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PUBLICATIONS

.^V -Of. _

NAT L INST. OF STAND & TECH

AlllOb 33TTfib

NBS TECHNICAL NOTE 1098

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

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'Headquaricrs and Laboratories ai Gaiihersburg, MD, unless oiherwise noted; mailing address Gaithersburg. MD 20899. 'Some divisions within the center are located at Boulder, CO 80.103.

•M oca ted al Boulder. CO. with some elements at Gailhersbure \/\n
Linear Gain - Standard Antennas

Below 1000 IVil-fz

R.G. FitzGerrell

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

/ \^ \

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

NBS

RESEARCH

INFORMATION CENTER

•• ; C '^ «^ g

Issued May 1986
National Bureau of Standards Technical Note 1098

Natl. Bur. Stand. (U.S.), Tech Note 1098, 44 pages (May 1986)

CODEN:NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1986

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

Page

1 . Introduction 1

2. Definitions and Equations 3

3. Gain-Standard Antennas 7

4. Examples of Gain-Standard Antenna Calculations 11

5. Conclusions 27

6. References 28

Appendix — Listing of Program HVD6 29

iix

LINEAR GAIN-STANDARD ANTENNAS BELOW 1000 MHz

R.G. FitzGerrell

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Gain and antenna parameters related to input impedance are

calculated using a computer program named HVD6. This program uses well documented equations to compute these parameters for gainstandard antennas used in r el at

ve- ga i n or ga i n- transfer

measurements at frequencies below 1000 MHz. The utility of this

program is that it calculates gain patterns and input impedances for

linear dipoles above perfect or imperfectly conducting plane ground

and in free space, and for monopoles on perfectly conducting plane

ground. Examples are included to illustrate the use of the program.

Uncertainties in the calculated parameters are estimated to be less

than those of the measured parameters.

Key words: antenna gain; dipole antennas; gain standards; monopole

antennas

1 . Introduction

"The power gain of an antenna, in a specified direction, is ^tt times

the ratio of the power radiated per unit solid angle in that direction to

the net power accepted by the antenna from its generator. This quantity is an inherent property of the antenna and does not involve system losses

arising from a mismatch of impedance or polarization.

"Antennas which are to be used for gain standards should have the

following characteristics:

(1) The gain of the antenna shall be accurately known.

(2) The antenna shall have a high degree of dimensional stability.

(3) The antenna's polarization should be linear or, for some applications, circular....

"Although any antenna meeting these criteria may be used as a gain

standard, the two universally accepted antenna types are the dipole and the

pyramidal horn. The gains of these antennas can be fairly accurately

calculated, and because of their mechanical simplicity they can be

manufactured with a high degree of reproducibility." [1]

The purpose of this document is to present an interactive computer

program, listed in the Appendix, for calculating power gain (the term gain

will be used henceforth) of dipoles used as gain standards over perfect or imperfectly conducting plane ground, and in free space, and of monopoles

used on perfectly conducting plane ground. In addition to gain versus
elevation angle, the computer program lists the following antenna

parameters:

(1) Input impedance

(2) Mutual impedance between the dipole and its image in ground

(3) Antenna factor

(M) Antenna VSWR

(5) Mismatch loss

The equations used to calculate gain and various antenna parameters are located in Section 2. As discussed in [2], monopoles should be considered

for use as gain standards only on electrically large, highly conducting

ground screens.

These standard antennas are used in gain-transfer measurements to

determine the gain of test antennas [1]. Below 1000 MHz, these measurements

are frequently performed outdoors because of the size of the antennas or the

expense of anechoic chambers large enough to simulate a free-space

environment at these frequencies. Measurements are also made outdoors

because the test antennas may be outdoors and, as an added complication, may

be within a few wavelengths of the ground. As a result, gain of the

standard antenna must be calculated taking the effect of ground into

account.

The electrical properties of the ground must be known to calculate the

gain of dipoles over imperfect ground. These properties may be estimated by

measuring soil samples and assuming the entire test site is uniform plane

ground exhibiting these properties. The curvature of the earth and the

effects of ground-wave propagation are neglected in these gain calculations.

It is often very difficult to measure the gain of standard antennas below

1000 MHz, therefore the calculated gain must be assumed to be correct in

many gain measurement situations.

Actual antennas having calculable gains are described in Section 3. Recent measurements of insertion loss between pairs of these antennas in the

30-MHz to 1000-MHz frequency range have been made using the NBS ground screen [3]. Comparisons of measured and calculated data imply that the
calculated gain, at or near the maximum, may have uncertainties on the order

of 0.4 dB or less. This does not mean that the entire gain pattern of a standard antenna will have this small an uncertainty.

Section 4 is a compilation of examples of the use of the computer

program. Most of the examples are for radiating elements with a half-length

of a quarter wavelength or less, which is typical of most gain-standard

antennas. The term half-length is used for the length of a single radiating

element. It is the distance from the dipole feedpoint to the end of one

radiating element, or the distance from the monopole feedpoint to the end of

its radiating element. Validity of the equations used in the computer

program is restricted to half-lengths less than one-half wavelength.

2. Definitions and Equations

All equations in this document are generally considered to be good

engineering approximations. They are presented in a format incorporating

the variable names and library functions used in the computer code while at

the same time retaining the conventional form of the equations as they

appear in the referenced material. The purpose of this somewhat mixed

format is to enable the reader to easily recognize the lines of code

embodying the equations from the references.

The radiating elements of the gain-standard antennas have a halflength, L, a circular cross section, may have a linear taper, have no internal losses, and no shunt admittance in the input region. The principal

quantity required for calculating most antenna performance parameters is

input impedance, ZR. It is obtained by calculating the intrinsic impedance,

ZI, and adding the mutual impedance between the antenna and its image in

ground if the antenna is located over ground. The intrinsic impedance is

the input impedance of a dipole in free space or a monopole on a perfectly

conducting ground plane. The mutual impedance between a dipole and its

image in ground, ZMB, is obtained by calculating ZML, the mutual impedance

between two free-space dipoles in echelon [4], one representing the image

dipole, and changing the reference from the loop current to the base

current. The mutual impedance, ZMB, is then multiplied by the reflection
coefficient of the ground evaluated at an elevation angle ij; = 90 deg and

denoted RH90 for horizontal polarization and RV90 for vertical polarization.

Because of the length of the mutual impedance equations, the reader is

referred to reference [4] and Subroutine Mutual in program HVD6 located in

the appendix.

The equations yielding intrinsic impedance are from [5]. All linear

dimensions and wavelength, A, are in meters. Upper-case variables, except M

and N, are the variable names actually used in program HVD6.

_ KA( (KA-M)cos(BL)+j(ZA+JWCT*KA^-jN)sin(gL)) _ ZINN , . 2

~ ZIND'

(ZA+JWCT*KA +jN)cos(6L)+j(KA+M)sin(6L)

where

B = 2it/A, and

KA = 120(log (2L/RT)-1

)

for antenna elements with a uniform cross section, and

KA = 120(log (2L/RB)+(RT/(RB-RT))log (RT/RB))

for antenna elements tapered from the base with radius RB, to the tip with

radius RT.

M = 60(Cin(26L)-1+cos(26L)) = MBL,

N = 60(Si(2BL)-sin(26L)) = NBL,

JWCT = JRT/30X, and

ZA = RABL+jXABL, where

Real(ZA) = RABL = 60Cin(2BL)+30(2Cin(2BL)-Cin(46L) )cos(2BL)

+30(Si(4BL)-2Si(26L)sin(2BL)), and

Imag(ZA) = XABL = 60Si (2BL)-30(Cin(4BL)-log 4)sin(2BL)-30Si (4bL)cos(2BL) .

In the preceding equations. Si and Cin (and Ci in Subroutine Mutual)

are functional notations for sine and cosine integrals. These integrals are calculated in Program HVD6 in Subroutine SCI using series expansions and

rational approximations given in [5].
For free-space dipoles,

ZR = ZI, (2)

and for raonopoles,

ZR = ZI/2. (3)

For horizontal dipoles over ground,

ZR = ZI+RH90*ZMB. - (4)

For vertical dipoles over ground,

ZR = Z1+RV90*ZMB. (5)

Antenna factor is the ratio, expressed in decibels, of the linearly

polarized field strength incident upon a copolarized antenna to the voltage

at the antenna terminals measured with a receiver having a characteristic

impedance, ZCHAR. Antenna factor is

AF = 20 log |(ZCHAR+ZR)/ZCHARl/(effective length of antenna) (6)

where | ( X/iT)tan(BL/2) ] is the effective length of a free-space dipole, and

I ( A/2tt ) tan( BL/2 )I is the effective half-length of a monopole on infinite,

perfectly conducting ground.

