 k-p Diagram for a Snyder Switched Parallel Array. Element Spacing

= 3/8 Wavelength 35


3/8 Wavelength 36

4.14 k.-P Diagram for a Snyder Unswitched Parallel Array. Element

Spacing = 1,4 Wavelength 37

4.15 Attenuation of a Snyder Unswitched Parallel Array. Element Spacing

= 1/4 Wavelength 38

4.16 k-p Diagram for a Standard Switched Parallel Array. Element

Spacing = 3, 8 Wavelength 40

4.17 Attenuation of a Standard Switched Parallel Array. Element Spacing

= 3/8 Wavelength 41

4.18 k-P Diagram Comparison 42

4. 19 Attenuation Comparison 43

I. INTRODUCTION

A. THE LOG-PERIODIC ANTENNA

The log-periodic antenna (LPA) is structured so that its impedance and radiation

characteristics repeat periodically as the logarithm of frequency. The variations over

the operational frequency are minor so that the LPA is considered to be frequency

independent.

The LPA design is based on relatively simple ideas that produce bandwidths of

operation that were considered impossible several decades ago. One of these ideas is

the angle condition which specifies an antenna array by angles only and not by specific

dimensions. In this case the antenna is self-scaling and eliminates the dependence on

its characteristic length and operating frequency. The second idea is that if an antenna

array's dimensions are scaled by a factor X, it will exhibit the same properties at one

frequency as at r times that frequency. These properties are a periodic function of the

logarithm of frequency with the period of log t. Thus the term log-periodic is used to

describe these types of antennas. [Ref. 1]

The first successful LPAs were discovered by R.H. DuHamel and D.E. Isbell in

the late 1950s. Many unsuccessful attempts were log-periodic but produced

unacceptable variations of pattern and impedance over a period. One of the first

successful LPAs was the log-periodic toothed planar antenna (Figure 1.1). Current

flows out along the teeth and is insignificant at the ends. The ratio of edge distance is

a constant factor given by:

T=Ra,l/

Rn<1 (eqnl.l)

The slot width is:

*=an/Rn <l (eqnl.2)

The scaling factor t gives the period of the antenna. The frequencies f j and f lead

to identical performance so the antenna is logarithmically periodic. [Ref. 2: p.290]

Figure 1.1 Log-periodic Toothed Planar Antenna (from Ref. 2).

B. THE LOG-PERIODIC DIPOLE ARRAY

After a few years of experimenting, Isbell developed the log-periodic dipole array

(LPDA), an array of parallel wire dipole elements of increasing length outward from

the apex feed point (Figure 1.2). He used a parallel load with switched phase from one

element to the next. This is still the most common method used, although other feed

types have also been used successfully. [Ref. 3: p. 55]

The switched feed in I shell's LPDA produces a 180 degree phase shift between

elements. The elements near the input nearly cancel since they are close together and

almost out of phase. As the spacing between elements (d) increases, the phase delay in

the transmission line combined with the 180 degree phase shift gives a total of

360(l-d.A* degrees. The radiated fields of the two dipoies are then d apart in phase in

the backward direction. Moving further out increases :!l1q phase deiay, causing the in-

phase direction to move from backward to broadside to forward radiation. If the

elements are resonant with the total phase delay from one element to the next equal to

about 360(1 -d/X) degrees, a good beam is generated off the apex. Due to this

condition, the transmission line power is exhausted before the phase changes very

much.

Figure 1.2 Log-periodic Dipole Array (from Ref. 2).

The antenna is fed by running a coaxial line inside one side of the boom and

connecting its inner conductor to the other side at the input (Figure 1.3) [Ref. 3: p. 71].

This forms a parallel feed with switched phasing between the elements. This method of

current feed will be investigated and applied in this thesis as will series switched and

parallel unswitched feeds.

Feed point

Figure 1.3 Connection of LPDA Elements (from Ref. 3).

10

C. CHARACTERISTICS OF SUCCESSFUL LOG-PERIODIC ANTENNASThere are several characteristics associated with log-periodic antennas. By

definition, the electrical properties must repeat penodicaily with the logarithm of the

frequency to help ensure broadband performance. To maintain frequency

independence, the electrical properties must vary only slightly over a period, and the

current must decay rapidly over an active region to eliminate end effects caused by

truncation of the electrical length of the antenna. The log-periodic antenna must also

produce backward wave radiation (towards the feed point). Backward radiation can be

determined by observing an antenna array with the feed point on the left. As the wave

travels to the right, backward radiation occurs if the magnitude of the current is

sharply attenuated as it moves across the left most element of the active region and the

phase increases in the element on the right. This will cause the antenna to radiate at

the feed point to the left with a null to the right. Thus the wave has propagated in the

backward direction. [Ref. 4]

