Reference

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NAT'L INST. OF STAND & TECH

A111DS T77AED

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*°*eau o* % NBS TECHNICAL NOTE 1082

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards
rp

M he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

/ft Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

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NATIONAL BUREAU OF STANDARDS

LIBRARY *

A Near-Field Array of Yagi-Uda

Antennas for Electromagnetic

Susceptibility Testing

David A. Hill

Galen H. Koepke

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

c

**rn<**

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued July 1985
National Bureau of Standards Technical Note 1082

Natl. Bur. Stand. (U.S.), Tech Note 1082, 82 pages (July 1985)

CODEN:NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1985

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
CONTENTS

Page

1. Introduction 1 2. Theory 2 2.1 Two-Element, Yagi-Uda Antenna 3 2.2 Array Element Excitations 6

2.3 Numerical Results 10

2.4 Mutual Coupling 12

3. Experiment 15

3.1 Array Construction 15

3 .2 Probe 16

3.3 Track 16

3.4 Instrumentation 17

4. Experimental Results and Comparisons with Theory 17

5. Conclusions and Recommendations 20

6. Acknowl edgements 21

7. References 21

Appendix A Far-Field Pattern of a Two-Element, Yagi-Uda Antenna 22

Appendix B Uniform Array 23

m

A NEAR-FIELD ARRAY OF YAGI-UDA ANTENNAS

FOR ELECTROMAGNETIC SUSCEPTIBILITY TESTING

David A. Hill and Galen H. Koepke

In electromagnetic susceptibility testing of electronic equipment,

the ideal incident field is a plane wave. To approximate this

condition, a seven-element array of Yagi-Uda antennas has been

constructed and tested at a frequency of 500 MHz. The element

weightings are determined by a near-field synthesis technique

which optimizes the uniformity of the field throughout a rectangular test volume in the near field of the array. The amplitude and

phase of the electric field have been measured throughout the test

volume with a short dipole probe, and the agreement with the

theory is excellent.

Key words: antenna array; array synthesis; dipole antenna;

electromagnetic susceptibility testing; mutual coupling; near

field; plane wave; Yagi-Uda antenna

1. Introduction

In electromagnetic susceptibility testing of electronic equipment, the

ideal incident field is a plane wave. Far-field antenna ranges are generally

unacceptable because they waste power outside the test volume and because the

far-field distance is often inconveniently large. An ideal test facility

would supply most of the power to the test volume containing the equipment

under test (EUT), and the test facility dimensions should not be too much

larger than the test volume so that it could be located indoors.

The compact range [1] uses a paraboloidal reflector to produce an approximately plane wave in the near field, but the compact range is most useful

at frequencies above 1 GHz. At low frequencies, transverse electromagnetic

(TEM) cells [2] and parallel plate transmission lines are used to produce TEM

fields which are uniform over a portion of their cross section. Such transmission line structures are most effective for testing EUTs that are electrically small. There exists a frequency gap (about 50 MHz to 1 GHz) between

the low frequency and high frequency methods where another method of producing

a plane wave is needed.

The feasibility of using phased arrays to fill the frequency gap has been

studied, and a near-field array synthesis method has been developed to compute

the array element excitations [3]. The method optimizes the field quality

1
throughout the test volume and also constrains the element excitations to

reduce the field strength outside the test volume. The synthesis method can

be applied to arbitrary array elements and geometries, and in this report we

apply the method to a seven-element, planar array of dipole antennas. To

check the theory and to gain experience in working with near-field arrays, we constructed a seven-element array of dipoles and tested it at a frequency of

500 MHz. In an actual electromagnetic susceptibility test, we might prefer

array elements with greater bandwidth, but dipoles were useful for verifying

the array theory because their characteristics are well understood. Earlier

experimental results have been obtained by Lynggaard [4] who built and tested

a five-element array of horns.

The organization of this report is as follows. Section 2 contains the

analysis and numerical results for the seven-element array. Mutual coupling

between the array elements is considered in section 2.4. Section 3 describes

the array construction and feed network and the method of probing the amplitude and phase of the electric field. Section 4 contains the experimental

results for the electric field measurements throughout the test volume and

gives some comparisons with the theoretical predictions of the electric

field. Section 5 summarizes the results of this study and makes recommendations for further work.

2. Theory

The geometry of the seven-element planar array is shown in figure 1. The

equally-spaced array elements are located at the vertices and at the center of

a regular hexagon in the x-z plane. This configuration can also be viewed as

a triangular arrangement of the array elements, and it is known to be very

efficient in filling the planar array surface without producing grating lobes

[5].

Only the driven elements are shown in figure 1, but each driven element

is accompanied by a passive reflector in order to reduce the radiation in the

backward (negative y) direction. Thus each array element is actually a twoelement, Yagi-Uda antenna as described and analyzed in section 2.1. The excitations of the Yagi-Uda antennas are chosen to optimize the plane wave character of the field in the rectangular test volume shown in figure 1. In
section 2.2, the previously developed near-field array synthesis method [3] is

applied to this array, and the optimum element excitations are determined. In section 2.3, the field distributions of the array are shown.

2.1 Two-Element, Yagi-Uda Antenna

Since the seven array elements are identical and mutual coupling is ne- glected in the initial analysis, it is sufficient to analyze a single isolated

Yagi-Uda antenna. The center element of the array is shown in figure 2, and

it consists of a driven dipole of half length h^ and a reflector of half

length h

p

. Both dipoles are z directed. The current distributions on both

the driven element I^U') ancl the reflector element I r (z') are assumed to be

sinusoidal :

I . I.(z') = -r-nTTT- sin kfh . - Iz

1 I]

d

v

' sin kh . ^ d ' ' J a and (1)

I

I (z') = . r

,

sin kfh - Iz' II,

r

v

' sin kh v r ' ' ; ' r

where k = w /uo e o = 2-n/X, y and e are the free space permeability and permittivity, and X is the free space wavelength. The time dependence exp (jut)

is suppressed. The current distributions in eq (1) are symmetrical in z

1 and are zero at the ends of the elements. A more precise form of the currents

could be obtained from three-term theory [6,7] or the method of moments [8],

but the sinusoidal assumption is adequate for dipoles of length on the order

of a half wavelength. The advantage of the sinusoidal current assumption is

that simple expressions are available for the near fields [9] and the self and

mutual impedances [10].

The base currents of the driven and reflector elements, 1^ and I p

, can be

obtained from the following circuit relations:

V , = Z.I , + Z , I d d d dr r and (2)

= Z , I . + Z I . dr d r r
In eq (2), V d is the voltage applied to the base of the driven element, Z d is

the self impedance of the driven element, Z

p is the self impedance of the

reflector element, and Z dr is the mutual impedance between the driven and re- flector elements. The voltage applied to the base of the reflector element is zero because it is passive. From the second equation in eq (2), the ratio of

the reflector current to the driven current is

I r /I d

= -Z dr /Z

r

. (3)

The other quantity of interest is the input impedance of the driven element

z in

V Z

2

S'n "

I . Ld Z

* l4;

d r

To calculate the self and mutual impedances, we use the mutual impedance ex- pressions given by King [10]. These expressions involve sine and cosine integrals, and efficient computer codes are available for evaluating these

integrals [11]. Self impedances are evaluated by computing the mutual impedance at a separation equal to the dipole radius a.

