CALIBRATION
OF
DIRECTIONAL
ANTENNAS
Abstract
Although directional antennas for electromagnetic field measurements are widely used, the problem of
antenna calibration in a frequency range below 1 GHz still has not been described satisfactorily in th
e literature
and in internationally accepted standardization procedures. The use of a typical substitution method is
considered for this purpose, and it is shown that, if applied, the method may lead to improved measurements,
particularly if it is carried
out with accuracy. The problem is discussed with an example of a log

periodic
antenna, but the method may be applied to any other type of directional antenna. The correct calibration
procedure does not assure accurate measurements under all conditions. The
problems of accuracy limitations
are discussed and solutions are proposed, applicable particularly for near

field measurements.
1. Introduction
Contemporary civilization may be characterized by an enormous growth of electromagnetic (EM) energy
applicat
ions. Every such application is linked to intended or unintended radiation of energy. A measure of the
radiated energy may be the natural EM environment pollution. Larger than other pollutants, and prevalent world

wide. Attention should be focused on the f
act that, in the majority of cases, it is an exceptional kind of pollution

it is intentional pollution playing a role of the information carrier. As a result, the all of civilization has to exist in
a condition of continuous exposure to that pollution. T
hat may create problems for human beings as well as for
their products.
The growth of EM energy applications was followed by the development of tools and methods for
electromagnetic field (EMF) measurements. The measurements are usually performed within t
hree areas of
involvement, i.e.:
1.
The measurement of propagating free waves in wireless communication, radiolocation (radar), navigation as
well as geophysical exploration. Here, the aim is to study propagation phenomena, properties of media, and
optimiz
ation of these systems (frequency, radiated power).
2.
EM interference measurements. Apart from the telecommunication, the interference often may be caused by
industrial devices and installations and even by non

obvious sources such as laser or ultrasonic
devices where a
transducer is excited from a RF power source.
3.
The measurement of the susceptibility of organisms, devices and matter to EMF; to design and to control the
necessary means of protection in a technical, legal, or organizational sense.
In t
he majority of cases, the measurements related to the latter group are performed in the near

field, using an
omnidirectional antenna that is sensitive to EM fields of arbitrary polarization. The antenna is needed because the
polarization and its spatial an
d time variations are not known
a priori
and signals of quasi

ellipsoidal polarization
(for instance due to multipath interference of elliptically polarized waves) may be present in the field. If we
neglect the above, published results and conclusions from
such measurements performed in the near

field using
horn, log

periodic, or similar directional antennas are of doubtful value. We will not comment here on whether
such measurements (and their results) make sense.
The second group of measurements are carr
ied out both in the near and the far

field. Here, measurements
performed using directional or resonant size antennas (as mentioned above) in the proximity of an interference
source are extremely controversial. In the first group, the measurements are usual
ly performed in the far

field,
where the directional antennas could be useful and where the use of the antennas has never aroused doubts.
Before analysing the metrological use of these antennas, we shall examine their methods of calibration.
Calibration o
f any type of antenna performed in an anechoic chamber, permits the use of typical procedures [1

2]. However, when larger antennas are to be calibrated and the calibration is performed on an open area test site
(OATS), the presence of the reflected ray can
not be neglected in the majority of cases. Thus, the influence of the
ray must either be limited or the presence of the ray must be made use of through suitable measures or
procedures. As an example of the first approach, one may cite the British procedure
s [3], where the antenna being
calibrated is placed in a specific position to eliminate the role of the reflected ray. The role of the latter is
emphasized in the work both in the case of calibration and during measurements.
2. A model of the directional a
ntenna
The expression 'directional antenna' requires a comment because it may suggest a possibility to construct a
non

directional one. One may assume that several types of antennas could be considered as more or less
omnidirectional ones, as an example
a new proposal of such a device will be outlined at the end of the paper.
However, it is the rule that an omnidirectional antenna fulfilling the reciprocity theorem is still unknown.
Directional antennas, because of their sizes, are usually used in metrol
ogy at frequencies above 200