D. THE LPDA WITH COAXIAL ELEMENTS

Many LPDAs have been designed and built over the last thirty years. What

makes this research unique is the use of dipoles made of coaxial transmission line. The

coax dipole was patented in 1984 by Mr. Richard D. Snyder and will be referred to as

the "Snyder dipole" throughout the remainder of this text to differentiate it from the

conventional wire dipole. The Snyder dipole (Figure 1.4) is constructed using coaxial

transmission line for the inner portions of its segments, connected so that the outer

conductor acts as part of the radiator, and the inner and outer conductors of the coax

form compensation stubs. The stubs' impedances vary with frequency in such a way as

to cancel the dipole reactance normally exhibited with frequency change, and can be

connected in series or parallel. The coax conductors are shorted together at one end of

the line so that the non-radiating conductor combines with the second conductor to

form an impedance modifying stub and the second conductor forms part of the

antenna segment [Ref. 5]. This leads to a larger operational bandwidth than in the

conventional aipole.

If an LPDA using Snyder elements proves successful, it will have many

advantages in field use over the conventional LPDA, particularly at lower frequencies

with long wavelengths. Advantages include allowing a larger deviation from the

operating frequency, lighter weight, more rugged, and more easily transportable since

the conventional LPDA would require much thicker (and therefore heavier) elements to

11

J^

Figure 1.4 The Snyder Dipole (from Ref. 5).

achieve the same bandwidth. Since many of the advantages are size and weight related,

the analysis presented herein will be performed on antenna arrays operating in the high

frequency (HF) band at 3.88 Megahertz (MHz) with a wavelength of 77.3 meters.

12

II. DEVELOPMENT OF THE SNYDER DIPOLE

A. THE NUMERICAL ELECTROMAGNETICS CODEAll antennas in this research were modeled on an IBM main-frame computer

using the Numerical Electromagnetics Code (NEC) version three. NEC was developed

by the Lawrence Livermore Laboratory for the Naval Ocean Systems Center (NOSC).

It is a user-oriented computer code used to analyze antennas or other metal structures

based on the use of numerical solutions of integral equations for currents induced on

the structure by an incident plane wave or a voltage source [Ref. 6]. Outputs from

NEC include current and charge density, voltage standing wave ratio (VSWR), near

electric or magnetic fields, and radiated fields. Single and double precision versions are

available for better accuracy as well as versions that allow for large numbers of

networks or wires.

B. PROCEDURE FOR OBTAINING OPTIMUM SNYDER DIPOLE

The goal for the optimum Snyder dipole was to achieve the widest bandwidth

possible with a VSWR no greater than 2:1 without exceeding size constraints. Since

the operational bandwidth of a dipole increases as the diameter increases, this effort

was restricted to 0.3 inches in diameter, about the size of standard coaxial transmission

cable. This way the design is consistent with the stated advantages of light weight,

ruggedness, and transportability.

The Snyder dipole was modeled on NEC as a standard dipole with two

transmission lines in parallel to simulate the coax segments of the antenna. The first

step was to model a standard half-wave dipole. It was based on a frequency of 3.88

MHz which has a wavelength of 77.3 meters. The dipole was modeled for free space

propagation with no ground plane and the transmission line segments were modeled as

one-fourth wavelength stubs. Both the dipole and the transmission lines were swept

through a frequency range of 3.5 to 4.2 MHz with a resulting output of admittance at

each frequency. The susceptance (imaginary part of the admittance) for the dipole was

capacitive below resonance and inductive above resonance. The susceptance for the

parallel transmission lines was inductive below resonance and capacitive above

resonance, the opposite of the dipole. The impedance of the transmission lines were

then varied until a value was found which provided maximum cancellation of the

13

dipole susceptance. The addition of the transmission line and dipole impedances are

shown in Figure 2.1. A value of 50 ohms for each of the parallel transmission lines

was found to best counter the susceptance characteristics of the dipole. The

transmission lines and dipole were then combined to model the Snyder dipole with the

transmission lines acting as the compensation stubs that cancel the antenna reactance

normally associated with frequency change. This is what makes the Snyder dipole

more broadband than the conventional dipole.

The next step entailed the modeling of the Snyder dipole using NEC, and

tweaking the input impedance, or balun load, so as to produce the largest bandwidth

possible with a VSWR not greater than 2:1. The model used for the Snyder dipole is

given in Appendix A, and the comparison of bandwidth for the Snyder dipole and the

standard dipole is shown in Figure 2.2. The standard dipole bandwidth is about 6

percent while the Snyder dipole bandwidth is over 16 percent. The standard dipole

diameter shown is equal to the thin segments of the Snyder dipole. A standard dipole

diameter equal to the thick portions of the Snyder dipole produced a bandwidth of

about 9 percent, so even in the worst case the Snyder dipole still gives a bandwidth

gain of well over 50 percent compared to a conventional dipole. The bandwidths are

based on the formula:

BW=2(f2-f

1)/(f

2+ f

1) (eqn2.1)

where f2and ^ are the upper and lower points where each frequency curve crosses the

line equal to a VSWR of 2:1. Hansen [Ref. 7] shows larger bandwidths in both cases,

but he used a much higher antenna diameter-to-length ratio. As mentioned earlier, this

effort was confined to coaxial transmission line diameter, but as a check a NEC run

was made using Hansen's diameter-to-length ratio. The resulting bandwidth was close

to that calculated by Hansen with NEC giving a slightly larger bandwidth. The Snyder

dipole was also run with a double precision version of NEC to check accuracy. The

results varied by less than two percent, so the remaining NEC runs used only single

precision to conserve computer resources and costs. The bandwidth displayed by the

NEC model of the Snyder dipole was consistent with Mr. Snyder's claim.

