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NAT! INST. OF STAND & TECH

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NBS TECHNICAL NOTE 1059

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

- QC

100

.U5753

Mo. 105'

1932
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress on March 3, 1901. The 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 basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

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'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. 'Some divisions within the center are located at Boulder, CO 80303.
OF STAHDARD3

UBHA3Y

DEC 15 1982

A Method to Quantify the Radiation

Characteristics of an Unknown

Interference Source

Mark T. Ma

Galen H. Koepke

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

e

•*FM0»»*

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued October 1982
National Bureau of Standards Technical Note 1059

Nat. Bur. Stand. (U.S.), Tech. Note 1059, 60 pages (October 1982)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1982

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

Price $4.75

(Add 25 percent for other than U.S. mailing)
CONTENTS

Page

1

.

I ntroducti on 1

2. A Short Summary of Fundamental Theory for Determining the Radiation Characteristics of an Electrically Small Source 2

3. Phase Considerations for Determining an Unknown General Source Consisting of Both Electric

and Magnetic Dipole Moments 7

4. Illustrative Examples 20

Example 1 A general simulated theoretical example 20

Example 2 A special simulated theoretical example 24

Example 3 A practical experiment 27

5. Conclusions 32

6

.

References 32

Appendi x 33

1 1

1

A Method to Quantify the Radiation Characteristics of an Unknown Interference Source

Mark T. Ma and Galen H. Koepke

Electromagnetic Fields Division

National Bureau of Standards

Boulder, Colorado 80303

A new method for determining the radiation characteristics of leakage from electronic

equipment for interference studies is described in this report. Basically, an unintentional leakage source is considered to be electrically small, and may be characterized by

three equivalent orthogonal electric dipole moments and three equivalent orthogonal magnetic dipole moments. When an unknown source object is placed at the center of a transverse

electromagnetic (TEM) cell, its radiated energy couples into the fundamental transmission

mode and propagates toward the two output ports of the TEM cell. With a hybrid junction

inserted into a loop connecting the cell output ports, one is able to measure the sum and

difference powers and the relative phase between the sum and difference outputs. Systematic measurements of these powers and phases at six different source object positions,

based on a well -developed theory, are sufficient to determine the amplitudes and phases of

the unknown component dipole moments, from which the detailed free-space radiation pattern

of the unknown source and the total radiated power can be determined. Results of simulated theoretical examples and an experiment using a spherical dipole radiator are given

to illustrate the theory and measurement procedure.

Key words: dipole moments; electrically small; interference source; leakage; phase

measurements; power measurements; radiation pattern; TEM cell; total radiated power.

1. Introduction

As part of a continuing effort to devise measurement methods for quantifying radio frequency

leakage from electronic equipment, a practical method has been developed. The measurement system

shown in figure 1 uses a transverse electromagnetic (TEM) cell to isolate the equipment under test

(EUT) from the environment while providing the coupling mechanism for the necessary power and phase

measurements.

The premise for this approach is twofold. The first is that the cell is well constructed and

operation is limited to the dominant TEM mode only. The second is that leakage currents on the

exterior surface of the EUT may be modeled with equivalent electric and magnetic short dipole sources

[1,2]. These dipoles may then be vectorially combined to yield a composite equivalent source con- sisting of three orthogonal electric and three orthogonal magnetic dipole moments as represented in

figure 2.

It has been shown that the total power radiated in free space by the unknown leakage source under

study can be determined with an experimental setup similar to that given in figure 1 by measuring the sum and difference powers [1,2]. The detailed radiation pattern, however, can be obtained only when

the unknown source is characterized by equivalent three orthogonal electric dipole moments or_ three

orthogonal magnetic dipole moments, but not both . The reason for this is clearly shown in the next

section. For a general unknown radiator characterized by a composite source consisting of both electric and magnetic dipole moments, such as that represented in figure 2, the amplitudes and phases of

the component dipole moments will be equally important for determining the radiation pattern for such

a composite source. Hence, it is the objective of this report to describe additional required

measurements and their theoretical justifications to determine uniquely the equivalent six unknown

amplitudes and six unknown phases displayed in figure 2.

To avoid the complication of having to establish a phase reference physically connected to the

EUT, the phase difference from sum to difference ports in figure 1, namely <j> E

- <)> A

, is measured for

1
each of the six EUT orientations required previously for power measurements. Thus, the measurement

setup described in this report remains essentially the same as before [1,2] except that an additional

instrument capable of measuring the relative sum-difference phase is inserted into the system.

For easy reference and clarity, the previous theoretical work is very briefly outlined in Section

2. It is there that the notation and definition of terms are also established. Section 3 describes

the power and relative phase measurements and shows how the individual phase information associated

with each component dipole moment (both types) can be extracted from these measurements. Specific

results for two theoretically simulated examples and an experiment using a spherical dipole are presented in Section 4. A computer algorithm giving instructions of measurement sequences and numerical

results is included as Appendix.

2. A Short Summary of Fundamental Theory for Determining the Radiation Characteristics of an Electrically Small Source

The electric and magnetic fields appearing at the output ports of a waveguide of arbitrary cross

section, such as one half of a TEM cell shown in figure 3, generated by a current source located inside the waveguide may be expressed as [1,2]:

E - the vector electric field appearing at the right-hand port (la)

n

n n

E = the vector electric field appearing at the left-hand port (lb)

-l b

n e'-'

n

n

fl = the vector magnetic field appearing at the right-hand port (lc)

t n n

n

H = the vector magnetic field appearing at the left-hand port

. v . ,-,(-) " I b

n Hi

_ n

(Id)

where I

~ and FT are respectively the vector orthonormal electric and magnetic basis functions

describing the field structure for each of the n modes that can exist in the waveguide, and a

n and bn are the expansion coefficients.

When the size of the waveguide cross section and operating frequency are such that only the

dominant TEM mode (n = 0) exists, and the current source is placed at z = 0, we obtain, with an application of the Lorentz reciprocity theorem for perfectly conducting waveguide walls [1],

a„ = bvn = -2-"' - 4- 5i • e n (2a)
when the source is a short infinitesimally thin current filament with an electric dipole moment

m = J 31 , edipole; orm - J 3£ , where J is a normalized filament current and 31 is the directed length vector of the short

e

aQ

= - bQ= - ?

jk (mm

x z) • eQ

(2b)

when the source is a small current loop with a magnetic dipole moment m = J'ds , where J

1 is the

normalized loop current, 3s is the vector loop area, k is the free space wave number, and z is the

unit vector along the direction of propagation.

In (2a) and (2b), e

n is the normalized transverse vector electric field inside the TEM cell.

Physically, it is the fundamental mode field generated at z = when a power of one watt is supplied

to the TEM cell. It has mostly the vertical component (y-directed) at the cell center. When the TEM

cell size and frequency are specified, enin v/m can be computed theoretically [3].

When a general EUT is represented by a combination of both small electric and magnetic di poles,

the principle of superposition yields,

aQ

= - -|- (m

e * jk M) • e

Q

(3a)

and

b

=

" \

(S

e

" jk R) ' ~e (3b)

where

R = m x z . (3c) m

The unit for m is in meters (or amp-m normalized with respect to a unit current), and that for m is

in meter-squares (or amp-nr normalized with respect to a unit current). The units for aQand bQ are

in volts.

Taking the sum and difference of (3a) and (3b), we obtain, for the sum power,

P s =

i aO + b

o|

2= K-~e

o|

2 (4a)

and for the difference power,

P d

= K-b |

2 =k2 |M.e | 2

• ' 4b)
Note that the sum power depends only on the electric dipole moment while the difference power depends

only on the magnetic dipole moment. Note further that only the components of rri and M that lie along

the direction of the transverse vector field e~ contribute to the output. From the analysis point of

view, when the current sources (rii and M) are specified, a~ and bu can be calculated to give the field

amplitudes at the cell output ports. Or equivalently, the sum and difference powers can be calculated

from (4). From the synthesis point of view, P

s and P^ are obtained from measurements, and m

e and M

can be determined from (4) to represent the unknown EUT. After m

e and PI (and hence nim

) are determined, the corresponding far-field power pattern radiated in free space may be written as [1]

P(e,4>) = -^J Um2ex+ k2 m

2

x

) (cos

2

e cos

2

* + sin

2 *)

r A

+ (m

ey

+ k2 m

my* ^ cos2e sir,2(t

> + cos

2

*) + ( m

eZ + ^ mmz ) sin2e

2{m

ex m

ey cos(^ex

- *gy

) + k^m^cosU^ - *my

)} sin 2

e sin* cos,

2^ey

m

ez

cos( V ^ez

) + k^m^ cos(^

my

- V)} sine cose sin*

2{m

e2 mex cosU

e2

- *ex

) + k

2 m

mz mmx cos(*mz

- *mx

)} sine cose cos,

+ 2k{rn ni sinU - * ) - m m sin(* - * )} cos( ex my

y exymy ey mx

rey

ymx

+ 2k{m m sin(* - * ) - m m sin(v - * )} sine cos<j ey mz

y eyymz ez myyezymy

+ 2k{m

ezm

mx sin(^

ez

- ^) - m^ s1n(*

ex

- *mz

)} sine sin*] , (5)

where m

ex , m

ey , and m

ez

are the amplitudes of the three orthogonal components of the electric dipole

moment m

Q

, * gx, * and ^ez

are the phases associated with the components of m; m , m , mmz

, ^ mx , ^my, and ^mz

have similar meanings for the magnetic dipole moment m ; A is the operating wavelength; r is the distance measured from the radiator; and and * are the spherical coordinates relative to a chosen origin at the radiator.

The total radiated power is given by

P T

= / P(e,*)dn

1 4tt
2 ^Z- {m 2 + m

2 + m2 + k2 (m2 + m2 + m2

)} 2 ex ey ez mx my mz

40tt 2

, ~72~" l mj 2 + k

2 ImJ

2

) . (6)

It is clear that the total radiated power in (6) depends only on the amplitudes of dipole moments, and

that the power pattern in (5) is much more involved.

Based on the above observation and various properties noted earlier for P

s and P d

, an experimental procedure was developed to measure the sum and difference powers for six different EUT positions, from which the total radiated power and the radiation pattern for an EUT made of one kind of

dipole moment can be determined [1].

Outlining this method, we establish a coordinate system (x,y,z) with respect to the TEM cell with

the origin at the geometric center of the cell, place the EUT at (0, y , 0), assign another coordinate

system (x

1 , y' , z') with respect to the center of the EUT. Initially, we align x-x' , y-y', and z-z'

as shown in figure 4a. We then rotate the EUT counterclockwise by an angle of tt/4 about the z'-axis

so that its position relative to the TEM cell can be seen in figure 4b, measure the sum and difference

powers, and designate them respectively as P

s

^ and P dl . Remembering the transverse electric

field en

= px + -1-1 qy , we see from (4) that only the x- and y-components of the "rotated" transverse

- electric field e' = — (p+q)x + —- (q-p)y and the x- and y-components of m and M contribute to P c1 U /2 /2

e and P dl .

We next rotate the EUT by an additional tt/2, also counterclockwise about the z'-axis as displayed

in figure 4c, and measure the sum and difference powers P s2 and P d2 . Clearly, this time

e~ = — (-p + q)x (p + q)y and the x- and y-components of lii and R make contribution to P

S 2 and

/2 /2~ P d2'

We then align the coordinate frames such that x = y', y = z' and z = x' as shown in figure 5a. Now, we rotate the EUT counterclockwise by an angle of tt/4 about the x'-axis to have a geometric

condition given in figure 5b, proceed to make the sum and difference power measurements, and call them

respectively P s3 and P d3 . Note the eA and the y- and z-components of m and R contribute to P s3 and

P d3 . The EUT is then rotated counterclockwise by another tt/2 about the x'-axis with its position displayed in figure 5c yielding measurements of P s4 and P d4 due to contributions by e'l and the y- and z- components of the dipole moments.

Finally, we align the coordinate frames in accordance with x = z' , y = x' , and z = y' , rotate in

a similar manner as indicated in figures 6a, b, c, and measure P s5 , P d5 , P s6 and P d6 . Now, eQ and the

x- and z-components of m

e and M contribute to P s5 and P d5 while e^ and the x- and z-components of m and M contribute to P s6 and P d6 .

After collecting the measured sum and difference powers, we obtain the following [1]:
and

where

(£,]

1*

• m

ez-

= EC] [P

s ]/2(p

2 + q2

) :7a!

' m

mx

mmy

m_4

EC] [P J/2k 2 (p

2 + q

2

) 7b)

f m m cos(ui - i> )

* ex ey ^ex v ey

ey ez

r eyr ez m m cosU - ib ) ez ex

v ez ^ex ;

[D] [P

$ ]/2(q

2

- p

2

) !7c)

m m cosU - i> )

*\ mx my ymx r my

m m cosU - \\> ) my mz ^my rmz m m coxU - it ) { mz mx vmz mux

= [D] [P d ]/2k

2 (q2

- p

2

) , (7d)

[P

s

]

' p sl

'

p s2

P s3

P s4

P s5

, P s6 ,

(7e)

CPhI

P d2

'dl

'd4

'd3

'd6

'65

(7f)
[C] =

[D]

1 1 -1 -1 1 1

1 1 1 1 -1 -1

1 -1 1 1 1 1

1 -1 f f -f -f

f -f 1 -1 f f

f f -f -f 1 -1

(7g)

7h)

and

f = 2pq/(p

2 + q2

) [71)

From (6) and (7a, b) we see why the sum and difference power measurements alone are sufficient to determine the total radiated power, in free space, of the unknown EUT. From (5) and (7c, d) we see why

the radiation pattern can also be determined by the power measurements under the condition that the EUT may be characterized by either m or m (but not both) even though the phases associated with the

component dipole moments have not been treated yet. For a general EUT consisting of a combination of

both types of dipole moments, the phases as well as the amplitudes of the component dipole moments

will be important for determining the radiation pattern in view of the last three lines in (5).

Before considering the phase measurements to be presented in the next section, we note from (7a)

that the electric dipole moment components are related only to the sum powers, and from (7b) that the

magnetic dipole moment components are related only to the difference powers. Thus, an observation of

the relative values of the measured sum and difference powers may reveal the basic characteristics of

the unknown EUT as to whether it is of electric type, magnetic type, or both.

3. Phase Considerations for Determining an Unknown General Source Consisting of Both Electric and

Magnetic Dipole Moments

The results in (7c, d) contain limited phase information already. Once the amplitudes of the

component electric dipole moments are obtained from (7a), application of (7c) yields

ill v

- $> = cos

ex

y ey H

P sl - P s2 + f(P

s3 + P s4 - P s5 - ^

2(q

2

- P

2

) m

ex m

ey

'el (8a)

U)y

- tfi = COS

ey rez

P., - P., f(-P

sl

- P s2

P s5

+ P s6 ) •1

[

r s3 ~ r s4 2(q

2

- P

Z

) m

ey mez

7 e2

(8b)

and
, r„«-lf

P s5 - P s6 + f(P

sl + P s2 - P s3 - P s4 ) ] . fl *ez " *ex

= cos

{ 7T2 2, m m J

=

e e3 ' (8c)

s 2(q - p ) m

ez mex

where the results have been designated as 9 ., i= 1,2, and 3.