The quantities in eqs (2) through (4) have been evaluated for the following parameters: h d /X = 0.25, h

r /x = 0.26, a/A = 5.29 x 10" 3

, and d/X

= 0.25. The value of a/X was determined from the experimental parameter of a

= 0.318 cm (0.125") and a frequency of 500 MHz. For the above parameters the

various impedances are:

Z d

= 7.31 + j 40.6 n,

Z

r = 82.2 + j 67.0 n, and

Z dr = 43.2 - j 29.8 a. (5)

By substituting eq (5) into eqs (3) and (4), the following values are obtained

for the current ratio and the input impedance:

I r /I d

= - 0.138 + j 0.476
and

Z in = 81.3 + j 65.2 n. (6)

Thus the input impedance is larger than the self impedance of the driven element given in eq (5). The fields of the two elements add constructively in

the forward direction (positive y) and cancel in the backward direction (negative y) because the phase of Ip/Ij is near 90 deg. The resultant far-field

radiation patterns in the two principal planes are shown in figure 3. The E plane is the yz plane, and the H plane is the xy plane. The patterns were computed from the far-field expressions derived in appendix A. The front-toback field ratio is 2.94 (i.e., 9.37 dB). Some calculations were done for

other values of d and h_, but not much improvement was observed.

In the following sections, the near fields of the Yagi-Uda antenna are required. For the sinusoidal current distribution given in eq (1), the electric field radiated by the driven element E is given by [9]

where

rE=xE+yE+zE, d r d r d rd ,.., — (7)

x

J y z '

v ;

E d , x d

= y_ E

x p p* y p p'

-jnI H [z - h.J expt-jkPx)

[- p 4tt sin kh, L p r x

(z + h ,) exp(-jkr 2 ) 2z cos kh . exp(-jkr ] + _ 9. 1 P r 2 p r

J

'

d -jnld expt-jkrj exp(-jkr 2 ) E

z = 4, sin kh

d

I Fi + F2

" 2 cos kh

d exp(-jkr )/r ],

r, = /p 2 + (z - h )2, r 2 = /p 2 + (z + h ) 2

,

r

Q = /p 2 + z 2

, p = /x 2 + y

2

, and r\ = /y /e

Q

.

The magnetic field radiated by the driven element H

d is given by [9]
H d

= x H

d + y Hd

, (8)

x

J y

v

'

where H

d = -=£ 1-T, Hd

= - HT, and

x p y y p <t>'

jl

d

H

6 =

4tt P sin kh [ exPHkr i) + exp(-jkr 2 ) - 2 cos kh

d exp(-jkr )J.

The same expressions apply for the fields of the reflector element, _E_r and _H_r

, if we replace I d by I r

, h d by h

p

, and y by y + d. The total fields of the

Yagi-Uda antenna, Ef ahd _H , are simply the sums of the fields of the driven

and reflector elements.

E

t = Ed + Er and H* = Hd + H

r

. (9)

The fields in eqs (7), (8), and (9) are those of the center element of the

array in figure 1, but the expressions are also applicable to any of the six

outer elements because all elements are identical. It is only necessary to

replace x by x-X; and z by z-z^ where the element is centered at (x^z.-) in

the xz plane.

2.2 Array Element Excitations

In this section we use the previously developed near-field synthesis

method [3] to determine the excitations of the array elements. The desired

field is a plane wave propagating in the positive y direction:

E=zE andH=xH, (10)

-=p pz -f> px'

where E = E exp (-jky) and H = — exp(-jky).

The array and test volume in figure 1 have two planes of symmetry, the xy

plane and the yz plane. Consequently, the excitations of the array elements

possess the same symmetry as shown in figure 1, and there are only three independent excitations. I is the base current of the driven element at the

origin, I is the base current of the four driven elements above and below the

x axis, and I is the base current of the two elements on the x axis at x = +

s. For later use in the synthesis procedure, we define a three-element column

matri x:
[I] =

IIh

I 3

(11:

The values of I , I , and I are to be chosen to approximate the plane wave

given by eq (10) within the test volume shown in figure 1. If we neglect

mutual coupling between the array elements, then the corresponding input voltages (v , v , and v ) are proportional to the base currents:

(12:

Vl Ii

v 2 = z. • inI 2

_

V 3_ _I 3 _

where Z^

n is given by eq (4). If mutual coupling is to be included, then Z- must be replaced by the appropriate impedance matrix as shown in section

2.4. Of course, we always include the mutual coupling between the driven

element and its reflector as given by eqs (2) through (4).

The first step in the synthesis procedure [3] is to define a column

matrix [P] of the desired plane-wave values on the surface S of the test

vol ume: Pi

[P] =

P2

^i

(13)

where —P. = (E . -nn x H )|

i

v -=^> tan -^p ' \r_ = r.

The subscript tan indicates the component tangential to S, and n is a unit

inward normal. The element _P. is a tangential vector evaluated at the point _r_

= _r\j as shown in figure 4. M is the number of points considered on S. In addition we define an M x 3 rectangular matrix [T]:

[T] =

Xl 1 Ii 2 .13 121 122 123

Im 1 Im2 Im 3

(14)
where Tj j = (E^ - n n xH)^.

The fields in the expression for JTjj are evaluated for I.- = 1 and all other

currents equal to zero. The actual expressions for the electric and magnetic

fields of the Yagi-Uda elements are given in eqs (7) through (9). The reason

for using the hybrid vector involving the tangential components of both the

electric and magnetic fields on S is that this particular hybrid vector pos- sesses the desired uniqueness properties when specified over a closed surface

[3].

The synthesis problem amounts to determining [I] when [P] (the desired

plane-wave field) and [T] (the solution to the forward problem) are known. We

can write the approximate relationship between [P] and [T][I]:

[T][I] - [P]. (15)

Since [P] is an M x 1 column matrix of two-component (tangential) vectors and

[I] is a 3 x 1 column matrix of scalars, eq (15) actually represents 2M equations in 3 unknowns. Normally, 2M is greater than 3, and eq (15) can only be

solved approximately. The least squares solution to eq (15) yields the best

approximation to the plane-wave field on the surface of test volume, and

uniqueness guarantees that the field is also optimized throughout the test

volume [3].

If the least squares solution to eq (15) yields large element excitations

and large fields outside the test volume, a more useful solution is obtained

when a constraint is placed on the source norm [3,12]. For the array in

figure 1, it is natural to define the following diagonal weight matrix [A] for

the source inner product:

[A] =

*1

a 2 as

(16)

where a = 1, a = 4, and a = 2,
The values of the elements a,- are chosen to equal the number of array elements

with base current I,-. The square of the source norm |[I]|| 2 is given by

3

||[I]|| 2 = [T] [A][I] =

I a.|I.|2. (17)

j=l J J

In eq (17), * denotes complex conjugate, and the tilde denotes transpose. The

constraint on the source norm is written [12]

||[I]|| 2

< C, (18)

where C is a positive constant to be chosen.

The least squares solution to eq (15) with the constraint eq (18) re- quires the eigenvalues X

n and the eigenvectors [<j>] n which satisfy

[T]*[T][*]

n = X

n [A][4>]

n

. (19)

Matrix multiplication in eq (19) has the usual meaning, and the dot product is

understood whenever the elements multiplied together are vectors. The matrix

[T] [T] is Hermitian, and efficient computer codes [11] are available for com- puting the eigenvalues and eigenvectors. The orthogonality relationship of

the eigenvectors i s:

Ri'wuij . t J; ; ; • • <20)

The constrained solution for [I] is [12]:

n=l n

where C

n = [?]*[T]*[P].

The Lagrange multiplier a satisfies
c - 1l , JX + a) n=l v n '

= 0. (22)

The left side of eq (22) is a monotical ly increasing function in a which is

real and positive, and the equation is easily solved numerically for a. If a

is set equal to zero, then eq (21) gives the eigenvector expansion of the

usual least squares solution of eq (15).