The next step in the analysis was to see if an LPDA built with Snyder dipole

elements would either increase the bandwidth or provide the same bandwidth with

fewer elements than the conventional LPDA. Before presenting the experimental

procedures, it is appropriate to discuss the characteristics of LPDAs.

14

PU

OP

sio-o oitro 500*0 OOO'O

SOHW900-0- OTO-0- QIO'O-

Figure 2.1 Dipole and Transmission Line Susceptances.

15

©o*

<>—

,

r*>o —

'

<* OWC/3

COOJ 273 ^g —

<

—

i

-20> >—

'

«« >, HU Q

co Z P0= W 2P3 JD CO

orIIH

s « <w fo i—

i

QQ

CO 03t">; Qn 2

F»4 COP-

n

toas

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—an

ovO

n

HMSA

Figure 2.2 Standard Dipole and Snyder Dipole Bandwidths.

16

III. K-BETA DIAGRAMS

A. K-BETA DIAGRAM DESCRIPTION

One of the characteristics of an LPDA mentioned in chapter one is that of

backward radiation. It is possible to tell whether or not an array possesses the

capacity for backward radiation by the use of a k-p diagram, also called a dispersion or

Brillouin diagram (Figure 3.1).

ki d

•Broads idahFast waveregion

|FWR|

— (3d

Figure 3.1 k-P Diagram (from Ref. 8).

This diagram is obtained by plotting the free space constant k versus the

propagation constant P (or kd versus Pd where d is the antenna element spacing). It is

only necessary to show one period since the log-periodic antenna characteristics repeat

every 27t. For free space propagation:

k=P =:-;"/. (eqn 3.1)

According to Mittra and Jones [Ref. 9: p. 20], the k-P diagram can be separated

into three different frequency regions. These are the propagation (P) region, the

complex (C) region, and the radiation (R) region. The propagation region corresponds

to the feed excitation region in the antenna and has little or no attenuation. The

17

complex region occurs at p = ±n and acts as a stopband where the attenuation is high

but coupling to space is poor, so the complex region does not facilitate radiation. The

third region, the radiation region, is where an antenna is an efficient radiator. It is also

where fast waves occur, that is, where k is greater than p. The radiation region can be

divided into an Rr region, for forward radiation (away from the feed), and the Rb

region, for backward radiation (towards the feed). The most successful iog-penodic

antennas have radiation occurring in the Rb

region near the line where P= — k. The

Rbregion should also have a large amount of attenuation to facilitate radiation into

space. It is these characteristics of the k-P diagram that will be used to determine if

the Snyder LPDA has the possibility of producing backward radiation with high

attenuation and becoming a good log-periodic antenna.

B. OBTAINING THE K-BETA DIAGRAM DATA USING NEC

To determine P, the amplitude and phase of the current along the transmission

feed line can be measured in the near field of the antenna array at different frequencies.

Early experimenters used a current loop placed in the near magnetic field of the

antenna elements and measured actual values for the current phase and amplitude in

relation to a reference point. For this thesis, "experimental data" was gathered by the

use of NEC to determine the amplitude and phase of the near magnetic fields. The

near field is usually considered to extend to O.lX. NEC requires near field calculations

be taken at no closer than 0.00 IX, so several runs were performed taking magnetic field

calculations at distances of 0.002X and 0.0 IX. A comparison of the two distances gave

a magnitude difference of less than two percent and a phase difference of less than ten

percent. All NEC information used in the final analysis was near field calculations

taken at a distance of 0.01X.

When NEC is programmed for near magnetic fields at one frequency, the output

is the magnitude in amps per meter and the phase in degrees. These values are given

for the X, Y, and Z directions at each antenna element. The X direction magnetic

fields were used for the analysis since the antenna array was placed in the X-Y plane

with "he wave propagating in the X direction. Using a plotting program, the phase

vaiues were plotted for each type of antenna feed at several different frequencies and

element spacings. The slope of each plot was then multiplied by the element spacing

(d) and converted to radians to produce one point on the k-p (or more specifically, kd-

Pd) diagram. The current magnitude output was used to derive a in the complex

propagation equation:

18

Y=a^-jP (eqn 3.2)

These values were plotted using the same plotting program as before. The ratio of

maximum to minimum amplitude was converted to decibels per meter, divided by the

distance over which it varied, and then multiplied by the antenna element spacing to

produce one point on the attenuation plot.