Similarly, we obtain the following with the aid of (7b) and (7d):

_-lf

- P dl + P d2 + f(P

d3 + P d4- P d5- P d6M n ,o , *mx " V

= cos

I ~

2,2 ~T, -I =

9 ml (9a)

2k (q - p ) m

mx m ^

, -1 f - P d3 + P d4

+ f( - P dl - P d2+ P d5+ P d6 } > V - V

= cos

I 91 2, 2 2, -

2k (q - P ) m m

mz

m2

!9b)

\|) y - i|> = cos

mz

rmx

' " P d5

+ P d6 + f(P

dl + P d2 " P d3 " P d4 )

2k V - p

z

) m

mx

mmz

3 m3

* (9c)

Note that (8) and (9) give some phase relationship between the component dipole moments of the same kind only . The phase relationship between the components of mixed types, which is also necessary for

determining the power pattern in (5), has to be obtained by other means.

To avoid the difficulty of having to establish a phase reference with respect to a physical point

on the EUT, and to keep the measurement setup simple, we only insert an additional instrument into the

previous system [1,2] that has the ability to measure the relative phase between the sum and difference ports, as shown in figure 1. We will now present the necessary derivations to demonstrate that

the relative sum and difference phases measured at the same six EUT orientations as those for measuring the sum and difference powers are sufficient to extract the individual phase information for the

component dipole moments.

Referring to (3a), (3b), and figure 4b where the first sum and difference power measurements are made, we have, for the sum port,

a + b

=

" S

e

* ~e

= ~

( * m

ex

e ** + *

m

ey

e ^ * { * p ' + ^q

' } (10a)

= -(Aj_ + jB

x

) ,

where

A., = p'm cosij; + q'm cosip (10b)

1 y ex

Y ex H eyy ey

5, = p m simj; + q'm si nil; 1 K ex

r ex H ey

Tey

8

(10c)
p

1 = pcosU/4) + q sinU/4) = (p + q)//2~ (lOd)

q

1 = qcosU/4) - p sinU/4) = (-p + q)//2~ (lOe)

and p and q are respectively the x- and y-components of the normalized transverse electric field

vector e

Q

.

For the difference port, we have

where

a

" b

=

~^ k ^ * ^0

=

~jk

^"m

x ^ ' %

= -k(C

x + jDx

)

(11a)

1 ^ mx mx r my

Tmy

(lib)

and

D, = -q'm cos<j> + p'm cosij;

1 ^ mx

Ymx

K my

Ymy

(lie)

The relative phase between the sum and difference ports for this first measurement orientation is

then,

j

= tan"

1 ^^) - tan

-1 ^/^) . (12a)

When the relation i> = i> - e , from (8a) is substituted above for A, and B-, , and

ey ex el i i'

i|> = i> + 6 . from (9a) is substituted for C^ and Dj, we obtain

tan" (B

1 /A1

) = *ex

- ^12b]

and

-1 tarfMD^) = + - gj (12c)

where

a-, = tan

-1

q' mow sinQQ i i ey el

+ q'm cc.

ex

M ey eJ

;9 el J 12d)

and

B n = tan

, f q'rn cosem1 - p'm

1 ^ mx ml r my

q mmv sin mx

J,MU

ml

12e)
Thus, equation (12a) becomes

'1 = *ex " a

l " ( V " h

] ' :i2f)

or

*ex " V

= *l

+ a

l " h ' (12g)

Note that a, and 3, are obtainable from the measured sum and difference powers in accordance with

(7a, b), (8a) and (9a). Since <h is also available through a direct measurement, the mixed phase

iji - ty required in (5) can then be obtained from (12g).

Alternatively, when the relation * = \p + e . and i|> = * - e . are used in (12a), we have

'1 = *ey " a

l " ( *mx " Bl

}

' or

12h)

*ey " *mx

= *1 + a

l " 3

1 * (121)

where

a,' = tan if -P' m

ex s1n9

el

p'm K cose , + q'm

ex el ^ ey

and

3l = tan

-1 r q' mm« - p' mmw cosem1 1 j mx my ml

iTm K sine , my ml

:i2j)

(12k)

Taking the difference between (12g) and (12i), and using (8a) and (9a) yields

5 el + 9 ml

= a

l " h ' (ai " B

l

} (124)

which may serve as a useful check to determine data consistency.

The truth of (124) may also be evidenced by showing

a

l " al 'el 12m)

from (12d,j), and

'1 p

l uml

(12n)

from (12e,k).

Clearly, either the set of (12d,e,g) or that of (12i,j,k) is necessary from the computation point

of view, provided, of course, that a measured <h is available. This means that we may either compute

10
the relative mixed phase y - y from (12d,e,g) and then obtain its counterpart y - <ji mx also

required in (5) by

iii Y -1(1 = ill -ill - e .. - e , , (12o)

ey

ymxr exy my el ml '

or compute i|» ey

- <ji mx

from (12i,j,k) and then obtain iji ex

- ^m

by

ill v -ill = ill -ill + 8 , + 9 , . (12p) ex ymy v ey

vmx el ml v

When the measured quantities (sum and difference powers, and the relative phase (Jm between the sum and

difference ports) are not contaminated by noise, there will be no inaccuracy contained in the computed

values. The computation from either of the above two sets is then equally good and yields identical

results. However, when the computed values are relatively inaccurate because of the noisy measured

quantities, more reasonable results may be obtained from one set of computations than the other, as will be evident later in Example 3. For this reason only, the derivations for both sets of

computations are presented above.

At the second measurement orientation shown in figure 4c, we have

a Q + bQ

= -m

e

• ej = -(A

2 + jB,,) (13a)

a Q

- bQ= -Jk(m

m

x z) • ej = -k(C

2 + jD

2

) , (13b)

where

and

A

2 = q'm

ex cos*

ex

- p'm

ey cos*

ey

(13c!

B„ = q'm si nil; - p'm si mp (13d)

2

H ex

T ex

K ey

r ey

co

=

P' mnw sini|»mv - q'ni siniji , (13e)

2 mx mx n my

r my

D„ = p'm cosili + q'm cosili . (13f)

2

K mx

y mx M my

ymy

Note that A

2

, B 2, C

2 and D

2 above can be obtained from (10b, c) and (llb,c) merely by replacing p' by

q

1 and q' by -p' in the latter expressions. This is so because the measurement orientation for EUT in figure 4c differs by 90° from that in figure 4b. Thus, the relative sum-to-difference phase now becomes

<fr 2

= tan"

1 (B

2 /A2

) - tan"

1 ^/^) , (14a)

which is of the same form as that in (12a) except a change in subscript from 1 to 2.

11
The same application of ^ ey

= i|> ex- e el and i> m

= $ + e ml

in (14a) yields

tan

_1

(B

2 /A2

) = ^ - Og , (14b)

tan

_1

(D

2 /C2

) = ^my

- 32

, (14c)

*2

= ^ex " a

2

- { % ~ B 2

)

' (Ud)

*ex " %

= *2

+ a

2

" e 2' (14e)

where w -p'm sine . ,

2 k q m

ex

- p m cose

el

J

or

and

-1 " p m

r °"> = tan -r- . 5 Z l -pv m sine , mx ml

. ( -p m cose , - q m > + ,„-! f mx ml H my I M . x So = tan irns—?m?r-——J • (U9 }

Note that (14e) and (12g) should give an identical result for ^ex

- y if no error is present in

the measured quantities. When errors are present because of the noisy measurement background,

inaccurate readings of the instruments, or other reasons, the results from (12g) and (14e) are no longer identical. The difference between them may be indicative of the quality of the measured

quantities involved. In practise, we may be forced to take the average of them as the final result

for ^ex " V*

Alternatively, we obtain the following, if the relations ip = i|» + e , and ^m

= \p mx- e m^ are used in (14a),

*2

= *ey " a

2

" <V " ^ > (14h)

or

where

*ey -*mx

= *2 +a2- e 2 ' (14i)

i < -Q'^v sine . .. a' = tan'

1 —, —** £} ] , (14j)

2 I q m

ex cose

el

- p m

ey

J

and

. •». -

1

, f -p m -q m cose , ^i 3' tan'

1 f g» JBL TMLj . (14k)

2 l *« m

my

sin9

ml j

The identities,

a

2

" a

2 = °el

12

(14A)
and

3» - e 2 - e ml

(14m)

may also be useful for the purpose of checking data consistency.

Furthermore, the equality of (12g) and (14e) also helps to establish the following important

phase relationships between e

1 and e , :

or

where

sine

ml

= M

12 /N12 (15a]

sine

el

= M^

2 /N^2

, (15b)

2 2 M

12

= 2(m

mx " mmy

) m

ex mey sin6el

+ (m ex" m

ey

)(mmxm

ly ] tan(

*l " *2>

2 2 M10 = - 2(m - m ) m m

12 ex ey mx my

+ 4rn nim m tan (<*>«- <i> ) sine . ex ey mx my

y

l Y2 el

M

12

= 2(m

ex

" m

ly ] Vm

my

sin6

ml

(15c)

(15d)

2 2 , , 2 2 W " m

ey

} (mmx " %•

(15e)

'"') ( m

mx " mmJ tan ^i " *2 }

and

N i2

=

" 2(mmx " m

my

} m

exm

ey

+ 4 m m m m tan(<f>, - <t> ) sine . . (15f)

ex ey mx my

T

l Y2 ml

The importance of (15a, b) can be seen when we refer to (8) and (9). In addition to the obvious

constraints,

e el + e e2

+ 6 e3

= ° (16a)

and

3 ml + 9 m2

+ 9 m3

= ° (16b)

there is still a sign ambiguity for 8 . and e ., i = 1,2,3, based on the power measurement data and

ei mi the operation of taking inverse cosines. Equation (15a) or (15b) will solve this problem of sign

ambiguity in the sense that only one particular choice of sign set will satisfy (15a) or (15b).

13
Similarly, the other four EUT orientations discussed in Section 2 yield:

<j> 1 = tan"

1 (B./A

i

) - tan

_1

(D./C.) , i = 3,4,5,6 (17)

where A3, B3, C3 and D3 may be obtained from (10b, c) and (llb,c) when the subscript x in the latter

expressions is replaced by y and y by z; A^, B^, C4 and D^ from (13c,d,e,f) by doing the same changes

in suscripts; A5, B5, C

5 and D5 from (10b, c), (llb,c) and Ag Bg, Cg and Dg from (13c,d,e,f) by

changing the subscript x to z and y to x.

More explicitly, we have

A

3

= p

' m

ey cos*ey

+ q

' m

ez cos

*ez ' (18a)

B

3 =

p

' m

ey s1n

*ey

+ q

' m

ez

s1r%z ' (18b)

Co = q'mm%/ si n^mw - p'mm, sin^m, , (18c)

3 my r my v mz rmz

3 my T my r mz mz

A

4

=

q

' m

ey cos

*ey " p

' m

ez cos*ez ' (19a)

B4

= q

' m

ey

sil%y " p

' m

ez

si %z » (19b)

c/i = -P' mmw sin* ' - q'mm, slna , (19c)

4 my my ^ mz mz

D/i =

P' mmw C0S,L„ + q' mm, cos^-, ;

( 19d ) 4 my T my ^ mz mz

A

5

= p'm

ez cos^ + q'm

ex cos^ , (20a)

B

5 =

p

' m

ez s1n

*ez

+ q

' m

ex s1n^ex » (20b)

C

5

= q

' m

mz

sin

*mz " p

' m

mx s1nV ' {20c)

14
Dc = -q'm cosui + p'm cosii; ; 5

H mz

vmz y mx mtix

' (20d)

and

6 ^ ez

y ez K ex yex

' (21a)

B c = q' m~, si ni^_ - p'ni sirni> , 6 ^ ez

r ez K ex

yex' (21b)

c

6

= "P' mmr sin^m7 "

q' mmv

s1ni|»mv , mz

T mz n mx

T mx

(21c)

Dc

=

P ,|TL, cosik + q'm cosi|» 6K mz

ymz M mx

rmx

(21d)

With the substitution of i|> = i|> w

- e » from (8b) and * = i + em0 from (9b) in (17) for i = ez ey e^ my mz mc. 3 and 4, we obtain:

and

> = i|) - a- - (i|> - e ) 3

y ey 3ymz 3 !22a)

4

= *ey " a

4

" ( *mz " e4

} ; (22b)

yielding

*ey " *mz

= *3

+ a

3

" e 3

= *4

+ a

4

" e 4 • [22c)

where

a- = tan

-1 q in sin

ez *'" ue2

I P' m

ey

+ q

" m

ez cos9

e2

>' (22d)

S, = tan

-1

q 'in cose _ - p'm

_ my m2 r mz qiL, sinem0 my mZ

(22e)

and

a. = tan

-1 -p in sin

ez °" ,u e2

Tr rr

q m

ey

- p m

ez cosee2

(22f)

3 4

= tan

r my m2 _ mz -p'm r mw sinem0 my m2 /

(22g)

15
In addition, equation (22c) also yields a relationship between e _ and e ?

Sin9

m2

= M

34

/N

34 !23a)

or

where

M

34

= 2(m

my

sine

e2

= M^/N^ ,

mm„ ) m^w m^, sine ~ mz ey ez e2

+ (% " m

ez

) (m

my " V) tan( *3 i) .

!23b)

(23c)

N - = -2(m - m ) m m

34 ey ez my mz

+ 4m m m m tan{i>~ - a.) sine „ ey ez my mz

y

3

r4 e2

(23d)

2 2 M 34

= 2(m

ey

" m

ez

) m

my

mmz

S1

' n6

m2

+ (m

ey

" m

ez

} (m

my " mmz

) tan( *3 " *4 }

(23e)

and

N' = -2(m2

- m

2

) m m

34 my mz ey ez

+ 4 m m m m tan (<)>., - a.) sine - ey ez my mz

y3

r4 m2

(23f)

Alternatively,J ' with the substitution of ^r = i> + e and \\> = \\> - e „ in (17) for i = 3 ey

r ez e2 ymzrmy m2

and 4, we obtain:

and

3 ez 3

rmy 3 (24a)

>4 = *ez " a

i

" { % ' 3 4

} ; (24b)

yielding

n ' ^ez " *ny

= *3

+ a

3

" 3 3

= *4

+ a

4

" '4 ' (24c)

where

, _ i I -P m

ey s1n6e2

a

3

" t p'm

ey cosee2

+ q"m

ez ) [24d]

$2 = tan"

q mmiJ - pnm7 cosem„

2 my r mz m2

p'ni r sinem0 mz m2

(24e)

16
•q' m

ey

S1

' n9 e2

k q m

ey cosee2

- p m

ez J'

(24f)

and

$\ = tan

-p m - q m cose „ -1 | K my H mz m2 qm„, sine„ ^ mz m2

(24g)

Of course, the second relation in (24c) yields the same relationship between - and e ? as those in

(23a,b). The following identities,

a

3

- a

3

= a

4

- a

4

= ^

and

p 3

- p 3

- p 4- p 4-

C|n2

may be useful for checking the correctness of various quantities,

(24h)

(241)

Applying the relationships of \\> = <|/ - 8 _ from (8c) and <jj = <|i + e _ from (9c) to (17)

with i = 5 and 6, we obtain:

and

5

y ez 5ymx 5 ' (25a)

yielding

>6 = *ez " a

6

" ( V " e 6

}

' !25b)

where

*ez " *mx

= *5

+ a

5

" B

5 = *6

+ a

6

" e 6 (25c)

etc = tan

-1 q ni sine "i H ex e3

„ p'm„ K + q'm cosTT"

ez

M ex e3 ' (25d)