The voltage reflection coefficient at the antenna terminals is

R = (ZR-ZCHAR)/(ZR+ZCHAR), (7)

and the voltage standing-wave ratio is

VSWR = (i+|r| )/(i-|r| ). (8)

The conjugate mismatch loss [7], expressed in decibels, is

LOSS = 10 log^Q(1/(l-|R^|)). (9)

Antenna gain is a function of input impedance, free-space effective

length, and radiation pattern of the array formed by the antenna and its
image in the ground. Based upon equations in [8,9,10,11], antenna gain is

expressed in decibels as

GAIN = 10 log^Q(120|E^|/Real(ZR)) (10)

where E is the effective length of a dipole over ground, multiplied by ir/X.

The three equations for E for a dipole with its feedpoint H meters

above ground and for a monopole on perfect ground are as follows:

Horizontal dipole over ground, H-plane

E = |tan(6L/2)|(eJ^""^'^^.RH e-^^""^"^) (11)

Vertical dipole over ground or monopole on perfect ground, E-plane

E = |(cos(3Lsinij;)-cos(6L))/(cosK;(sin6L))|(e-^^"^^"'^+RV e"^^"^^'^''') (12)

(Monopole gain is computed using the value of E for a vertically polarized

dipole in free space.)

Horizontal dipole over ground, E-plane

E = |(cos(BLcos4;)-cos(6L))/(sinijj(sin6L))l(e-^^"^^"'''-RV g"-^^"®^'^^) (13)

The vertical and horizontal reflection coefficients [8] for the ground

plane or test site ground are

RV = (((EPSN-jX)sini^)-TSQ)/(((EPSN-jX)sinil;)+TSQ) , and (14)

RH = (sin4;-TSQ)/(siniJ;+TSQ), (15)

where

X = 17.975 SIGMA/FREQ,

FREQ = frequency, in MHz,

SIGMA = a = conductivity in millisiemens/m (abbreviated mS/m, and

originally millimhos/m in past usage),

EPSN = e = relative dielectric constant, and

r

TSQ = (EPSN-jX-cos^4;)^^^.
3. Gain-Standard Antennas

Half-wave gain-standard dipoles and quarter-wave monopoles are

fabricated using rigid metal tubing above about 30 MHz and tensioned wires

below this frequency. This approximate frequency crossover may be reduced

when using electrically small antennas. The feedpoints are electrically

small, and the amount of low-loss dielectric material used as a support is

kept to a minimum. The dipole balun (balanced-to-unbalanced transmissionline transformer) is removable for calibration.

Figures 1 and 2 show dipoles used for insertion loss measurements in

the 30-MHz to 1000-MHz frequency range [31. The feedpoint assembly is a dielectric cylinder 8.9 cm (3.5 in) long and 2.54 cm (1 in) in diameter.

Two, small, coaxial panel jacks (Type SMA) form the feedpoint, and banana

jacks soldered to the inner conductors provide a simple slip fit to the

radiating elements. Below about 97 MHz, the radiating elements are

extensible whips used down to about 30 MHz. Above 97 MHz, thin-wall brass

tubing is used for elements up to 1000 MHz. Precision attenuators (pads)

and equal length, 50-ohm, coaxial cables connect the dipole terminals to the

collinear (0 and 1 80 deg) ports of a coaxial hybrid junction serving as the

dipole balun. Figure 3 shows the monopole antenna using the same radiating

elements as the dipole.

Figure 4 shows how the hybrid junction, cable, and precision attenuator

assemblies are calibrated for use with the dipole antennas. The initial

received signal level at the spectrum analyzer is measured with the cables,

shown attached to the E-ports, joined with a coaxial adapter. The final

received signal level is measured as shown, and the difference between the

two levels is the total insertion loss of two assemblies providing the

spectrum analyzer and signal generator have input- and output-port

impedances that are matched to the impedance of the cables. It is assumed

that the assemblies are identical, and that the loss of a single assembly is

just one-half the total measured loss. The 3-dB attenuators are used at the

dipole feedpoint end of the cables to force the actual value of ZCHAR toward

the 100-ohm value assumed for the calculations.
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Insertion loss between pairs of these antennas has been measured using

the 30-m by 60-m NBS ground screen. See reference [3] and Example //? in

Section 4 for a comparison of part of the measured and calculated data. In

the 30-MHz to 1000-MHz frequency range of interest, the results imply that

the mean difference between measured and calculated gain is typically

^ 0.05 dB, with a value ^ 0.42 dB on the outside. This result is for

dipoles with O.IX ^L^ 0.25X and for monopoles with L = 0.25A, assuming the

effective lengths are correct. Effective length is the only quantity used

for calculating gain that is not used explicitly for calculating insertion

loss. However, insertion loss between pairs of antennas in free space is

precisely the quantity obtained using the antenna gains in Friis's

transmission formula [5], assuming the mismatch losses are zero. Therefore,

antenna gains are implicit in the more general insertion loss equations.

Comparing measured and calculated insertion-loss data is a valid method of

determining the uncertainty in the gain-product of two linear antennas.

4. Examples of Gain-Standard Antenna Calculations

#1 Thin X/2 Dipole and A/4 Monopole - 299.792458 MHz

The computer program assumes all free-space dipoles are "horizontal"

and calculates both the E- and H-plane patterns. For this example, the

half-length of the dipole and monopole are exactly A/4 and the radii are

m. Since the program must have some nonzero dimension for the radius, a value of input for the requested radius results in the program setting the

-30

value to 1 m. Figure 5a shows the dipole gain is a constant 2.14 dB in

the H plane and exhibits a quarter-section of the "figure-eight" pattern in

the E plane. Figure 5b shows the monopole gain is 5.14 dB and its pattern

is an inverted copy of the dipole pattern.

11
The following data are copied from the computer screen during program

execution:

TYPE THE REQUESTED DATA AFTER EACH ? FREQUEHCY, MHZ

• 299.792458

ANTENNA HALF-LENGTH < LAMBDA/2, M

? .25

ANTENNA RADII, FEEDPOIHT THEN END, M

??TYPE 1. FOR DIPOLE, 8 FOR MOHOPOLE

? 1. TYPE 1. FOR GROUND, 6 FOR FREE SPACE

7 e IMPEDANCE OF T-LIHE ATTACHED TO ANTENNA, OHMS

? 108. INPUT IMPEDANCE =« 73.32e9+JC 42.6559J0HMS

ENTER NEW HALF-LENGTH, OR ENTER 6

? 8 ANTENNA FACTOR ASSUMING A 108.e0-OHM RECEIUER

AND A l:l BALUH ARE EMPLOYED » 14.98 DB USWR = 1.7850

MISMATCH LOSS » .3595 DB PRESS RETURN FOR GAIN US PHI, OTHERWISE TYPE CNTL T PAUSE

7ELEU ANCLE INCREMENT FOR BELOM 10 DEG AND THE ADDITIONAL INCREMENT FOR ABOUE 10 DEG

? 2.

? 3.