300
MHz. For instance these are: Yagi

Uda, log

periodic (LP), spiral and horn antennas and their versions. The
directional properties of the antennas are a function of their electrical sizes while their widebandness depends
upo
n the type of an antenna. Because of quite good widebandness and directional properties, within frequency
range 0.3

1 GHz, the log

periodic antennas are in wide use. Such an antenna was chosen as a model for the
considerations presented.
The DAMZ

4 type
LP antenna works within frequency range 300

1000 MHz, its gain in relation to a half

wave dipole is about 7 dB and front to back ratio exceeds 20 dB [4]. Its radiation pattern in planes E and H,
measured at 500 MHz, is shown in Fig. 1.
180
o
150
o
120
o
90
o
60
o
30
o
30
o
60
o
90
o
120
o
150
o
E
H
dB
dB
dB
0
o
Fig. 1 Radiation pattern of the chosen LP antenna
For theoretical estimations the normalised pattern in H

plane, with an accuracy of 1 dB for
j
< 70
o
and for
(important here) the main lobe direction, i.e
.: for
Q
= 0, was approximated in the form:
2
cos
1
)
,
F(
2
(1)
Of course, the pattern is specific for the type of the antenna used and is a function of frequency and sizes of
the antenna. If considerations are
repeated for another type of antenna or more accurate results are required, the
experimental data of the pattern may be used instead of formula (1). The formula was introduced only to illustrate
the considerations. However, the approximation is accurate en
ough for a wide class of LP antennas.
3. The method of calibration
Calibration of EMF meters with directional antennas may be performed using the standard field method or the
standard antenna (substitution) method. Because of the accuracy of the proced
ure and its simplicity the latter one
is preferred, in our case an additional advantage of the method is its reduced sensitivity to the presence of the
reflected ray and a possibility to increase the field strength by the use of a directional antenna for t
ransmission as
well. In the method the EMF is generated with the use of an arbitrary transmitting antenna (TA). The standard
receiving antenna (SRA) is placed at a distance, in the case of primary standard it is usually a thick half wave
dipole. Then SRA i
s replaced by an antenna under test (AUT) as shown in Fig. 2.
G
Vmeter
Vmeter
TA
SRA
AUT
counter
Fig. 2 The substitution method in antennas' calibration
Replacing SRA and AUT it is assumed that the EMF intensity is not changed during the procedure and a
s a
result of it. The method is widely used for calibration of dipole antennas and we won't discuss here the accuracy
of the method as it may be found in the literature [5]. We will focus our attention on the case when the TA and
AUT are different from a s
ingle dipole. Then, an additional error of the method will appear due to the geometry
of propagation, directional properties of these antennas, and their more than one dimensional sizes.
We should notice here that the basic requirement in the calibration
is the minimal distance between the
antennas, i.e. the far

field condition should be fulfilled:
d
>
2
D
2
/
(2)
where:
d
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R
1
= R
2
= d (for free space). Then, for quasi

far

field conditions, (3) may be expressed as:
)
,
F(
d
jkd)
exp(
E
E
0
(4)
where: E
0
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The geometry of propagation in an open

