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U56 NO 87-3068 1987 V19C.1 NBS-P k f \ ^ A M A DD A\/ r* W Mi^nLi uio Ur AIM AnnAY Ur

LOG-PERIODIC DIPOLE ANTENNAS FOR

GENERATING TEST FIELDS

Galen H. Koepke

David A. Hill

Mark T. Ma

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303-3328

June 1987

“QC

100

. U56

#87-3068

1987

NBSIR 87-3068

ANALYSIS OF AN ARRAY OF

LOG-PERIODIC DIPOLE ANTENNAS FOR

GENERATION TEST FIELDS

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303-3328

June 1987

Sponsored in part by

Naval Surface Weapons Center

Dahlgren, Virginia 22448

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

Galen H. Koepke

David A. Hill

Mark T. Ma

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

Abstract 1

1. INTRODUCTION... 1

2. LOG-PERIODIC DIPOLE ANTENNAS 2

2.1 Design Characteristics and Analysis 3

2.2 Radiated Fields.... 7

3. AN ARRAY OF LOG-PERIODIC DIPOLE ANTENNAS

3.1 Array Geometry

3.2 Element Excitation 1

4. NUMERICAL RESULTS 10

4.1 Comparison with Single LPDA 10

4.2 Effect of Phase Variation 12

4.3 Frequency Dependence 13

5. CONCLUSIONS AND RECOMMENDATIONS 14

6. ACKNOWLEDGMENTS 15

7. REFERENCES 15

iii

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^

UD

ANALYSIS OF AN ARRAY OF LOG-PERIODIC DIPOLE ANTENNAS

FOR GENERATING TEST FIELDS

Galen H. Koepke, David A. Hill, and Mark T. Ma

Electromagnetic Fields Division

National Bureau of Standards

Boulder, CO 80303

An analysis of log-periodic dipole antennas was extended to

study their use in arrays designed for electromagnetic

susceptibility measurements. Parameters of an array of five

log-periodic dipole antennas were calculated and in some cases compared to a single log-periodic dipole antenna. These

parameters were used to evaluate the tradeoffs that exist in the

design of an optimum transmitting antenna for susceptibility

measurements

Key words: broadband antenna; electromagnetic susceptibility;

log-periodic dipole antenna; near-field phased array.

1 . INTRODUCTION

A method has been developed to synthesize a desired field distribution

over a limited volume for electromagnetic susceptibility (EMS) testing [1],

This technique uses an array of elements fed in such a manner that a given

field distribution (typically a plane wave) is generated in the near-field

region of the array. An array designed in this manner is known as a near- field phased array. The technique has been verified with an array of YagiUda antennas [2] and has shown good agreement with theory and experiment.

The ability to generate a given test field at a particular fixed frequency

[2] is useful for verifying a concept, but a general purpose EMS facility

should perform over a broad range of frequencies. There is a need for wide

frequency coverage in order to perform measurements with a minimum of

mechanical adjustments and equipment changes. The motivation for this study

is to examine the possibilities of constructing an array of broadband

elements in an effort to extend the usable bandwidth of the array and to

1
determine what enhancements can be obtained to the field strength at a particular test point by using an array instead of a single broadband

element.

Devices such as transverse electromagnetic (TEM) cells [ 3 ] and

parallel plate transmission lines are useful for frequencies below about 50

MHz and compact ranges [4] for use at higher frequencies above 1 GHz which

can be used to produce TEM fields for testing purposes. There is a range of

frequencies between 50 MHz and 1 GHz where this near-field phased array may

find greatest application, and the attention will be given to that band.

A common, proven broadband antenna that radiates linear polarization

and is used in this frequency range is the log-periodic dipole antenna

(LPDA). This antenna design has received considerable attention [5,6,7,8,91

and has been modeled theoretically. For these reasons the LPDA was chosen

for the elements of the phased array. Some of the other frequencyindependent antennas [10] are not useful for our purposes because they

radiate circular polarization. The TEM horn [11] is broadband and radiates

linear polarization, but its field distribution is difficult to calculate.