3 5 = tan

1 f q' mm, C0S6m-3 -P' mmv

N -1 ^ mz m3 r mx

q mm, sin mz m3

(25e)

and

•pm

ex sinee3

a

6 = tan

L q'm

ez

- P -m ex cos^ !25f)

B 6 = tan

r mz m3 mx -p'm r m, sinemQ mz m3 / (25g)

Also, equation (25c) yields a relationship between 8 _ and 9 _ ,

17
or

where

Sin6

m3

= M

56 /N56

s1n6

e3

= M

56 /N56

(26a)

(26b)

2 2 M

56

= 2( V " V)mezm

ex sinee3

+ (mez

" m

ex

)(mmz

" V) tan( *5 " V '

(26c)

.2 _2

N 56

= - 2(m

ez

" m

ex

)mmzm

mx

+ 4m

ezmex m

mzmmx

tan( *5 " V sin9

e3 ,

( 26d)

2 2 M

56

= 2(m

ez

" m

ex

) Wsine

n,3

+ (mez

" m

ex

)(mmz " m

mx

) tan((f> 5

" H] (26e)

and

N 56

=

" 2( V " V)mezm

ex

+ 4m

ezmexW tan( *5 " *6 )sin9m3

(26f)

Alternatively,J if we use \j> = ib + - and ij* = to - 8 - in (17) for i = 5 and 6, we obtain;

ez ex e3 mx mz m3

and

*5

= ^ex"

a

5

" { *mz ' 3 5

}

' (27a)

) 6

- ^ ex- aj - hm

- 3') ; (27b)

yielding

to - to = <b r + a'r - 3r = i> c + a!. - $'

r c exT mz

y

5 5 5

r 6 6 6 !27c)

where

-If

" p m

ez sin9e3

a

5 = tan

{ p'ni cose - + q'tn ez e3 H ex

(27d)

3c = tan 2 mz mx m3

p'mmv sin e r mQ mx m3

(27e)

al = tan

-1 q'm

ez sinee3

q m

ez cosee3

- p m

ex

(27f)

and

18
i *,„-l mz ^ mx m3

r - tan

6 ^ m

mx

sine

ni3 (27g)

Of course, equation (27c) yields the same relationship between e - and - as given in (26a, b). The

following identities for possible checking purpose are also obvious,

* 5

- »

5

- »

6

- *6 " G e3 » and

a r - a r = ar - a^ = i _., , (27h)

3 5

" 3

5 =

3 6

" 3 6

= 9 m3

' (27i

In addition, from (12f), (14d), (22a, b) and (25a, b), we have another useful checking relationship:

*1 " *2

+ ^3 " <f) 4 + *5 " *6

= a

2 + a4

+ a

6

" ^ a

l + a

3 + a5^

+ e

1 + 3 3 + e 5

- (3

2 + b 4 +Bg

)

Similarly, from (12h), (14h), (24a, b) and (27a, b), we also have

>1 -

<i>2 + *3 " *4 + ^5 " *6

= a

2 + a4 + a6

" ^ a

l + a

3 + a5^

+ 3

1 + e 3 +e5

" (3

2 + 3 i + e 6*

(27j)

(27k)

Thus, the phases obtained in (12g) [or (14e)], (12i) [or (14i)], (22c), (24c), (25c) and (27c)

together with (7a-d) derived previously constitute the complete set of information characterizing an unknown emitter being investigated, from which the detailed radiation pattern may be plotted in accordance with (5).

After the rather lengthy formal derivations presented above, it is instructive to summarize a few

points, (i) The sum and difference power measurements taken at the proposed six EOT positions are sufficient to determine the equivalent six unknown dipole moments amplitude (mex , m

ey , m

ez ; m^, n^y,

m^), and the total power radiated by the unknown EUT in free space, (ii) The same power measurements are not enough to determine the detailed radiation pattern if the EUT is made of both types of

dipole moments. To achieve this objective for the general case, the relative phase measurements

between the sum and difference ports taken at the six prescribed EUT positions are required, (iii)

An examination of the power pattern expression given by (5) shows that all phase terms appear as relative quantities (i.e., i|» - <|; )• This permits specifying one phase angle as a reference,

assigning an arbitrary value to it, and resolving the five remaining angles relative to the chosen

reference. Of course, the reference value assigned will have no effect on the final radiation power

pattern, (iv) To extract the remaining five relative phase angles from the measured power and phase

data (P si) P di , ^, i=l,2 6), after choosing one of the six phases i|/ ex>

^ey

, <J> ez

; ^m, ^my

, \z as

a reference, it is necessary to use:

19
(A) One set of three equations from either (8) or (9) with the constraints

given by (16a) or (16b),

(B) (12g) or (He),

(C) one of the relations in (22c)

and

(D) one of the relations in (25c)

for a total of five independent equations. The sign ambiguity in (8) or (9) is solved by (15a),

(23a), and (26a) [or (15b), (23b), and (26b)].

Three examples are given in the next section to illustrate the above summary.

4. Illustrative Examples

Since the equations required for extracting the unknown phases are quite involved, we wish first

to verify their usefulness and validity by two simulated theoretical examples so that the problem is not futher complicated by practical considerations such as measurement inaccuracy caused by the background noise and imperfect readings of the instrument.

Example 1 . Suppose the equivalent electric and magnetic dipole moments in meters and square-meters

respectively and phases in degrees representing an unknown EUT are:

m = 1.6, <() = 0, ty 80

,

v

= 60 ; ez

yex' rey' yez m = 0.4, i> = -80

,

ip = -60

,

\L> = -45 . mz

' rmx' ymy' rmz

In addition, suppose the particular TEM cell used has a cross-sectional area of 1.2mX1.2m so that at

the frequency of 30 MHz, only the dominant TEM mode can propagate and the vector transverse electric

field is computed as e

Q

= xp + yq, where p = and q = 11.83 v/m [3].

In accordance with the material presented in Section 2, we have the following sum and difference

powers,

P sl

= K^ex + m

ey

+ 2m

exmey cos( ^ex " V3 = 425 ' 107856

' (28a)

m

ex

= ^ rn =1.8

ey m

mx

= °' 8 ' m = 0.6

my

P s2

= b

[mex

+ m

ey

" 2m

exmey cos( *ex " V] = 302 ' 626424 (28b)

P s3

= r1 Cmey

+ m

ez

+ 2m

ey mez cosU

ey

" ^ez )] = 784 - 597583 » (28c)

20
P s4

= KCmey

+ m

ez

" 2"ear n,ez

cos(

*€af

" *ez )] = 27 ' 106038

• (28d)

P s5

= K[mez

+ m

ex

+ 2m

ez mex

cos( *ez " *ex )] = 473.027282 , (28e)

P s6 = K[mez

+ 4 " 2m

ezm

ex

cos( *ez " *ex )] = 159.541746 , (28f)

P^i = ik

2

q

2 [m2 + m2

- 2m m cos(i|> - y )] = 2.704333 , (28g)

dl 2

H mx my mx my

ymxymy

' 3

Pao = ic2 q

2 Cm2 + m2 + 2m m cosU - it )] = 52.545279 , d2 2 M mx my mx my miix ymy

(28h)

P,n = iK2 q

2 [m2 + m2

- 2m m cosU -*„,)] = 1.556813 ,

( 281

)

d3 2

M my mz my mz

ymy

ymz

p = k

2

q

2 [m2 + m2 + 2m m cos{^ - « )] = 27.172985 , (28j)

d4 2

M my mz my mz

ymyrmz

P = ik2

q

2 [m2 + m2

- 2m m cosU - * )] = 7.617338 , (28k)

d5 2 M mz mx mz mx

ymz miix

and

p Hfi = ^V^L + m

2 + 2mm

m cosU - *mv )3 = 36.582351 . (28*)

do 2 mz mx mz mx mz mx

The relative sum-to-difference phases in degrees can be obtained from (12f), (14d) and (22a),

(22b), (25a) and (25b) in Section 3 as:

<j. 1 = -103.0261 , <(> 2

= -77.0300 , *3

= -113.5502, (29)

$4

= 105.5593 , 4> 5= 48.1116 , <j> 6 = 91.9132.

We, now, assume that the EUT is unknown and the values given in (28) and (29) are the "measured" sum and difference powers and phases. The problem at hand is then to verify the validity and

usefulness of the development presented in Sections 2 and 3 to see whether the unknown dipole moments

and phases can be recovered to compute the radiation pattern. Using (7) with p

= and q = 11.83, we obtain

4 = (P sl + P s2 " P s3 " P s4 + P s5 + P s6 )/(2

^ =

l ' 96 (3 ° a)

21
m

ey

= (P sl + P s2 + P s3 + P s4 " P s5 " P s6 )/(2q2) = 3 ' 24

• (30b)

.2 , n n.n.n.n.n W,o_2 m

iz

= ( " P sl "

P s2 + P s3 + P s4

+ P s5 + P s6 )/(2 ^ ] = 2 ' 56

• (30c)

mL

= (P dl + P d2 " P d3 " P d4

+ P d5 + P d6 )/(2k ^2) = °' 64 (30d)

m

my

= (P dl + P d2 + P d3

+ P d4 " P d5 " P i6 )/{2k ^2)

= °' 36 (30e)

m

mz

=

( " P dl " P d2 + P d3 + P d4

+ P d5 + P d6 )/(2k2q2) = °' 16 > (30f)

cos( *ex " *ey ) = (P sl " P s2 )/(2q2m

exmey

) = °' 173648 < 30 9>

or ibv

- ib = 6 , = + 80° , ex

y ey el '

cos ^ey

_ *ez ] = (P s3 " P s4 )/(2q2m

eymez

) = °' 939693 ( 30h >

or

*ey " *ez

= 9 e2= * 20 ° •

cos( *ez " *ex } = (P s5 ' P s6 )/(2q2"1 ezm

ex

) = °- 500000 (30i)

or ibr -ib =6 = + 60° , ez

y ex e3 '

cos( <W " V = (P d2 " P dl )/(2k2q2V%) = °- 939693 {30j)

or

*mx " *my

= 9 ml= * 20 °

'

cos( <W " «> = (P d4 " P d3 )/{2k2q2%V} = °' 965926 (30kl

or V " *mz

= 9m2

= *

15 °

'

C0S( V " V = (P d6 " P d5 )/(2k2q2W) = °' 819152 (3(U)

or *m ~ *mx

= 9 m3

= * 35 °

•

22
Clearly, all the amplitudes of dipole moments have been recovered, (16a, b) can be satisfied with two possibilities for each. The sign ambiguity for e ei and emi-, i = 1,2,3 may be resolved by (15), (23)

and (26).

Case 1. Choosing 9 gl

= 80°, e g2= -20°, and e g3

= -60° for (15a), (23a) and (26a), we obtain

sine - = -1.428572, no solution ;

sine ~ = -1.140644, no solution ;

sine _ = 1.070753, no solution .

Case 2. Choosing e ^ = -80°, e g2

= 20°, and e g3

= 60° for (15a), (23a) and (26a) we obtain

sine

ml

= -0.342020 ,

sine

m2

= -0.258819 , (31a)

sine - = 0.573605 , m3

which yield

e ml

= - 20 °' e m2= - 15 °> 9 m3

=35° (31b)

or

6 ml

= - 160 °' 9 m2= - 165 °' 6 m3

=145 ° (31c)

A quick check of (16b) and (30j,k,£) confirms that the solution in (31b) is correct. The false

solution in (31c) should be discarded. Thus,

*ex "*ey

=

" 80 °' *ey " *ez

= 20 °' *ez " *ex= 60 °

• (32)

^mx" V"200

' %' *mz

= - 15 °» k"*«- 35 °

'

Should we start with e ., e ? and e 3 obtained in (30j,k,£) and then use (15b), (23b) and (26b), we would reach the same conclusion.

The application of (12d,e,g), (14e,f,g)," (22c,d,e,f ,g) and (25c,d,e,f ,g) yields

a

x = -45.9877° , B

x = 150.9862° , (33a)

a

2

= 58.4730° , 3 2 = -78.5570° , (33b)

23
and

a

3

= 9.4057° , B3 = 130.8555°

a

4

= -61.5510° , 3 4= -80.9917°

a

g = 27.7958° , Bg

= -64.0926°

a

6

= -53.4132° , Bg = -101.5000°

\py - i|> =60°,^ - * = 125° , ib - i> = 140° . ex

Tmy ' y eyrmz ' rez

rmx

The application of (12i,j,k), (14i,j,k), (24c,d,e,f ,g) and (27c,d,e,f ,g) yields

(33c)

(33d)

(33e)

(33f)

(33g)

and

a^ = 34.0123°

a'z

= 138.4730°

-10.5943°

-81.5511°

a£ = -32.2042°

a

6

= -113.4132°

Bj = 130.9862°

$2 = -98.5570°

3 3

= 115.8554°

e 4

= -95.9917°

3

5 = -29.0926°

6' = -66.5000°

*«„ " *mv

= 160 °

» K, ~ <L»

= 120 °

. K* ' *», = 45 ° • ey

r mx ez

T my exT mz

(34a)

(34b)

(34c)

(34d)

(34e)

(34f)

(34g)

Note that the quantities obtained in (32), (33g) and (34g) fulfill the relative phase requirement for

the radiation pattern in (5). Note further that the relationships in (12£,m,n), (14£,m), (24h,i), and

(27h,i,j,k) are all exactly satisfied.

If, in addition, \b = is chosen as the phase reference, the other phases will be \|> ey

= 80°,

4>T = 60°, to = -80°, i|» = -60°, and ib = -45°, which are exactly the ones assigned in this

ez mx Y my

' r mz 3 particular example.

At this point, one may doubt the validity of the formal presentation if some of the six amplitudes of the dipole moments vanish. To eliminate this doubt, another theoretical example is given

below.

Example 2 . Suppose the input data remain the same as those presented in Example 1, except that m^ =

0. Naturally, under this condition, \|» has no meaning. The sum powers and the first two difference

powers should also remain as those obtained in (28) because they do not involve m^. The other

difference powers will be different. They are:

d3

r d4

: ^my72 = 9 - 944930 (35a)

24
and

P d5

= P d6= kVn£x /2 = 17.679876 . (35b)

By the same reason, <f>- and $- should have the same values as those given in (29). The other sum-todifference phases in degrees may be obtained from (17) as:

4> 3 = -139.4057, 4> 4

= 111.5511, ^ = 22.2042 and $

fi = 103.4132 . (36)

Note that, for this special case, we not only have P.- = P.. and P.

5 = P.g as given in (35), but also

have 2(P .- + P.r) - P .. - P . ? = 0. In fact, these relations insure m^ = as can be easily seen from

(7). The sum-to-difference phases <j>. have, however, no simple relationship.

Again, from the testing point of view, we assume that the powers given in (28a through h) and

(35a, b) and the sum-to-difference phases given in (36) together with <h = -103.0261° and ^^ ~ -77.0300° are the "measured" values. Obviously, all the dipole-moment amplitudes can be totally

recovered by the same exercise presented in (30a through f). The relative phases associated with the

electric dipole moments also remain the same as before, namely, Q Q ^ = +80°, e e2

= ±20°, and e e3

= +60°. The only relative phase associated with the magnetic dipole moment is still Q m± = +20°. The

other relative phases associated with the magnetic dipole moments, 8 „ and 6 _, are undefined because

they both involve the meaningless quantity ty . Fortunately, they are not required, as can be seen

later.