H-PLANE ELEUATIOH ANGLE IN DEGREES DEG AND GAIN IH DB HORIZONTAL POLARIZATION

2.800 2.140

4.008 2.148

6.088 2.140

8.808 2.148

18.888 2.148

i5.eee 2.148

28.880 2.140

25.908 2.140

38.808 2.140

35.088 2.148

48.088 2.148

45.000 2.140

50.000 2.140

55.000 2.140

60.000 2.140

65.888 2.148

78.080 2.148

75.000 2.148

80.000 2.140

85.000 2.140

98.000 2.148

E-PLANE ELEUATION ANGLE IN DEGREES AND CAIN IN D UERTICAL POLARIZATION

2.000 -29.100

4.080 -23.076

6.008 -19.550

8.000 -17.046

10.000 -15.100

15.000 -11.554

20.000 -9.025

25.000 -7.054

30.800 -5.441

35.800 -4.881

40.000 -2.913

45.000 -1.982

58.880 -1.825

55.000 -.268

60.000 .379

65.000 .920

70.000 1.361

75.000 1.702

80.000 1.945

85.000 2.091

90.000 2.148

12
o

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in

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DIPOLE GRIN VS ELEVATION ANGLE... E^H PLANES

;'

HALF-LENGTH, .250 M

FREE SPACE

- HP \ / D VP

y —" ' --""

--'''

--30.0 -25.0 -20.0 -15.0 -10.0

GAIN, DB

5.0 0.0 5.0 10.0

Figure 5 a. Calculated gain versus elevation angle for a thin, X/2 dipole in

free space. A=1 m

13
Jil^uJK^vrSUP''' '''' '''^^ '''" • E-PLANE ELEUATIOH ANGLE IN DEGREES AND GAIN IN DB

^ 299.792458 UERTICAL POLARIZATION

AHTEHHA HALF-LENGTH < LAMBDA/-2, M 2.998 5.142

7 ,25 4 699 5 119

AHTENNA RADII, FEEDPOINT THEN END, M 6!899 5!e88

; 2 8.999 5.926

TYPE 1. FOR DIPOLE, 8 FOR MONOPOLE IsigM 4! 712

IMPEDANCE OF T-LINE ATTACHED TO ANTENNA, OHMS 25!988 3! 931

- -®: 39! 989 3.' 389

INPUT IMPEDANCE = 36.6685+JC 21.3279D0HMS 35.899 2.742

_ __ 49.898 1.985

ENTER NEW HALF-LENGTH, OR ENTER 8 45.888 1.188

? 8 59.998 .897

55.888 -1.878

ANTENNA FACTOR ASSUMING A 5e.e8-0HM RECEIVER 69.888 -2.431

AND TRANSMISSION LINE ARE EMPLOYED = 21.08 DB 65.899 -4.944

USWR = 1.7858 70 aaa -6 014

MISMATCH LOSS = .3595 DB 75.999 -8!543

PRESS RETURN FOR GAIN US PHI, OTHERWISE TYPE~CNTL T 85!999 -ll'lls

7 ^'^^^^ 99! 998 -128.' 890

ELEU ANGLE INCREMENT FOR BELOW 18DEGANDTHE

ADDITIONAL INCREMENT FOR ABOUE 19 DEG

? 2.

? 3.

o

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MONOPOLE GRIN VS. ELEVRTION RNGLE. . „ E-PLRNE

"~

-----_

---___

^^- '^-.^

HRLF-LENGTH, „ 250 M

FREE 5PRCE

^,

\ / D

V

Vr

-30.0 -25.0 -20.0 -15.0 -10.0 -5.0

GRIN, DB

0.0 5.0 10.0

Figure 5 b. Calculated gain versus elevation angle for a thin, A/4 monopole

fed against an infinite, perfectly conducting, plane ground.

A = 1 m

14
#2 A Vertical Dipole Over Imperfect Ground - 485 kHz

In 1979, an extensive set of measurements were made near Dateland,

Arizona, to determine the gain of various medi um- frequency antenna

configurations at low elevation angles. The 485-kHz test signal was

transmitted from an electrically short (61 m), vertical sleeve dipole

suspended by a helicopter. An optical tracker provided elevation and

azimuth angle data for these measurements.

The gai n- standard antenna was a vertical sleeve dipole, with

3 L = 152.4 m, supported by a 25-m helium-filled blimp. A large toroidal

choke suppressed undesired currents on the outer conductor of the antennato-receiver cable at ground level. The gain pattern of this antenna, shown

in Fig. 6, is calculated for o = 10 mS/m and e =50 based upon soil samples

from the dry lakebed test site.

Measurements were made at a range of 1620 m, and, because of the strong

ground-wave component in the electromagnetic field at the test site, the

resulting data are "gain" values relative to the particular reference dipole

measured at that specific range. In fact, "the concepts of power gain,

directive gain, radiation resistance, and radiation efficiency are not

directly applicable in this situation. . ."[1 ]

.

15
The following data are copied from the computer screen during program

execution:

TYPE THE REQUESTED DATA AFTER EACH ? FREQUENCY, MHZ

7 0. 485 ANTENNA HALF-LENGTH < LAf1BDAx2, M

? 152.4 ANTENNA RADII, FEEDPOINT THEN END, M

7 9.992

? 9.992

TYPE 1. FOR DIPOLE, 9 FOR MOHOPOLE

? 1. TYPE 1. FOR GROUND, 8 FOR FREE SPACE

? 1. DIPOLE FEED-POINT HEIGHT ABOUE GROUND, M

? 153. TYPE 1. FOR HORIZONTAL POLARIZATION, 8 FOR UERTICAL

? e TYPE 1. FOR PERFECT GROUND, 8 FOR IMPERFECT GROUND

? 8 GROUND CONDUCTIUITY, MILLISIEMENS/M

? 19. GROUND RELATIVE DIELECTRIC CONSTANT

? 50. IMPEDANCE OF T-LIHE ATTACHED TO ANTENNA, OHMS

? 59. INPUT IMPEDANCE « 96. 1373+ JC 31.142730HMS

ENTER NEU HALF-LENGTH, OR ENTER 8

? 8

ANTENNA FACTOR ASSUMING A 58.88-OHM RECEIVER

AND A 1:1 BALUN ARE EMPLOYED - -36.18 DB MUTUAL IMPEDANCE DUE TO THE DIPOLE'S IMAGE

IN THE GROUND - 25.849e+JC 15.8547D0HMS

USHR « 2.1875

MISMATCH LOSS « .6489 DB PRESS RETURN FOR GAIN OS PHI, OTHERHISE TYPE CNTL T PAUSE

7ELEU ANGLE INCREMENT FOR BELOU 18 DEG AND

THE ADDITIONAL INCREMENT FOR ABOUE 18 DEG

? 2.

? 3. E-PLANE ELEVATION ANGLE IN DEGREES AND GAIN IN DB UERTICAL POLARIZATION

2.888 -1.826

4.888 1.998

6.888 3.164

8.888 3.787

18.888 3.949

15.888 3.885

28.888 3.268

25.888 2.237

38.888 .866

35.888 -.846

48.888 -2.988

45.888 -5.358

58.888 -8.221

55.888 -11.598

68.808 -15.598

65.888 -20.395

78.888 -26.187

75.888 -32.821

88.888 -38.727

85.888 -44.480

98.888 -128.888

16
DIPGLE GRIN VS ELEVRTION RNGLE„ .

E-PLRNE

).0

ELEVRTIGN

RNGLE,

DEG

0.0

15.0

30.0

45.0

60.0

75.0

9C

1

1

1

1

1

~" - ~~-. -,_

HRLP-LENGTH, 152.4 M

IMPEREEGT GRGUND

~~--

~^~-^

\ / n VP ^^-.^

''\

;'

30.0 -2^J.O -2C].o -lei.O -ic

GRIN

).0 -5

, DB

.0 .0 5 .0 IC

Figure 6. Calculated gain versus elevation angle for a vertical dipole over imperfect ground with lower tip of dipole at ground level.

X=6l 8 m; a=10 mS/m; e =50

r

17
#3 A Horizontal Dipole Over Imperfect Ground - 11.555 MHz

The Table Mountain test site is located near Boulder, Colorado.

Frequent high winds make the use of a blimp-supported vertical reference

impractical in the high-frequency band, so a horizontal wire-dipole,

stretched between two wooden poles, was used as a gain-standard antenna for some measurements performed in 1977.