This report is organized in the following manner. Section 2 details

the analysis of the LPDA including geometry and circuit models. This

section includes a description of the LPDA used for the array study and

describes the important characteristics of the antenna. Section 3 details a simple array configuration and describes the calculations used to arrive at

the field in front of the array. Section 4 gives the comparisons of the

array of LPDAs vs a single LPDA at various operating frequencies and test

points. Section 5 draws some conclusions and makes recommendations for

future work.

2. LOG-PERIODIC DIPOLE ANTENNAS

Log-periodic dipole antennas belong to a class of antennas that

exhibit nearly frequency-independent char acter i st i cs [12]. They are

2
actually arrays of dipole antennas, but we refer to the array as an antenna

in order to avoid confusion later when we form an array of LPDAs . The input

impedance and radiation pattern of a properly designed LP DA vary

periodically with the logarithm of frequency and the variation within the

logarithmic period is negligible [13]. These frequency- independent

properties are bandlimited by the fact that the actual antenna is a truncation of an infinite structure, but given enough properly sized and

spaced elements the bandwidth is arbitrarily large.

2.1 Design Characteri sties and Analysis

A typical log-periodic dipole antenna is shown in figure 1. The

antenna is an array of parallel center-fed linear dipoles lying side by side

in a plane. The lengths and radii of dipole elements form a geometric

progression with a common ratio x, called the scale factor:

h a t-2- = —— = x, n = 1 ,2,3, • • • *N-1 , 0<x<1 , (1)

n + 1 3

n+1

where h^ is the half-length, a^ is the radius of the nth dipole, and N is

the total number of dipoles in the antenna. The ratio of half-length to

radius is constant for all dipoles. (However, in examining several

commercial antennas the radius appears to be constant over the entire

antenna using the same materials for all dipoles. This analysis assumes the

antenna is constructed with the radius of each dipole satisfying equation

1.) A line through the ends of the dipole elements makes an angle a with

the array axis at the virtual apex 0. The spacing factor o’ is defined as the ratio of the distance between two adjacent elements to twice the length

of the larger element and is constant for a given LPDA . The geometry of

figure 1 relates a* to x and a:

a

' = Hh

n+1

yn+l'yn 4h . n+1

(hn+r

h

n )cot a

1,„ , Im— = ¥

(1"T)cot a. n+1

(2)

3
The following analysis is drawn from Ma [8] and is based on the work

of Carrel [ 7 ]. The calculations treat the LPDA as a parallel circuit

combination of two distinct parts, the feeder circuit which is a balanced

constant-impedance feed line and the dipole antennas which are connected

such that the phase reverses for adjacent dipoles. The voltages and

currents at the input terminals of the dipole elements are determined by

solving circuit equations. A schematic representation of the circuit

elements is shown in figure 2. The current-voltage relations for the dipole

element circuit (figure 2a) can be written as

[VI = [Z ][I ] or [I ] = [Z ] ’[V] (3) a a a a a a

where

_I

1 a" V *

Z 2 a and 1

—

< 1

1 n V

2a

X Na_ >.

are Nxl column matrices representing, respectively, the driving base

currents and response voltages for the dipole elements, and

Z

1a

Z 12 aZ 1Na

tZ

a

] ‘ Z

21 a

Z 22 a* * * Z 2Na

Z N1a ZN2a * *Z NNa

is the associated NxN open-circuit impedance matrix.

The main diagonal of [Z ] in (5) represents the self-impedances of the

3. dipoles while the off-diagonal elements represent the mutual impedances

between dipoles indicated by the indices. All of these impedances can be

4
calculated (Ma [8], eq 4.32 or eq 4.33 and eq 4.38 or eq 4.44). These

impedance calculations are derived by the induced-etnf method with the King

and Wu [14] three-term assumption for the current distribution on the dipole

antennas.

The cur rent- voltage relations for the feeder circuit shown in figure

2b can be expressed by

[I

f

] = [Y

f

][V

f

] - [Y

f

][V

a

3, (6)

where

1

hH JL.

I

< J V

[I

f

] =

1 2f II i > i— L c "O 1 V

2f = V

2a

i

i—

z

*

1 -V

Nf- -VNa_

are the driving currents and response voltages, respectively, for each

section of the transmission line which constitutes a complete feeder

circuit, and

"y

1 1f

Y

1 2f

Y INf

[Y

f

] - Y

21 f

Y 22f• • • Y 2Nf

Y NlfYN2f • • • Y NNf

is the associated NxN short-circuit admittance matrix of the feeder. The

matrix elements of [Y^.] in (8) depend on the lengths of the transmission

line in each section and the characteristic admittance Y

Q

, which is known

for a given transmission line. The elements of [Y ] can be calculated by (Ma

[8] eq 5.9).