The k-p and attenuation diagrams for the Snyder uniform array are presented

and discussed in the next chapter. By comparing the diagrams of the Snyder array with

those of a conventional array, it will be possible to determine whether or not the

Snyder array shows any improvement over the conventional uniform array.

19

IV. EXPERIMENTAL PROCEDURES AND RESULTS

A. CHARACTERISTICS OF UNTAPERED ARRAYS

The LPDA is made up of elements tapering in length from the longer, low

frequency elements to the shorter, high frequency elements at the feed point. An

untapered version of the LPDA, called a uniform array, was used to simplify the

modeling necessary for NEC. Mittra and Jones [Ref. 9: p. 21] describe the k-0

characteristics required of the untapered counterpart of a potentially successful tapered

log-periodic antenna.

Starting from small values of k, the untapered antenna shall have a continuous P

region, immediately beyond which it moves into an Rb

region. If the Rb

region

is quite efficient (if the coupling to space for the wave in this region is farily (sic)

effective), it is immaterial what the k-p properties of the structure are beyond the

R region. However, if the P region is interrupted by a C or Rfregion ahead of

the Rb

region, the tapered structure derived from it will be a potentially

unsuccessful broadband antenna. It is therefore quite important to distinguish

between the C and R regions as previously defined.

It is also important to have high attenuation in the Rbregion for proper coupling of

the wave to space. These guidelines will be applied to the k-0 diagrams derived from

the NEC runs for the various antenna array configurations.

B. DEVELOPMENT OF THE SNYDER LPDA

The antenna modeled as the Snyder uniform array contains 10 elements, each

identical to the Snyder dipole (see the NEC code in Appendix A). Each element

consists of a 1/4 wavelength (at 3.88 MHz) center section and a 1/8 wavelength section

on each end. The center section is 0.296 inches in diameter and simulates the coaxial

transmission line section of the Snyder dipole by connecting the middle segment to 1/4

wavelength stubs. These are rhe stubs that were described earlier that cancel the dipole

reactance in the Snyder dipole. They are open-circuited at the element end and short-

circuited at the stub end to produce the desired results. The 1/8 wavelength end

sections are 0.144 inches in diameter, barely stretching the NEC requirement that

adjacent wire segments not vary in size by more than two to one. A 300 ohm

transmission line connects each element and the voltage source.

20

The elements were laid horizontally in the X-Y plane with the voltage source 1/4

wavelength from the array in the minus X direction, and the 300 ohm transmission line

terminated in a matched impedance 1/4 wavelength from the array in the plus X

direction. The near magnetic fields were calculated in the Z direction at 0.8 meters,

approximately equal to 0.01X, above the center of each element. The near field values

were calculated for several different frequencies for each array configuration. As

mentioned in the section on k-p diagram data, the plotted values for each frequency

form one point on the k-P and attenuation diagrams. Other sets of k-P and

attenuation diagrams were formed by changing the distance between the elements in

the array. If the elements can be spaced further apart in the Snyder LPDA without

losing any bandwidth, then maybe fewer elements would be necessary than in the

conventional LPDA. Different types of voltage feed were also modeled on NEC for

comparison and discussion in the next section (Figure 4.1). The use of the word "feed"

may be a poor choice since it refers to the way the elements are loaded, not the order

in which the voltage is supplied to the elements. All of the antenna configurations

modeled in this thesis receive excitation by means of a coaxial transmission line

running between adjacent elements.

C. EXPERIMENTAL RESULTS

1. Switched Series Array

The switched series feed connects the antenna array elements in series with a

180 degree phase shift between each element. This method is not commonly used for

LPDAs, but was tried since suggestions in various conversations led to the idea that

the switched series feed might produce good results when using Snyder dipole elements.

The k-P and attenuation diagrams for a switched series fed array are presented

in Figures 4.2 and 4.3. The element spacing (d) is 1/8 wavelength for a frequency of

3.88 MHz, which is the resonant frequency of the dipole element. All array element

spacings in the remainder of this study will also be in reference to the resonant

frequency of the dipole element. Following the guidelines of the previous section, these

figures show two areas of backward radiation, one extending from the low kd vaiues up

to 0.77 and the second from 0.82 to high kd values. The kd value of 0.77 corresponds

to a frequency of 3.81 MHz and 0.82 equals 4.04 MHz. Even though both of the

backward radiation (Rb ) regions are preceded by a propagation region, the attenuation

never goes above 5 decibels (dB), which is not enough to facilitate coupling of the wave

into space. An attenuation of about 15 dB or higher in the Rbregion is necessary for

21

-*-

Switched Series

-r

Switched Parallel

Unswitched Parallel

Figure 4.1 Types of Voltage Feed.