The test antenna was a vehicular omnidirectional antenna mounted on a large van which was placed on a turntable rotating at about 1 rpm during the

measurements. The test site was illuminated with an electrically-small,

reflector-backed, vertically-polarized antenna mounted between the skids of

a helicopter. This antenna pivoted so the main beam always pointed at the

test site. The helicopter flew over the test site on a radial in the

vertical plane through the gain-standard antenna. Test antenna gain data

were presented as mean vertical-plane patterns with horizontal bars

indicating the standard deviation of the sampled data measured in specific,

elevation-angle increments. Figure 7 shows the gain of the standard,

h orizontal , A/2 dipole, positioned at a 6.3-m height, used as a vertically

polarized reference. That is, the E-plane gain-pattern of the dipole was used as the gain-transfer standard. Toroidal chokes are required in the

dipole feed cable to reduce radiation by any currents on the outer conductor

of this cable.
The following data are copied from the computer screen during program

execution:

TYPE THE REQUESTED DATA AFTER EACH ? FREQUENCY, MHZ

? 11.555 ANTENNA HALF-LENGTH < LAMBDA/2, M

? 5.7 ANTENNA RADII, FEEDPOINT THEN END, M ? 8.89125

? 8.88125

TYPE 1. FOR DIPOLE, 8 FOR MOHOPOLE

? 1. TYPE I. FOR GROUND, 8 FOR FREE SPACE

? 1. DIPOLE FEED-POINT HEIGHT ABOUE GROUND, M

? 6.3 TYPE 1. FOR HORIZONTAL POLARIZATION, 8 FOR UERTICAL

? 1. TYPE 1. FOR PERFECT GROUND, 8 FOR IMPERFECT GROUND

? 8 GROUND CONDUCTIUITY, HILLISIEMENS/M

? 28. GROUND RELATIUE DIELECTRIC CONSTANT

? 5. IMPEDANCE OF T-LINE ATTACHED TO ANTENNA, OHMS

? 188. INPUT IMPEDANCE 58.9441+JC -123.485130HMS

ENTER NEH HALF-LENGTH, OR ENTER 8 ? e ANTENNA FACTOR ASSUMING A I88.e8-0HM RECEIUER

AND A l:l BALUN ARE EMPLOYED » -18.68 DB MUTUAL IMPEDANCE DUE TO THE DIPOLE'S IMAGE

IN THE GROUND = 9.8674+JC 15.232930HMS

USWR = 4.6582

MISMATCH L0SS'= 2.3588 DB PRESS RETURN FOR GAIN US PHI, OTHERWISE TYPE CNTL T PAUSE

7ELEU ANGLE INCREMENT FOR BELOU 18 DEC AND

THE ADDITIONAL INCREMENT FOR ABOUE 18 DEG

? 2. ? 3.

E-PLANE ELEUATIOH ANGLE IN DEGREES AND GAIN IN DB H-PLANE ELEUATION ANCLE IN DEGREES AND GAIN IN DB

UERTICAL POLARIZATION

2.eee -24.484

4.eee -19.563

6.886 -16.826

8.868 -14.965

18.666 -13.486

15.666 -16.429

26.666 -7.726

25.866 -5.274

36.868 -3.163

35.866 -1.226

48.866 .373

45.866 1.719

56.866 2.839

55.868 3.762

68.866 4.511

65.668 5.187

78.688 5.569

75.666 5.912

88.666 6.148

85.888 6.286

98.886 6.331

HORIZONTAL POLARIZATION

2.688 -17.466

4.668 -11.439

6.668 -7.991

8.666 -5.577

16.666 -3.737

15.686 -.515

26.686 1.612

25.686 3.116

36.686 4.192

35.666 4.975

46.666 5.533

45.686 5.918

56.666 6.171

55.666 6.322

66.666 6.397

65.866 6.421

76.868 6.412

75.688 6.387

86.868 6.366

85.868 6.339

96.688 6.331

19
o

O -I eno

Ln - CD ^

LJ

CZl o

N CD - LJ ^

_l

CDZ o

^°

LlJ

Ln -

o

o _

DIPOLE GRIN V5 ELEVRTIGN RNGLE. , .E^H PLRNE5

).0

;'

;'

HRLP-LENGTH, 5.7G0 M

IMPEREECT GROUND

1 1 n> \ / Ri

/

/

/

f /

Hh ^ Vr

,''

..---'' 2________

1 1 1 1 1 30.0 -25.0 -20.0 -15.0 -10.0 -5.0

GRIN, DB

1 1 0.0 5.0 IC

Figure 7. Calculated gain versus elevation angle for a horizontal dipole

with its feedpoint 0.24 A above ground. X=25.9 m; 0=20 mS/m; e =5

r

20
#4 Horizontal Dipole Over Imperfect Ground - 392.5 MHz

Reference [12] describes measurements of buried, vertically polarized

antennas in the 225-MHz to 400-MHz frequency range. The gain-standard

dipole used for the measurements at Table Mountain was a horizontal A/2

dipole positioned 2.6 \ above the ground. A rotatable, reflector-backed

dipole was used to illuminate the test range enabling the use of the H-plane

pattern as a gain-transfer standard for these vertically polarized test

antenna measurements [13]. Figure 8 shows the calculated gain versus

elevation angle for the gain-standard dipole. This dipole was positioned at

a height chosen to place its main beam at a 5-deg elevation angle to insure

accurate measurements near this elevation angle. It is difficult to make

accurate ga i n- trans fer measurements near the nulls of gain-standard

antennas.

21
The following data are copied from the computer screen during program

execution:

TYPE THE REQUESTED DATA AFTER EACH ? FREQUENCY, MHZ

? 392.5 AHTEHHA HALF-LENGTH < LA(1BDA/2, M ? 0.172 ANTENNA RADII, FEEDPOINT THEN END, M

? 9.883

? 8. 983 TYPE 1. FOR DIPOLE, 8 FOR MOHOPOLE

? 1. TYPE 1. FOR GROUND, 9 FOR FREE SPACE

? 1. DIPOLE FEED-POINT HEIGHT ABOUE GROUND, M ? 1.987 TYPE 1. FOR HORIZONTAL POLARIZATION, 8 FOR UERTICAL

? 1. TYPE 1. FOR PERFECT GROUND, 8 FOR IMPERFECT GROUND

? 8 GROUND CONDUCTIUITY, MILLISIEMENS/M

? 29. GROUND RELATIUE DIELECTRIC CONSTANT

? 4. IMPEDANCE OF T-LINE ATTACHED TO ANTENNA, OHMS

? 188. INPUT IMPEDANCE - 51.9938+JC 2.02763OHMS

ENTER NEW HALF-LENGTH, OR ENTER 8 ? 8 ANTENNA FACTOR ASSUMING A 109.00-OHM RECEIUER

AND A l:l BALUN ARE EMPLOYED = 17.22 DB MUTUAL IMPEDANCE DUE TO THE ANTENNA'S IMAGE

IN THE GROUND :> -.9154+JC -.e99530HMS

USHR = 1.9617

MISMATCH LOSS = .4839 DB PRESS RETURN FOR GAIN US PHI, OTHERWISE TYPE CNTL T PAUSE

7ELEU ANGLE INCREMENT FOR BELOW 19 DEG AND THE ADDITIONAL INCREMENT FOR ABOUE 18 DEG

? 2. ? 3.

E-PLftHE ELEVATION ANGLE IH DEGREES AND GAIN IH DB H-PLAHE ELEUATIOH ANGLE IH DEGREES AHD GAIN IN DB UERTICAL POLARIZATION

2.088 -24.536

4.000 -24.565

6.890 -26.223

8.808 -16.298

19.888 -11.768

13.888 -11.692

28.898 -8.484

25.898 -6.865

38.888 -4.715

35.888 -4.689

48.888 -1.319

45.889 -.892

58.809 -3.859

55.000 .917

60.009 2.981

65.900 1.752

70.000 -,951

75.000 -1.256

89.999 .672

85.999 2.884

98.898 2.422

HORIZONTAL POLARIZATION

2.888 2.908

4.888 7.238

6.888 7.792

8.888 5.384

18.808 -2.896

15.888 6.282

28.888 2.928

25.888 2.686

38.888 5.779

35.888 -4.242

48.888 3.891

45.888 4.171

58.888 -2.596

55.888 3.684

69.899 5.288

65.989 3.163

79.999 -.533

75.990 -1.131

88.888 .889

85.808 2.848

90.088 2.422

22
DIPOLE GniN VS ELEVRTION RNGLC.E^H PLANES

o • en

CD

LJQ

ino

LiJ _1

CD

01

o

en>

LJ

_J

LJ

o

LD -

o

LO

HRLF-LENGTH, „ 172 M

IMPERFECT GROUND

HP , VP

-30.0 -25.0 -20.0 -15.0 -10.0 -5.0

GRIN, DB

0.0 5.0 10.0

Figure 8. Calculated gain versus elevation for a horizontal dipole with its

feedpoint 2.6 A above ground. A=0.76 m; o=20 mS/m; e

=i| r

23
#5 Antenna Factor Calculation For Comparison With Measured Data - Monopole

A simple 1-m monopole antenn,a was fabricated using brass tubing with a 0.002-m radius. The antenna factor of this monopole was measured on the NBS

ground screen during the calibration of a commercial active monopole in the

0.014-MHz to 72.5-MHz frequency range. The following table gives the

results at six selected frequencies in this range.