5
The feeder and antenna circuits are connected in parallel at the

dipole bases. Hence there is no difference between the feeder voltage

matrix [ V ] and the antenna voltage matrix [V ], and [V] is used to

I d

represent both, as shown in figure 2c.

Adding (3) and (6) we obtain the total input current matrix:

[I] = [I ] + [I-] = { [U] + [Y ][Z ] } [I ] , (9) d I Ida

where [U] is the NxN unit matrix.

The matrix elements of [I] represent the input currents to each node

point (dipole base) at the point where the antenna and feeder circuits are connected. The dipole base current matrix [I ] can be determined from (9)

3

by matrix inversion:

[I ] = { HU] + [Y„][Z ]} ^I]

d Id ( 10 )

where the elements of [I] are all zero except for the driving current to the

array at the base of the smallest dipole, which is assumed to be 1 A.

The response voltages appearing at the dipole bases can then be

determined by substituting (10) into (3). The input impedance Z^

n of the

entire array, which is numerically equal to the voltage across the feed

point since the input current is assumed to be 1 , is

Z.in

= V = N

I

i = 1

Z. . I.

1 la la

= R in JX,in ( 11 )

Figure 3 shows the details of an 1 8-element LPDA for use in the 200-

600 MHz frequency range. This antenna is given as an example in ([9],

example 6. 3. pg. 299) and has characteristics that are of interest in this

6
study. The base currents of the dipole elements at 300 MHz calculated by

the above method are shown in figure 4, and comparisons are made with moment

method calculations by Stutzman and Thiele [9] for a transmission line

impedance of 83 ft as given in [9] (this impedance is changed to a more

common value of 50 ft for all subsequent calculations). The data in figure 4 show the relative base currents for each dipole in the antenna and

illustrate the three different regions of the LPDA [7]. The first region is

called the transmission region which includes the feed point (dipole 1) and

the first few elements that have very low base currents. The dipoles in

this region have the smallest physical dimensions and define the upper

frequency limit of the antenna. The second region is referred to as the

active region. Here the dipoles have relatively high base currents, and

this is where the majority of radiation takes place. The dipoles in this

region have lengths close to one-half wavelength. The remaining longer

dipoles are in the unexcited region. This region defines the lower

frequency limit of the antenna.

2.2 Radiated Fields

The radiated fields of the antenna can be calculated using assumed

current distributions on the dipoles, the relative amplitudes of the base

current for each dipole, and the geometry of the array. The components of

the far-field can be evaluated in closed form ([8], section 5.2) for the

three-term current. However, for this application the region of interest

includes close distances in front of the array. The integrals for terms

that include the higher inverse powers of distance, which become more

significant at close distances, cannot be easily evaluated analytically and

a numerical integration becomes necessary.

The formulation for the fields radiated by any segment of a particular

dipole can be derived in terms of the vector potential [15, 16, 17]. The

electric and magnetic field components are found by performing the required

mathematical operations on the vector potential function. The rectangular

cartesian coordinate system is chosen with the dipole orientated along the

7
x-axis. The vector potential A at a field point (x,y,z) for this

configuration can be expressed as

h -*j kr a a

x b l I(x') dx', (12)

-h

2 2 2 2 where a

x is the unit vector in the x direction, r = (x-x') + y

+ z , and

I(x’) is the current distribution along the antenna. The electric field (E)

and the magnetic field (H) are related to A by

E = —j a) A

-

cope V(V*A) and H = - (VxA),

U

(13)

where u> is the radian frequency, with e^

wt

as the time dependency, p is the

permeability, and e is the permittivity of the transmission medium (free

space). The indicated derivatives are performed retaining all the higher

inverse powers of r. The resulting integrals are then evaluated numerically

with Simpson’s 1/3 rule [18] using the current weightings derived for each

dipole. The fields from each dipole in the LPDA are summed together at a given test point to give the total field from the array of dipoles.