Case 1. Choosing 9 . = 80°, Q^ = -20°, and e e3

= -60° for (15a), we have

sine . = -1.428572, no solution.

Case 2. Choosing 9gl

= -80°, Q q2

= 20°, and e g3

= 60° for (15a), we have

sine

ml

= -0.342020, or e - = -20°,

which implies that the correct solution should be:

(h _ ,h = -80°, 4> - ill =20°,^ -ill = 60°, and ill - $ = -20° . (37a)

Note that the other possible solution of e = -160° is discarded in view of (28g) and (28h). So long

as P d2

>P

dl , we always have

| 9 ml | <90°«

25
The conditions (12g) and (12i) yield respectively

and

the condition (24c) yields

*ex " V

= 60 ° • < 37b > V " *mx

= 160 ° ; (37c)

* ez " % - 120 ° • ' 37d >

and the condition (25c) yields

*ez " *mx

= 140 ° ' (37e)

The relative phases so extracted above are all required by (5) for computing the power pattern for the

emitter being considered. The other conditions, (22c) and (27c) are meaningless in this case. Note

that the values for a., a'. , (i = 1,2,3,4,5,6), p., p„, pJ, pi remain the same as those given in (33)

and (34) since they involve only 6 . (i = 1,2,3) and 8 . . The other p. and p! become

P

3

, p., Pg, pg undefined,

(38)

P 3

' = 90° , p^ = -90° , P 5

= -90° , P6

= -90° .

Of course, when <|> = is chosen as the phase reference, we obtain from (37)

4>r = 80°, <|> = 60°, i|) = -80° and <|i = -60° (39) ey ' r ez ' ymx

rmy

Thus, we demonstrated that the theoretical development presented in this report is also

applicable to the special case when one of the component dipole moments vanishes. The same conclusion

is valid when any one of the other five component dipole moments is zero. For example, when m^ = 0, we will have P dl

= P d2 , P d3= P d4 , and 2(P dl + P d3 ) - P d5 - P d6 = 0; and e ml and 9 m2 will be

meaningless. As another example, if m

ex

= 0, we will then have P

s

^ = P s2 , P

S 5

= P

s s, and 2(P

S

^ + P s5 )

- P

S 3

- P s4 = 0; and e e

^ and e e3 will have no meaning.

The formulation is also good when any two or more of the six component dipole moments vanish.

For example, when mmy

= m^ = 0, we will have P.. = P

rf2 = P d5

= P d6 , and P.- = P.. = 0; and

all 8 . (i=l,2,3) will have no meaning. Then e . , e ?

, e _, and \\> - i> from (25c) will be

sufficient to give the correct solution. As another example, if m = m = 0, we then have P

S 3

=

P s4> P s5

= P s6* 2 ( p s3 + P s5> " P sl " P s2

= Q > P d3

= P d4> P d5 = P d6> 2 < P d3

+ P d5> " P dl " P d2

= °> and

26
'e2» °e3 : >m2 : an d m3 will all have no meaning. Then, 8 ., (12g), ( 1 4 i )

, and (15a) will give an unambiguous solution for the relative phases.

After demonstrating the usefulness and validity of the theory and computation procedures outlined

in Sections 2 and 3 by two theoretical examples, we now give a practical example based on actual

experimental data. It should be anticipated that the procedures involved will not be as straightforward as those for the theoretical examples because the measured inaccuracy and noise will

mask the consistency required by various equations.

Example 3 . In this experiment, the unknown EUT is represented by a spherical dipole radiator with a radius of 5 cm. The radiator consists of two hemispherical shells which are fed at the poles and held

together by threading onto a dielectric disc such that there is a gap of 3 mm between them. The

electronic circuitry feeding the dipole is enclosed within the shells and consists of a batteryoperated power supply and a 30-MHz crystal oscillator followed by an amplifier. Thus, the radiator is self-contained and no external connections are needed.

The radiator, with an arbitrary orientation, was placed at the center of the upper chamber of a TEM cell of 1.20 m X 1.20 m X 2.40 m. The measured sum powers in watts, difference powers in watts,

and relative phases in degrees between the sum and difference outputs at the six positions depicted in figures 4, 5, and 6, as recorded by the computer in the experimental system, are as follows:

P sl

= 9.935735(10" 6

), P s2

= 8.855233(10" 10

)

, P s3

= 2.224334(10" 6

)

P s4

= 2.674238(10" 6

), P s5

= 2.329164( 10" 6

)

, P s6

= 2.80027K10"6

)

,

'd2d5

P dl

= 2.640584(10"°),

P d4 = 5.91153K10"9

), P

<!>]_ = -32.94, i> 2

<)>3 = 166.5, <j>4

<j>5 = 168.66, <|>g

5.391381 (10

-12

) 5.268658U0"9

),

'd3

>d6

5.031529(10" 9

), 1.179506(10"°);

= unstable because of weak levels of P

S 2 and P^-.

= -13.5

= -48.6.

An examination of the relative values of the sum and difference powers confirms that this

radiator is essentially an electric-type source, as it should be. We, nevertheless, treat it as a combination of both types even though the magnetic dipole moments are not as important as the electric

counterparts. The frequency of 30 MHz assures that only the dominant mode may exist inside this

cell. The size of the radiator is, indeed, small compared to the cross section of the cell and to the

wavelength of 10 m. The normalized transverse electric field at the radiator center for this

particular example is estimated at e

Q

= 11.825y v/m [3]. That is, p

= 0, q= 11.825, and the field is

purely y-directed.

The amplitudes of the dipole moments extracted from these measurement data in accordance with

(7a, b) are:

m

ex

= 1.906736U0" 4

), m

mx

= 1.716559U0" 5 ),

m

ey

= 1. 862939 (10"4

),

"to

1.35566K10"5

),

'"ez

"Viz

= 0.180769(10"4

), = 0.380153(10" 5

). (40)

27
The relative phases between the dipole components of the same kind may be extracted in accordance

with (7c, d) [or (8) and (9)] as:

cose el =1.0, e el

= * ex

- *ey

= 0°, cose e2 = -0.477711, e e2 = *ey

- ^ez= + 118.5360°,

cose e3

= -0.488734, 6 e3= ^ez- ij> ex= +119.2574°,

cose ml = -1.0, 8 ml = ^mx

- ^my= ±180°,

cose m2

= 0.154661, 6 m2= ^my

- x\> mz

- ±81.1028°,

cos6m3 = 0.905867, 6m3 = r|>mz

- ^mx- ±25.0596°. (41)

Since the measurement data involve inaccuracies due to background noise, instrument errors, etc.,

obviously we should not expect a perfect satisfaction of various restraining equations as for the

theoretical examples considered previously. For example, to satisfy (16a), we may choose (a) 9 e

^ = 0,

e e2 = 118.5360°, and 6 e3 = -119.2574°, or (b) e el = 0, 6 e2 = -118.5360°, and e e3 = 119.2574°. Either

of these two cases yields a small error of less than 1°, which implies that the accuracy on the

measured sum powers and the values of m

ei

- , i = 1,2,3 deduced from them is quite acceptable. However,

the values of e mi

- do not nearly meet the requirement in (16b). In fact, the smallest deviation among

various combinations of emi

- from (16b) is of the order of 74°. This is not surprising in view of the

relatively weak levels of m^- . Since cose m^ involves P d2 - P^ and the measured P d2 is a few orders

smaller than the measured P d

j, we are certain that |eml l>90°. Whether or not the absolute value of

e m^ is closer to 180° as obtained in (41) depends naturally on the actual accuracy. Similarly, since

the measured P dg is quite stronger than the measured P d

g, we may be certain that cosem3 determined by

P dg

- P^g is positive, giving an absolute value for 6 m3 smaller than 90°. Of course, the true value

for e m3 may be much different from 25° as approximately shown in (41). As for e m2 , the situation is

very different from e ml and e m3 . Since the measured values for P d3 and Pd^ are quite close, the true value for cosem2 determined by P d4

- P d3 may be small -positive or small -negative. Thus, the absolute

value for e m2 may be greater or smaller than 90°. The above analysis explains that the condition

(16b) is still likely to be met if the accuracy involved in the measurement of difference powers is more reasonable. In any case, we still have other conditions such as (15), (23), and (26) to be

examined.

Case 1. Choosing e el = 0°, 8 e2

= 118.5360°, and 8 e3= -119.2574°, we obtain respectively from (23a)

and (26a):

sine m2

= -0.282754 yielding 6 m2 = -16.4246° or -163.5754°

and

sine m3 = 9.364986/4.105186 = 2.281247, no solution.

In examining (26a) more closely for this case, we find that the result of an unrealizable e m3 is

mainly due to the chosen negative sign for e e3 even though the values for m

ex , mez , m

mx , m^ and the

measured <t>g and <t>g are all somewhat responsible. Even a substantial deviation in all of these values

in view of the implicit measurement errors is not likely to yield a realizable value for e m3 so long

as a negative sign is chosen for e e3 .

28
The value for e m^ cannot even be determined from (15a) because it requires <^ and <f> 2

, and yet the

weak levels of P s2 and P d2 f ai"l t0 Produce a stable measured value for <t>o. Thus, we are forced to use

9 ml

= 180° as obtained in (41).

Case 2. Choosing e el

= 0°, e e2= -118.5360°, and e e3= 119.2574°, we obtain from (23a)

sinem2 = 0.282754 giving 9 m2 = 16.4246° or 163.5754°,

and from (26a)

sine m3 = 5.994492/5.299348 = 1.131175.

Although 9 m3 also appears unrealizable for this case, the situation is rather encouraging because only

a small deviation in m

ex , mez , m

mx , mmz , $§, ij>g, or 9 e3 will make sin9m3 approach to 1.0, yielding 9 m3

= 90°.

Thus, from the above considerations, it is more reasonable to choose Case 2 to represent the

unknown radiator. Even so, the sum of 9m1-, i = 1,2,3 is still approximately 74° off the ideal

condition (16b). This amount of deviation is considered too excessive to deduce any meaningful

results for other mixed phases. To make a compromise in this regard and in view of the previous

comment that the absosolute value for e m2 may be greater or smaller than 90°, we take, for e m2 , the

arithmetic average of 81.1028° obtained in (41) with the actual measured difference powers ( p d4 >p d3^ and 163.5754° obtained from (23a) by allowing the possibility that the true value for P d3 could well

be greater than the true value for P^. That is,

6 m2

= 1/2 (81.1028° + 163.5754°) = 122.3391° . (42a)

Similarly, for e m3 , we take the arithmetic average of 25.0596° obtained in (41) based on the measured

P d5 and P^g and 90° obtained from (26a) with a minor adjustment in measured quantities to account for

the measurement inaccuracy,

8 m3

= 1/2 (25.0596° + 90°) = 57.5298° . (42b)

Now, the sum of e ml

= 180°, e m2 in (42a) and 6 m3 in (42b) almost satisfies (16b).

With this important constraining condition almost satisfied, we then proceed as follows.

From (12d,e,g,j,k,i) we obtain

c^ = 0, 3

1 = -90°, c^ = 0, ej_ = 90° , (43a)

and

Note that for this case,

di - tt = 6. + <x. - p. = 57.06° , (43b) y ex

ymyr

l 1 1 '

* - y = , + ol\ - p! = -122.94° . (43c) v ey

ymx

Y

l 1 1

29
«! - «i = ° = e ei> e

i " ei = 180 ° = emi

' (43d)

which exactly satisfy (12m,n).

Equations (14e,i) are useless under the current measurement condition because we do not have a stable measured value for <t>2. Therefore, (43b) is the only computed value for i|> ex

- ^m

, and (43c)

for *ey " W

From (22d,e,f ,g,c) we have

<* 3 = -5.1081°, 3 3

= -43.9804 u

, a

4

= 4.6576°, 34= 163.2360° , (43e)

*ey " *mz

= *3 + a

3

" e 3

= - 154 - 6277 ° • («f)

*ey ' V

= *4 + a

4

" 34

= - 172 ' 0784 ° • < 43 9>

and

The reason that the result in (43f) does not agree exactly with that in (43g) is because of the

approximation for 6 m2 used in (42a). Again, taking the arithmetic average of (43f) and (43g) gives

*ey ' *mz

= - 163 - 3530° • < 43h )

From (24d,e,f ,g,c), we have

a

3

= 113.4279°, S 3= 78.3587°, a

4

= 123.1936°,

4

= -74.4249°, (43i)

*ez

_ *my

= *3 + a

3

" 3 3

= - 158 ' 4308 ° > («j)

and

*ez " *my

= *4

+ a

4

" 3 4

= " 175 - 8815 ° {45k)

Taking the arithmetic average of (43j) and (43k) yields

*ez " +my

= "167.1562° . (434)

Also, note that

a

3

- a

3

= a

4

- a

4

= -118.5360° = 9^, ^ - 63 = 3 4

- B4= 122.3391° = 6^ (43m)

which are the results expected from (24h,i).

From (25d,e,f ,g,c) , we have

aK = 114.3005°, p c = -78.0276°, a, = -56.2228°, fi K

= -99.4802° (43n)

and

*ez " *mx

= *5

+ a

5

" e

5 = °' 9881 ° ' (43o)

*ez " V = *6

+ a

6

" e 6

= " 5 - 3426 ° * (43p)

30
Taking the arithmetic average of (43o) and (43p) yields

*ez " *mx

= "2.1773° . (43q)

Finally, from (27d,e,f ,g,c), we have

a's

= -4.9569°, p£ = -20.4978°, a'6

= -175.4802°, 3g = -41.9504° , (43r)

*ex " V =h +a5-^= -175.7991° , (43s)

and

*ex " V =h + %- *6- "182.1298° . (43t)

Taking the arithmetic average of (43s) and (43t) yields

*ex " *mz

= "178.9645° (43u)

Note that,

a

5

" a

5

= a

6

" a

6

= 119 - 2574 ° = e e3' e 5

" h = *6 " h

= 57 ' 5298 ° = 9 m3

(43v)

which are the results expected from (27h,i).

In summary, the results of ^ex

- i|> ey= 0, ^ ey

- yez

= -118.5360°, i|> ez

- ij; ex

= 119.2574°, i|» mx-

i|; m

= 180°, ty - \j)mz= 122.3391°, i|i mz

- ^mx

= 57.5298°, together with those in (40) and

(43b,c,h,£,q,u) are all we need in computing the radiation pattern (5) for the spherical dipole

radiator being analyzed.

In addition, the total dipole strengths and orientations can also be determined as follows:

(i) for the electric type,

m*r

= (<"?« + mL + mL

)1/2 = 2.671865(10"4

) m (actually, amp-m (43w)

normalized to a unit current) ,

e e

= cos

_1

(mez

/mer

) = 86.12°, ^ = tan

_1

(mey /m

ex

) = 44.33° ; (43x)

(ii) for the magnetic type,

m

mr

= 2.220114(10" 5

) m

2 (actually, amp-m2 relative to a (43y)

unit current) ,

e m

= 80.14° <(. m

= 38.30° . (43z)

It is significant to note that the electric dipole strength obtained in (43w) agrees very well (within

+1%) with that deduced from another measurement method [4], and that the orientation obtained in (43x)

is approximately (within +2%) equal to that of the spherical dipole radiator (relative to the TEM cell

31
coordinates) placed originally inside the TEM cell to begin with this experiment. This kind of con- firmation certainly helps to establish a good degree of confidence in the proposed method. Since

there is no a priori knowlege about the equivalent magnetic dipole vector associated with the

spherical dipole radiator, we have no way to determine the accuracy for the results obtained in

(43y,z).