site case is shown in Fig. 3. Of course, during the calibration in the
free space conditions (or in an equivalent case of calibration pe
rformed in an anechoic chamber) the role of the
reflected ray should be neglected.
TA
SRA
(AUT)
h
t
h
r
d
r
Fig. 3 Geometry of propagation in an OATS
If assume that an AUT is of D length and taking into account, in first approximation, the lin
ear EMF
variations in space as given by (4) then the relative change of EMF intensity at the length of the antenna may be
expressed as:
E
E
D
d
(5)
The formula requires a comment. It presents EMF intensity variations at the length of the
antenna in the
relation to the field strength on one of the antenna ends. The total length of the discussed DAMZ antenna is 70
cm, it would mean than the EMF homogeneity within 1% at the antenna length requires D>70m. Thus, a
generation of measurable EMF
would need an excitation of TA at kilowatt level. Is it really indispensable?
If we take into considerations the fact that the EMF variations at the antenna length are almost linear and we
will refer the homogeneity estimations to the center of the activ
e part of the antenna, then the error will be much
lower as a result of the EMF averaging by the antenna, and it should be negligible for distances fulfilling the
condition (2). To prove the hypothesis a series of measurements were performed in an anechoic
chamber and on
an OATS. It was found that the accuracy reduction of an AUT calibration at the lowest frequency, i.e.: 300 MHz,
does not exceed 1%, even at distance d = 1m. The use of the distance is not advised, however, it illustrates well
the role of th
e antenna length. A trick here is important: during replacing the SRA: the AUT should be placed
exactly in such a distance from the TA that its active dipole replaces the SRA.
5. Calibration on an OATS
In case of calibration an OATS the resultan
t field E
s
is the sum of the direct ray E
d
and the reflected one E
r
:
r
d
r
d
2
r
2
d
s
cos
E
E
2
E
E
E
(6)
where:
F
d
and
F
r
represent phases of both rays.
E
d
may be estimated directly using formu
la (4) as, for the direction of the maximal radiation in the case of
directional TA, we have F(
Q
,
j
) = 1. E
r
is a function of the length of the reflected ray (r), radiation patterns of the
ant
ennas used as well as the reflection coefficient (R).
Lets consider three cases here:
a. both TA and the SRA (AUT) are dipoles, then:
R
r
e
E
E
j kr
0
r
(7)
b. TA or AUT is directional one, then:
E
E
e
r
F
(
)
R
r
0
j kr
(8)
c. TA and AUT are directi
onal and their patterns are identical, then:
E
E
e
r
F
(
)
R
r
0
j kr
2
(9)
If we accept (for simplification only) identical altitudes of the antennas, i.e.: h
t
= h
r
, then the ratio E
s
/E
d
, for
instance for case b, is given by the following formula:
cos
cos
1
R
r
d
R
2
cos
1
r
d
1
E
E
2
2
2
2
2
d
s
(10)
where:
D
F
=
F
d
F
r
The formula is identical with presented by Crawford [6]. It permit
s to estimate the EMF distribution in the
area of the AUT. Because of computational possibilities on the ground of formula (10) a large number of curves
may be generated; that would be very spectacular, however, their usefulness is very limited. Let's anal
yse the
point.
The phase difference
D
F
is a function of easy to define electrical lengths of both rays: kd and kr and much
more difficult to estimate phase of the radiation pattern of a TA (t
he latter was neglected in formula (1) and the
phase of the reflection coefficient. Of course, it is possible to find all of them with required accuracy and take
into account in final EMF estimations, however, their temporal and spatial alternations as wel
l as their frequency
dependence limits remarkably the applicability of such an approach. Usually R =
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dd
is:
O
E
E
d
r
R
dd
s
d
1
(11)
b. for dipole and LP antenna O
dl
:
R
2
cos
1
r
d
1
E
E
O
2
d
s
dl
(12)
c. for two LP antennas O
ll
is:
R
2
cos
1
r
d
1
E
E
O
2
2
d
s
ll
(13)
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1
2
3
5
7
10
15
m
0
0,5
1
1,5
2
d
Fig. 4 Envelopes O
dd
捯n瑩tuous,
dl
broken and O
ll
dotted line
The goal of the considerations is to find the role of the reflected ray in the calibration accuracy estimations.
The role is not a result of the ray existence but different radiation patterns of AUT a
nd SRA. The role must not
be neglected while a directional AUT is being calibrated. The SRA is always a dipole in the primary standards.
Thus, the curves in Fig. 4 make it possible to analyse the problem in two cases: while TA is a dipole antenna
(a. and
b.) and while TA and AUT are directional ones (b. and c.).
In order to find the optimal calibration conditions we will take into account the loop of waves, i.e.: O
ii
>1 over
a perfectly conducting terrain. For a dipole TA the additional error of the method
d
is:
1
2
dd
dl
dd
d
cos
+
1
cos
sin
1/2
O
O
O
(14)
Similarly for two LP antennas
l
is:
1
2
2
2
dl
ll
dl
l
cos
1
cos
2
sin
cos
1
cos
1/2
O
O
O
(15)
Both errors are plotted, as a function of d, in Fig. 5.
0
5
10
1
2
3
5
7
10
15
m
d
[%]
h
Fig. 5
d
捯n瑩tuous慮d
l
dashed versus d
A doubt may appear because of the 'radiowave' approach which was used here. However, the problem was
analysed by Kawana and Miyajima [7