A normalized squared error E

n can be defined as

where [F] = [T][I] =

1 lf_- - M2

|[F] - [Pill 2

_ i=l "

' ||[P]|| Z " "M

I IP,-

2 1=1 n

Ll

li

^M

(23)

It has been shown [12] that as C is decreased both a and E

n increase. However, it is often the case that large decreases in the source norm j|I|i can

be achieved with only small increases in E

n

. A useful value of C can be obtained by considering a uniform array where 1=1=1= I u

. In this case,

C is given by

c-7|g*. (24)

The value of I u is derived in appendix B

2.3 Numerical Results

A computer program was written to solve for [I] by eq (21). Because of

the double symmetry, the match points were taken over only one quarter of the

surface S of the test volume as shown in figure 4. The number of points in

the x, y, and z directions are M

x

, NL, and M

z

, respectively. Consequently,

the spacings of the points in the x, y, and z directions are B/(2M Y ), A/Mr

10
and C/(2M

Z ), respectively. The numerical results were found to be insensitive

to M

x

, M

y

, and M

z for spacings less than or equal to A/4. There are M

X MZ points on the front and back faces (y = y ± C/2), M

y M

z points on the side

face (x = B/2), and M

X M points on the top face (z = A/2). Thus the total

number of points M is

M = 2M M + M (M + M ). (25)

x z y

x x z'

v '

The numerical results in figures 5 through 15 apply to the following

array parameters: s = A, h d = d = A/4, h

p = 0.26 A, and a = 5.29 x 10" 3 A.

In figures 5 through 11, the test volume is a 1.5 A cube (A = B = C = 1.5 A)

which is centered 1.75 A from the array (y = 1.75 A). Thus the front of the

test volume is one wavelength from the array (y - C/2 = A). The magnitudes

and phases of the synthesized currents are shown in figure 5. For this particular case, the constraint has no effect because the unconstrained currents

(a = 0) satisfy eq (18). The currents in figure 5 are normalized to the current of the uniform array I as given in appendix B. The center current I has the largest magnitude, and this was true for all cases which were studied.

For the synthesized currents in figure 5, the normalized squared error E as given by eq (23) is 0.077 compared to E

n = 0.385 for the uniform array.

This difference in the quality of both the magnitude and phase of the electric

field is evident in figures 6 through 11. In all cases the plane-wave value

is shown over the extent of the test volume for comparison. The decay in the

field for x and z outside the test zone in figures 7 and 8 is about the same

for the synthesized and uniform arrays. In the z = plane, the electric

field has only a z-component, and there are no cross-polarized components.

For z * 0, there is a small cross-polarized field (E

y

) as shown in

figure 12. (Here we refer to either orthogonal component of the electric

field, E x or E , as a cross-polarized component. In propagation theory, E is more often called a longitudinal component producing a wave tilt.) In general

the amplitude errors in figures 6 through 8 tend to be more significant than

the phase errors in figures 9 through 11. Although not shown here, the errors

in the magnetic field have similar characteristics.

There are several ways to reduce the size of the field errors: (1) in- crease the number of array elements, (2) decrease the size of the test volume,

11
(3) move the test volume farther from the array. An increase in the number of

elements gives more degrees of freedom for the synthesis procedure, but

increases the cost and complexity of the array. A decrease in the size of the

test volume makes it easier to maintain a uniform field, but limits the size

of the test object. In figures 13 through 17, we show numerical results for

y = 2.75 X. Thus the front face of the test volume is now two wavelengths

from the array. All other parameters remain the same. The synthesized currents both with and without a constraint are shown in figure 13. For this

case, the normalized squared error E

n is 0.020 for the unconstrained synthesized array, 0.046 for the constrained synthesized array, and 0.340 for the

uniform array. Thus the errors are smaller, as expected, when the test volume

is farther from the array. The magnitude of the electric field is shown along

the three axes in figures 14 through 16, and the errors are seen to be smaller

than those in figures 6 through 8. The cross-polarized component is shown in

figure 17, and it is seen to be smaller than in figure 12.

Because it is difficult to display fields throughout a volume, only the

fields on the three centerlines of the cube have been shown. However, the

normalized squared error E n which represents the surface field errors is a good indicator of average field errors throughout the volume.

Some cases were run for different values of the element spacing as shown

in figure 1, and the best results were obtained for s = X. For smaller values

of s, the array size gets smaller, and it becomes necessary to decrease the

size of the test volume. For larger values of s, undesirable grating lobes

begin to form. If we assume that spacings on the order of one wavelength are

good for broadside arrays which are not electronically scanned, then the width

of the test volume must be somewhat less than /N X, where N is the number of

elements. In other words, the width of the array must be somewhat greater

than the width of the test volume.

2.4 Mutual Coupling

In the previous sections, the optimum values of the base currents were determined. When mutual coupling between the array elements is neglected, the

input voltages are proportional to the base currents as shown in eq (12). In this section we derive more accurate expressions for the input voltages which

12
include the effect of mutual coupling. The results tell us when mutual

coupling is important and how to account for it.

The base currents I,- and input voltages v^ for the seven-element array

are shown in figure 18. The voltages and currents satisfy the following

matrix relationship:

Vl

v 2

• =

•

•v 7

Zh

Z21

Z71

Z12

Z 2 2

17

•77

(26)

The mutual impedances Z- • are defined as

v. (27)

where all base currents except I- are zero The reflector currents are assumed to satisfy the approximate relationship given in eq (3). Thus the

mutual impedance in eq (27) can be written as the sum of two terms:

I z.. = 1.: ^ z

i (28)

where Z^ • is the mutual impedance between the i and j driven elements and

Z^^ is the mutual impedance between the i driven element and the j re- flector. The ratio (I /I^) is approximately given by eq (3). A more accurate

expression for (I

r /I^) can be obtained by adding seven more equations to eq

(26) and solving the entire set of equations simultaneously [7], but we have

found that the resultant value for (I./Ij) varies little from that given by

eq (3). The expressions for Z^ _• and Z

n

- - r in eq (28) are those for dipoles in

echelon [10],

Because of the double symmetry of the array, many of the voltages and

currents in figure 18 are equal:

v 2

= v H= v 5 = v 7 , v 3 = v 6 ,

13
I 2 = I4 = I 5 = I 7 » and I 3 = I 6

. (29)

Thus there are only three independent voltages (v , v , v ) and currents (I

I , I ) as shown ii duced to three rowsI , I ) as shown in figure 1, and the matrix equation in eq (26) can be re-

"Vi"

v 2 = V3

Zil

Z21

Z31

12 17

37

~h~

I 2

I 3

I 2

I 2

I 3 _I 2 _

Z11 (Z12 + Z u + Z 15 + Z 17 ) (Z 13 + Z 16 ) Z21 (Z22 + Z 24 + Z 2 5 + Z 27 ) (Z 23 + Z 26 ) Z31 (Z32 + Z3i+ + Z35 + Z37) (Z33 + Z 36 )

~Il

h

13

Many of mutual impedances are equal

and

z n z 22 z 33 ,

7^12 =7 =7 =7 =7 =7 =7 =Z ^14 L lb L \7 ^21 ^"23 ^"32 ^i*'

Z 13

:: Z 16 Z 27 ~ Z 3i .

(30)

Z 26

=: Z 37 " Z 35* (31)

By substituting eq (31) in eq (30), we have

Vl

v 2 V3

Zn 4 Z 12 2 Z 13

Z12 (z n + z 13 + Z 24 + Z 25 ) (Z 12 + Z 26 ) Z13 2(Z 12 + Z 26 ) (Z n + Z 36 )

"Il

h

13

32)

14
Z in eq (38) is equal to Z

q

- n in eqs (4) and (12). Thus, eq (32) reduces to

eq (12) only when the mutual impedances U » Z i3, Z , Z25> Z 26 , and Z

3fe

) are

all zero. These mutual impedances decrease in magnitude as the interelement

spacing s is increased.