Frequency, MHz Measured AF, dB Calculated AF, dB

0.1 75.7 75.58

1 .0 55.5 55.58

10.0 35.6 35.42

20.0 28.8 28.88

30.0 25.6 24.44

50.0 15.8 16.32

#6 Antenna Factor Calculation For Comparison With Measured Data - Dipole

A commercial dipole was calibrated in the NBS anechoic chamber in the

400-MHz to 1000-MHz frequency range. This dipole consists of extensible

radiating elements permanently attached to a balun. The element lengths are set using a scale provided by the manufacturer, and the larger radius

sections are used to form the elements as specified. Calculations assume

the antenna input impedance is 50 ohms, and the balun transformer ratio is

1:1. The following table gives the results at nine selected frequencies.

Frequency, MHz Measured AF, dB Calculated AF, dB

400.0 20.6 20.41

500.0 22.6 22.48

550.0 21 .9 23.26

600.0 22.4 24.10

650.0 23.8 24.74

700.0 25.9 25.48

800.0 26.2 26.64

900.0 27.0 27.76

1000.0 28.7 28.70

24
These comparisons of measured and calculated data show the difference

between the actual antenna factor and the "ideal" or calculated antenna

factor.

Uncertainties in the antenna factor calibration technique may be

determined by measuring the antenna factor of gain-standard dipoles and

monopoles and comparing measured and calculated data.

#7 Site Attenuation Using Gain-Standard X/2 Dipoles

Site attenuation is the minimum insertion loss between two copolarized

antennas located above a test site. It is measured with one antenna at a fixed height, while the other antenna is located at a specified horizontal

distance away and scanned vertically over a specified range of heights.

Gain-standard A/2 dipoles, fabricated as described in Section 3, were

used to measure site attenuation of the NBS ground-screen test site at ten

frequencies from 30 MHz to 1000 MHz [14]. These dipoles are required for

obtaining measured site-attenuation data that are used for comparison with

calculated data. Calculated data are shown as the solid lines and + + + symbols, and measured data are shown as circles, in Fig. 9.

Although site attenuation calculations do not involve gain directly

(some measurements are actually made in the near-field where gain is not

defined), the input and mutual impedance formulations are the same as those

used in the gain calculations. Program HVD6 is used to calculate the length

of the gain-standard dipoles, given the radii of the radiating elements.

This length is somewhat arbitrarily chosen to make the calculated, freespace value of ZR (ZI) purely real when the element length is near A/4.

25
CO

CD

COcno

CD

LlJ en

o

Lno

o

o

o

o

o

o

OD

CD

OD

CO

CD

o

LD

O

LTi O

o

O c;

LlJ CO

o

to

o

o

o

o

o

0'

0'

SITE RTTENUflTION VS FREQUENCY HP

SOURCE HEIGHT, 2.0 M

DI5T = 3, 10, ^ 30 M

10^ 0'

VP

SOURCE HEIGHT, 2.0 M

DIST = 3, 10, ^ 30 M

10

EREOUENCY, MHZ

0"

Figure 9- Minimum insertion loss -vs. frequency for A/2 dipoles horizontally

polarized, HP, and vertically polarized, VP. Scan heights are

1 to 4 m for the 3 and 10 m distances and 2 to 6 m for the 30 m distance.

Solid line — calculated for infinitely thin A/2 dipoles

+ + + + + — calculated using the actual dipole dimensions

o o o o o — measured using gain standard dipoles

26
5. Conclusions

The examples given in Section 4 illustrate the usefulness of Program

HVD6. It is written in the FORTRAN programming language because of the ease with which this language handles complex arithmetic. It is used on the

large, main-frame computer installed at the NBS Boulder Laboratories, but it

should run properly on any computer with a FORTRAN compiler.

The well documented equations used in this program are based upon

conventional engineering approximations. It is the author's opinion that

gain-standard antenna parameters, that is, parameters for thin linear

dipoles with removable baluns, positioned over ground or in free space, and

monopoles on highly conducting ground, can be calculated with less

uncertainty than they can be measured. That is, the calculated parameters

may more accurately represent the actual antenna performance than the

measured parameters because of the difficulty of making accurate

measurements in the frequency range below 1000 MHz.

27
6. References

[I] IEEE Standard Test Procedures for Antennas. IEEE Std 149-1979

(Revision of IEEE Std 149-1965). New York, NY: IEEE, Inc.; 1979.

[2] FitzGerrell, R.G. Limitations on vertically polarized ground-based

antennas as gain standards. IEEE T-AP-23: 284-286; March 1975.

[3] FitzGerrell, R.G. Standard linear antennas, 30 MHz to 1000 MHz.

Fifth International Conference on 'Electromagnetic Compatibility.'

1986 Sept. 29 - Oct. 2; University of York, York, England.

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

IEEE T-AP-5: 306-313; 1957 July.

[5] Schelkunoff, S.A.; and Friis, H.T. Antennas, Theory and Practice.

New York, NY: John Wiley & Sons; 1952.

[6] Abramowitz, M.; and Stegun, I. A. Handbook of Mathematical Functions

With Formulas, Graphs, and Mathematical Tables. Nat. Bur. Stand.

(U.S.) Appl. Math. Ser. 55; Washington, D.C.; 1964. 231-233.

[7] Beatty, R.W. Insertion loss concepts. Proc. IEEE. Vol 52: 663-67I

;

1 964 June.

[8] Jordan, E.G. Electromagnetic Waves and Radiating Systems. Englewood

Cliffs, NJ: Prentice-Hall; 1950.

[9] Ma, M.T. Theory and Application of Antenna Arrays. New York, NY:

John Wiley & Sons; 1974.

[10] Ma, M.T.; and Walters, L.C. Power gains for antennas over lossy

ground. ESSA Tech. Rept. ERL 104 - ITS 74. U.S. Govt. Printing

Office, Washington, D.C.; 1969.

[II] Berry, L.A.; and Chrisman, L.E. Linear high frequency antennas over

a finitely conducting spherical earth. ESSA Tech. Rept. ITSA No. 8.

U.S. Govt. Printing Office, Washington, D.C.; 1966.

[12] FitzGerrell, R.G.; and Haidle, L.L. Design and performance of four

buried UHF antennas. IEEE T-AP-20: 56-62; 1972 January.

[13] FitzGerrell, R.G. Gain measurements of vertically polarized antennas

over imperfect ground. IEEE T-AP-15: 211-216; 1967 March.

[14] FitzGerrell, R.G. Site attenuation. IEEE T-EMC-28: 38-40; 1986

February.

28
Appendix — Listing of Program HVD6

00100 PROGRAM HVD6 ( INPUT, OUTPUT, TAPE50)

001 1 00******************************************************************

001 200* GAIN VERSUS ELEVATION ANGLE AND IMPEDANCE RELATED PARAMETERS * 001 300* FOR VERTICAL AND HORIZONTAL DIPOLES OVER GROUND AND MONOPOLES * 001 400* ON PERFECT GROUND R.G. FITZGERRELL (303) 497-3737 * 001 50C* TAPE50 IS USED IN A PLOTTING PROCEDURE FILE. DELETE THE FOUR * 001 60C* CALLS TO FILE AND SUBROUTINE FILE IF DESIRED. * 001 70C******************************************************************

00180 DIMENSION ARG( 2) ,01 ( 2) ,CIN( 2) , SI( 2)

001 90 COMPLEX E, J, JWCT, R, RH, RV, RH90, RV90, TSQ, ZA, ZIND , ZINN, ZML, ZR, ZI , ZMB

00200 REAL KA, LAMBDA, L, L2 , LOSS, NBL,MBL, MONO

0021 00***********************************************************

002200* USER SPECIFIES ANTENNA GEOMETRY. ANTENNA ELEMENTS MAY * 00230C* HAVE A LINEAR TAPER OR A ZERO (1.E-30) RADIUS. * 002400***********************************************************

00250 10 F0RMAT(*TYPE THE REQUESTED DATA AFTER EACH ?*)

00260 PRINT 10

00270 20 FORMAT(*FREQUENCY, MHZ*)

00280 PRINT 20

00290 30 F0RMAT(F12.4)

00300 READ 30,FREQ

00310 40 FORMAT(*ANTENNA HALF-LENGTH < LAMBDA/2, M*)

00320 PRINT 40

00330 READ 30,

L

00340 50 FORMAT(*ANTENNA RADII, FEEDPOINT THEN END, M*)

00350 PRINT 50

00360 READ 30, RB

00370 READ 30, RT

00380 IF(RT.EQ.O. )RT=1 .E-30

00390 IF(RB.EQ.O. )RB=1 .E-30

00400 60 F0RMAT(*TYPE 1. FOR DIPOLE, FOR MONOPOLE*)

00410 PRINT 60

00420 READ 30, MONO

00430 IF(MONO.EQ.0)POLAR=0.

00440 IF(MONO.EQ.O) GO TO 140

00450 70 FORMAT(*TYPE 1. FOR GROUND, FOR FREE SPACE*)

00460 PRINT 70

00470 READ 30, GF

00480 IF(GF.EQ.0.)P0LAR=1

.