From (43x) we realize that the electric dipole is approximately located in the plane of $ = 45°

and <(> = 225°. The normalized radiation pattern in this particular plane, in accordance with (5), is

presented in figure 7. Clearly, the maximum radiation is approximately in the direction perpendicular

to the dipole axis as expected. The presence of some magnetic dipole moments causes a minor unsymmetry of the pattern. The total power radiated by this spherical dipole is, in accordance with (6),

about 0.283 uw.

The relative phases extracted in this example are relatively consistent, though not perfect,

under the practical measurement circumstance. It is felt that a general composite interference source with comparable strengths of electric and magnetic di poles will give even better results. Corresponding results due to a source of essentially magnetic type are to be reported on in the future.

5. Conclusions

The theoretical development and measurement procedures have been presented to determine the freespace radiation characteristics, both the total radiated power and detailed radiation pattern, for a general unknown emitter. The success of this proposed method relies on the measurements of powers and

phases at six different emitter positions when it is placed inside a TEM cell. One of the main

requirements is that the emitter is electrically small compared to the wavelength and the TEM cell

size. The other requirement is that the frequency is low enough such that only the dominant mode is

propagating inside the TEM cell. Both theoretical and experimental examples have been given to demonstrate the usefulness and validity of the method. An error analysis of the final experimental

results should be made in the future to gain insight into the accuracy of the method due to background

noise and other practical imperfections involved in the measurements.

6. References

[1] Sreenivasiah, I.; Chang, D. C; Ma, M. T. Characterization of electrically small radiating

sources by tests inside a transmission line cell. Nat. Bur. Stand. (U.S.) Tech. Note 1017; 1980.

[2] Sreenivasiah, I.; Chang, D. C. ; Ma, M. T. Emission characteristics of electrically small

radiating sources from tests inside a TEM cell. IEEE Trans, on Electromag. Compat., EMC-23,

No. 3: 113-121; August, 1981.

[3] Tippet, J. C. Model characteristics of rectangular coaxial strip line. Ph.D. Thesis, University

of Colorado, Boulder; 1978.

[4] Crawford, M. L. ; Workman, J. L. Predicting free-space radiated emissions from electronic

equipment using TEM cell and open-field site measurements. IEEE Internat. Synp. on Electromag.

Compat. Record 80-85; 1980.

32
Appendix

100 REM THIS ROUTINE WILL COLLECT RHD ANALYZE OR SIMPLY ASSIST IN T ^E

105 REM.... ANALYSIS OF POWER AND PHASE DATA AS OUTLINED IN THIS NBS TECH NOTE.

110 REM.... THE RADIATION PATTERN FOR THE EQUIPMENT UNDER TEST

115 REM IS ALSO DEVELOPED. THIS PROGRAM IS WRITTEN ON THE HP 9330 WITH

120 REM.... THE HP 9362A PLOTTER. 8568A SPECTRUM ANALYZER. THE INPUT/OUTPUT

125 FEM COMMANDS MUST BE MODIFIED TO ACTUAL EQUIPMENT USED. THE PHAsE

130 REM IS INPUT MANUALLY WHEN PROMPTED BY THE COMPUTER.

135 REM

140 REM

145 DEF FNA<X>=ATN<X/SQR<:i-X*X+lE-99>>

150 DEF FNBOO=ATN<Si'!R<1-X*X>/<X+1E-99>>+2*ATN1E+99*<X<0>

155 REM INITIALIZE ALL MATPICIES

160 DIM A*[ 1O3>6*C103»C$C903

165 DIM PC63,QC63,CC3»63»DC3.63,EC33,F[33»MC33,NC33

170 DIN SC185.23.UC100.23.WC63.ZC6.63

175 MAT S=ZERC 185.23

ISO MAT U=ZERC 1O0.2 3 185 MAT W=ZERC6 3 190 MAT Z=ZERC6,6 3 195 DATA l.l.-l.-l.l.l.l.l.l.l.-l.-l.-l.-l.l.l.l.l

200 DATA 1.-1.0, 0.0.0, 0.0.1. -1.0.0.0.0, 0.0.1.-1

205 MAT READ CC 3, 6 3, DC 3, 6

3

210 MAT P=CONC6 3 215 MAT Q=CONC6 3 220 MAT E=CONC3 3 225 MAT F=CONC3 3 230 MAT M=CONC3 3 235 MAT N-CONC3 3 240 REM IF POWER AND PHASE DATA ARE TO BE COLLECTED USE THE NEXT SUBPOUTlUfc

245 REM AND SKIP THE READ DATA COMMANDS. IF DATA IS TO BE STUDIED AFTER

250 REM.... COLLECTION, USE DATA READ WITH UPDATED INFORMATION. (EO.F0 ALSO'.

255 REM.... AND SKIP THE DATA COLLECTION SUBROUTINE. (USE OR DELETE LINE 260)

260 GOTO 275

265 GOSUB 4200

270 GOTO 3O0

275 REM READ IN DATA FROM THE DATA COMMANDS AT THE END

280 GOSUB 4910

285 E0=11.83

290 FQ=3E+07

295 REM END DATA INPUT

300 FIXED 4

305 PRINT "FREQUENCY*" <F0/1E+06)J "MHZ. CELL FACTOR EO="5E0

310 PRINT

315 QO=EO/ 1.4 142 13562

320 PO=Q0

325 KO=<2*PI*FQV3E+0S

330 K2=1.'-<2*E0T2)

335 Kl=l/<2*K0T2*E0t2)

340 FLOAT 4

345 MAT E=C*P

350 MAT E=(K2>*E

355 MAT M=C*Q

360 MAT M=(K1)*M

365 MAT F=D*P

370 MAT F=-:K2)*F

375 MAT N=D*Q

380 MAT N=<K1)*N

385 FOR C=l TO 3

390 IF ECC3>0 THEN 400

395 EC C 3=0

400 IF MCC3>0 THEN 410

405 MCC3=0

410 NEXT C 415 PRINT

420 PRINT

425 FPINT "THE SUM POWERS ARE!"

430 PRINT "PSl = "!PCi35"PS2=";PC23;"PS3="5PC33

435 PRINT "PS4="5PC4 3;"PS5="!PC5 3;"PS6="JPC6 3 440 FPINT

33
445 PRINT

450 PRINT "THE. DIFFERENCE POWERS ARE5"

455 FT: INT " PD 1 =

" ? Of 2 ] 5 " PD2= " ? Q[ 1 ] 5 " PD3= ; Q[ 4 3 460 PRINT "PIi4="»Qt3i; ,, PB5=', ;Gl6 3; "PD6="Q[5]

465 PRINT

470 FIXED 4 475 PRINT

480 PRINT "THE PHASE ANGLES' SUM TO DIFFERENCE POWERS ARE <l-6>»

405 PRINT IJ[ 1 ]iU[2];U[3]iU[4]IU[5]fUC6 3; "DEGREES"

490 FOR 0=1 TO 6

495 UCC]«<MtC]/180)*PI

SO* NEXT C 505 PR I NT U[ 1 ] ? til 2 3 \ til 3 3 5 Wf 4 3 5 W[ 5 ] 5 til 6 3!" RAD I RNS " 510 PRINT

515 PRINT

520 FLOAT 4

5 PRINT "THE ELECTRIC DIPOLE MOMENTS ARE!".

O PRINT "MEX=";SQR<E[1 3>» "MEY^ ? SQR<E[

2

3>5 "MEZ=" ! SORCEC 3 3> 535 PRINT

54U PRINT

545 PRINT "THE MAGNETIC DIPOLE MOMENTS ARE?"

550 PRINT "MMX'»"tSQR<W[13>»"MMYB M *SQR<ML2]>l M l1MZ=

,, iSQR<ML3 3> 555 PRINT

566 PRINT

565 PRINT "THE ELFCTRIC DIPOLE MOMENT CROSS TERMS APE!

570

575

PRINT "THE ELECTRIC D I POLE MOMENT CROSS TERM!

PKINl "MLJ{Y="»FC 1 ];"MEYZ«"?FC£3f "MEZK= ,, jF[ 3 3 npiTiiT PRINT

5S0 PRINT

585 PRINT "THE MAGNETIC DIPOLE MOMENT CROSS TERMS ARE!"

590 PRINT ' MhSY="?HC 1 3? "MMYZ=" 5 NL 2

3? "MNZX=" 5 N[ 3

3

595 Ai=E[ 1 ]+<K6t2>*ME 13

600 H2=E[2 3+(i.:Ci12>*f1[2 3 605 A3=EL3 3-+a-:0t2)*M[3 3 610 h4=FL 1 3+<K0t2>*H[ 13

615 A5=F[2 3+<K0T2>*N[2 3 620 A6=FL 3 3+ •. K0T2 > *N[ 3 3 625 P9- >: 10^KOT2)*CA1+A2+A3>

630 PRINT

635 PRINT

640 PRINT ' AKT2=', ;A15"AY12="5A2;"AZ12= ,, ;A3

645 PRINT

650 PR I NT " A KY= " » A4 J " A YZ= " 5 A5 ! " A ZK=? A6

655 PRINT

660 PRINT

665 PRINT

670 PRINT 'THE TOTAL RADIATED ROWER IN FREE SPACE IS"P9"WATTS

675 PRINT

680 PRINT

685 PRINT

690 REM GO DEVELOP THE E TO M CROSS TERMS

695 GOSUE IS 90

TOO REM DEVELOP THE B TERMS FOR THE PATTERN

705 GOSUB 3125

710 REM ...THE RADIATION PATTERN IS DEVELOPED HERE

715 REM THETA=I» PHI=J» LAMDA=L

720 REM ALL ANGLES IN DEGREES...

725 DEG

730 C'FLAG 2 735 L-3E+O8/F0

740 D1SP "RADIAL DISTANCE IN METERS????";

745 BEEP

750 INPUT R 755 DISP "VARY THETA OR PHI? (T/'P)*'!

760 BEEP

765 INPUT A*

770 IF Aftl3="P" THEN 795

775 IF AH13="T" THEN 765

780 GOTO 755

785 GOSUB 1545

34
790 GOTO yOu

795 GO SUE! 1755

£80 GOSUB 940

805 GOSUB 1200

810 PRINT

815 PIXEL 2 820 IF A*! 1 3="F" THEN 855

825 PRINT "THE RADIATION PATTERN FOP PHI=" J-180"DEG AND R="R" METERS"

820 PRINT "HAS THE FOLLOWING MAXIMUM AND RELATIVE MAXIMUMS?"

835 PRINT

840 FORMAT 5X* F8. 0< 6X« F12.

845 PRINT "THETA DEGREES RADIATED POWER CUB WATTS BELOW MAX)"

850 GOTO 875

855 PRINT "THE RADIATION PATTERN FOR THETA=" I "KEG. AND R="R"METERS"

860 PRINT "HAS THE FOLLOWING MAXIMUM AND RELATIVE MAXIMUMS!"

865 PRINT

870 PRINT " PHI DEGREES RADIATED POWER <DB WATTS BELOW MAX.'" 875 PRINT

8S0 FOR Z=l TO Q

885 WRITE <15-&40>U[2.1].UrZ*2]

890 NEXT Z 895 PRINT

900 PRINT

905 DISP "REPEAT RADIATION PATTERN? I'Y/NVi

910 BEEF

915 INPUT EM 920 IF Btt 1 ]='*Y" THEN 740

925 DISP "THATS ALL FOLKS 1 "; 938 STOP

935 END

940 REM.... THIS SUBROUTINE WILL FIND THE MAXIMUM VALUE IN THE RADIATION PATTERN

945 REM THEN IT WILL REFERENCE ALL. VALUES TO THIS MAXIMUM? CONVERT EVERY

950 REM ENTRY TO DB BELOW THE MAXIMUM AND FINALLY FIND ALL RELATIVE MAXIMUMS

955 REM THAT EXIST FOR THE PATTERN CALCULATED IN MATRIX S. ... 960 REM

965 IF NOT FLAG2 THEN 995

970 DISP "REFER TO NEW MAXIMUM* <¥/N)."l

975 BEEP

SCO INPUT Bt

985 IF EtC 1 3="Y" THEN 995

990 GOTO 1030

995 D2-SC1? 1

1000 FOR C=2 TO K 1005 IF SLC2 3,D2 THEN 1015

1010 L£-SCC»2]

1015 NEXT C 1020 SFLAG 2 1025 FLOAT 4 1030 PRINT "THE MAXIMUM POWER RADIATED FOR ONE DIRECTION^' > D25 "WATTS •'MT2" 1035 PRINT

1040 PRINT

1045 FOR C=l TO K 1050 SEC»2 3=<i.'D£>*S[C»2]

1055 IF S[C»2 3>lE-50 THEN 1665

1060 SCC-2]=lE-50

1 065 SI C « 2 3= 1 6*LGT ( SC C . 2 3 > 10?O NEXT C 1075 IF SCK»2KSC1»2] AND St 2»2KSC 1 12 D THEN 1090

lOSO Q=l

1085 GOTO 1165

109O Ut 1- 1 ]=SC 1)13

1095 UC l»2>St 1»2 3 11O0 0=2

1105 FOR C=2 TO K-l

1110 G=C-1

1115 D=C+1

1120 IF SCG»23<SEC2] AND S[ D. 2 3<S[ C>2 3 THEN 1130

1125 G010 1145

1130 UCQ) 1 3=SECt 1 3

35
1135 UEC!>2]=SLC»2]

1 140 Q=CH i

1 145 NEXT C 1150 REM . ..RlL MAXIMUMS FOR D TO 179 LEG ARE FOUND..

