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IR 89-3922

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IR 89-3923

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N I STIR 89-3924

NEAR-FIELD GAIN

OF PYRAMIDAL HORNS

FROM 18 TO 40 GHz

David A. Hill

Richard L. Ehret

National Institute of Standards and Technology

U.S. Department of Commerce

Boulder, Colorado 80303-3328

November 1989

N I STIR 89-3924

NEAR-FIELD GAIN

OF PYRAMIDAL HORNS

FROM 18 TO 40 GHz

David A. Hill

Richard L. Ehret

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

November 1989

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Acting Director

CONTENTS

Page

Abstract 1

1. INTRODUCTION 1

2. THEORY 2

3. MEASUREMENTS 4

4. CONCLUSIONS 6

5 . REFERENCES 6

iii

NEAR- FIELD GAIN OF PYRAMIDAL HORNS

FROM 18 TO 40 GHZ

David A. Hill and Richard L. Ehret

Electromagnetic Fields Division

National Institute of Standards and Technology

Boulder, CO 80303

Generating a standard electromagnetic field requires knowledge

of the gain of the transmitting antenna. Using the two -antenna

method, we have measured the near -field gain of pyramidal horns

at frequencies from 18 to 40 GHz. The discrepancy between the

measured and theoretical near-field gain is typically within

±0.3 dB for distances from 0.5 to 4 m from the horn aperture.

An accurate laser alignment of the horns was necessary to obtain

this level of agreement.

Key words: anechoic chamber; electric field; near-field gain;

pyramidal horn; two -antenna method.

1 . INTRODUCTION

Anechoic chambers are currently in use for a variety of indoor antenna

measurements, electromagnetic interference (EMI) measurements, and

electromagnetic compatibility (EMC) measurements. The main requirement is

that a transmitting antenna located within the chamber generate a known

field throughout a volume of sufficient size to perform antenna

measurements

.

The methodology for standard electromagnetic field measurements using

the National Institute of Standards and Technology (NIST) anechoic chamber

has been described in previous publications [1-3]. Measurements in an

anechoic chamber are usually performed in the near field of a standard

transmitting antenna, and for frequencies above 450 MHz NIST uses a series

of pyramidal horns for transmitting antennas. In this report we compare

theoretical and measured near-field gains of pyramidal horns for frequencies

from 18 to 40 GHz. The theory [4,5] and measurement techniques [1-3] are

the same as those previously used at NIST at lower frequencies (below 18

GHz) .

1
In section 2 we review the theory for the near- field gain of pyramidal

horns, and in section 3 we present measured results for the near-field gain

for frequencies from 18 to 40 GHz. The good agreement between the two

indicates that the NIST anechoic chamber performs well over this frequency

range

.

2 . THEORY

The geometry of a pyramidal horn is shown in figure 1. The width and

height of the rectangular aperture are a and b, and the slant lengths are £

and £ . The near- field gain of pyramidal horns can be derived either in

terms of the electric field on the horn axis [4,5] or in terms of the power

transfer between a pair of identical horns [6]. We choose the electric

field derivation because it is more relevant to our application of

generating a standard electric field and because it involves simpler

mathematical functions.

Jull's expression for the near field gain G is [4,5]

G - ^ RA, (1)

where A is the free space wavelength and R and R^ include the gain

reduction due to the E and H plane flare of the horn as well as the effect

of finite range. The gain reduction factors are

C

2

(w) + S

2

(w)

2

w

* { f C(u) Cfy)!

2

+ fSfu)

4(u - v)

2

S (v)

1

2

1

}

( 2 )

where w = b/(2A i')^2

, h

2
v

1 " I

(AiH

/2)1/2 1 a/< 2A -6 H

)1/2,

V

E

di

K

d + V

di

H

d + V

and d is the on-axis distance from the aperture plane. The Fresnel

integrals C and S are defined as

w

C(w) - jS(w) = J* exp(-j7rt

2

/2) dt. (3)

0

In our computer program for (l)-(3), we have used the approximations of

Boersma [7] to compute the Fresnel integrals, and we have checked our

results with Jull's curves and tables for R and [4,5]. Larsen and Ries

[8] have derived polynomial fits for R^ and R^ that are easy to compute, but

these polynomial fits are not accurate for large values of w and u. Consequently, we use the Fresnel integral formulation in ( 1

)

- ( 3

)

because

they have no such limitation.