00490 IF(GF.EQ.O) GO TO 140

00500 80 F0RMAT(*DIP0LE FEED-POINT HEIGHT ABOVE GROUND, M*)

00510 PRINT 80

00520 READ 30, H

00530 IF(H.LE.L)P0LAR=1

.

00540 IF(H.LE.L) GO TO 95

00550 90 FORMAT(*TYPE 1. FOR HORIZONTAL POLARIZATION, FOR VERTICAL*)

00560 PRINT 90

00570 READ 30, POLAR

00580 95 CONTINUE

00590 100 FORMAT(*TYPE 1. FOR PERFECT GROUND, FOR IMPERFECT GROUND*)

00600 PRINT 100

29
00610 READ 30, GND

00620 IF(GND.EQ.1 . ) GO TO 130

00630 110 FORMAT(*GROUND CONDUCTIVITY, MILLISIEMENS/M*)

00640 PRINT 1 10

00650 READ 30, SIGMA

00660 120 FORMAT(*GROUND RELATIVE DIELECTRIC CONSTANT*)

00670 PRINT 120

00680 READ 30,EPSN

00690 GO TO 150

00700C***********************************************************

0071 OC* PERFECT GROUND AND FREE-SPACE APPROXIMATIONS ARE MADE. * 00720C***********************************************************

00730 1 30 SIGMA=1 .E30

00740 GO TO 145

00750 1 40 SIGMA=0,0

00760 1 45 EPSN=1 .0

00770 150 CONTINUE

00780 160 FORMAT(*IMPEDANCE OF T-LINE ATTACHED TO ANTENNA, OHMS*)

00790 PRINT 1 60

00800 READ 30,ZCHAR

0081 J=CMPLX(0. ,1 .)

00820 LAMBDA=299.792458/FREQ

00830 BETA=6.2831853/LAMBDA

00840 X=17.975*SIGMA/FREQ

00850 170 F0RMAT(* *)

00860 PRINT 170

00870c*********************************

00880C* THE CALCULATIONS BEGIN HERE * 00890c*********************************

00900 200 B=2.*BETA*L

00910 BL=BETA*L

00920 DO 210 M=1 ,2

00930 ARG(M)=M*B

00940 210 CALL SCI( ARG(M) , SI(M) ,CI(M) ,CIN(M)

)

00950c*****************************************************************

00960C* COMPUTE SELF-IMPEDANCE, ZI, USING SCHELKUNOFF 'S EQN. I3-IO8 * 00970c*****************************************************************

00980 IF(RT.EQ.RB)KA=120.*(AL0G(2. *L/RT)-1 ,

)

00990 IF(RT.NE.RB)KA=120.*(ALOG(2*L/RB)+(RT/(RB-RT))*ALOG(RT/RB))

01000 MBL=60.*(CIN(1)-1 .+C0S(B))

01010 NBL=60.*(SI(1)-SIN(B))

01020 RABL=60.*CIN(1)+30.*(2.*CIN(1)-CIN(2))*COS(B)+30.*(SI(2)

01030+ -2.*SI(1))*SIN(B)

01040 XABL=60.*SI(1)-30.*(CIN(2)-AL0G(4.))*SIN(B)-30.*SI(2)*C0S(B)

01050 ZA=RABL+J*XABL

01060 JWCT=J*RT/(30.*LAMBDA)

01 070 ZINN=KA*( (KA-MBL) *C0S( BL) +J*( ZA+ JWCT*KA*KA-J*NBL) *SIN( BL)

)

01080 ZIND=(ZA+JWCT*KA*KA+J*NBL)*COS(BL)+J*(KA+MBL)*SIN(BL)

01090 ZI=ZINN/ZIND

01 1 OOC********************************************************************

01110c* COMPUTE ANTENNA INPUT IMPEDANCE, ZR. SUBROUTINE MUTUAL RETURNS * 01 1200* MUTUAL IMPEDANCE REFERRED TO THE LOOP CURRENT, ZM, BETWEEN TWO * 01 130c* FREE-SPACE DIPOLES. SIN(BL)**2 CHANGES REFERENCE TO BASE CURRENT*

01140C********************************************************************

30
01150 IF(SIGMA. EQ.O. AND. MONO. EQ.

1

.)ZR=ZI

01160 IF(MONO.EQ.O. )ZR=ZI/2.

01170 IF(MONO. EQ.O. OR. SIGMA. EQ.O.) GO TO 2^0

01180 CALL MUTUAL( BETA, H, J, L,ZML, POLAR)

01190 ZMB=ZML/(SIN(BL)**2)

01200 IF(H.GE.0.1*L) GO TO 230

01210 HI =0.0001 *LAMBDA

01 220 P0LAR1 =1 .0

01230 CALL MUTUAL(BETA,H1 , J,L,ZML,P0LAR1

)

012^10 ZI = ZML/(SIN(BL)**2)

01250C***********************************^**************************

01 260C* THE ABOVE 5 LINES HELP PREVENT NEGATIVE VALUES OF ZR FOR * 01270C* DIPOLES NEAR THE GROUND BECAUSE SCHELKUNOFF 'S ZI DOES NOT * 01280C* CONVERGE TO THAT OBTAINED USING SUBROUTINE MUTUAL. * 01290C**************************************************************

01 300C* COMPUTE REFLECTION COEFFICIENTS FOR PSI=90 DEG * 01310c****************************************************

01 320 230 RV90=((EPSN-J*X)-CSQRT(EPSN-J*X))/((EPSN-J*X)+CSQRT(EPSN-J*X))

01 330 RH90=(1 .-CSQRT(EPSN-J*X))/(1 . +CSQRT( EPSN-J*X)

)

013^0 IF( POLAR. EQ.1 .AND. MONO. EQ.1 . ) ZR=ZI+RH90*ZMB

01350 IF ( POLAR . EQ . . AND . MONO . EQ . 1 . ) ZR=Z I + RV90 *ZMB

01 360 240 CONTINUE

01370 250 FORMAT(*INPUT IMPEDANCE =*F1 2. i|*+ J[ *F1 2. 4*]0HMS*)

01 380 PRINT 250, ZR

01390 PRINT 170

01400 260 FORMAT(*ENTER NEW HALF-LENGTH, OR ENTER 0*)

01410 PRINT 260

01 420 READ 30, L2

01430 IF(L2.GT.O) L=L2

01440 IF(L2.GT.O) GO TO 200

01 450c*****************************************************************

01460C* COMPUTE ANTENNA FACTOR; MUTUAL IMPEDANCE; VSWR; MISMATCH LOSS*

01 470c* ANTENNA FACTOR = VOLTAGE DIVIDER FACTOR/EFFECTIVE LENGTH *

01 4 80c*****************************************************************

01490 IF(MONO.EQ.0. ) AF=(CABS( ZCHAR+ZR)/ZCHAR)/ABS( ( 1 . /BETA) *TAN( BL/2 . )

)

01 500 IF(M0N0.EQ.1 . ) AF=(CABS( ZCHAR+ZR)/ZCHAR)/ABS( (2. /BETA) *TAN( BL/2 . ))

01510 PRINT 170

01520 300 FORMAT(*ANTENNA FACTOR ASSUMING A *F6.2*-0HM RECEIVER*)

01530 310 FORMAT(*AND A 1:1 BALUN ARE EMPLOYED =*F8.2* DB*)

01540 320 FORMAT(*AND TRANSMISSION LINE ARE EMPLOYED =*F8.2* DB*)

01550 PRINT 300,ZCHAR

01560 IF(M0N0.EQ.1 .) PRINT 310, 20. *AL0G1 0( AF)

01570 IF(MONO.EQ.O.) PRINT 320, 20 . *AL0G1 0( AF)

01580 330 FORMAT(*MUTUAL IMPEDANCE DUE TO THE DIPOLE'S IMAGE*/

01590+*IN THE GROUND =*F1 2 . 4*+ J[ *F1 2. 4*]0HMS*)