8]. The convergence of radiow
ave method and other approaches was
confirmed by Borsero and Nano [9]. It was shown that the method assures required accuracy, particularly at
frequencies above 300 MHz, and while d exceeds 2
l
.
As it may be seen from Fig.
5 the error of the method may be negligible in many cases. It may be reduced
with the use of technical means or applying calculated correction coefficients. If the means are insufficient, a full
insulation from external EM environment is required or while
the measurements should be performed with no
regard to the meteorological conditions, then an anechoic chamber will be irreplaceable [10].
6. EMF measurements
Many services and institutions are involved in EMF measurements and concerned in possibility
to calibrate
the meters applied. The doubt, regarded to the applicability of the typical methods for calibration of the meters
with directional antennas, was expressed by them to the author. The above presented considerations lead to the
conclusion that t
he situation is not bad and the use of relatively simple means may even improve it. It is full
answer to the question regarded to the calibration. Here the work could be terminated. A bit contradictory
question arises, however. What is an accuracy of the E
MF measurement with a well

calibrated meter? An
analysis of the problem is presented below in two typical cases. The measurement in free space and a single path
propagation, as trivial, was neglected.
6.1 Measurements in the conditions of slightly disturb
ed propagation
In the most general case, in conditions of multipath and multiple reflections' propagation, a signal from a
source reaches the point of observation on an arbitrary way, as shown in Fig. 6. Each of the rays may be reflected
in the way an ar
bitrary number of times. The i

th ray produces at the observation point E

field component E
i
'seen' by the receiving antenna:
E
E
F
(
,
)
e
r
R
i
0
j kr
i
ij
j
=
0
n
i
1
1
A
i
(16)
where:
1
A
and
1
i
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†††
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†††
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ij
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††
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,
⤠
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慰p汩敤.
A
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A琠瑨攠s慭攠瑩t攠瑨攠敡氠l

f楥汤捯mpon敮琠to敬慴edw楴ii

瑨慹E
i
is:
E
'
E
e
r
R
i
0
j kr
i
ij
j
=
0
n
i
(17)
The sum of 'i' E

field components given by (17) [E'] represents the resultant E

field i
n the observation point
while the sum of values given by (16) [E] represents the field components measured with the use of an antenna
that may be characterised by its radiation pattern and polarizational properties. The ratio E/E' is a measure of an
error
associated with the use of the antenna.
In the simplest case two rays come to the point of observation. If accept that the polarization of both rays is
conform, then the E may be estimated with the use of (6). At large distances from a source the phase di
fference of
the rays varies slowly and as a result the measuring errors, due to directional properties of a measuring antenna,
for similar incidence angles of the rays, are negligible. We may summarise that in these conditions the directional
properties of
the receiving antenna do not reduce remarkably the accuracy of the measurement.
6.2 Measurement of quasi

ellipsoidally polarized field
In the majority of cases the measurements are done within a diversified terrain, covered by natural or/and
man

made
forms. Signals come to a point of observation by ways impossible to univocal fixing, sometimes the
direct ray may not exist at all. Because of reflections from moving objects or due to multiple reflections of
frequency modulated signals a spatial rotation
of the polarization ellipse may appear that leads to the quasi

ellipsoidal polarization. In the field the ratio E/E' may take arbitrary small values. It leads to the necessity to use
methods specific for the near

field measurements [11], where the receivi
ng antenna must be insensitive to the
direction of the coming ray and to the polarization of the ray. A concept of such a device is presented in Fig. 7. It
contains three synchronous receivers. Every one of them is fed from one of three mutually perpendicu
lar short
dipole antennas. After squaring in an IF amplifier their output voltages are added.
MIX
IF
V
2
MIX
IF
V
2
MIX
IF
V
2
LO
a
b
c
Fig. 7 An example of omnidirectional pattern synthesis
Lets imagine three spatial E