In Jull's derivation of R and R^, he included quadratic phase terms in

the evaluation of the aperture integration, but neglected cubic and higher

order terms. For the cubic terms to be small, the following inequality must

be satisfied

2 2 2 k(a + b

z

) 128d3

« 1 , (4)

where k = 2?r/A. For given horn dimensions and frequency, (4) places the

following requirement on the range d

d »

2 2 2

r k(a + b^r 1/3

L 128 J (5)

3
Similarly, Jull neglected quadratic amplitude terms which means that the

following inequality must be satisfied

2

a « 1 . ( 6 )

For given horn dimensions, (6) places the following requirement on d

2 2 1/2

d » [(a + b )/8] ' . (7)

Taken together, (5) and (7) place a minimum value on the range d for ( 1

) - ( 3

)

to be valid. Jull [9] has also studied the effect of edge diffraction on

horn gain, but this effect tends to be fairly small.

3 . MEASUREMENTS

Gain measurements were made in the NIST anechoic chamber using pairs of

identical pyramidal horns. The gain as determined by the two-antenna method

is [1]

G

4fl~d

A <W1/2

( 8 )

where d is the distance between the horn apertures, P^_ is the net power

delivered to the transmitting horn, and is the received power. Details

of the NIST methods of power measurement have been discussed previously [1].

Normally (8) is used for the far-field gain, but here we also use (8) for

the near-field gain G.

In figures 2-4, we show the theoretical and measured near- field gains

as a function of distance d for frequencies of 18, 22, and 26.5 GHz. The

horn dimensions are: a = 10.43 cm, b = 7.88 cm, i = 19.09 cm, and

hi

2 2 = 20.34 cm. The nominal far-field distance, 2 (a + b ) /A

,

is also shown

n

4
in each figure caption, and some gain reduction is evident even at this

distance. The small oscillations in the measured curves are caused by

multiple reflections between the horns, and they could be smoothed out by

averaging over an integer number of half wavelengths. The measured curve at

22 GHz in figure 3 shows evidence of a more complicated interference pattern

that probably involves an additional reflection. No attempt was made to

determine the source of this reflection or to assess the effectiveness of

the chamber absorber in this frequency range.

Further comparisons of theoretical and measured near- field gains are

shown in figures 5-7 at frequencies of 26.5, 33, and 40 GHz. For these

results the horn dimensions are: a = 6.89 cm, b = 5.27 cm, = 12.73 cm,

hi and i = 14.00 cm. Small multiple reflections are again evident in the

rl measured results, and some indication of a more complicated interference

pattern appears at 40 GHz in figure 7. An accurate laser alignment was

required to obtain the agreement shown in figures 5-7. Our first attempts

at these frequencies gave measured results approximately 1 dB below the

theoretical gain, and rotation and movement of the antennas indicated that

alignment was a problem. In the laser alignment, we sight down the

waveguide of the transmitting horn to the waveguide of the receiving horn.

In future calibrations of small probes or other antennas, the same method of

sighting down the waveguide of the transmitting horn should work equally

well

.

The agreement of the theoretical and measured near- field gains

generally falls within the range of 0.1 to 0.3 dB, and this uncertainty is

adequate for generation of a standard electric field strength for future

antenna measurements. We cannot expect agreement any better than about

0.1 dB because the theory has errors of about that magnitude [9].

For the horn dimensions and frequencies in figures 2-7, the

inequalities (5) and (7) yield a minimum distance d of about 0.5 m. For

smaller distances, the theory is not reliable. Even though the theoretical

near-field gain is based on the on-axis electric field [4,5] rather than

horn-to-horn transmission [6]

,

the agreement with measured gain is roughly

independent of distance for distances in the range of validity (> 0.5 m)

.

For smaller distances, Jull [4] has indicated that the near- field reduction

5
factors for the on-axis electric field are greater than those for horn-tohorn transmission [6].

4. CONCLUSIONS

Using the two-antenna method, we have measured the near-field gain of

pyramidal horns at frequencies from 18 to 40 GHz. The discrepancy between

the measured and theoretical near- field gain is typically within ± 0.3 dB

for distances from 0.5 to 4 m from the horn aperture. An accurate laser

alignment of the horns was necessary to obtain this level of agreement, and

the same alignment method should be used for generating standard fields with

horn transmitting antennas.