01600 IF(SIGMA.GT.O.) PRINT 330, ZR-ZI

01610 R=(ZR-ZCHAR)/(ZR+ZCHAR)

01 620 VSWR=(1 .+CABS(R))/(1 .-CABS(R))

01630 340 FORMAT(*VSWR =*F12.4)

01 640 PRINT 340, VSWR

01650 LOSS=10.0*ALOG10(1 .0/(1 . 0-CABS(R*R) )

)

01660 350 FORMAT(*MISMATCH LOSS =*F12.4* DB*)

01670 PRINT 350, LOSS

01 680 PRINT 170

31
01 6 90 C****************************************************

01700C* COMPUTE GAIN VERSUS ELEVATION OR EXIT PROGRAM. *

01 71 00****************************************************

01720 400 FORMAT(*PRESS RETURN FOR GAIN VS PHI, OTHERWISE TYPE CNTL T*)

01730 PRINT 400

01740 PAUSE

01750 410 FORMAT(*ELEV ANGLE INCREMENT FOR BELOW 10 DEC AND*/

01760+*THE ADDITIONAL INCREMENT FOR ABOVE 10 DEG*)

01770 PRINT 410

01780 READ 30, ENC

01790 READ 30, ENC2

01800 CALL FILE(ENC, ENC2,L, POLAR, SIGMA, 0. ,0. ) 01810 IF(SIGMA.EQ.O. ) H = 1 . 01820 BH=BETA*H

01830 IF(POLAR.EQ.O) GO TO 530

01840 PRINT 170

01850 420 FORMAT(*H-PLANE ELEVATION ANGLE IN DEGREES AND GAIN IN DB*)

01860 PRINT 420

01870 430 FORMAT(*HORIZONTAL POLARIZATION*)

01880 PRINT 430

01890 PSI=0

01900C*****************************

01910C* HORIZONTAL POLARIZATION *

01 92 00*****************************

01 930 500 PSI=PSI+ENC

01940 IF (PSI.LT.10.1 ) GO TO 510

01950 PSI=PSI+ENC2

01960 IF(PSI.GT.90. ) GO TO 530

01970 510 PSIRAD=0.01745329252*PSI

01980 SNPSI=SIN(PSIRAD)

01990 CNPSI=COS(PSIRAD)

02000 TSQ=CSQRT(EPSN-J*X-(CNPSI**2))

02010 RH=(SNPSI-TSQ)/(SNPSI+TSQ)

02020C****************************************************************

02030C* RH & RV ARE HORIZONTAL AND VERTICAL REFLECTION COEFFICIENTS * 02040C****************************************************************

02050 EFLH=ABS(TAN(BL/2.))

02060 E=EFLH*(CEXP( J*BH*SNPSI)+RH*(CEXP(-J*BH*SNPSI) )

)

02070 E2=120.*CABS(E*E)/REAL(ZR)

02080C*****************************************************************

02090C* THE GAIN EQUATION IS BASICALLY JORDAN'S EQN. 12-18 USING * 021 OOC* (EFFECTIVE LENGTH) *PI/LAMBDA DENOTED AS E AND APPROPRIATELY * 021 IOC* DEFINED FOR THE ORIENTATION OF THE DIPOLE. * 021 20C*****************************************************************

02130 GAIN=10.0*ALOG10(E2)

021 40 520 FORMAT(2F15.3)

02150 PRINT 520, PSI, GAIN

02160 CALL FILE(-1 . ,-1 . ,-1 .,-1 . ,-1 ., PSI, GAIN)

02170 GO TO 500

02180 530 PRINT 170

02190 IF(POLAR.GT.O) PAUSE

02200 540 FORMAT(*E-PLANE ELEVATION ANGLE IN DEGREES AND GAIN IN DB*)

02210 545 FORMAT(*VERTICAL POLARIZATION*)

02220 PRINT 540

32
02230 PRINT 545

022^10 PSI=0

022500*********^*****************

02260C* VERTICAL POLARIZATION * 02270C***************************

02280 550 PSI=PSI+ENC

02290 IF (PSI.LT.10.1) GO TO 560

02300 PSI=PSI+ENC2

02310 IF (PSI.GT.90.) GO TO 580

02320 560 PSIRAD=0.01745329252*PSI

02330 SNPSI=SIN(PSIRAD)

02340 CNPSI=COS(PSIRAD)

02350 TSQ=CSQRT(EPSN-J*X-(CNPSI**2))

02360 RV=(((EPSN-J*X)*SNPSI)-TSQ)/(((EPSN-J*X)*SNPSI)+TSQ)

02370 IF(P0LAR.EQ.1 .) GO TO 570

02380 EFLV=ABS(COS(BL*SNPSI)-COS(BL) ) / (CNPSI*SIN( BL)

)

02390 E=EFLV*(CEXP(J*BH*SNPSI)+RV*(CEXP(-J*BH*SNPSI)))

02400 E2=120.*CABS(E*E)/REAL(ZR)

02410 IF(E2.EQ.O.) E2 = 1.E-12

02420 GAIN=10.0*ALOG10(E2)

02430 PRINT 520, PSI, GAIN

02440 CALL FILE(-1 . ,-1 . ,-1 . ,-1 . ,-1 ., PSI, GAIN)

02450 GO TO 550

02460C***************************************************

02470C* VERTICAL POLARIZATION FOR A HORIZONTAL DIPOLE * 024 80 C***************************************************

02490 570 EFLVH=ABS(COS(BL*CNPSI)-COS(BL))/(SNPSI*SIN(BL))

02500 E=EFLVH*(CEXP(J*BH*SNPSI)-RV*(CEXP(-J*BH*SNPSI)))

02510 E2=120.0*CABS(E*E)/REAL(ZR)

02520 GAIN=10.0*ALOG10(E2)

02530 PRINT 520, PSI, GAIN

02540 CALL FILE(-1 . ,-1 . ,-1 . ,-1 ., -1 ., PSI , GAIN)

02550 GO TO 550

02560 580 PRINT 170

02570 END

02 5 80 C************************************************************

02590 SUBROUTINE MUTUAL( BETA, H, J, L, ZML, POLAR)

02600C* COMPUTES MUTUAL IMPEDANCES BETWEEN DIPOLES IN ECHELON * 0261 OC******************************************^*****************

02620 DIMENSION ARG(5) , SI( 5) ,CI ( 5) ,CIN( 5)

02630 REAL L,L1 ,L2,L3,L4

02640 COMPLEX J, ZML

02650c*****************************************************

02660c* COMPUTE ARGUMENTS FOR SINE AND COSINE INTEGRALS * 02670c*****************************************************

02680 Y0=0.

02690 X0=2.*H

02700 IF( POLAR. EQ.O. ) GO TO 1 02710 Y0=2.*H

02720 X0=0.

33
02740C* XO IS THE SEPARATION BETWEEN THE FEEDPOINTS OF THE VERTICAL * 02750C* DIPOLE AND ITS COLINEAR IMAGE. YO IS THE SEPARATION BETWEEN * 02760C* THE HORIZONTAL DIPOLE AND ITS IMAGE. * 02770c*****************************************************************

02780 1 B=BETA

02790 Y02=Y0**2

02800 HL1 =X0-2.*L

0281 HL2=X0-L

02820 HL3=X0

02830 HL4=X0+L

02840 HL5=X0+2.*L

02850 ARGd ) =B*( SQRT( Y02+HL1 **2)+HL1 ) 02860 ARG(2)=B*(SQRT(Y02+HL2**2)+HL2)

02870 ARG(3)=B*(SQRT(Y02+HL3**2)+HL3)

02880 ARG(4)=B*(SQRT(Y02+HL4**2)+HL4)

02890 ARG(5)=B*(SQRT(Y02+HL5**2)+HL5)

02900 DO 10 1=1 ,5

02910 10 CALL SCKARGd) ,SI(I),CI(I) ,CIN(I))

02920 IFCPOLAR.EQ.O. ) GO TO 20

02930c**********************************************************

02940C* COMPUTE MUTUAL IMPEDANCE FOR HORIZONTAL POLARIZATION * 02950c**********************************************************