22

propagation. The highest attenuation of 7.5 dB occurs in the forward radiation (Rf)

region which will not allow proper radiation from the antenna.

Figures 4.4 and 4.5 show results for a switched series fed array with the

element spacing equal to 1/4 wavelength. The k-P diagram is basically the same as for

1/8 wavelength except it is shifted up in frequency (up the kd axis). The major

difference here is that the attenuation is occurring in the Rbregion where it is needed,

but it is too low to readily induce radiation into space. It should be noted that the

NEC run at 3.81 MHz (kd= 1.54) was not used in the diagrams since the NEC

calculations showed characteristics of a standing wave or improper impedance that is

nonconducive to a successful LPDA.

In the k-P and attenuation diagrams for an element spacing of 3/8 wavelength

(Figures 4.6 and 4.7), the attenuation is fairly strong in the Rb

regions, particularly

between 2.4 and 2.6 (3.96 to 4.29 MHz). This is still a relatively low attenuation value

with a narrow bandwidth. The results of the switched series feed models show very

little potential for a successful log-periodic antenna. The near field NEC plots for the

various switched series arrays are shown in Appendix B.

2. Switched Parallel Array

The switched parallel voltage feed is the most common method used to excite

LPDAs. This method consists of loading the array elements in parallel and inducing a

180 degree phase shift between each element. The switched parallel feed was the one

used by Isbell to produce the first successful LPDA.

The diagrams for a switched parallel feed with an element spacing of 1/8

wavelength (Figures 4.8 and 4.9) show a broad Rb

region, but the attenuation is never

any greater than about 5 decibels. Prospects for a successful LPDA are poor in this

case due to the low attenuation.

23

Figure 4.2 k-p Diagram for a Snyder Switched Series Array.

Element Spacing = 1/8 Wavelength.

24

0.0 1.3 2.0 3.0 4.0 5.0 -3.0 7.0 3.0 9.0 10.0 11.0 12.0 13.0

ATTENUATION (DB)

Figure 4.3 Attenuation of a Snyder Switched Series Array.


25

03

Q •

N

03

i\ N

2.4 -2.0 -1.6 -1.2 -0.3 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4

BETA D



26

CO

o

Q «

flO

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0

ATTENUATION (DB)



27



28

Q 9

1 1 1 \! i II II I

^—

"""rrt44 Mill|

|

H; Mill|| X M II M !

0.3 1.0 2.0 3.0 4.0 5.0 6.0 7.0 3.0 9.0 10.0 11.0 12.0 13.0

ATTENUATION (DB)



29

N

=3

G

gq

j :

; :

/

d

d

-2.4 -2.0 -1.6 -i.2 -0.;) -0.4 0.0 0.4 0.3 1.2 L.8 2.0

BETA D

Figure 4.8 k-p Diagram for a Snyder Switched Parallel Array.


30

Q

w

:: I ::[•;! :

—

CO H 1 :: MiO ~

«0

b -

d

0.0 1.3 2.0 3.0 4.0 5.0 6.0 7.0 8.0 3.0 LO.O 11.0 12.0 13.0

ATTENUATION (DB)

Figure 4.9 Attenuation of a Snyder Switched Parallel Array.


31

The k-{3 and attenuation diagrams for a 1/4 wavelength element spacing

(Figures 4.10 and 4.11) show much improvement over those of the 1/8 wavelength

spacing. A broad Rb

region exists up to kd equal 1.65 (4.10 MHz) with high

attenuation in at least part of that region. This is conducive to backward radiation, a

key characteristic of successful log-periodic antennas. The second area of high

attenuation occurs in an Rfregion and thus that portion of the frequency band would

not radiate well.

Figures 4.12 and 4.13 show a switched parallel array with the elements spaced

3/8 wavelengths apart. This configuration produced the highest attenuation in an Rb

region indicating good coupling to space, but the backward radiation region is only

from 2.2 to 2.45 which corresponds to 3.63 to 4.04 MHz. This antenna meets the

requirements of being a backward radiator with high attenuation but does not meet the

design goal of having a broad operating frequency.

A switched parallel feed NEC run was made with the elements spaced at 1/2

wavelength with poor results. Almost every frequency contained characteristics of a

standing wave or improper input impedance to the elements. There were no k-j5 or

attenuation diagrams produced for this configuration, but plots of the NEC results are

included in Appendix C with the other switched parallel antennas.

3. Unswitched Parallel Array

An unswitched parallel or straight feed configuration at 1/4 wavelength

element spacing (Figures 4.14 and 4.15) did not produce good results. In this case,

there is no phase shift between the elements. Phase shift seems to be a necessary

characteristic of a good log-periodic antenna as Isbell found out when he designed his

first LPDAs. The k-p diagram shows a very broad band Rbregion but the attenuation

is too low to accomplish radiation. The results in this case were as expected. The near

field plots for this array make up Appendix D.