5 . REFERENCES

[1] Nahman, N.H.; Kanda, M. ; Larsen, E.B.; Crawford, M.L. Methodology for

standard electromagnetic field measurements. IEEE Trans.

Instrumentation Meas . , IM-34: 490-503; 1985.

[2] Kanda, M. ; Orr, R.D. Near-field gain of a horn and an open-ended

waveguide: comparison between theory and experiment. IEEE Trans.

Antennas Propagat., AP-35: 33-40; 1987.

[3]

Kanda, M. ; Driver, L.D. An isotropic electric - field probe with tapered

resistive dipoles for broad-band use, 100 kHz to 18 GHz. IEEE Trans.

Microwave Theory Techniques, MTT-35: 124-130; 1987.

[4] Jull

,

E , V

.

Finite -range gain of sectoral and pyramidal horns.

Electronics Letters, 6: 680-681; 1970.

[5] Jull

,

E.V. Aperture Antennas and Diffraction Theory. Stevenage:

Peter Peregrinus Ltd.; 1981.

[6] Chu, T.S.; Semplak, R.A. Gain of electromagnetic horns. Bell Syst.

Tech. J. , 44: 527-537; 1965.

[7] Boersma, J. Computation of Fresnel integrals. Math. Comp., 14: 380;

1960.

[8] Larsen, E.B.; Ries, F.X. Design and calibration of the NBS isotropic

electric- field monitor (EFM-5), 0.2 to 1000 MHz. Nat. Bur. Stand.

(U.S.) Technical Note 1033; 1981.

6

Figure 1. Geometry and dimensions of a pyramidal horn antenna.

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Theoretical

and

measured

near-field

gain

of

a

pyramidal

horn

at

26.5

GHz.

Horn

dimensions:

a

=

6.89

cm,

b

=

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cm,

=

12.73
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13

Figure

6.

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and

measured

near

-field

gain

of

a

pyramidal

horn

at

33

GHz.

Horn

dimensions:

a

=

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cm,

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14

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7.

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and

measured

near-field

gain

of

a

pyramidal

horn

at

40

GHz.

Horn

dimensions:

a

=

6.89

cm,

b

=

5.27

cm,

=

12.73
NIST-1 14A

(REV. 3-89)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BIBLIOGRAPHIC DATA SHEET

PUBLICATION OR REPORT NUMBER

NISTIR 89-3924

PERFORMING ORGANIZATION REPORT NUMBER

3. PUBLICATION DATE

November 1989

4. TITLE AND SUBTITLE

Near-Field Gain of Pyramidal Horns from 18 to 40 GHz

5. AUTHOR(S)

David A. Hill and Richard L. Ehret

6. PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

GAITHERSBURG, MD 20899

7. CONTRACT/GRANT NUMBER

8. TYPE OF REPORT AND PERIOD COVERED

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE, ZIP)

10. SUPPLEMENTARY NOTES

DOCUMENT DESCRIBES A COMPUTER PROGRAM; SF-185, FIPS SOFTWARE SUMMARY, IS ATTACHED.

11. ABSTRACT (A 200-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBLIOGRAPHY OR

LITERATURE SURVEY, MENTION IT HERE.)

Generating a standard electromagnetic field requires knowledge of the gain of the

transmitting antenna. Using the two-antenna method, we have measured the near-field

gain of pyramidal horns at frequencies from 18 to 40 GHz. The discrepancy between

the measured and theoretical near-field gain is typically within +0.3 dB for distances

from 0.5 to 4 m from the horn aperture. An accurate laser alignment of the horns was

necessary to obtain this level of agreement.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITALIZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

anechoic chamber; electric field; near-field gain; pyramidal horn; two-antenna method

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ORDER FROM SUPERINTENDENT OF DOCUMENTS, U.S. GOVERNMENT PRINTING OFFICE,

WASHINGTON, DC 20402. ORDER FROM NATIONAL TECHNICAL INFORMATION SERVICE (NTIS), SPRINGFIELD, VA 22161.

14. NUMBER OF PRINTED PAGES

20

15. PRICE

ELECTRONIC FORM

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