A sample calculation for the electric field along the boresite (vs -y

at x = z = 0) of the LPDA using the asymptotic expression for the fai—field

and the complete expressions containing the near-field terms evaluated via a numerical integration routine is shown in figure 5. These data are useful

for comparing the two calculations and verifying the near-field derivation

and integration routines. The data also illustrate the region where farfield calculations are no longer adequate and produce incorrect results.

The remaining calculations utilize the near-field terms and should be valid

at all distances.

8
3. AN ARRAY OF LOG-PERIODIC DIPOLE ANTENNAS

The single LPDA with its endfire radiation pattern and fixed geometry

does not provide means to vary the field structure. A desired flexibility

can be gained by constructing an array of LPDAs with the amplitude and phase

of the feed current, number of elements, and the array geometry providing

the necessary parameters required to control the radiated field. These

parameters are somewhat arbitrary yet interrelated. The intended use of the

array will, in most cases, determine practical choices for the array

parameters. This application requires the array to be easily handled, thus

limiting the overall size; to provide a maximum field strength for a given

input power; and to provide acceptable field uniformity over the test

volume. After considering the array geometry, the maximum field strength vs field uniformity compromises will be discussed.

3.1 Array Geometry

The array geometry shown in figure 6 details a planar five-element

broadside array of LPDAs. This configuration is a minimum sized array that

will provide some flexibility in the control of the field structure in a small test volume. Additional elements would increase this capability but

at the expense of feed complexity and ease of handling. The five elements

are arranged with the outer four on the corners of a square and one in the

center. The symmetry of this geometry permits the simplest possible feed

network with the center element as one feed value and the outer four

elements taking another value. The need to illuminate a volume of cubic or spherical proportions has ruled out other possible geometries such as arranging the elements in a linear fashion. The elements are spaced

sufficiently far apart (on the order of a wavelength) such that effects from

mutual coupling between the LPDA elements can be neglected. Mutual coupling

was found to be negligible in an earlier near-field array [2], and there are

no corrections for these effects in this analysis.

9
3.2 Element Excitation

As mentioned above, the five-element array has only two values of the

feed current, with the outer four elements requiring an identical value.

The near-field synthesis technique can be used to determine what the feed

should be for a given field structure. Typical improvements in field

uniformity for a similar array can be found in [2] and a similar analysis

for this array is not repeated here. It should be noted that the near-field

synthesis technique tends to prescribe feed values that are not well matched

to the common 1/2 - 1/2 power splitters [2]. Attenuators are then required

increasing the losses in the feed system. For an application where field

uniformity or prescribed structure is the most important feature, these

additional losses can easily be tolerated or a feed system specif ideally

designed based on these requirements. However, for the purpose of this

study emphasizing the frequency dependent nature of the array along with the

potential application requiring the maximum field strength for a given input

power for which attenuators in the feed system should be avoided, the

amplitude weightings are chosen such that common power splitters may be

used. The array elements are then assumed to be fed with equal splitting

where the center element receives 1/2 and the outer four elements each

receive 1/8 of the power. The relative phase is adjustable and will be

examined. The phase can be determined by hot-spot theory [19] which results

in the outer elements leading the center such that the field is in phase at

the test point. Alternatively, the phase of the outer elements can be

retarded relative to the center to produce a more uniform field over a wider

area. The actual phase chosen for the array will be determined by the

application.

4. NUMERICAL RESULTS

4.1 Comparison with Single LPDA

The intended use for an array of LPDAs is to produce a specified field

environment for EMS testing. A typical measurement involves positioning the

10
equipment under test (EUT) and the transmitting antenna such that the EUT is

exposed to the specified field to be generated by the transmitting antenna.

In many situations the EUT may be quite large (e.g.,. aircraft) and it is

more practical to move the transmitting antenna rather than the EUT to

provide various illuminations for the EUT. A single LPDA is obviously more

convenient than an array of several LPDAs and in some situations may be a good choice.