02960 R12=30.*(C0S(2.*B*L)*(CI(1)+CI(5)-2.*CI(2)-2.*CI(4)+2.*CI(3))

02970+ +SIN(2.*B*L)*(-SI(1)+SI(5)+2.*SI(2)-2.*SI(4))

02980 + +4 . *CI ( 3

) -2 . *CI ( 2) -2 . *CI ( 4 )

)

02990 X12=30.*(C0S(2.*B*L)*(-SI(1)-SI(5)+2.*SI(2)+2.*SI(4)-2.*SI(3))

03000+ +SIN(2.*B*L)*(-CI(1)+CI(5)+2.*CI(2)-2.*CI(4))

03010+ -4.*SI(3)+2.*SI(2)+2.*SI(4))

03020 ZML=R1 2+J*X12

03030 RETURN

03040C********************************************************

03050c* COMPUTE MUTUAL IMPEDANCE FOR VERTICAL POLARIZATION * O3O6OC********************************************************

03070 20 L1=AL0G(HL2/HL1

)

O3O8O L2=AL0G(HL4/HL3)

03090 L3=ALOG(HL2/HL3)

03100 L4=ALOG(HL4/HL5)

031 10 B1 =B*HL1

03120 B2=B*HL3

03130 B3=B*HL5

03140 B4=B*HL2

03150 B5=B*HL4

031 60 R12 = 15.*(C0S(B1 )*(CI(1)-CI(2)+L1 )+SIN(B1 )*(SI(1 )-SI( 2) ) +C0S( B2)

03170+ *(CI(3)-CI(4)+L2)+SIN(B2)*(SI(3)-SI(4))+COS(B2)*(-CI(2)+CI(3)

03180+ +L3)+SIN(B2)*(-SI(2)+SI(3))+COS(B3)*(-CI(4)+CI(5)+L4)+SIN(B3)

03190+ *(-SI(4)+SI(5))+2.*COS(B*L)*COS(B4)*(-CI(2)+CI(3)+L3)+2.

03200+ *COS(B*L)*SIN(B4)*(-SI(2)+SI(3))+2.*COS(B*L)*COS(B5)*(CI(3)

03210+ -CI ( 4

) +L2 ) +2 . *COS ( B*L) *SIN( B5 ) *( SI( 3

) "SI ( 4 ) )

)

34
03220 X12=15.*(C0S(B1 ) *(-SI( 1 ) +SI(2) ) +SIN( B1 ) *(CI ( 1 )-CI (2)-L1 )+C0S(B2)

03230+ *(-SI(3)+SI(i|))+SIN(B2)*(CI(3)-CI(4)-L2)+C0S(B2)*(SI(2)

03240+ -SI(3))+SIN(B2)*(-CI(2)+CI(3)-L3)+COS(B3)*(SI(4)-SI(5))

03250+ +SIN(B3)*(-CI(M)+CI(5)-L4)+2.*COS(B*L)*COS(B4)*(SI(2)

03260+ -SI(3))+2.*COS(B*L)*SIN(B4)*(-CI(2)+CI(3)-L3)+2.*COS(B*L)

03270+ *(-SI(3)+SI(4))+2.*COS(B*L)*SIN(B5)*(CI(3)-CI(4)-L2))

03280 ZML=R12 + J*X12

03290 RETURN

03300 END

0331 OC*********************************** *****************************

03320 SUBROUTINE SCI( ARG, SI , CI ,CIN)

03330c* COMPUTES THE SINE, COSINE, AND MODIFIED COSINE INTEGRALS * 033i|0C*** ****************************************************** *******

03350 DIMENSION T( 42) , S( 20) ,C (20)

03360 K=1

03370 T(1 )=1 .0

03380 DO 10 M=1 ,42

03390 K=K+1

03400 10 T(K)=M*T(K-1)

03410 IF(ARG.GT. 1 .) GO TO 25

03420c***************************************

03430c* COMPUTE THE INTEGRALS FOR 0<ARG<1 * 03440c***************************************

03450 DO 20 N=1 ,20

03460 20 S(N)=((-1)**N)*(ARG**(2*N+1 ))/((2*N+1 )*T(2*N+2))

03470 SI=ARG+S(1)+S(2)+S(3)+S(4)+S(5)+S(6)+S(7)+S(8)+S(9)+S(10)

03480+ +S(11)+S(12)+S(13)+S(14)+S(15)+S(16)+S(17)+S(18)+S(19)+S(20)

03490 DO 30 N=1 ,20

03500 30 C(N)=((-1)**N)*(ARG**(2*N))/((2*N)*T(2*N+1 ))

03510 SA=C(1)+C(2)+C(3)+C(4)+C(5)+C(6)+C(7)+C(8)+C(9)+C(10)+C(11)

03520+ +C(12)+C(13)+C(14)+C(15)+C(16)+C(17)+C(18)+C(19)+C(20)

03530 CI=0. 57721 5665+AL0G(ARG)+SA

03540 CIN=-SA

03550 GO TO 40

03560c**********************************************

03570c* COMPUTE THE INTEGRALS FOR 1<ARG<INFINITY * 03580c**********************************************

03590 25 FZ=(ARG**8+38.027264*(ARG**6)+265.187033*(ARG**4)

03600+ +335. 67732*(ARG**2) +38.1 02495) /(ARG*((ARG**8)

03610+ +40. 021 433*(ARG**6) +322. 62491 1*(ARG**4)

03620+ +570. 23628*(ARG**2) +157. 105423))

03630 GZ=(ARG**8+42.242855*(ARG**6) +302. 757865 *(ARG**4)

03640+ +352.018498*(ARG**2)+21 . 821 899)/ ( ( ARG**2) *( ( ARG**8)

03650+ +48. 196927*(ARG**6)+482.485984*(ARG**4)+1 1 14.978885

03660+ *(ARG**2)+449. 690326))

03670 SI=1 .570796327-FZ*C0S(ARG)-GZ*SIN(ARG)

03680 CI=FZ*SIN(ARG)-GZ*COS(ARG)

03690 CIN=-CI+0. 57721 57+AL0G( ARG)

03700 40 RETURN

03710 END

35
03730 SUBROUTINE FILE( ENC, ENC2, L, POLAR, SIGMA, PSI, GAIN)

03740C* WRITES DATA ON TAPE50 FOR PLOTTING USING PROCEDURE FILE ^T * 03750c******************************************************************

03760 N=AINT(10./ENC+80./(ENC+ENC2)

)

03770 10 F0RMAT(I5)

03780 20 FORMAT(2F10.3)

03790 30 F0RMAT(F10.3)

03800 40 F0RMAT(E9.3)

03810 IF(ENC.GT.O) WRITE(50,10)N

03820 IF(ENC.GT.O) WRITE(50,30)L

03830 IF(ENC.GT.O) WRITE(50,30)P0LAR

03840 IF(ENC.GT.O) WRITE( 50, 40) SIGMA

03850 IF(ENC.LT.O) WRITE(50,20)PSI,GAIN

03860 RETURN

03870 END

Note: If file TAPE50 is not wanted, delete line 00100, calls to FILE in

lines 01800, 02160, 02440, and 02540, and the entire Subroutine FILE.

36

U S. GOVERNMENT PRINTING OFFICE: 1986—671-745/45,198 REGION NO. 8
NBS-114A (REV. 2-8C1 U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS/TN-1098

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

May 1986

4. TITLE AND SUBTITLE

Linear Gain -Standard Antennas Below 1000 MHz

5. AUTHOR(S)

R. G. FitzGerrell

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

I I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here)

Gain and antenna parameters related to input impedance are calculated using a computer program called HVD6. This program uses well documented equations to

compute these parameters for gain-standard antennas used in relative-gain or gaintransfer measurements at frequencies below 1000 MHz. The utility of this program

is that it calculates gain patterns and input impedances for linear dipoles above

perfect or imperfectly conducting plane ground and in free space, and for monopoles

on perfectly conducting plane ground. Examples are included to illustrate the use

of the program. Uncertainties in the calculated parameters are estimated to be less

than those of the measured parameters.

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

antenna gain; dipole antennas; gain standards; monopole antennas

13. AVAILABILITY

JX^Un limited

I I For Official Distribution. Do Not Release to NTIS

[X] Order From Superintendent of Documents, U.S. Government Printing Off ice, Washington, D.C.

20402.

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

14. NO. OF

PRINTED PAGES

44

15. Price

USCOMM-DC 6043-P80



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