1155 G=K-1

1160 IF 8[Gf23<SLK»2] AND SL" 1.2KSE K.2] THEN 1175

1165 0=0-1

1170 RETURN

1175 U[Qi 1 >Sn.. 1 3 use u[q«2]=s[Kj2j

1185 RETURN

1190 STOP

1195 END

1200 REM THIS ROUTINE HILL PLOT AND LABEL THE RADIATION PATTERN.

1205 REM

1210 REM

1215 DISP "INSTALL PAPER AND SET BOUNDS"!

1220 BEEP

1225 STOP

1239 SCALE -36« 370s -34 »

6

1235 FOP C=l TO K 1240 PLOT SCC»13»SCC»23

1245 NEXT C 1250 PEN

1255 DISP '• LAEEL CURVE •: Y/N>??" ? 1260 BEEP

1265 INPUT Bf

1270 IF Bltl.l ]="Y" THEN 1285

1275 PEN

1280 RETURN

1285 MAX IS -30.20j0.36O

1290 VAX IS 368. +2. -30.

2

1295 XAXIS 2.-28.360.0

1380 VAX IS 0.-2.2. -30

1305 PEN

1310 FORMAT "FREQ ="»F7.2." MHZ PHI*" .F6. 1 » "

. "tF6. It " DEC. MAX=" . E9.2. " W.'Ht2' 1315 FORMAT F4.0

1320 FORMAT "FREQUENCY*" . F8. 2t "MHZ. THETA^-" . F6. 1 - " DEC. MAX="?E9. 2« "WATTS/MI 2' 1325 FOR C=-2S TO O STEP 4 1330 PLOT -25.C-0.3)-l

1335 LAPEL <1315>C

1340 NEXT C 1345 PEN

1350 PLOT -30i -15.-1

1355 LAEEL <*>"HB"

1360 PLOT 158.-33.-1

1365 IF A*t"l]="P" THEN 1470

1370 LABEL <*) THETA DEGREES"

1375 FORMAT "RHI="»F6.1

1380 PLOT 40 . -33.-1

1385 LABEL U 375 X J- 188)

1390 PLOT 288. -33.-1

1395 LABEL (1375)

J

1400 0.9=180

1405 FOR C=20 TO 340 STEP 40

1416 IF Oiee THEN 1438

1415 PLOT C-12»-31»-l

1428 LABEL <1315>C

1425 GOTO 1445

1438 09=09-40

14 35 PLOT C-12. -31.-1

1440 LABEL < 1315)09

1445 NEXT C 1450 PLOT 18.3.-1

1455 LABEL (1310) <F0/lE+06>i J-188. J.H2

1460 PEN

1465 GOTO 1518

1470 FOR C=0 TO 360 STEP 40

1475 PLOT C- 12. -31.-1

36
1430 LABEL (133 5>C

1435 NEXT C 1490 REM

1495 LflEEL £*>"PHI DEGREES"

1560 PLOT 10?

f -1 1505 LABEL a320><:F0/lE+06J>»I»D2

1516 niSP "INPUT TITLE. 60 CHAR MAX. "I 1515 INPUT C*

1520 Plot i0«5j-1

1535 LABEL 0>C*

1530 RETURN

1535 STOP

1540 END

1545 REM.... THIS ROUTINE CALCULATES THE RADIATION PATTERN FOP A FIXED PHI 1550 PEN WITH THETA VARIED FROM 6 TO 186 DEGREES IN STEPS OF 2 DEGREE

1555 REM THE DATA IS DEPOSITED IN MATRIX S 1566 REM

1565 REM

1570 DEG

1575 DISP "INPUT ANGLE PHI (DEGREES)"!

15S0 BEEP

15S5 INPUT J 1590 J1=C0SCJ)

1595 J2=SIN<J>

1600 PRINT "PLEASE BE PATIENT WHILE THE RADIATION PATTERN IS CALCULATED

1605 PRINT

1616 PRINT

1615 PRINT

1620 K=0

1625 FOP 1=0 TO 186 STEP 2 1636 K=K+1

1635 II- cos a>

1640 1 2=S IN (I;' 1645 PS=A1-'. I1T2*J1T2+J212)+A2*', IlT2*J21-2+Jlt2) + (A3*12T2'+Bl*ll

1656 P7=2*A4*I2t2*Jl*J2+2*A5*Il*12*J2+2*fl6*Il*I2*Jl-B2+I2*Jl-B3*-I2*J2

1655 P6*<a5*PI>'<Rt2*Lt2>>*<P8-P7>

1660 sn« 1 ]=I

1665 S[K<2]=P6

1670 NEXT I 1675 J=J+180

1656 J1=C0S(J>

1685 J2-SIN<J>

1690 09=180

1695 FOR 1=178 TO 6 STEP -2

1700 09=09+2

1705 K=K+1

1716 I1=C0S<I>

1715 I2=3IN(I>

1720 P8=Al*aiT2*Jlf2+J£t2>+A2*ait2*J2t2+JlT2> + <A3*I212>+Bl*Il

1725 P7=2*A4*I2t2*Jl*J2+2*A5*Il*I£*J2+2*A€*Il*I2*Jl-B2*I2*Jl-B3*I2*J2

1730 R6=((l5*FI>/(Rt2*L12>>*(P8-P7>

1735 StKil]=Q9

1740 SCK»2]«P6

1745 NEXT I 1750 RETURN

1755 REM THIS ROUTINE CALCULATES THE RADIATION PATTERN FOR A FIXED THETh

1766 REM WITH PHI VARIED FROM 6 TO 360 DEGREES IN STEPS OF 2 DEGREE

1765 REM LATA IS DEPOSITED IN MATRIX S 1770 REM

1775 REM

1786 DISP "INPUT ANGLE THETA (DEGREES) "5 1785 BEEP

1796 INPUT I 1795 Il=COSvI>

I860 I2=SINa>

1805 PRINT "PLEASE BE PATIENT WHILE THE RADIATION PATTERN IS CALCULATED

1816 PRINT

1815 PRINT

1826 PRINT

37
1825 l->0 1833 FOR J-0 TO 360 STEF 2

1833 K*K+1

184 J

1 -COS (J)

184 5 J2=?1N'.:J':' 1856 r8=fil*<ll12*Jlt2+J212)+fl2*ait2*J2T2+Jlt2) + <R3*I2t2>+Bl*ll

1855 F7=2*A4*I2t2*Jl*J242*R5*I 1*12* J2+2*R6*I 1*12* J1-B2*I2*J1-B3*I2*J2

I860 P6-(<15*Pl)ARt2*Lt2>)*CP8-P7>

iees srf • i 3-j

1879 SEF«2 3=R6

1375 NEXT J 1880 RETURN

1835 STOP

1890 REM THIS ROUTINE CALCULATES THE E TO M CROSS TERMS

1895 FIXED 4 1900 FOR C=l TO 3

1805 EEC3=SGR(EEC3>

1910 Mm-SQRCMCC])

1915 NEXT C 1930 REM THIS ROUTINE IS DESIGNED TO LAUNDRY FAULTY DATA

1925 FOR C=l TO 3

1930 IF EEC3#0 THEN 1946

1935 EEC ]=lE-20

1940 IF H[C3#0 THEN 1950

1945 MrOlE-20

1950 NEXT C 1955 E1=FE 1 3-'CEE 1 3*EE2 3> i960 IF fiBSCEl) <= 1 THEM 1975

1965 PRINT "ERROR***INCGMPATIBLE DATA POINTS REQUIRE flCOS OF CE1 > =

" SE1

1970 tl-El-'ABSCEl > 1975 El-FNBkEl J» 1930 Mi=NE i ]-'<Mt 1 3*ME2 3> 1985 IF AESail) <= 1 THEN 2000

1990 PRINT "ERROR***INCOMPATIBLE DATA POINTS REQUIRE ACQS OF (Ml >=" 5M1

1995 Ml=Ml/AE3ail)

2000 N1-FNBCM1)

2005 E2=FE2 3-CEE2 3*EE3 3> 2010 IF ABSCE2) <= 1 THEN 2035

2015 PRINT "ERF.OR***INCCiMPATIBLE DATA POINTS REQUIRE ACQS OF CE2>*"*E2

2020 E2-E2-'ABS(E2>

2035 E2=FHB<F2>

2030 M2=NE2 3- CME2 3*ME3 3> 2035 IF F!BSai2) <= 1 THEN 2050

204 PR INI "ERROR*** INCOMPATIBLE DATA POINTS REQUIRE ACQS OF <M2>="?M2

2045 H2*H2/ftBS<M2)

2050 M2=FNB<M2>

2055 E3=FE3 3-'CEE3 3*EE1 ])

2060 IF AESCE3) <= 1 THEN 2075

2065 PRINT "ERROR*** INCOMPATIBLE DATA POINTS REQUIRE ACQS OF (E3)="»E3

2070 E3=E3/RBSCE3>

2075 E3=FNBCE3>

2080 M3=NE 3 ]" < MC 3 3*M[ 1 3

>

2085 IF ABSCM3> <= 1 THEN 2100

2090 PRINT "ERROR***INCOMPATIBLE DATA POINTS REQUIRE ACQS OF <M3>»"iM3

2095 M3=N3 'ABSCM3>

2100 M3=FNBCM3>

2 1 05 PR INT "E 1 . Ml = "5 CE 1 /P I ) * 1 80 ? C M

1

/? I > * 1 SO

211© PR I NT " E2 » M2= " ! CE2/P I > * 1 80 ? ( M2/P I > * 1 80

2115 PRINT M E3iM3=";<E3/PI>*l 80S (MS/PI)* 180

2120 PRINT

2125 FOR C=l TO 6

2130 IF RESCUE C 3X1. 5706 OR RESCUE C 3) >1. 571 THEN 2170

2135 S=UEC3/ABSCUEC3)

2140 UEC3=RBSCUEC3>

2145 IF WEC3 <= 1.570796 THEN 2160

2150 NEC 3=1.571

2155 GOTO 2165

2160 NEC 3= 1.5706

2165 UEC3=S*UEC3

38
2:1 7-0 NEXT C £175 M:P "BELIEVE El» Ml OR BOTH?";

£180 3 Mr UT B* £185 IF £:*[ 3 ]=-B" THEN £345

2190 Tl--Tfinai[ 1 ]-W[£3>

£195 U=l

2 £@0 \'~ £ ££95 IF E«1»2:="M1" THEN £286

££10 IiISF "SIGN El? -r 1 » - 1 ?" 5 ££15 INF'iJT SI £££0 El=Si*El

£££5 Te=SlHCEl)

££30 S2=SGN(0C1 ]-Q[£]>

££35 GOSUB £835

££48 IF HOT FLFlGl THEN ££60

££45 PRINT "NO SOLUTION FOR Ml FROM El = "? (El PI >*1S0J " SIN<M1 >-" » Ml

£350 E1=S1-E1

££55 GOTO £175

££80 PRINT "FOR El = "

5 (El-'FI >*188» " Ml =

" ££85 GO SUB £930

££?0 Mi = T4

££75 GOTO £345

££30 II ISP 'SIGN Ml » + 1 ? — 1 '? "

•££85 INPUT SI ££90 Ml=Sl*Mi

££95 7 8=33 Is < Mi > 2300 3£ = SGN(P[ 1 ]-PE£]>

£305 GO SUE £946

£310 IF NOT FLRG1 THEN £330

£315 PRINT 'NO SOLUTION POP El FROM M J = "

? (Ml/pi >* ISO!

' : SIN'.El ': = "

? M

2320 M1=S1*M1

2335 GOTO £1,5

£330 PRINT "FOR Mi=" 5 <M1/PI >*18P; " El="

£335 GO SUB £9 SO

£840 E1=T4

£345 D1SP 'BELIEVE E£< M£ OR BOTH?"?

£350 INPUT B*

£355 IF Bid ]="B" THEN £515

£380 Tl=TflH<WL3]-WE4 3) 2365 U=£

2370 V=3

2375 IP B*L 1 .£]="fl£" THEN £450

2380 LISP "SIGN E2> +1»-1?"J

23S5 INPUT SI 2330 E£=S1*E£

2395 T6=SIN(E£.:'

£400 S£=SGNO:'[3]-Q[4]>

2405 GOSUB £885

£418 IF NOT FLHG1 THEN £438

£4 15 PRINT "NO SOLUTION FOR M£ FROM E2=" ! (E2/PI >*180> " SIN(E£>=" • Ul

2420 E£=S1*E£

2425 GOTO 2345

£430 PRINT "FOR E£="5 (E£.PI>*130; " M2="

2435 GOSUB 2988

£440 M2=T4

2445 GOTO £515

2-50 LISP "SIGH M£i +l»-l^"j

£455 INPUT SI £468 112=81 *M2

2485 T0=SIN-'M£>

24 70 S2=SGN' PL3 3-PL4D)

2475 GOSUB 2948

2480 ir HOT FLHG1 THEN 2500

2485 PRINT "HO SOLUTION FOR E£ FROM M£=" » (M£/P1 >*1805 " SIN<E2>="»W1

2438 M2-S1*M2

2495 GOTO 2345

2500 PRINT "FOR M2=" » <f12/PI)*l605 " E£="

2

C 85 GOSUB 2980

£510 E£=T4

39
25 15

2528 INPUT E*

2525 IF B*[l 3="B" THEN 2635

2530 Tl*TflN<WL5 3-WL6 3> 2535 U=3

2540 V=l

2545 IF B«1»2:="M3" THEN 2626

2550 DISP "SIGN E3» +1>-1? M

; 2555 INPUT SI 2560 E3=S1*E3

2565 T0=SIN<E3)

25'0 S2=SGIHC![5 3-C![6 3> 2575 GOSUB 2885

2530 IF NOT FLftGl THEN 2600

2585 PRINT "NO SOLUTION FOR H3 FROM E3=" » (E3/PI >*180? " 3IN(h3>=" 5 141 2550 E3=S1*ES

2595 GOTO 2515

260O PRINT "FOR E3=" 5 <E3-'PI >*186 i " M3="

2605 GOSUB 2930

2610 N3-T4

2615 GOTO 2685

2620 DISP "SIGN 113 1 +1.-1?"

5

2625 INPUT SI

2636 M3=S1*M3

2635 T6=SIN<M3>

2640 S2=SGH<PE5 3-P[6 3> 2645 GOSUB 2940

2650 IF NOT FLHGl THEN 2676

2655 PRINT "NO SOLUTION FOR E3 FROM M3=" ! <M3-'PI >*186? " SIN(E3J = "iMl

2660 H3=S1*M3

2665 GOTO 2515

2670 PRINT "FOR N3=" ? (MS-PI':'* 180? " E3="

2675 GOSUB 2980

26S0 E3=T4

2635 REM NEW E ft HI" M TERNS CALCULATED.

2696 PRINT "EIjMU"; <E1/PI>*180! (M1-'PI>*180

2695 PRINT "E2 t M2=" ! <E2/PI >*186! (M2/RI H186

2706 PRINT "E3!M3="» <E3/PI>*180;ai3/PI>*180

2705 PRINT

2710 DISP "SELECT OTHER CHOICE? Y.'N"i

2715 INPUT B$

2730 IF B*[13="H" THEN 2860

2725 D ISP "E1»E2»E3»M1»M2jM3: l»2»3»4»5i6?"i

27 30 INPUT 26

27 35 GOTO Z6 OF 2740 j 2760 > 2786 j 2800 > 2826 < 2840

2740 DISP "INPUT El"?

2745 INPUT El

2756 E1 = ';E1/180)*PI

2755 GOTO 2685

2766 DISP "INPUT E2"5

2765 INPUT E2

2776 E2=(E2-180>*PI

2775 GOTO 2685

2780 DISP "INPUT E3"5

2785 INPUT E3

2796 E3='.E3/180>*P1

2795 GOTO 2685

2806 DISP "INPUT Ml";

2805 INPUT Ml

2816 M1 = (M1 -180)*PI

2815 GOTO 2685

2820 DISP "INPUT M2"»

2825 INPUT M2

2830 M2=ai2/186>*PI

2335 GOTO 2685

2846 DISP "INPUT M3"!

2845 INPUT M3

2850 H3=<M3/180>*PI

2855 GOTO 2685

40
Cfc't't1 2S70

2 1 8 6

O c C- *" 2890

2995

2900

2905

2910

2915

2920

2925

2 9 SO

2995

2940

2945

2950

2955

29 c" 29C5

2970

2975

2990

2990

2995

3000

3005

3010

3015

3020

3025

3090

3025

3040

J '.' 4 5 3050

3055

3060

3 Or.5 3070

3075

3030

3035

3090

3095

2 1 3105

3110

3115

3120

2125

3130

3135

3140

2145

3150

3155

3180

3 It 5 3170

3175

3130

3185

3190

3195

3200

LISP "REPEAT E AND M CALCULATIONS? Y-N "5

INF!.:-! Bf

IT Lil 1 3="Y" THEM 1955

RETURN

3 TOP

REM CALCULATE N FROM E TERNS.