Many susceptibility tests require high field strengths to simulate

real environments that exist where the equipment is to be used. Higher

field levels obviously require larger power amplifiers, but some enhancement

may also be attained by reducing the distance between the transmitting

antenna and the EUT. Figure 7 details what happens to the ratio of the

dominant far-field components (E /H ) as this distance is varied. The E /H

X Z X z ratio begins to deviate from the free space impedance value of 120tt ft at

about 2 wavelengths separation distance for both the single LPDA and the

array of 5 LPDAs whose individual LPDAs are fed in-phase. This deviation

from 120-rr ft indicates the deterioration of the plane wave field structure

into a complex near-field environment. Figure 7 indicates that either

antenna may be usable to a fraction of a wavelength with relatively minor

deviation of the wave impedance. However, it is not practical to operate an antenna at such close distances to a typically reflective EUT because of the

interaction and mutual coupling that will occur between the antenna and the

EUT.

The array has some advantages in terms of field strength in the test

zone, control over field uniformity, and flexibility in the size of the test

zone. The enhancement in field strength is demonstrated in figure 8 for the case where the array elements are fed in phase. The dominant electric field

component (E

x

) is calculated for a single LPDA and for the array of 5 LPDAs

along the boresite of each. The array is able to concentrate more energy in

the test zone for the same total input power than a single LPDA. The

improvement in field strength can be seen as a function of distance in

figure 9 where the ratio of E

x from the array to E

x produced by the single
antenna is shown. An approximate theoretical maximum for the far-field gain

of the array over that of the single LPDA is 10 log N = 7 dB. The far-field

result in figure 9 is within half of one decibel of this maximum.

A comparison of the electric field patterns perpendicular to the

propagation direction is shown in figures 10 and 11, here the array is fed

in an in-phase manner with the same input power as the single LPDA. The

ability to vary the test volume by changing the phase of the array feed

system will be discussed in section 4.2. The single LPDA has no provisions

for changes in the radiation pattern that could alter the field in the test

zone

4.2 Effect of Phase Variation

The effects of changing the phase of the feed system as discussed in

section 3.2 can be seen in figures 12 and 13. The data in figure 12 show

the transverse amplitude variation in E

x parallel to the LPDAs at a distance

of 3 meters in front of the array for differing phase of the outer four

elements with respect to the center element. The highest field strength at

the peak of the beam is obtained when the outer elements have a leading

phase angle. This angle can be determined by requiring all contributions at

a particular test point to add in phase. The most uniform field can be seen near the phase value of -99.7 degrees. The test area of ±1 meter for this

case is not as uniform as the single LPDA of figure 10. However, if the

test area is extended to ±3 meters the array shows substantial improvement

over the single LPDA at the perimeter. The array would show improved field

uniformity in both the transverse direction shown here and in the

longitudinal direction (figure 5) if the amplitude and phase of the element

weightings were determined by the synthesis technique [2]. The phase angle

for E^ at corresponding locations is shown in figure 13. Similar data for

the H-plane pattern are shown in figures 14 and 15. These curves

demonstrate the tradeoffs that exist between maximizing power density and

generating a uniform field in the test zone.
4.3 Frequency Dependence

The characteristics of the array change as a function of frequency.

The assumption here is that the mechanical dimensions and connections are

not altered as the frequency changes. The electrical dimensions of the

array obviously then depend on frequency; the spacing of elements in terms

of wavelengths is less at low frequencies and greater at high frequencies,

and in the case of log-periodic elements, the actual point of maximum

radiation will move along the length of the LPDA. The array cannot

therefore be labeled as broadband in the same sense as the LPDA. The useful

range of frequencies over which the array may be used is limited by how much

variation can be tolerated.

The input impedance is one parameter that does not change dramatically

with frequency as it is more a function of the element characteristics than

of the array. The data shown in figure 16 are for a single 18 element LPDA

over the band of 200-600 MHz. This input impedance will become part of the

array feed network which can be designed to avoid frequency dependent

behavior

The relative distribution of base currents within a single LPDA is

shown in figure 17 at several frequencies. The active region of the LPDA

clearly moves along the length of the LPDA. This active region radiates the

majority of power so the effect here is one of varying the separation

distance of the array to the EUT. This would change the amplitude of the

signal but would not, in itself, change the field structure except at very

close distances.

The parameter that does have a pronounced effect upon the field

structure, given a fixed feed system, is the spacing of the individual LPDA

array elements. The array in this example is designed with a one-wavelength

spacing at the middle frequency (400 MHz). This translates to 0.5

wavelength at 200 MHz and 1.5 wavelength at 600 MHz. The effects on the

field structure are shown in figures 18 and 19. Again the data are for a separation of 3 meters between the antenna origin and the test plane.