Since the currents (I , I , I ) are already known from eq (21), the re- quired input voltages (v , v , v ) can be obtained directly from eq (32) by

matrix multiplication. The resultant input voltages are shown in figures 19

and 20 for the same parameters which were used to obtain the currents in

figure 5 and the constrained currents in figure 13. The voltages are normalized to the voltage v

u for a uniform array which is given by

v

u = I u Z in , (33)

where I u is given by eq (B-7) and Z.,- n is given by eq (4). The voltages in

figures 19 and 20 which do not include mutual coupling were computed from eq

(12). Thus the differences between the dashed and solid results are an indication of the importance of mutual coupling. The differences occur primarily

in the phases, but this is not necessarily true for other cases. The effect

of the interelement spacing s on mutual coupling has been studied, and the

mutual coupling has been found to decrease as s is increased as expected.

This is why the hexagonal geometry was chosen to allow a larger interelement

spacing [5],

3. Experiment

The array as described in section 2 and shown in figures 1 and 2 was con- structed, and a series of measurements was performed throughout the test

volume shown in figure 1. A test frequency of 500 MHz was chosen for convenience, although the array can be adjusted for any frequency from 100 to

1000 MHz.

3.1 Array Construction

Each of the seven two-element Yagi-Uda antennas was constructed as shown

in figure 21. The driven dipole element is fed with a dual coaxial transmission line as described in [13], The coaxial lines were in turn fed with a

15
0° - 180° hybrid junction (power splitter), as shown in figure 22, to provide

optimum excitation of the dipole. Each dipole antenna was then tuned for resonance at 500 MHz by adjusting the length of the telescoping arms on the

dipole. The driven to reflector distance d and the reflector length 2h

p (figure 2) were then adjusted according to dimensions in section 2.3; d = A/4

and h

p = 0.26 X, based on the physical length of the driven element (X/2).

The masts for the seven Yagi-Uda antennas were attached to the structure

shown in figure 23. This particular arrangement allowed easy positioning of

all the elements for any chosen frequency (100 to 1000 MHz), with 500 MHz

chosen for this experiment. The dual -coaxial lines from each antenna extended

back and perpendicular from the driven element to a wall of rf absorber

(figure 24). The rf source, power splitting network, and instrumentation are behind the absorber wall and outside the anechoic chamber.

The feed system (power splitting network) consisted of 13 broadband

hybrid junctions, two phase shifters, and two variable attenuators. Six junctions were connected as in-phase power splitters and seven were used to feed

the dual -coaxial lines from the antennas; hence these were connected to

utilize the 0° and 180° ports. The system is better described in figure 25.

3.2 Probe

The rf probe construction duplicated the driven element of the Yagi-Uda

antennas. Here the dipole length was 1/10 X (approximately 6 cm) rather than

X/2 used for the resonant antenna. The same dual-coaxial feed system was used

and these cables were carefully positioned to minimize interactions with the

rf field being measured. As near as was practical, the cables were hidden

behind sections of rf absorber. The signal from the probe then traveled

through coax line along the floor of the anechoic chamber and out through the

door to the instrumentation. Both amplitude and phase of the electric field

components were measured.

3.3 Track

The probe moved through the test volume on a nonconducti ve motorized

track. The motor for the track sat on the base and, through a series of belts

16
and pulleys, moved the probe in a horizontal linear direction. The motor also

drove a precision potentiometer. The resistance of the potentiometer was then

used, after careful calibration, to determine the position of the probe along

the track. The details of the track may be seen in the photograph in figure

26. The direction of the track was aligned with the z axis of the array

coordinates, thus all scans are along this axis. The x position can be

changed by moving the cart (a feature of the anechoic chamber) along the y

coordinate, perpendicular to the array. Thus by selecting an x and y position

and scanning the z direction, the test volume can be mapped. The amplitude

and phase measurements were taken by manually controlling the track position

via a switch located outside the anechoic chamber. At every selected location, the computer was triggered to accumulate the data and store it on disk. A single scan read 60 to 80 data points. A more elaborate arrangement

would have allowed the computer to control the track also; however, this system proved adequate for these measurements.

3.4 Instrumentation

The measurement system (fig. 24), used a vector analyzer (phase amplitude

receiver), digital multimeter to read ohms and hence track position, and a computer/instrument controller. As indicated, the track was positioned manually but all the information was read with the computer. The computer read

both the field parameters and the track position at every test point. The

data were then saved on floppy disk for later processing.

4. Experimental Results and Comparisons with Theory

Four sets of element weightings were applied to the seven element

array. These amplitude and phase feeding schemes were calculated using the

synthesis techniques outlined in section 2. The calculations used two cubic

(A = B = C = 1.75 X in figure 1) test volumes at different distances from the

array, each with and without mutual coupling adjustments. We identify the

four sets of element weightings as feeds 1-4 described below:

Feed 1. Test volume centered at x = 0, y = 1.75 X, and z = without corrections for mutual coupling between array elements (fig. 19).

17
Feed 2. Same as 1, but with corrections for mutual coupling between array

elements (fig. 19).

Feed 3. Test volume centered at x = 0, y = 2.75 x, and z = without correc- tions for mutual coupling between array elements (fig. 20).

Feed 4. Same as 3, but with corrections for mutual coupling between array

elements (fig. 20).

The test results are shown in figures 27 to 53. In all cases, the mea- sured quantity is shown as a function of the z coordinate, f(z). Figures 27

through 41 show both theoretical and measured values. Figures 42 to 53 are measured values only and show more detail throughout the test volumes. All

figures are scans parallel to the z axis at some distance y from the array and

lying in an x = constant plane. Feed 1 was probed in the x = -0.75 X, x = 0,

and x = +0.75 X planes, while feeds 2, 3, and 4 were probed only in the x = plane. All amplitude and phase values are referenced to the center of the

test volume; values there are dB and deg. The test volume boundaries are shown by the vertical columns of dots.

Figures 27 through 29, respectively, show scans in the plane x = along

the near face (y = 1.0 X), center (y = 1.75 X), and far edge (y = 2.5 X) of

the test volume used for feed 1. All three electric field components (E

x

, E , and E

z

) were calculated and measured for each of these locations. The calculated curves (shown by the symbol +) are obviously not those of a perfect

plane wave; rather they represent the best approximation to the plane wave as determined by the synthesis technique for an array of only seven elements. As

the number of elements increases, the field becomes closer to that of a plane

wave [3].

A uniform plane wave would have a constant E z with no E x or E components; hence, E x and E may be considered error fields for this experiment.

Theory predicts an E y component at these close distances to the array and mea- surement confirms it. E is strongest closest to the array (y = 1.0 X) and

decreases as the distance increases. E x is predicted to be zero; the measurement shows that it is small, but not zero (10 to 20 dB or more below E y

).

These data may indicate the effectiveness of the rf probe in being able to

18
resolve the field components or other measurement errors. Hence, little or no emphasis should be placed on interpretation of the E x data.