D. COMPARISON OF SNYDER ARRAY TO CONVENTIONAL ARRAYThe results of the previous section indicate the switched parallel array with 3/8

wavelength element spacing holds the most potential for becoming a successful LPDA.

It produced high attenuation in the Rbregion as is required for a log-periodic antenna.

To determine if the design goal of producing more bandwidth than a conventional

LPDA has been met, a uniform array with standard elements was modeled in NEC.

All characteristics were modeled exactly the same as the Snyder dipole except that

32

cvi"

=

-2.4 -2.0 -1.6 -1.2 -0.8 -0.4- 0.0 0.4 0.8 1.2 1.6 2.0 2.4

BETA D



33

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10. 11.0 12.0 13.0

ATTENUATION (DB)



34

N

T)

n

—

: /

: /

: /

3.0-2.8-2.2-1.8-1.4-1.0-0.6-0.2 0.2 0.6 1.0 1.4 1.8 2.2 2.6 3.0

BETA D



35

M

aN~

**

e\i~

o

—

Q •

—

CD

d -

1 ! 1

d -

C _

1 2 3 4- 5 8 7 3 9 10 11 12 13 14 15 18 17 13

ATTENUATION (DB)


Element Spacing =3/8 Wavelength.

36

CM

CM

Q *

a

-2.4: -2.3 -i.o -1.2 -0.3 -0.4 0.0 0.4 Q.3

BETA Dl.d 2.0 2.4

Figure 4.14 k-p Diagram for a Snyder Unswitched Parallel Array.


37

PS"

o

evi

CD

O

SO

c

CM

d

0.0 1.0 2.0 3.0 4.0 5.0 d.O 7.0 3.0 9.0 iO.O 11.0 12.0 13.0

ATTENUATION (DB)

Figure 4.15 Attenuation of a Snyder Unswitched Parallel Array.


38

there are no coaxial transmission line sections and the input impedance to each

element is 73 ohms, the same as that used in the standard dipole in chapter two. The

same values were used for the physical dimensions, element spacing, transmission feed

lines, voltage excitation, near field measurements, and frequencies.

The resulting k-P diagrams for the conventional array are Figures 4.16 and 4.17.

These diagrams show very similar results as those for the 3/8 wavelength Snyder array

(Figures 4.12 and 4.13). The Rband R

fregions are about the same in both cases, as

are the attenuation curves. The highest attenuation in both cases is about 17.5

decibels in the Rb

region. The frequency bands of the Rbregions are almost identical

so that there appears to be no bandwidth gain in the Snyder array. A direct

comparison of the two arrays is presented as Figures 4.18 and 4.19.

A standard dipole array with 1/2 wavelength element spacing was also modeled

with NEC, but the results were as poor as the 1/2 wavelength Snyder switched parallel

array. The near field plots for the 3/8 and 1/2 wavelength standard dipole arrays are

included as Appendix E.

39

3.6

Figure 4.16 k-P Diagram for a Standard Switched Parallel Array.


40

o

i

-i

!

_a-

| \

-

i \

KD

i)

06

1.2

18

2

-

o_^

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ATTENUATION (DB)

Figure 4.17 Attenuation of a Standard Switched Parallel Array.

Element Spacing =3/8 Wavelength.

41

Figure 4.18 k-P Diagram Comparison.

42

ATTENUATION (DB)

Figure 4.19 Attenuation Comparison.

43

V. CONCLUSIONS AND RECOMMENDATIONS

This thesis examined the feasibility of designing a log-periodic dipole array with

more operational bandwidth per element than the LPDAs currently in use. To

accomplish this, a Snyder dipole made of coaxial transmission line was modeled using

the Numerical Electromagnetics Code (NEC). It was then placed in a uniform array

and different configurations were tried by varying the type of feed and the element

spacing. The performance of each antenna was then based on the k-P and attenuation

diagrams created from the NEC output.

The first conclusion one can draw from the NEC results is that a Snyder dipole

can be designed and built with an operational bandwidth greater than that of a

standard dipole. This greater bandwidth will then allow a larger deviation in the

operating frequency without serious degradation of the impedance match. Another

advantage of the Snyder dipoie is chat it achieves the same bandwidth as a standard

dipole of larger diameter, and therefore reduces the weight.

The second conclusion drawn from the research is that the NEC model for the

Snyder dipole is accurate since the results are consistent with the designer's claims and

other antenna models. Since nothing was found in the literature to reference on the

use of coaxial transmission line elements in. uniform arrays, it is assumed the NEC

model for the array is also accurate. The k-P and attenuation diagrams showed that

backward radiation was produced at some frequency for every kind of feed and element

spacing used, but the attenuation was often so low that no radiation from the antenna

could occur. For the case where there was high attenuation, the bandwidth was no

better than that of a standard array of the same element spacing. This leads to the

final conclusion; the Snyder dipole does not improve the bandwidth of a conventional

uniform array.