field components E
x
, E
y
and E
z
in Cartesian co

ordinates:
E
A sin
t
E
B cos
t sin
t
E
C cos
t cos
t
x
y
z
(18)
where:
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.
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瑨攠瑨敥慮瑥tn
慳Ⱐ椮i.㨠
a
, V
b
and V
c
are given by:
V
a
A sin
t cos
(
a
,
x
)
B cos
t sin
t cos
(
b
,
x
)
C cos
t cos
t cos
(
c
,
x
)
V
b
A sin
t cos
(
a
,
y
)
B cos
t sin
t cos
(
b
,
y
)
C cos
t cos
t cos
(
c
,
y
)
V
c
A sin
t cos
(
a
,
z
)
B cos
t sin
t cos
(
b
,
z
)
C cos
t cos
t cos
(
c
,
z
)
a
b
c
(19)
where: A, B, C
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sph敲楣慬ipo污l楺慴楯n,慮d瑨攠楤敮瑩瑹of慮y散敩e楮g捨慮n敬e椮i.㨠愠㴠b㴠挠,瑨敮瑡t楮g愠sumofsqu慲敳eof
瑨攠vo汴慧敳
19w攠w楬氠i慶攠慮ou瑰u琠to汴慧攠of瑨攠d敶楣攠嘺
V
K V
KV
KV
a
A
K
a
2
b
2
c
2
2
2
(20
If瑨攠慭p汩瑵d敳eA,B慮dC数敳敮琠瑨攠慭p汩瑵d攠v慲楡瑩insdu攠瑯楴imodu污瑩ln瑨攠po捥du攠p敳敮瑥t
捯u汤 b攠us敤 fo d整散瑩tn 慮d 瑨攠d敶楣攠m慹 p污l 愠o汥lof omn楤楲散瑩tn慬a po污l楺慴楯n 楮s敮s楴楶攠A䴠
散敩e敲.In捡s攠of慮䙍Fs楧n慬a瑨攠
d敶楣攠shown楮䙩F.7n敥ds愠mod楦楣慴楯n.Ins瑥慤ofI䘠squ慲楮g瑨攠I䘠
慭p汩l楥is慲攠汯慤敤byd整散瑯s慮d瑨攠wokof瑨攠d敶楣攠楳瑨敮楤敮瑩捡氠w楴i瑨攠楤敡ofd楶敲s楴i散数瑩tn.
Ap慲琠fom瑨攠poss楢楬楴y瑯d楲散瑬tm敡su攠瑨攠sp慴楡氠E

晩
敬e捯mpon敮瑳,愠敳e汴慮琠v慬a攠m慹b攠ob瑡楮敤
by瑨攠w慹of捡汣l污瑩lnof瑨攠sumofsqu慲敳fs数慲慴攠vo汴慧敳e
7. Conclusion
The starting

point of the considerations were the doubts related to the applicability of the typical EMF
standards for
directional antennas calibration. It was shown that it is possible to use the standards with a slight
reduction of the calibration accuracy and the latter may be improved by the use of simple means.
The basic problem with the use of directional antennas
for electromagnetic field measurements is the
multipath propagation. In simple case of two rays (although not always) meters with arbitrary antennas may be
used. For the measurement of fields of complex time

spatial structure the use of omnidirectional ant
ennas is
indispensable. Appropriate concepts are presented above. A doubt may be formulated here if assumption of the
short antennas use and (even non mentioned) the pattern distortion by feeders were correct. With no proof we
may say that it all may be ac
ceptable. But another step is necessary here. The mentioned sum of E

field
components given by formulas (16) or (17) should be extended to the frequency domain as the instantaneous E

field vector in a point is a sum of any E

fields including the electrosta
tic one [12]. Proposal of such a device has
already been presented; it is based upon the photonic technology [13].
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