CFLAG 1 W=-T 1 * ( ( EC U 3* ME V 3 >T2- ( EC LI 3*MC U 3 ) 12- (EC V 3*M[ V ] > 12+ (EC V ]*M[ U ] > 12 > U=-h+ ( 2- : HC U 3*ME U ]-MC V 3*. ML V 3 J* E[ U 3*El V ]*T0

)

l.^l.j <4*T8*T1*EC U 3^-EC V 3*MC U 3*MC V 3-2*MC U 3*HC V 3* (EC U 3*EC U 3-EC 7 3-EC V J > . IF FiBStW) <= 1 THEN 2930

U1=W

W=SGN(IJ>

SFi_AG 1 RETURN

STOP

REM CALCULATE E FROM M TERNS.

CFLflG 1 W=-T 1 > i. (EC U 3*M[ V 3 > 12- (EC U ]*l"|[ U 3 > 12- (EC V 3*ME V 3 > 12+ ( EC V 3*MC U 3 > T2 ':> W=U+ ( 2* ( EC U 3^EC U 3-EC V 3*EC V 3 >*HC U 3+NC V 3* TO

)

W=iJ.(4*T0*Tl*E[ LI 3*EC V 3*MC U 3*NC V 3-2* EC U 3*EC V 3*(MC U ]*MI U 3-MC V 3*MC V 3> > GOTO 2910

RETURN

STOP

REM DETERMINE CORRECT QUAD FOR INVERSE SINE FUNCTION.

T2=FNfl- U)

IF U<e THEN 3005

T3=P1-T2

GOTO 3010

T3=--(PI+T2>

IF S2<6 THEN 3025

T4=T2

GOTO 3030

T4=T3

PRINT "POSSIBLE ANGLES"* (T2/P1 >*180? "

» "5 (T3/RI >*180? " CHOSEN=">' T4/PI>*1 SO

PRINT

RETURN

STOP

END

REM DETERMINE CORRECT QUAD FOR INVERSE TANGENT FUNCTION.

IF AES(E> >lE-25 THEN 3070

B=(SGN(B))*lE-25

IF P <= THEN 3035

Z4=ATN(A.-B>

RETURN

Z4=PI+ATN(A.B)

RETURN

STOP

REM TRIE ANGLES BETWEEN +- ISO DEGREES.

IF ABS(?5> <~ PI THEN 3115

25=Z5-(SGN(Z5>*2*PI>

RETURN

STOP

REM TEST EQUATIONS FOR (EX-MY).

A=OQ*EC2 3*SIN(El>

B=F'0*E[ 1 3+Q0*EE2 3*COS(El>

GO SUB 3055

Zl" 1«23=24

fl=QO*Mt3*C0S(M1>-P0*NC2 3 E=00*MC 1 ]*SIN<M1>

GO SUB 3055

ZC 1*33=24

Z5=UC1 3^ZC1»2 3-2C1»33

GOSUB 2100

ZC 1 » 1 3=25

Z0=(UC13PI>*180

2l=(2tl > 2 3/PI>*180

22= (2[ Ir33-PD*180

22=(ZE1»1]'PI)*180

41
3285

3216

32 1

3220

3225

3238

3235

3240

3245

3250

3250

3265

3270

32 SO

^. •% o c- 3290

3295

3300

3305

231Q

3315

3320

S3 40

!345

S358

S355

;°60

S365

5370

;. - -? c( J388

3400

3405

3410

3s 15

3420

3425

34 30

3435

3440

3445

3450

3455

3460

3465

3470

34 75

3430

3425

34 90

3495

35O0

3505

3510

3515

3520

3525

3530

3525

3540

3545

WRITE (15«32lO> , 'EX-rrv'=

, ;ZO! " +";Z1S" -" FORMAT 4F9.3

fl=-P8*EC2]*SIN<El)

Ef=Q0*EE 1 3-P0*E[2:*COS<El>

GOSUE 3055

rr i!5 3=24

fl»-<P6*Mt 1 ]*COS<Hi)+Q0*HC£]>

B=-P0*Mi 1 ]*SIN<M1)

GOSUE 3055

21 1 « 6 3=24

Z5=WC £ 3-t-Zt l*5]-2[ 1»6'3 GOSUE 3100

ZE 1-4 3=Z5

28=<W[£].'PI>*1S0

Z1 = (Z[ 1.5],'PI>*1S0

Z2=(Z[ 1j61F'I>*180

Z3=(Z[ 1.4]/PI)*180

WRITE <15>3210>"EX-MY=";ZO;" +"5215" -" PRINT

REM TEST EQUATIONS FOR (EY-MX).

A=-P0*EE 1 ]*SIN<E1)

B=P0*E[ 1 ]*COS<E1)+Q0*E[2']

GOSUE 3055

ZL2>23=Z4

Fi=Q8*M[ 1 3-P0*ME 2 3*C0S<M1 > B=P0*ML2]*SIN<M1'>

GOSUE 3055

Z[2?3]=Z4

Z5=ur 1 3+ZC2»2 3-2[2»3 3 GOSUE 3100

Z[2j13=Z5

Z6=<WC

3'PI>*180

Zl=<ZC2>2]/Pi>*180

Z2»<Z[2»33/PI)*180

Z3=':Z[£'! 1 ]/Pl>*lS0

WRITE <15«3210>"EV-MK=";Z0; " +"?zi;" -" n=-08*EC 1 ]*SIN<E1)

B=O0*EE 1 ]*C0S<El>-Pfl*EC2]

GOSUE 3055

Z[ 2*5 3=24

A=-'PG*ML 1 ]+Q0*M[2 3*C0S(Ml>>

E=U0*I1[2]*SIH'..M1>

GOSUE 3055

ZL2»6 3=Z4

Z5=WL2 3+Zt2»5 3-Z[2»6 3 GOSUE 3100

Z[ 2- 4 3=25

Z0=(W[2]/PI>*180

Zl=(Zr2j53/PI)*188

22= (Zt 2j6 3/PI)*180

Z3=';Z[2.<4 3/PI>*180

WRITE <15j32ie)"EY-MJ<;=";20;" +";Z15" - PRINT

REM TEST EQUATIONS FOR (EV-MZ).

fl=Q0*EC3 3*EIN(E2)

E=PO*E[2 3+Q0*E[3 3*COS(E2)

GOSUE 3055

ZL 3*2 3=24

A=G8*M[23*COS(M2>-P0*M[33

B=Q0*M[2 3*SIH<M2>

GOSUE 3055

Zr 3> 3 3=24

25=W[3 3+2[3>2 3-2[3»3 3 GOSUE 3100

5 225" ="?Z3

ZC3«13=

Z0=<W[3 3/PI)*180

Z1 = ''Z[3j2 3.'PI)*180

Z2=(2[3»3 3/PI>*180

Z3=<2t3»13/PI>*180

42
V c~'fi

C; r c Cj ? bee

3 5£5

C 576

<^. r?c

^ 58Q

3 585

^; 55

*D 595

^ £ O

O £05

^ 6 1 j £ 1

5

2 £20

3625

£ 630

c £35

J £40

t £45

". £50

£ £55

1 ££0

1 ££5

1 £70

J i 00

J705

5710

J715

J720

;• "7 o c:

374

3745

3750

O"• c; c

3770

3775

3780

3785

3790

3755

38O0

3805

3810

3815

3820

C« Q *£ c* W*C£ -' 3830

3835

3840

3845

3850

3855

SS£0

38£5

3870

3875

3830

3835

3890

write a5.32i0>"EY-MZ=";z0; " +

m ;zi;"

fi=-P0*E[3 3*?IN<E2)

B=Q0*Et2 3-PO*E[3 3*COS<E2)

GOSUE 3055

Z[3«5 3=Z4

fi=- > P0*ri[2]*COS<H2>+Q0*M[3]>

E=-P0*ML2 3*S1H(M2)

GOSUE 3055

ZL3;£]=Z4

Z5=U[4 3+2[3«5 3-Z[3i6]

GOSUE 3100

Zr3>4 3=Z5

Z0='-Ur4]-F'I>*180

Zl=<ZL3s53/Pl>*180

Z2=>:Z[3j£]/PI>*180

Z3=<Z[3'4]/PI)*180

WRITE (15»3210)"EY-MZ="«Z0; " +"?Z1!"

PRINT

REM TEST EQUfiTIONS FOR <EZ-MY>.

fl=-P0*EC2 3*£IN<E2)

B=P0*E[ 2 ]*C0S CE2) +G0*E[ 3 ] GOSUE 3055

Z[4>2 3=Z4

fl=Q0*H[ 2 3-P0*H[ 3 3*C08<M2>

B=P0*M[3 3*SIR(H2)

GOSUE 3055

ZL 4,2 3=24

Z5=Wi3 3+ZC4,2 3-Z[4,3 3 GOSUE 3100

ZC4- 1 3^Z5

Z0=':H[3 3/PI>*130

Zi = ';ZE4»2 3/Pr>*180

Z2='Z[4»33/FI)*180

73='-ZL4. 1 3/PI>*180

WRITE C15»3216)"EZ-HY=";Z0» " +'•:zl;

,, fi=-0.0*Ei:2 3*SIH/.E2)

B=Q0*E[2 3*COStE2>-Pe*E[3 3 GOSUE 3055

Z[4-5]=Z4

fl=-=:P0*Mt 2 3+Q0*M[ 3 3*C0S ':M2> > B=G0*M[3 3*SIN<M2)

GOSUE 3055

ZL4-£3=Z4

Z5=UE4 3+ZC4j53-Z[4»6 3 GOSUB 3100

Z[4»4 3=Z5

ze=aj[4 3'Pi>*i80

Z1 = ':Z[4,53.'PI>*180

Z2=':Z[4<£]''PI)*180

Z3=(ZI4j4 3 'PI'* ISO

WRITE (15f3210>"EZ-riY-";Z0;" +"»21t"

PRINT

REM TEST EQUATIONS FOR <EZ-MK>.

fi=G'0*E[ 1 3*SIN<E3)

B=P0*EI 3 3+QG*E[ 1 3*COS<E3)

GOSUE 3055

ZC5»2 3=Z4

fl=Q0*M[3 3*COS<M3)-Pe*MI 1

3

B=Q0*HE3 3*SIN(M3)

GOSUE 2055

Z[5'3 3=Z4

Z5=WC5 3+Z[5»2 3-Zt5»3 3 GOSUE 3100

Zt5i 1 3=Z5

Z0=(WC53/PI)*180

Z1=<Z[5*23/PI>*180

Z2=':Z[5j33/PI>*186

Z3=a[5jl3/PI>*180

WRITE (15«3210> , 'EZ-MX="5Z0; " +"!Z15

t cd.%

» *.£» =

43
3895 fl=-P0*EC13*SIN<E3>

39O0 B=QO*E[ 3 3-P0*EC 1 3*COS<E3>

3905 GOSUB 3055

3919 ZC5<53=Z4

3915 A=-<F0*M[3 3*COS<M3>+Q0*MC13)

3920 6=-P0*M[3]*SINai3>

3925 GOSUB 3055

3930 ZC 5.(51=24

3935 Z5=NC6J+ZC5>5 3-ZC5.6 3 3940 GOSUB 3100

3945 ZC5»4 3=Z5

3950 Z0=<W[6 3. PI>*130

3955 Z1=<ZC5»5]/PI>*180

3960 Z2='Z[5.6].PI>*1S0

3965 Z3=<ZC5.4]/PI>*180

3970 WRITE (15»321O>"EZ-MX="5Z0; M +";Z1?" -"5Z2?" = "?Z3

3975 PRINT

3930 REM TEST EQUATIONS FOR. CEX-MZ).

3985 A=-P0*EC33*SIN<E3>

3990 B=P0*EC 3 ]*COS(E3)+Q0*EE 1

3

3995 GOSUB 3055

4OO0 ZC6>23=Z4

4O05 M=Q0*HC3 3-P0*M[ 1 3*COS<f13>

4010 B=P0*MC13*SIN<M3>

4GU5 GOSUB 3055

4020 ZC6>3 3=Z4

4025 Z5=WC5 3+ZC6»2 3-ZC6.3 3 4O30 GOSUB 3100

4035 ZC6»13=Z5

4040 Z0=':WC5 3/PI>*130

4045 21 = (ZC6.2 3.'PI>*180

4O50 22= < ZC € j 3 ]/P

) * 1 SO

4055 Z3-< ZC6-13- PI>*180

4060 WRITE <15»3210)"EK-MZ=";Z0;" +";Zi;" - M ;Z2;" = ">Z3

4065 A=-Q0*EC3 3*SIN<E3)

4O70 B=QO*E[ 3 3*CGS'E3)-P0*EC 1 3 4075 GOSUB 3055

4O30 ZC6>5 3=Z4

40S5 A=-<PO*MC 3 3+Q0*M[ 1 ]*C0S<M3;)

4O90 B=Q0*MC13*3IH<M3>

4095 GOSUB 3055

4100 ZC6>63=Z4

4105 Z5=WC6 3+ZC6>5 3-ZC6j6 3 4110 GOSUB 3100

4115 ZC6>43=Z5

4120 Z0='W[6 3/PI)*180

4125 Z1 = (ZC6.53.'PI)*1S0

4130 Z2=(ZC6»6 3/PI>*130

4135 Z3='.ZC6.4 3/PI>*180

4140 WRITE a5>32l0)"EX-MZ="5Z0i" +"5Zi; M -"5Z2i" ="5Z3

4145 PRINT

4150 PRINT

4155 Bl=2*K0*'::EC13*MC23*SIH':ZClfl3)-EC23*hC13*SIH<ZC2»13>>

4160 B2*2*K0*(EC2 3*MC3 3*SIH<ZC3»13>-EC3 3*MC2 3*SIN(ZC4»13>>

4165 B3=2*K0*<EC3 3*MC13*SIN<ZC5>13>-EE13*MC3 3*SIN<ZC6»13>>

4170 WRITE <15>4175)"BXY-BVX="5Bi;" BYZ-BZY=" 5 B25 " BZX-BXZ«"IB3

4175 FORMAT 3E12.4

4130 PRINT

4185 PRINT

4190 RETURN

4195 STOP

420O REM BEGIN THE MEASUREMENT PROCEDURE AS OUTLINED IN THIS NBS TECH NOTE.