The results of the Snyder uniform array data are disappointing, but before

completely disregarding the Snyder dipoie as an LPDA element, it is recommended that

the effort of this study be continued by modeling a uniform array over various grounds

to see if there is any advantage in using the Snyder dipole in that situation. It is also

recommended that a Snyder LPDA be modeled on NEC. This study showed that the

Snyder uniform array performed no better than a standard uniform array, but the

44

characteristics of the mutual impedance of the Snyder LPDA elements may prove

advantageous in a tapered array. Modeling a Snyder LPDA may require a new set of

design nomograms based on input impedance since the nomograms currently used for

standard LPDAs may not be applicable. If the same conclusions are reached as those

from this research, the Snyder dipole array should be removed from consideration as a

potentially successful LPDA.

It should be noted that even though the Snyder dipole failed as a uniform array,

it did produce excellent results as a single dipole. The Snyder dipole should be

considered for any use where an increased dipole bandwidth is desired or necessary,

particularly if coaxial transmission cable can be used to maximize the performance.

45

APPENDIX ANEC DATA SETS

CM

CM THE SNYDER DIP0L5 (WITH DOUBLE RADIUS SEGMENTS,

CM COMPARED TO SNYDER'S DIMENSIONS;

CM

CM 3.540 - 4.234 MHZ

CM

CM HALF HAVE HIGH IN FREE SPACE

CM

CM LI » 31.46*

CM 01 * .296"

CM L2 » 31. 66'

CM 02 « .144-

CM 20 » 25 OHMS (TWO SO OHM LINES IN PARALLEL;

CM

CM ZNORM « 145 OHMS (BALUN LOAD)

CM

cs

GW 1,5. -63.32.0.0, -31.66,0,0, .006 END PORTION/EQUAL LENGTH SEGS

GM 2,15. -31.66.0.0. 31.66.0,0. .0124 CENTER PORTION/EQUAL LENGTH SEGS

GW 1,5, 31.66.0.0, 63.32,0,0, .006 OTHER END

GM 0,0. 0,0.0, 0.0.131.5. 001.003 RAISE UP TO HALF WAVE

GW 90.1. 0.0,0. 0.0.1. .0001 T.L. SHORT CIRCUIT WIRE

GM 0.0, 0,0,0, 2000,0.0. 090.090 MOVE IT WAY OUT

GS 1 FT TO METERS

GE

PT -1.1.1.1 SUPPRESS CURRENT PRINTOUT

TL 2.3.90.1. 25.0,19.30. 0.0.1ES.1E6 T.L. STUB

EX 0.2.8.01. 1.0.145 FEED CENTER/ASK FOR IMPEDANCE TABLE

FR 1.30.0.0. 3.560.1.006 30 FREQS/MULTIPLICATIVE STEPPING

xo

EN

46

JNIFORM SNYDER OIPOLS ARRAY

(SWITCHED SERIES FSED3

OIPOLE: LENGTH* 1/4 LAMBDA AT FREO* 3. 88 MHZ

SEGMENT LENGTHS* 31.66 FT

THIN DIAMETER" 0.i«- » 0.30133 METER RADIUS

THICX DIAMETER* 0.296" * 0.00376 METER RADIUS

10 ELEMENT ARRAY

ELEMENT SPACING * 1/3 WAVELENGTH (23.95 METERS)

20* CS OHMS (TWO 50 OHM LINES IN PARALLEL.

12.5 3ESIDE 12.5 IN PARALLEL)

Z-NORM * 145 CHMS (BALUN LOAD)