The E x and E components are low enough as to have an insignificant

effect on typical EM susceptibility measurements. So the remaining figures

(30 to 53) detail only the z-di rected electric field E

z

. The figures are paired to show amplitude and phase under the same conditions; i.e., figures 30

and 31 show amplitude and phase for feed 1 in the x = plane at y = 1.0 X,

1.75 X, and 2.5 X, figures 32 and 33 show the same for the x = -0.75 X plane,

and figures 34 and 35 are for the x = +0.75 X plane. The amplitude data, as presented, can be interpreted as follows. Each grid line directly above any

given pair (calculated and measured) of curves for a particular y value cor- responds to dB. For example, figure 30 shows three pairs of curves, one each for y = 1.0 X, y = 1.75 X, and y = 2.5 X. The center value for

y = 1.75 X is dB as this is the reference point. The center value for

y = 2.5 X is near dB for the measured and about -0.7 dB for the calculated

value. The values for y = 1.0 x at the center are about -3 to -4 dB. Again,

these values are measured from the grid line directly above the curves, with

10 dB between grid lines. It is interesting to note that the field amplitude

does not fall off as 1/r as one proceeds away from the array, but rather

increases initially and then decreases more slowly than 1/r. This trend is

shown in more detail for the theoretical results in figures 6 and 14. Feed 2 results are shown in figures 36 and 37 for the x = plane.

Feed 3 refers to the more distant test volume, and figures 38 and 39 show

data for the x = plane at the near face (y = 2.0 X), center (y = 2.75 X),

and the far boundary (y = 3.5 X) of the test volume. The final pair of graphs

with both theoretical and measured values compared (figs. 40 and 41) detail

feed 4 for the same locations as feed 3.

The agreement shown between experiment and theory in figures 27 to 41 is

quite good. There is one set of data (figs. 32 and 33), howver, where an apparent error in positioning the probe caused a shift in the experimental

data for y = 1.0 X. Feeds 2 and 4 were used to account for mutual coupling

between the elements, but mutual coupling effects are so small that little

improvement is seen in figures 36, 37, 40, and 41. Mutual coupling would be more important if the elements were more closely spaced.

19
In general the measurement agrees well enough with theory that the re- maining measurement data for additional locations are presented alone.

Figures 42 and 53 repeat the same locations as shown in figures 27 to 41 with

additional traces added to show every 1/4 wavelength in y for each chosen x plane. Again, the amplitude and phase values are referenced to the center of

the test volume, the amplitude traces have a dB line directly above each

one, and the corresponding phase for each amplitude trace is on the following

figure. This density of traces is shown to indicate the field uniformity

along the y dimension in addition to the z scan. The amplitude curves can be

visually grouped to show a third dimension and give the viewer a feel for the

field intensity anywhere in the constant x planes.

5. Conclusions and Recommendations

A general near-field array synthesis technique [3] has been applied to a seven-element array of Yagi -Uda antennas in order to optimize the field uniformity throughout a rectangular test volume. The array was constructed and

tested in an anechoic chamber at a frequency of 500 MHz to verify the theory

and to gain experience in controlling the amplitude and phase of the array

elements. The agreement between the measurements and theory was excellent for

both the amplitude and phase of the electric field. The effect of mutual

coupling between the array elements was sufficiently small that the feed cor- rections to account for mutual coupling produced a negligible change in the

measured fields.

There are a number of logical extensions to this work. The magnetic

field could be probed throughout the test volume with a small loop probe. The

Yagi-Uda array was chosen for convenience of analysis and construction in

validating the theory. However, to make the phased array useful for electromagnetic susceptibility testing, we need to be able to scan the frequency over

a large bandwidth, perhaps one or two octaves. This probably can be achieved

by computing frequency-dependent weightings for the array elements, but dipoles might not be the most useful elements because of their frequencydependent input impedance. To achieve very wide bandwidths on the order of a decade, wide-band elements would probably be required. In order to avoid

having to rotate the test object, the angle of arrival of the plane wave could

be scanned electronically, and angular scanning would require a larger number

20
of elements. Also, the appropriate geometry for angular scanning would re- quire further study.

6. Acknowledgements

The authors are grateful to Dr. M. T. Ma for technical discussions during

the course of this work and to W. D. Bensema, E. J. Vanzura, and A. E.

Wainwright for assistance in the construction and evaluation of the array. We

also thank C. K. S. Miller for his continued interest and support.

7. References

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

measurements. IEEE Trans. Antennas Propag. AP-17: 568-575; 1969.

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

cells. IEEE Trans. Electromagn. Compat. EMC-16: 189-195; 1974.

[3] Hill, D. A. Theory of near-field phased arrays for electromagnetic sus- ceptibility testing. Nat. Bur. Stand. (U.S.) Tech. Note 1072; 1984.

[4] Lynggaard, S. K. Plane wave synthesis for antenna measurements. Technical University of Denmark (in Danish), M.S. Thesis; 1982.

[5] Sharp. E. D. A triangular arrangement of planar-array elements that

reduces the number needed. IEEE Trans. Antennas Propag. AP-9: 126-129;

1961.

[6] King, R. W. P.; Wu, T. T. Currents, charges, and near fields of cylindrical antennas. Radio Sci . 69D: 429-446; 1965.

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

Wiley & Sons; 1974.

[8] Harrington, R. F. Field computation by moment methods. New York:

Macmillan; 1968.

[9] Jordan, E. C; Balmain, K. G. Electromagnetic waves and radiating systems. Englewood Cliffs: Prentice Hall; 1968.

[10] King, H. E. Mutual impedance of unequal length antennas in echelon.

IEEE Trans. Antennas Propag. AP-5: 306-312; 1957.

[II] Boisvert, R.; Howe, S.; Kahaner, D.; Knapp-Cordes, J.; Knapp-Cordes, M.

Guide to available mathematical software. Center for Applied

Mathematics, Nat. Bur. Stand. (U.S.); 1981.

[12] Mautz, J. R.; Harrington, R. F. Computational methods for antenna pattern synthesis. IEEE Trans. Antennas Propag. AP-23: 507-512; 1975.

[13] Kraus, J. D. Antennas. New York: McGraw-Hill; 1950, Sec. 14-24.

21
Appendix A. Far-Field Pattern of a Two-Element, Yagi-Uda Antenna

In the far field, the Yagi-Uda antenna of figure 1 radiates only a theta

component of electric field. In spherical coordinates (r, e, <(>), the farfield of the driven element E

Q

d is given by [9]

, jnl . exp(-jkr) cos(kh , cos e) - cos kh , F d

= 9 [ L 9 9.1 (i\_i)

Q 2ttt sin kh, L sine J

* lM l) a

The far-field of the reflector element E

Q r is given by

jnl . exp(-jkr ) cos(kh cos e) - cos kh

E

r = 9 L_ f C Hi ri_o) L

e 2ttt sin kh L sin e

J ' K

' r

where r r = r + d sin 8 sin <f>. The total far-field E fi t can be written

t r d r r jnI

d

GX P("J' kr ) E

e " V + E

e " 2,r

P < 6 '*>

^

where

, cos(kh.cose) - cos kh

sinkh , d

I [cos(kh cose) - cos kh ]exp(-jkd sine sin<j>) + s. C C 1 I. sinkh '* d r

The total magnetic field H.^ is given by

H

* = EgVn. (A-4)

The pattern in the E plane (yz plane) is obtained from P(e, tt/2), and the

pattern in the H plane (xy plane) is obtained from P(tt/2, <f>). For the case plotted in figure 3 where d = x/4 and the phase (l

r /l(i ) is near tt/2, the maximum of |P| occurs at e = <j> = it/2.

22
Appendix B. Uniform Array

In order to determine the actual value of the base current for uniform

excitation I u

, we first consider the equivalent smoothed current density^.

From the previous results [3], J,, is

2 E J = 2 y x H I n -s J -p|y=0

o

- - z. (B-l)

The effective dipole moment of each element ^_ shoul d then equal the sheet current times the area of a hexagonal cell, /3 s 2 /2:

v^ s 2 E . £= «

z - (B-2)

The effective dipole moment of the driven element jd^ is given by

^ -z j I <z') dz',

- h d

where

(B-3)

I.(z') = I d

v

' u

sin k(h

d

- |z|)

sin kh.