13
5. CONCLUSIONS AND RECOMMENDATIONS

An analysis of log-periodic dipole antennas was extended to study

their use in arrays designed for electromagnetic susceptibility

measurements. The near-field contributions to the radiated field components

were included to allow the test volume to be in close proximity of the

array. The computer code developed was then used to study an array of five

LPDAs. The characteristics of the array were compared to a single LPDA in

terms of wave impedance of the radiated fields vs distance, field strength

in the test zone, field uniformity, and size of the test zone. The

radiation pattern of the array for various feed phasings was examined to

illustrate the compromises between field strength and field uniformity.

These calculations were repeated using the in-phase case for three

frequencies to show the variations that an array of fixed geometry would

experience as the operating frequency is changed. The array characteristics

will change with frequency and the useful bandwidth is determined by the

tolerances allowed. A possible alternative to the bandwidth limitation is

to adjust the mechanical spacing of the broadband elements to compensate for

the change in frequency.

This information is needed to evaluate the tradeoffs that exist in the

design of an optimum transmitting antenna for susceptibility measurements.

An array of broadband elements can increase the field strength in the test

zone, or broaden the area of uniform illumination, as compared to a single

element. The advantages of the array solution must be weighed against the

increased complexity and bulk of the array. This analysis is limited to the

relatively simple case of a five-element array due to size and handling

considerations. The flexibility provided by an array would increase as the

number of elements is increased, but for the case of EMS testing the

disadvantages of increased size make a large array less practical.

Some of the more sophisticated features of the near-field phased array

method, synthesizing the field structure, scanning the test volume, and

constraining the fields external to the test volume are not addressed in

this report. Near-field synthesis techniques tend to prescribe element
weightings of odd values [2]. The goal here was to examine an array fed in an efficient manner without additional attenuation of the driving signal in

the feed network in order to maximize the energy delivered to the test zone. We recommend designing a five-element array of LPDAs and testing the array

over a wide bandwidth (perhaps an octave). Measurements of the input

impedance and the near-field distribution would be useful in testing the

validity of neglecting mutual coupling. Further theoretical calculations of

other array geometries would also be interesting. Nonuniform spacings of

the array elements [8] might be helpful in increasing the bandwidth of the

array .

6. ACKNOWLEDGMENTS

The authors are grateful to L. C. Walters for the use of the computer

code that provided the core of calculations for the LPDA evaluation and

saved untold hours in implementing the analysis used in this report, and to

J. Bean and the staff of the Naval Surface Weapons Center, Dahlgren,

Virginia, for their interest and support of this work. We also thank C.K.S.

Miller for his continued interest and support.

7. REFERENCES

[1] Hill, D.A. Theory of near-field phased arrays for electromagnetic

susceptibility testing. Nat. Bur., Stand. (U.S.) Tech. Note 1072;

1984.

[2] Hill, D.A.; Koepke, G.H. A near-field array of Yagi-Uda antenna for

electromagnetic susceptibility testing. Nat. Bur. Stand. (U.S.) Tech.

Note 1082; 1985.

[3] Crawford, M.L. Generation of standard EM fields using TEM

transmission cells. IEEE Trans. Electromagn. Compat . EMC-16: 189-195;

1984.

[4] Johnson, R. C.; Ecker, H. A.; Moore, R. A. Compact range techniques

and measurements. IEEE Trans. Antennas Propag. AP— 1 7 : 568-575; 1969.

[5] Isbel, D. E. Log-periodic dipole arrays. IRE Trans. Antennas and

Propagation. AP-8(3): 260-267; I960 May.

15
[ 6 ] Carrel, R. L. The design of log-periodic dipole antennas, IRE

National Convention Record, part 1. Vol. 9: 61-75; 1961.

[7] Carrel , R. L. Analysis and design of the log-periodic dipole antenna.

University of Illinois Technical Report No. 52; Urbania, IL. 1961.

[8] Ma, M. T. Theory and application of antenna arrays. New York, NY:

John Wiley & Sons; 197*1.