4205 LISP "PLACE EUT IN TEM CELL AT CENTER"

4210 BEEP

4215 STOP

4220 DISP "INPUT TEM CELL FACTOR <E0>";

4225 BEEP

-t_ jO INPUT EO

4235 REM ...INITIALIZE SPECTRUM ANALYZER AND SET OPERATING FREQUENCY.

44
42 4 3 GOSUE sOOO

4245 LISP ALIGN X-X' »Y-Y' >Z-Z' "5 4256 DEEP

4255 STOP

4266 LISP "ROTATE 45 DEC CCW REOUT Z <Z'>"

4265 BEEP

4Z'?0 sTQP

4275 REM REflU THE SPECTRUM ANALYZER AND GET FSls PM» ANL PHASE 1. 42S3 GOSUE *i690

4285 FT 1 3=Pi

4296 QL2 3=P2

4295 W 1 ]=P3

4200 LISP "ROTATE 90 LEG COW ABOUT 2 <Z'>"

4:? 05 PEEP

4210 ST OF 4215 REM REAL THE SPECTRUM ANALYZER HUH GET PS2> PH2« AND PHASE 2. 4320 Li SUB 4690

4225 P[2 3=P1

4330 Q[ 1 3=P2

4335 WL2 3=P3

4340 DISP "ALIGN X-Y* » Y-Z' »Z-X'

434 5 BEEP

4350 STOP

4355 DISP "ROTATE 45 LEG CCW ABOUT Z (X'V

4360 PEEP

4 265 STOP

4370 REM READ THE SPECTRUM ANALYZER AND GET PS3i PL2< AND PHASE 3 4375 GOSUE 4690

4330 F'[3]=P1

4335 Ci[4 3=P2

4390 UC3 3=P3

4395 LISP "ROTATE 90 LEG CCW ABOUT Z f.X'>"

4 4d? BEEP

4405 STOP

4410 REM REAL THE SPECTRUM ANALYZER AND GET PS4> FL4, ANL PHASE 4. 4415 GOSUE 4690

4420 F[4 ] = P1 4425 uL2 3=P2

4430 U[4 3=P3

44?5 LISP "AlIGN X-Z'»Y-X'jZ-Y'"

4440 BEEP

4445 STOP

4450 LISP "ROTATE 45 LEG CCW ABOUT Z <Y>>"

44 55 BEEP

4460 STOP

44 65 REM REAL THE SPECTRUM ANALYZER ANL GET PS5» FL5« AND PHASE 5. 4470 GOSUE 4690

4475 R[5 3=P1

44 86 OE6 3=P2

4485 WL5 3=P3

4490 LISP "ROTATE 90 LEG CCW ABOUT Z <Y»>"

4495 BEEP

4500 STOP

4505 REM PEAL THE SPECTRUM ANALYZER ANL GET PS6> PL6» ANL PHASE 6. 4510 GO SUB 4690

4515 PE6 3=P1

4520 0[5 3=P2

4525 W[6 3=P3

4530 REM

4535 REM THIS CONCLUDES THE GATHERING OF LATA FOP THE EMISSIONS CHARACTERIZATION

4540 RETURN

4545 END

4550 REM THIS ROUTINE INITIALIZES THE SPECTRUM RNALYZER

4555 REM THIS IS WHERE THE NECESSARY FREQUENCY INFORMATION IS GATHERED

4560 CML "?U2"

45 65 FORMAT 3B

4570 OUTPUT U3f45£5>256t4i512

4075 CML "?U2'VVB 16 KZ FA 2 HZ FB 266 MZ M2 EK"

45S0 WAIT 500

45
n j ; -> JML "?Ui-'5 "El"

4590 DISP "HOVE MflRKER TO DESIRED FREQUENCY";

4 5?5 STOP

4600 CMD "?U2"j "MT1"

460-5 WAIT 500

4610 CUE 'yu2'«"SF 2 MZ R& 30 KZ HD" 4615 WfilT 500

4620 CMD "?U2"i "MF"

4625 CMD "?R5"

46 30 ENTER < 1 3 » * > FCi 4635 CMD , "?U2". "M2.E1"

4640 FIXED £

4645 PRINT "FREQUENCY*" 5 <F6 /1E+06) ? " MHZ"

4650 FLOAT 2

4655 DISP 'INPUT AMPLITUDE THRESHOLD (MM)"!

4660 BEEP

4665 INPUT Zl

4670 PRINT

4675 RETURN

46 SO STOP

46S5 END

4690 REM READ THE RMPLITUDE INFORMATION FROM THE SPECTRUM RNRLYZER

4695 REM

4700 REM

4705 HIST' "SET COAX SNITCH TO THE SUM PORT "5 47 10 STOP

4715 CMD "?U2") " El. MR"

47 20 CMD -?R5"

4725 ENTER <13»*>P1

4730 DISP "SET COAX SWITCH TO DIFFERENCE";

4735 STOP

4740 CMD "'"U2"» "El MR"

4745 CMD "?R5"

4750 ENTER (13.*>P2

4755 DISP "INPUT PHASE (SUM-DIFF)"!

4760 INPUT P3

47 65 FIXED 4 4770 PRINT "PS="5Pi; "DEM. PD=" » P2? ' DBM THRESHOLD*" 'Zl

4775 PRINT

47S0 PRINT "WITH R CORRECTION FOR LOSSES. THE POWER LEVELS RRE5

4735 IF PKZ1 THEN 4S00

4790 Pl=Rl+3.6845

4795 GOTO 4805

4300 P1=0

4305 IF P2<Z1 THEN 4 320

4310 P2=P2+3.8345

4315 GOTO 4825

4820 P2=B

4325 PRINT

4830 IF P1=0 THEN 4840

4835 Pl = 10T'.v.Pl-'lO>-3)

4840 IF P2=9 THEN 4850

4345 P2=lOto:.F2/10>-3)

4350 FLOAT 10

4855 PRINT "PS«"IP1I"M PD="5P2»"W"

4860 PRINT

4365 FIXED £

4870 PRINT "PHASE ="5P3;"DEG " J (P3'180>*PI ? " RRD"

4875 P3=<P3 '180)*PI

4880 PRINT

4885 PRINT

4390 PRINT

4895 RETURN

49O0 STOP

4905 END

4910 REM RERD IN POWER AND PHASE DATA? SUM 1-6, DIFFERENCE 1-6. PHI 1-6

4915 DATA 4 . 8978E-06, 3. 4674E-08. 7. 0795E-06

4320 DATA 4. 1687E-07, 7. 9433E-0G. 2. 2387E-07

4925 DATA 9. 7724E-09. 3. 62E-09. 1 . 2023E-08

46
4938 DATA 3.31 13E-10) 1.4125E-88* 1.5488E-89

4935 READ Ft 1 3< PC 2 3> Ft 3 3»PE 4 ]»P[ 5 3» PL 6]

4940 READ GE2 3»0T 1 3j GE 4 3? QE 3 3» GE 6 3»QE5 3 4945 DFITfi 96.4976? -162. 7023 j 103.6022

4956 DflTfi - 144. 5' -30. 4627' -91 . 1973

4 955 READ ME 1 ] » WE 2 3 » Ml 3 3 > ML 4 3 • WE 5 3 « ME 6 3 4960 RETURN

4965 END

Fl SAMPLE OUTPUT FROM THE ABOVE PROGRAM,

FFEQUENCY= 30.0688 MHZ. CELL FACTOR E8= 11.6388

THE SUM POMERS ARE!

PS1= 4.8978E-86 PS2= 3.4674E-88 PS3= 7.8795E-86

FS4 = 4.1687E-87 PS5= 7.9433E-86 PS6= 2.2387E-07

THE DIFFERENCE POMERS APE!

PD1= 9.7724E-89 PD2= 3.8268E-69 FD3= 1.2023E-0S

PD4= 3.3H3E-18 PD5= 1.4125E-0S PD6= 1.54SSE-09

THE PHASE ANGLES) SUM TO DIFFERENCE POMERS ARE <l-6>>

96.4976 -i62.?623 183.6022 -144.5800 -SO. 4027 -91.1'

DEGREES

1 . 634; - 1 . 7925 1 . 8882 -2 . 5220 - 1 . 4033 -1.5917 RAD i HNS

the electric dipole moments are; mex= k4149e-b4 hey= 1.2339e-84 mez= 1.95s0e-84

the magnetic dipole moments are?

MriX= 1.2875E-85 MMV= 9.2509E-86 MMZ= 1.1742E-85

THE ElECTRIC DIPOLE MOMENT CROSS TERMS ARE?

MEXY= 1.7375E-68 MEVZ= 2.3S84E-8S MEZX= 2.7579E-88

THE MAGNETIC DIPOLE MOMENT CROSS TERMS ARE?

MMXY=-6. 1188E-11 MMVZ=- 1 . 85S1E-10 MMZX=-1. 1381E-18

AX12= 2.8877E-88 AYT2= 1.5266E-88 AZt2= 3.8394E-88

A XY- 1.7351E-88 A Y2= 2.3762E-68 A ZX= 2.7535E-68

ThE TOTAL RADIATED POMER IN FREE SPACE IS 2.9187E-87 WATT:

E1«M1= 5.6248 123.1319

E2-M2- 9.8623 166.7139

E3jM3= 5.4354 143.3872

47
FOR Ei--S*624& Ml = POSSIBLE ANGLES 4.5135 > 175.4865 CHOSEN* 175.4865

FOR E2- 9.8623 M2 = POSSIBLE; ANGLES 15.6733 . 164.3367 CHOSEN* 164.3367

FOP E?=-5.4354 M3=

POSSIBLE ANGLES-O. 1456 j-179.8544 CH0SEN=-179. 8544

E 1 -

M

I =-5 . 6340 175. 4865

E2*M2= 9.8633 164.3367

E:-»M3=-5.4 354 -179.8544

E1jM1=-5.6240 4.5135

E3 1 M3- 9 . 3623 1 64 . 3367

E3iM3=-5.4354 -179.8544

EX-MY= 96.498 + -2.620 - 71.123 = 22.756

EX-MY= -162.783 + 32.903 - 267.445 = 22.756

EV-H;:= 96.498 + 3.004 - 75.635 = 23.866

EY-M;:= -102.703 + 38.537 - -88.041 = 23.866

EY-MZ= 103.603 + 6.053 - -83.096 = -167.250

EY-MZ- -14-1.500 + 205.754 - 228.504 = -167.250

E2-MY= 103.602 + -3.810 - 81.231 = 18.561

E2-lr.= -i44.500 + 195.692 - 32.831 = 16.561

EZ-MX= -86.403 + -2.280 - 269.923 = 7.389

E2-H?1= -91.197 + 13.706 - -84.660 = 7.389

E

.

' - N

Z

- -80.403 + 3.156 - 90.074 = -167.321

EX-MZ= -91.197 + 19.142 - 95.265 = -167.321

BXY-BYX= -1.2081E-10 BYZ-BZY= -1.1270E-09 B2X-BXZ= 8.4037E-10

PLEASE BE PATIENT WHILE THE RADIATION PATTERN IS CALCULA1 EH

THE MAM I HON POWER RADIATED FOR ONE DIRECTION" 3.8429E-09 WATTS.TIT

2

THE RADIATION PATTERN FOR PHI= 45. OO PEG AND R= 3.00 METER' HAS THE FOLLOWING MAXIMUM AND RELATIVE MAXIMUMS!

THETh DEGREES RADIATED POWER CUB WATTS BELOW MAX)

134 -0.01

314 O.OO

THE END

48
TEM CELL

INSTRUMENTATION

FOR POWER AND

PHASE MEASUREMENT

Figure 1. Emissions testing measurement system,

49
mex/:Aex

m

m

5y /

y

ey

3z/

y

ez

mmx/^

mx

"Viy/^my

mmzAz

Figure 2. Unknown equipment under test (EUT) is made of

equivalent three orthogonal electric and three orthogonal

magnetic dipoles.

y

c

E

+

z =

Figure 3 . An arbitrary current source

inside one half of a TEM cell.

50
One half

TEM cell

(b)

Figure 4. Two EUT orientations in the TEM cell

51
Y i z

One half

TEM cell

(a)

(b)

Figure 5. Another two EUT orientations in the TEM cell

52
lY/X'

One half

TEM cell

x

(a)

(b)

Figure b. Final two EUT orientations in the TEM cell

53
I I I I > I I I I I > I > I I I I

-12 •

DB

-IB

-20 -

-2H--

-2B -•

t i i i

PHI« HS.B

IBB 1MB

THETP, DEBREE5

IBB BB 2B

PHI- 22S.0

Figure 7. Calculated power pattern in the phi = 45°,

225 plane for a spherical dipole radiator, based on

measured data.

54
NBS-M4A (rev. 2-80) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS TN-1059

2. Performing Organ. Report No 3. Publication Date October 1982

4. TITLE AND SUBTITLE

A Method to Quantify the Radiation Characteristics

of an Unknown Interference Source

5. AUTHOR(S)

Mark T. Ma 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

~2 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) A new method for determining the radiation characteristics of leakage

from electronic equipment for interference studies is described in

this report. Basically, an unintentional leakage source is considered

to be electrically small, and may be characterized by three equivalent

orthogonal electric dipole moments and three equivalent orthogonal

magnetic dipole moments. When an unkonown source object is placed at

the center of a transverse electromagnetic (TEM) cell, its radiated

energy couples into the fundamental transmission mode and propagates

toward the two output ports of the TEM cell. With a hvbrid junction

inserted into a loop connecting the cell output ports, one is able to

measure the sum and difference powers and the relative phase between

the sum and difference outputs. Systematic measurements of these

powers and phases at six different source object positions, based on a well-developed theory, are sufficient to determine the amplitudes and

phases of the unknown component dipole moments, from which the detailed

free-space radiation pattern of the unknown source and the total

radiated power can be determined. Results of simulated theoretical

examples and an experiment using a spherical dipole radiator are given

to illustrate the theory and measurement procedure.

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

dipole moments; electrically smalT; interference source; leakage; phase measurements; power measurements; radiation pattern; TEM cell; total radiated power.

13. AVAILABILITY

faTl Unlimited

| | For Official Distribution. Do Not Release to NTIS

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

20402. Q Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

15. Price $4.75

*U.S. GOVERNMENT PRINTING OFFICE: 1982-0-676-648/35 USCOMM-DC 6043-P80

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various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and industrial practice (including safety codes) developed in cooperation with in- terested industries, professional organizations, and regulatory

bodies. Special Publications—Include proceedings of conferences sponsored by NBS, NBS annual reports, and other special publications

appropriate to this grouping such as wall charts, pocket cards, and

bibliographies. Applied Mathematics Series—Mathematical tables, manuals, and

studies of special interest to physicists, engineers, chemists,

biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides quantitative data on the physical an'' chemical properties of materials, compiled from the world s literature and critically evaluated. Developed under a worldwide program coordinated by NBS under

the authority of the National Standard Data Act (Public Law

90-396).

NOTE: The principal publication outlet for the foregoing data is the Journal of Physical and Chemical Reference Data (JPCRD)

published quarterly for NBS by the American Chemical Society

(ACS) and the American Institute of Physics (AIP). Subscriptions,

reprints, and supplements available from ACS, 1 155 Sixteenth St., NW, Washington, DC 20056.

Building Science Series—Disseminates technical information developed at the Bureau on building materials, components,

systems, and whole structures. The series presents research results,

test methods, and performance criteria related to the structural and

environmental functions and the durability and safety characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures

published by the Department of Commerce in Part 10, Title 15, of

the Code of Federal Regulations. The standards establish nationally recognized requirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NBS administers this program as a supplement to the activities of the private sector standardizing

organizations. Consumer Information Series—Practical information, based on N BS research and experience, covering areas of interest to the con- sumer. Easily understandable language and illustrations provide

useful background knowledge for shopping in today's tech- nological marketplace. Order the above NBS publications from: Superintendent of Documents. Government Printing Office, Washington, DC 20402. Order the following NBS publications—FlPS and NBSIR's—from

the National Technical Information Services. Springfield. VA 22161

Federal Information Processing Standards Publications (FIPS

PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register

serves as the official source of information in the Federal Govern- ment regarding standards issued by NBS pursuant to the Federal Property and Administrative Services Act of 1949 as amended,

Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 11717(38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal Regulations).

NBS Interagency Reports (NBSIR)—A special series of interim or

final reports on work performed by NBS for outside sponsors

(both government and non-government). In general, initial dis- tribution is handled by the sponsor; public distribution is by the National Technical Information Services, Springfield, VA 22161,

in paper copy or microfiche form.
U.S. Department of Commerce

National Bureau of Standards

Washington, D.C. 20234

Official Business

Penalty for Private Use $300

POSTAGE AND FEES PAID US. DEPARTMENT OF COMMERCE

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