The integration in eq (B-3) can be performed to yield

2(1 - cos kh.) „ ^d '' l u k sin kh,

z * (B-4)

Similarly, the effective dipole moment of the reflector element _p_p is

2(1 - cos kh

r

) A

£-r = 1 r k sin kh

Zo (B-5)

where I p

= -I

u l^r /lr

. Since the reflector parameters are chosen to yield an in-phase contribution in the forward direction, the total effective dipole

moment jjj. i s

fit

2 1 (1 - cos kh ,) U r V sin kh

dr (1 - cos kh ) LLl

sin kh J

* (B-6)

23
I u is determined by equating jdj. in eq (B-6) with g_ in eq (B-2)

I =

u

-E ks 2 /3 (1 - cos khj

2n sin kh

"dr

(1 - cos kh ) n Lli-1

sin kh J (B-7)

24
Test

volume

s

Figure 1. Seven-element (equally spaced) array in the xz plane. The

rectangular test volume (A x B x C) is centered on the y-axis at

= y ._ Because of symmetry, there are only three independent excitations (1,1L 2' V25
Reflector

2h. 2h.

Field

point

Driven

element

Figure 2. Two-element, Yagi-Uda antenna. Both the driven and reflector

elements are cylindrical dipoles of radius a.

26
Figure 3. Normalized

antenna in the two

h /A = 0.26, d/X =

far-field pattern

principal

0.25, and

of a two-element, Yagi-Uda antenna

planes. Parameters:

a/X = 5.29 x 10 -3

h d /X = 0.25,

27
Figure 4. Closed surface S of test volume with. two planes of symmetry. The match points are located at r, , and n is the unit inward normal.

For this case, M = M = 2 aTTd M = 4.

28
^ -10° —

3

-20°-

co

Q_

30'

-40<

i

lu

2.0

1.5

1.0

0.5

A=B=C=1.5 X

y =i-75X

2

j

Figure 5. Magnitude and phase of the synthesized currents

the constraint has no effect.

For this case

29
Ez

2.5

/

Uniform array

0.5

Synthesis

/

Plane wave

Y =1.75 X

A=B=C=1.5\

x=z=0

1.0 1.5 2.0

y/X

2.5 3.0

Figure 6. Normalized magnitude of the electric field for a synthesized array

and a uniform array. The perfect plane wave is shown for

comparison.

30
2.5

2.0

1.5

1.0-

0.5-

Uniform array

— X

y =i.75 X

A=B=C=1.5 X

\

\

\

\

\

\ _ Synthesis \

-/ ^

^X A

y=i.75X

z=0

Plane wave \*^^_

I I

\ , -

I _L

0.25 0.5 0.75 1.0 1.25

X/X

Figure 7. Normalized magnitude of the electric field for a synthesized array

and a uniform array. The perfect plane wave is shown for

comparison.

31
^.o

Uniform array

2.0 _ \

y=yo=1 - 75 X

A=B=C=1.5X

x=0

\

\

\

\

\

1.5 — Synthesis \

^

\ ^^

\

\

1.0

Plane wave

^^^^

v -»-^_ ^ ^^^^ *** ^^,*,,,,,"^ 0.5

n I I

I i 0.25 0.5 0.75 1.0 1.25

Z/X

Figure 8. Normalized magnitude of the electric field for a synthesized array

and a uniform array. The perfect plane wave is shown for

comparison.

32
180'

120'

N

^

Oh

<D

CO

j2-60<

a.

-120°

-180°

Uniform

array

3.0

Figure 9. Phase of the electric field for a synthesized array and a uniform

array. The perfect plane wave is shown for comparison.

Parameters: A = B = C = 0, y Q

= 1.75X, and x = z = 0.

33
150'

LU°120°

N

111

CO

CO 90°-

60"

y = y =1.75X

A = B = C=1.5\

z =

/

// \

\

/ X .i~:

\

/

/

/

/

/

/

Synthesis

Uniform

array

1.25

Figure 10. Phase of the electric field for a synthesized array and a uniform

array. The perfect plane wave is shown for comparison.

34
150"

o

LU 120°

N

111

CO

05 90'

60*

y=y =1.75X

A=B= C=1.5\

x = \

Uniform

array

/

Synthesis Plane

wave

0.25 0.5 0.75

Z/X

1.0 1.25

Figure 11. Phase of the electric field for a synthesized array and a uniform

array. The perfect plane wave is shown for comparison.

35
0.5

0.4

0.3-

0.2

0.1

A = B = C=1.5\

y=y =1.75\

Uniform n

array^ x_u

r\\

\

/ \ _ f

Synt u • \ lesis \

/ A-\ \ /^ 1 / >v \ x~

I / N. J\

/ / \w / \

1 / '

\ / // \ /

// Test \ /

]/ volume <—

0.25 0.5 0.75 1.0 1.25

Z/X

Figure 12. Normalized cross-polarized component of electric field for a synthesized array and a uniform array.

36
CO

CO

\J_

lu

-20°

-i

-40° —

-60°

-80°

3.0

A = B = C = 1.5\

y = 2.75\

2.0 —

1.0

n

I

I

I

•

1

1

1

Fi gure 13.

j

Magnitude and phase of the synthesized currents with and without a constrai nt.

37
2.5

2.0-

1.5 -

1.0

0.5 —

Uniform array

Constrained synthesis

Synthesis

Plane wave

yG =2.75 \

A=B = C=1.5 \

x = z=0

1

1.5 2.0 2.5 3.0 3.5 4.0

y/X

Figure 14. Normalized magnitude of the electric field for a synthesized

array, a constrained synthesized array, and a uniform array,

perfect plane wave is shown for comparison.

The

38
2.0

Uniform array

i—-y

1.5

1.0 —

0.5

y =y=2.75 X

A=B=C=1.5 X

z=0

Plane wave

Constrained

synthesis \

\

0.25 0.5 0.75 1.0 1.25

X/X

Figure 15. Normalized magnitude of the electric field for a synthesized

array, a constrained synthesized array, and a uniform array. The

perfect plane wave is shown for comparison.

39
2.0

Uniform array

0.5

y =y=2.75 X

A=B=C=1.5 X

x=0

Plane wave

Constrained

synthesis

1

0.25 0.5 0.75

Z/X

1.0 1.25

Figure 16. Normalized magnitude of the electric field for a synthesized

array, a constrained synthesized array, and a uniform array,

perfect plane wave is shown for comparison.

The

40
Figure 17. Normalized cross-polarized electric field for a synthesized array,

a constrained synthesized array, and a uniform array.

41
v

2

,l 2 v

7

,l

V3^3 v

1-'l

V6»'6

VU° v5-'' "5

Figure 18. Voltages and currents for the seven-element array.

42
204

S

-20*

CO

a.

-40°

Vi

u

2.0 —

1.5

1.0-

0.5

Without Mut. Coup.

With Mut. Coup. -

A=B=C=1.5 X

y =1.75 X

J

Figure 19. Magnitude and phase of the voltages with and without mutual

coupling. These voltages correspond to the currents in figure 5

43
^

-20° —

COco -40°-

-60°-

3.0-

2.0

V;

V

u

1.0 —

—

I

I

l

I

T

I

I

Without Mut. (^oup.