[9] Stutzman, W. L. ; Thiele, G. A. Antenna theory and design, New York,

NY: John Wiley & Sons; 1981.

[10] Rumsey, V. H. Frequency independent antennas. New York, NY: Academic

Press; 1966.

[11] Kanda , M. The effects of resistive loading of "TEM" horns, IEEE

Trans, on EMC. EMC-2*4(2); 1982 May.

[12] Rumsey, V. H. Frequency-independent antennas, IRE National Convention

Record, part 1. Vol. 5: 11*4-118; 1957.

[13] DuHamel , R. H. ; Isbel , D. E. Broadband log-periodic antenna

structures, IRE National Convention Record, part 1. Vol. 5: 119-128;

1 957.

[1*1] King, R. W. P.; Wu, T. T. Currents, charges, and near fields of

cylindrical antennas. Radio Sci. Vol. 69D ( 3 ) : 429—446 ; 1965 March.

[15] Johnk, C. T. A. Engineering electromagnetic fields and waves. New

York, NY: John Wiley & Sons; 1975.

[16] Jordan E. C.; Balmain, K. G. Electromagnetic waves and radiating

systems, second edition. Englewood Cliffs, N.J: Prentice-Hall, Inc.;

1968 .

[17] Harrington, R. F. Time-harmonic electromagnetic fields. New York,

NY: McGraw-Hill; 1961.

[18] LaFara, R. L. Computer methods for science and engineering. Rochelle

Park, N.J: Hayden Book Company, Inc.; 1973.

[19] Gee, W.; Shung-wu Lee; Bong, N. K.; Cain, C. A.; Mittra, R. ; Magin, R. L. Focused array hyperthermia applicator: theory and experiment.

IEEE Trans, on Biomedical Engr. BME— 31 ( 1 )

198*4 January.

16
Figure 1 . Geometry of a log-periodic dipole antenna.

17
Dipole Elements

t M

a.) Dipole element circuit

c) Complete circuit

Figure 2. Circuit model of a log-periodic dipole antenna.

18
E

<S)

in

(S3 oo

lO • cs o4-> o

un oo n CM 4-> ISJ eo II o

<M

N

<U oc 3 03

t- - O t—

Cm t—

O'*

03 • C o C II <D t- 4-> C •» 03 bO0) 0) "O i—I o b—

Ol II •rH a

•oo CO

•rH 1

•o II o 2

•rHtC3 £

CL -C 1 •rH bOO

rH

N2 < S

on

03£-3

bO

•H

Cx-i

19
RELRTIVE

DIPOLE

BRSE

CURRENT

AMPLITUDES,

300

MHz

T

TT

T

ID inT

s'Q s Q - Q B

CDN

^4

ID

inmw

(9^4

0)

CDN

(0

a:umEDZHZuEUJuuJo

Q.HP

in

«•

cnN

cnB

3ani.i“idwu

mQ

cvj Q

Figure

4.

Relative

dipole

base

currents

for

the 1

8-element

LPDA

shown

in

figure

3,

except Z= Z=

83

ft.

The

operating
Near &

Far—

-field

Comparison

along Q

IINQnXX

XpUI cu0>

id3Uu2

CEFwMQ

CD sz

<UioE3E

•Hx

03EE

o)<D £3

CD • sz a

-l-> o

bO LPi CO II r-H 4-> 03 N

X3 II >-1

O

CDN

•Ho

•H

c.

4-> o

CD

•o

CD

03 I 1 3Of—

03 O

to

CD

s.3

bO •H

U-t

HP) *3

21

LPDA

of

figure 3

with
Figure 6. A five-element array of LPDAs.

22
WRVE

I

MPEDRNCE

vs

Csuiqo) 2H/X3

23

Figure

7.

Wave

impedance

(Ex

/Hz )

for

both

a

single

1

8-element

LPDA

and

an

array

of5

in-phase

LPDAs.

The

operating

frequency

is

H00

MHz.
T G

G

G if) * m

Q in G in rn oj cu ~ C^/a EP) *3

G in

24

Figure

8.

Electric

field

strength

of

a

single

18-element

LPDA

and

an

array

of5

in-phase

LPDAs

at

HOO

MHz

for

the

same

input

power.
ID ID in in

GP

n n

0

0

X

•pCDc

0

t)> 0 (0 - 3W

0

u

c

Id V

W

p

OJ

25

Figure

9.