Z-FEED LINES » 300 OHMS

CM

CM

CM

CM

CM

CM

CM

CM

CM

CM

CM

CM

CM

CM

CM

CM

CM

CE

GW 10.5. 0.-19.30.0. 0.-9.65.0. 0.00183

GM 20.16. 0.-9.65.0. 0.9.65.0. 0.00376

GM 30.5. 0.9.65.0. 0.19.30,0. 0.00183

GM 1.9. 0.0.0. 28.95.0.0. 010.030

GW 40.1. 0.0.0. 0.0.1. 0.0001

GM 1.21. 0.0.0. 28.95.0.0. 040.040

GM 3.3. 3.3.3. '.300.3,3. 340.361

3M 3.3. 3.3.3. 3. 0. 38.a. 310.361

GE 3

TL 20.8.40.1.12.5.19.30.0.0.1E6.1E6

TL 20,9,41.1.12.5.19.30.0,0.1E6,1E6

TL 21,a.42.:,I2.5.19.30.0.3.1E6.;E6

TL 21.9.43.i.l2.S.;9.30.3.a.IE6.iE6

TL 22.8.44. 1. 12. S, 19. 30. 3.3.;E6.;E6

TL 22, 9, 45, 1,12.5.19. 30. 3,3, 1E6.1E6

TL 23.3.46.1.12.5.19.30.0.0.1E6.1E6

TL 23.9.47.1.12.5.19.30.0.0.1E6.1E6

TL 24.3.48.1.12.5.19.30.0.0.1E6.1E6

TL 24.9.49.1.12.5.19.30.0.0.1ES.1E6

TL 2S.8.50.1.12.5.19.30.0.0.IE6.1E6

TL 25.9.51.1.12.S.19.30.0.0.1E6.1E6

TL 26.8.52.1.12.5.19.30.0.0.1E6.1E6

TL 26.9.53.1.12.5.19.30.0.0.1E6.1E6

TL 27.8.54.1.1Z.5.19.30.0.0.1E6.1E6

TL 27.9.55.1.12.5.19.30.0.0.1E6.1E6

TL 28.8.56.1.12.5.19.30.0.0.1E6.1E6

TL 28.9.57.1.12.5.19.30.0.0.1E6.1E6

TL 29.8,S8,1.12.5.19.30.0.0.1E6,1£6

TL 29.9.59.1.12.5.19.30.0.0.1E6.1E6

TL 60.1.20.8.300.19.30.0.0,0.0

TL 23.9.21,8,300, ,0,0.0,0

OR

TL 21,9,22,3,300, ,0,0,0,0

TL 22,9.23.8,300, ,0.0,0,0

TV. 23, 9,24,3.330. .3.3.3.3

TL :'-. 5,25.3,333, .J. J, 3.

3

It, ;5.9.25,<J,.:33, .3,3.3.3

n. 25,9.27,3,300. ,3.i,i,0

TL 27.9.23,8.300. ,0.0.0.0

TL 28.9.29.8.300. .0.0.0,0

TL 29.9.61,1,300. 19.30.0,0.0.0033.0

EX 0.60.1.01.1.0. 145

FR 0.1.0,0,3.33.0

PL 2.2,1.1

NH 0,10,1,1,0,0.0 .8.23.95.0.0

XQ

EN

FIRST THIN SEGMENT

MIDDLE THICX SEGMENTS

OTHER THIN SEGMENT

9 MORE, 3/3 LAMBDA APART

TL SHORT CKT STUB S FEED LINES

19 MORE TL SLU3S * 2 FEEDS

MOVE TL STUBS 1 FEED LINES OUT

RAISE ARRAY LAMBDA/2 HIGH

TL STUBS (2 PER ELEMENT)

TL STUBS COMPLETE

FEED LINE TO THE ARRAY

START SWITCHED SERIES FEED

STRAIGHT LINE METHOD USED

FOR 3LANK T.L. LENGTH

FEED LINES END 9 MTCHD IMPDNCE

EXCITE ARRAY/ASK FOR IMP TABLE

1 FREQUENCY

STORE NEAR FIELD X-COMPONENT

NEAR FIELD DATA, 0.8 METER UP

47

APPENDIX BNEAR-MAGNETIC FIELD PLOTS FOR SNYDER SWITCHED SERIES

ARRAYS

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LIST OF REFERENCES

1. Johnson, Richard C. and Jasik, Henry, Antenna Engineering Handbook, McGraw-Hill Book Company, New York, 1984.

2. Stutzman, Warren L., and Thiele, Gary A., Antenna Theory and Design, John

Wiley and Sons, New York, 1981.

3. Rumsey, Victor H., Frequency Independent Antennas, Academic Press, New York,

1966.

4. Johnsen, John Richard, An Investigation into the Potential for Developing a

Successful Log-periodic Half Square Antenna with Dual-feed, V1SEE Thesis, Naval

Postgraduate School, Monterey, California, December 1986.

5. Snyder, Richard D., Broadband Antennae Employing Coaxial Transmission Line

Sections, U.S. Patent 4,479,130, 23 October 1984.

6. Naval Ocean Systems Center Technical Document 116 volume 2, Numerical

Electromagnetics Code (NEC)-Method of Moments, January 1981.

7. Hansen, Robert C, "Evaluation of the Snyder Dipole", IEEE Transactions on

Antennas and Propagation, vol. AP-35, no. 2, February 1987.

8. Collin, Robert E., and Zucker, Francis J., Antenna Theory Part 2, McGraw-Hill

Book Company, New York, 1969.

9. Mittra, Raj and Jones, Kenneth E., "How to Use k-P Diagrams in Log-Periodic

Antenna Design", Microwaves, pp. 18-26, June 1965.

162

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DUDLEY ED RYNAVAL POSTGRADUATE SCHOOLMONTEREY, CALIFORNIA 93843-8003

ThesisT1386c.l

TarletonThe use coaxial trans-

mission line elements in

log-periodic dipolearrays.

Thesis

T1386

e.l

TarletonThe use coaxial trans-

mission line elements in

log-periodic dipole

arrays.

Documents

Theses and Dissertations Thesis Collection - core.ac.uk · Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 1987 The use of coaxial transmission line