With Mut. Cc>up. _ A=B=C=1.5 X

—

y =2.75 X

—

I

I

1

I

I

1

1

1 2

j

Figure 20. Magnitude and phase of the voltages with and without mutual

coupling. These voltages correspond to the currents in figure 13,

44
RG55U

Coaxial

Cables

Reflector

Element

TWO ELEMENT

YAGI-UDA ANTENNA

Fiberglass

;pL Tube

Cover removed to

expose feed point

Driven Dipole

Figure 21. Construction of two-element, Yagi-Uda antenna,

45
in

Rn/2

180°

To Dipole

Antenna

Pin /2

^

Figure 22. Dipole feed using dual coaxial lines and 0°

junction.

- 180° hybrid

46
Figure 23. Seven-element array and support structure,

47
RF

SOURCE

FEED

SYSTEM

REFERENCE

SIGNAL

TRRCK

CONTROL

LEFT

RIGHT

RNECHOIC CHAMBER

7 ELEMENT ORRRY

e—

-e—

-e—

-e—

-e—

COMPUTER

RF PROBE

TRACK —

CRRT

O O

DIGITAL

MULTIMETER

VECTOR

ANALYZER

Figure 24. Measurement system.

48
-t-> in>>

(/> a

aia;

<T3

CM

ai

49
Figure 26. Experiment hardware:

seven-element array.

probe positioner (track mechanism) and

50
RMPLITUDE (Feed #1)

10

-10

m

u

Q

D

h

M

J

Q_

E

d

-20

-30

-40

-50

60

-2X

1 r— i 1

1 i—i—i

1 -T n 1 ]

1 1 1

. Theo ry + + + + +

, Me asu red

^-vEz^^K

I /

II \ II \ r \\

II

\ Vy Ex^

\

f ' \ II H i Wi • \

\ r\ r\ A-l

\ / ' ^\l

. . , i

1 1 1 1 i i i i i j.. _i —X Center X

Scan the Z dimension

Data -For f CZ) , X = , Y= 1 .

2X

Figure 27. Theoretical and measured electric field amplitude at the center

surface of the test volume (y = X).

51
RMPLITUDE (Feed #1)

m

u

p

D

H

H

J

£L

E

-2\ —X Cen-tar X

Scan "the Z dimension

Data -For -F ( Z ) , X = , Y-1.75

Figure 28. Theoretical and measured electric field amplitude at the far

surface of the test volume (y = 1.75 X).

52
AMPLITUDE (Feed #1)

m

u

Q

H

J

(L

E

£E

-20

-30

40

-50

-G0

-2X —X Center X

Scan the Z dimension

Data -For f (Z), X = , Y=2 . 5

Figure 29. Theoretical and measured electric field amplitude at the near surface of the test volume (y = 2.5 A).

53
Ez AMPLITUDE (.Feed #1)

c

W

>P

\

m

"0Q

-2X —X Center X

Scan the Z dimension

Lines=0 dB relative to Z=0 , X=0 , Y=l . 75

Figure 30. Theoretical and measured amplitude of E

z at three distances from

the array.

54
Ez PHASE (Feed #1

)

360

270

180

90

0)

0)

u

CEI

Q_ -90

-180

-270

360

t 1 1

1 1 1 11 1 1 1

1 1 1 r Theory +H- + + Measured

J L -2X

Y=l .

Y=l . 75

Y = 2 . 5

» ' I I l I L J U —X Cen t. e r X

Scan the Z dimension

Data for fCZ), X =

2X

Figure 31. Theoretical and measured phase of E

z at three distances from the

array.

55
Ez RMPL E (Feed #1

)

>P

\

1 1- x=-

1 1

. 75

i 1 r 1

1 r

Y=l .

1

1

1 1 i Theo r y + + + + + •Measured

y .j. * * \.

/ \ /

! Y=l . 75

//

Y = 2 . 5

1- J » '

-I, _ "- J 1 J J J L 1 1 1 -2X —

Cen ter X

Scan "the Z dimension

Lines=0 d B relative to Z=0, X=0

2X

Y= 1 .75

Figure 32. Theoretical and measured amplitude of E

z at three distances from

the array for x = 0.75 X.

56
Ez PHASE (Feed #1

)

360

270

160

90

0)

t) T3

Id

I

Q. -90

-180

-270

-360

-2X —

Center X

Scan the Z dimension

Data -for f (Z), X = -.75

Figure 33. Theoretical and measured phase of E

z at three distances from the

array for x = -0.75 X.

57
Ez AMPLITUDE (Feed #1)

c

M

>P

\

ra

*o

is

-2X —X Center X

Scan "the Z dimension

Lines=0 dB relative to Z=0, X=0, Y=l.?5

Figure 34. Theoretical and measured amplitude of E

z at three distances from

the array for x = 0.75 X.

58
Ez PHRSE (Feed #1

)

360

270

180

90

U)

o

u

a:i

Q. 90

-180

-270

-360

-2X —

Center X

Scan the Z dimension

Data -for f (Z) , X = +.75

Figure 35. Theoretical and measured phase of E

z at three distances from the

array for x = 0.75 X.

59
Ez AMPLITUDE (Feed #2)

c

•r"M>P

\

m

"0Q

-2X —

Center X

Scan the Z dimension

Lines=0 dB relative to Z=0 , X=0 , Y-1.7S

Figure 36. Theoretical and measured amplitude of E z at three distances from

the array. Mutual coupling effects are included in the feed.

60
Ez PHRSE (Feed #2)

0) 13

u

en

CEi

Q.

360

270

180

90

-90

-180

270

-360

t r t r t r t r T

-2X

Y=l .

Y=l .75

Y = 2 . 5

Theory ++++-

Me asured

—

C&n ter X

Scan the Z dimension

Data -for f (Z) , X =

Figure 37. Theoretical and measured phase of E

z at three distances from the

array. Mutual coupling effects are included in the feed.

61
Ez RMPLITUDE (Feed #3)

o

>P

\

m

&

i r t 1 r X = 0.

Y=2 .

Y=2 . 75

Y = 3 . 5

t —i i r- Theory ++++•

Me asured

-2X —X Cent. a r X

Scan "the Z dimension

Lines=0 d B relative to Z = , X=0 , Y=2.75

Figure 38. Theoretical and measured amplitude of E

z at the boundaries

(y = 2.0 X, 3.5 X) and the center (y = 2.75X) of the more distant

test volume.

62
Ez PHASE (Feed #3)

360

270

180

90

•ou

in

x

x

Q. -90

-180

270

-360

III] 1 1 1

1

1 1

1

Y = 2 .

1 |

1 T 1 Theory + + + + +• Me ssured

,-

/

/" ^

Y=2 . 75

/^

Y = 3 . 5

1 1 1 1 ' ' 1 J- -i— i 1 i l _i

-2X —

Ce n t e r X

Scan the Z dimension

Data for -F(Z), X =

2X

Figure 39. Theoretical and measured phase of E

z at the boundaries (y = 2.0 X,

3.5 X) and the center of the more distant test volume.

63
Ez RMPLITUDE (Feed #4)

c

>p

\

m

Q

T T T T

X = 0.

Y = 2 .

Theory ++++

Me asu red

Y = 3 . 5

I J

-2X -X Center X 2X

Scan the Z dimension

Lines=0 dB relative to Z=0 , X=0 , Y=2.?5

Figure 40. Theoretical and measured amplitude of E

z at the boundaries and the

center of the more distant test volume. Mutual coupling effects

are included in the feed.

64
Ez PHRSE (Feed #4)

360

270

180

90

0)

U

U)

CEI

Q. -90

180

-270

360

1

1 r t 1 r ~i 1 r t

1 r

-2X

Y = 2 .

Theory +•- Me asu red

Y=2 . 75

Y = 3 . 5

—

Cen ter X

Scan the Z dimension

Data for f (Z), X=0

Figure 41. Theoretical and measured phase of E

z at the boundaries and the

center of the more distant test volume. Mutual coupling effects

are included in the feed.