Cain

In

field

strength

of

an

array

of5

ln-phase

LPDAs

over

a

single

18-element

LPDA.
3m,

z

B

0m,

F"400

MHz

(w/A HP) *3

26

Figure

10.

E-plane

electric

field

for

a

single

18-element

LPDA

and

an

array

of5

in-phase

LPDAs

for

the

same

input

power.
3m.

x=0m.

F°400

MHz

(uj/a HP) *3

27

Figure

11.

H-plane

electric

field

for

a

single

18-element

LPDA

and

an

array

of5

in-phase

LPDAs

for

the

same

input

power.
3m.

z

=0m

,

F-400

MHz

(UJ/A QP *3) P18U 31^3813

28

Figure

12. E

plane

electric

field

amplitude

for

an

array

of

five

LPDAs

fed

with

various

center

to

outer

element

phase

angles

(degrees).
3m,

z

B

0m,

F“=

a

400

MHz.

29

Figure

13.

E-plane

electric

field

phase

for

the

same

conditions

as

figure

12.
at

y

=

— 3m

,

x

=0m

, F

=

400

MHz

m

L

I) P

I)E

w

X

0

I N

("/A QP *3> P l ® 1 J- oinoaG

30

Figure

1*1.

H-plane

electric

field

amplitude

for

the

same

conditions

as

figure

12.
19 (9 0 0 0 0 0 0 0

(9 in 0 in 0 in 0 in

* m m (M OJ • <

( ss@ jBep ) sse L|d p i s [ j. o| j;ob(3

31

Figure

15.

H-plane

electric

field

phase

for

the

same

conditions

as

figure

12.
INPUT

I

MPEDRNCE

for

200-600

MHz

LPDR

with

Zt=50,

Zo

=

50

I

N

I

E

>-U

z

u

o

u

O'L

(suumo) 3DNUQ3dWI IfldNI

32

Figure

16.

Input

impedance

of

a

single

1

8-element

LPDA

as

detailed

in

figure

3.
relative

dipole

BASE

CURRENT

AMPLITUDES,

Zt-50

T

Bannidwu

33

Figure

17.

Relative

dipole

base

currents

for

the

18-element

LPDA

for

various

operating

frequencies.
L

L.

(UJ/A BP ><3) P1»U 3jnsei3

W

L

C

P

0

E

C

100

0)

W

X

QZ

X

34

Figure

18.

Frequency

variation

of

the

E-plane

field

amplitude

3

meters

In

front

of

an

array

of5

in-phase

LPDAs.
E

Q

in

m

OJ

Q

l

(\j

l

m

ml

in

a)L

L (uj/a SP ><3) P » l J- a | j^ob 13

w

L

13 +J0

E

C

a

u

in

V)x

<rN

35

Figure

19.

Frequency

variation

of

the

H"plane

field

amplitude

3

meters

in

front

of

an

array

of5

in-phase

LPDAs
NBS-114A [REV. 2-80

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publ ication Date

SHEET (See instructions) NBSIR 87-3068 June 1987

4. TITLE AND SUBTITLE

Analysis of an Array of Log-Periodic Dipole Antennas for Generating Test Fields

5. AUTHOR(S)

Galen H. Koepke, David A. Hill, and Mark T. Ma

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Sponsored in part by

Naval Surface Weapons Center

Dahlgren, Virginia 22448

10.

SUPPLEMENTARY NOTES

] Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gn i fi cant

bi bliography or literature survey, mention it here)

An analysis of log-periodic dipole antennas was extended to study their use in

arrays designed for electromagnetic susceptibility measurements. Parameters of an array of five log-periodic dipole antennas were calculated and in some cases compared to a single log-periodic dipole antenna. These parameters were used to

evaluate the tradeoffs that exist in the design of an optimum transmitting antenna

for susceptibility measurements.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

broadband antenna; electromagnetic susceptibility; log-periodic dipole antenna;

near-field phase array

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

| y| Uni imited

| | For Official Distribution. Do Not Release to NTIS

H Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

40

15. Price

[X] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

U.S. GOVERNMENT PRINTING OFFICE: 1987-776-306/65212 USCOMM-DC 6043-P80