65
MERSURED RMPLITUDE CF&ed #1)

c

M>o

m

o

Scan the Z dimension

Lines=0 d B relative to Z=0 , X=0 , Y-1.75X

Figure 42. Measured amplitude of E

z at X/4 spacings throughout the test

volume.

66
MEASURED PHASE (Feed #1)

c

>p

\

W

ID

I)i.D)

ID P

5)01

-2X —

Center X

Scan "the Z dimension

ZERO Phase at Z=0, X=0 , Y=1.75\

Figure 43. Measured phase of E

7 at x/4 spacings throughout the test volume

67
MERSURED AMPLITUDE (Feed #1)

c

w

>a

\

m

Q

r—i

1 1

1 1 1

1 1 1 1

1

1 r—« X-+.75X

Y=l . 0X

Y-l

25X ^

*

\ Y=1.5\

> j>

! Y=l

75\ ~^^^

s

: y=2 . ex

s

' Y = 2

25X

X

X ; Y=2.5X X

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -2X -X Center X 2X

Scan "the Z dimension

Lines=0 dB relative to Z = , X = , Y=l .75>,

Figure 44. Measured amplitude of E

z at A/4 spacings throughout the test

volume for x = 0.75 A.

68
MERSURED PHASE (Feed #1)

c

>P

\

n

Q)

0)L

m

Q) P

S

en

2X -X Center X 2X

Scan the Z dimension

ZERO Phase at Z-0 , X=0 , Y=1.75X

Figure 45. Measured phase of E

z at X/4 spacings throughout the test volume

for x = 0.75 X.

69
MERSURED AMPLITUDE (Feed #1)

c

V)

'I* >n

m

is

1 1 1 1 X--.75Xi 1 1

1 1 1

Y-i . aX

' 1 ' —

1

Y=l

25X

Y«l . 5X

Y-l

75X

J^

Y=»2.0X

^

^ \

Y »g . 2 5 X

^

-^ \ y=2.5\ ; ^

,i,l i i J ± __j i 1 1 I l -2X —X Center X 2X

Scan the Z dimension

Lines=0 d B relative to Z = , X = , Y=1.75X

Figure 46. Measured amplitude of E z at X/4 spacings throughout the test

volume for x = -0.75 X.

70
MEASURED PHRSE (Feed #1)

c

w>p

\

V)

0)

IDL

0)

01 P

S

01

~2X —X Cent. e r X

Scan the Z dimension

ZERO Phase at Z=0 , X=0 , Y-1.75X

Figure 47. Measured phase of E

z at X/4 spacings throughout the test volume

for x = -0.75 X.

71
MERSURED AMPLITUDE (Feed #2)

c

IA

>Q

\

m

Q

-2X

1 1 r —[ i

1 1

1

1 1 1 j i—i 1 X-0.0X

Y-l . 0X

/ Y=l . 25\

/ / Y=1.5\

S ' Y=l . 75X

y< ! Y = 2.0X

,/ ', Y = 2.25\

y^ '. Y = 2 . 5X x\

- Is ^N

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 —X Center X 2X

Scan the Z dimension

Lines=0 dB relative to Z=0, X=0 , Y=l .75X

Figure 48. Measured amplitude of E

z at x/4 spacings throughout the test

volume. Mutual coupling effects are included in the feed.

72
MEASURED PHASE (Feed #2)

^——

c

o

>p

\

\A

ID

0)Lm

03 P

Q

-2\ —X Csn ter X

Scan the Z dimension

ZERO Phase at Z=0 , X=0 , Y=1.75X

Figure 49. Measured phase of E

z at X/4 spacings throughout the test volume,

Mutual coupling effects are included in the feed.

73
MEASURED RMPLITUDE (Feed #3)

c

(4

>P

\

m

Q

-2X —

Cen ter X

Scan the Z dimension

Lines=0 d B relative to Z=0, X=0 , Y=2.75\

Figure 50. Measured amplitude of E

z at A/4 spacings throughout the more distant test volume (2.6 A < y < 3.5 A).

74
MERSURED PHRSE (Feed #3)

c

w

>a

\

w

tu

QJL

m

iu P

Q

CD

—

1 1 1 X=0. 0X

1 1 1

1 1 11

Y = 2 . 0\

|iii

—^—^*^TM" / Y = 2 . 25\ _ __

Y=2 . 5\

"\

Y=2 . 75X

^\

Y=3 . 0X

/^ ; Y=3 . 25X

Y=3 . 5X

1 1 <

i 1 < 1 1 1 1 1 1——

1 1 — 2X —X Center X 2X

Scan the Z dimension

ZERO Phase at Z = , X=0 , Y=2.75\

Figure 51. Measured phase of E

z at A/4 spacings throughout the more distant

test volume.

75
MERSURED AMPLITUDE (Feed #4)

c

>p

m

T3B

1 1 1

1 X-0. 0\

i 1 1

1

1 1

Y = 2 . 0X

I | . . .

Y = 2

25X

Y=2 . 5X

Y=2

75\

^

\

Y=3 . 0\

N

Y=3

25X

N

^^\^

Y=3 . 5X

\^

i i i 1 i i I _j j _i_ J —i 1 1 -2X — 2X

Cen ter X

Scan the Z dimension

Lines=0 dB relative to Z=0, X=0 , Y=2.?5A

Figure 52. Measured amplitude of E

z at A/4 spacings throughout the test

volume. Mutual coupling effects are included in the feed.

76
MERSURED PHRSE (Feed #4)

c

M

>n

\

VI

03

0)i-U)

0) p

Q

en

1 1

1 1 X=0. 0X

i r i —|

1 1

1

y=2 . aX

i ]

1 1 1

Y=2

25X

Y=2 . 5X

. \

Y=2

75X

Y=3 . 0X

Y=3

25X

N

Y=3 . 5X \

1 A. 1 1 1 1 1 1 1 1 1 1 1 1 1 — 2X —X Center X

Scan the Z dimension

ZERO Phase at Z=0 , X=0 , Y=2.75X

2X

Figure 53. Measured phase of E z at A/4 spacings throughout the test volume,

Mutual coupling effects are included in the feed.

77
NBS»114A (rev. 2-ec) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS TN-1082

2. Performing Organ. Report No. 3. Publication Date

July 1985

4. TITLE AND SUBTITLE

A Near-Field Array of Yagi-Uda Antennas for

Electromagnetic Susceptibility Testing

5. AUTHOR(S)

David A. Hill and Galen H. Koepke

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)

10. SUPPLEMENTARY NOTES

1\ 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 significant

bibliography or literature survey, mention it here)

In electromagnetic susceptibility testing of electronic equipment, the ideal

incident field is a plane wave. To approximate this condition, a seven-element

array of Yagi-Uda antennas has been constructed and tested at a frequency of

500 MHz. The element weightings are determined by a near-field synthesis technique

which optimizes the uniformity of the field throughout a rectangular test volume

in the near field of the array. The amplitude and phase of the electric field

have been measured throughout the test volume with a short dipole probe, and the

agreement with the theory is excellent.

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

antenna array; array synthesis; dipole antenna; electromagnetic susceptibility testing;

mutual coupling; near field; plane wave; Yagi-Uda antenna.

13. AVAILABILITY

\jQ Unlimited

| | For Official Distribution. Do Not Release to NTIS

[~X~| Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

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

14. NO. OF

PRINTED PAGES

82

15. Price

USCOMM-DC 6043-P80

ir U. S. GOVERNMENT PRINTING OFFICE: 1985—579-804/25293 REGION NO. 8


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