7
Chapter 2. Antenna Theory
8
2.1 Introduction
An antenna is defined by the IEEE Standard Definition [5] as “a means for radiating
or receiving radio waves”. It transforms electric energy to electromagnetic energy and
vice versa. In other words the antenna enables the transition of energy between a
guiding device, such as coaxial line or a waveguide to free-space as shown in
Fig. 2.1[6]. In a radio link the antenna is the final block on the transmission side and
is the first block on the receiving side. Thus, the antenna is a fundamental and
essential component of all wireless communication systems.
The most fundamental antenna element is the Hertzian dipole. It will then be used to
define the common antenna parameters and terminology. Antennas can be classified
according to their radiation principle, physical structure, manufacturing technology
and/or radiation characteristics. In this chapter the antenna fundamental parameters
are discussed and in order to complement the next chapters the helical antenna
parameters are also discussed.
Fig. 2.1 Antenna as a transition device.
9
2.2 Fundamental Parameters of Antenna
To describe the performance of an antenna, definitions of various parameters are
necessary. Some of the parameters are interrelated and not all of them need be
specified for complete description of the antenna performance.
2.2.1 Antenna Impedance
The antenna impedance, Za, is defined as the ratio of the voltage at the feeding point
of the antenna V(0) to the resulting current flowing in the antenna I as in (2.1).
(2.1)
where Xa is the antenna reactance and Ra = Rr + Rl is the antenna resistance, Rr is the
radiation resistance and Rl is the ohmic loss occurring in the antenna. The equivalent
circuit for an antenna system is depicted in Fig. 2.2.
Fig. 2.2 Equivalent circuit of an antenna.
2.2.2 Impedance Matching
In order to deliver maximum power from the source to the antenna, the antenna
impedance should be matched to the generator impedance. This means that the
conditions in (2.2) should be satisfied.
Pref
V I
Zin
Pin
Antenn
a
-------------------------------------
---
Rs Xs Xa
Rf
Rl
Source
10
(2.2)
2.2.3 Reflection Coefficient
Reflection coefficient is a measure of effectiveness of power delivered to a load such
as the antenna. If the power incident on the antenna is Pin and the reflected power
from the antenna to the source is Pref the degree of mismatch between the reflected
and incident power is given with (2.3).
(2.3)
2.2.4 Antenna Bandwidth
Antenna bandwidth is defined as “the range of frequencies within which the
performance of the antenna, with respect to some characteristics, conforms to a
specified standard” [5]. It can be determined either as absolute bandwidth or as a
fractional bandwidth. Taking fl and fh as the lower and higher ends of the bandwidth
the absolute bandwidth is simply defined as the difference of the two ends .
It is within this range that the antenna characteristics such as input impedance,
pattern, beamwidth or gain are within the acceptable values specified by the standard.
The fractional bandwidth is expressed as the percentage of the frequency difference
over the centre frequency as shown in (2.4).
(2.4)
An antenna is classified as narrowband if the fractional bandwidth is below 1%
otherwise it is wideband [7]. Generally, in wireless communications, the impedance
bandwidth is defined as the range of frequencies over which the antenna reflection
coefficient is less than -10 dB. However, for wireless device-integrated small
antennas such as digital video broadcasting- high definition (DVB-H) antennas the
standard is relaxed due to the limitations and the reflection coefficient of -6 dB and
even lower may be acceptable [8]. It is important to note that the reflection coefficient
is a measure of reflected power at the antenna port. Therefore, low reflection
coefficient shows that most of the incident power is not reflected to the port.
11
However, it does not show if the power radiated or dissipated. Thus, the reflection
coefficient is not sufficient for characterizing the antenna and other parameters such
as efficiency, gain, radiation pattern, which should also be taken into consideration.
2.2.5 Radiation Pattern
According to the IEEE standard definition, the antenna radiation pattern is “a
mathematical function or a graphical representation of the radiation properties of the
antenna as a function of space coordinates. In most cases, the radiation pattern is
determined in the far-field region and is represented as a function of the directional
coordinates”. The two- or three-dimensional partial distribution of radiated energy in
the coordinate is of most concern. The three-dimensional pattern is shown in Fig. 2.3.
It can be constructed using multiple two-dimensional patterns. In practice, few plots
of pattern at certain and θ values are used to derive the required information.
For a linearly polarized antenna, performance is often described in terms of its
principal E-plane and H-plane patterns. The E-plane is defined as “the plane
containing the electric field vector and the direction of maximum radiation,” and the
H-plane as “the plane containing the magnetic-field vector and the direction of
maximum radiation” [5].
Fig. 2.3 Antenna Radiation Pattern.
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The antenna radiation pattern can be described using three main radiation patterns. A
hypothetical lossless antenna having equal radiation in all directions provides an
isotropic pattern [5]. Such radiator is not physically realizable; however, it is often
taken as a reference for expressing the directive properties of actual antennas. A
directional pattern is provided by an antenna, which radiates or receives
electromagnetic waves more effectively in some directions than in others. In case, that
the pattern is essentially non-directional in a given plane and directional in any
orthogonal plane then the pattern is called omni-directional. An omni-directional
pattern is then a special type of directional pattern.
Polarization of an antenna in a given direction is defined as “the polarisation of the
wave radiated by the antenna.” Polarization of a radiated wave is defined as “that
property of an electromagnetic wave describing the time-varying direction and
relative magnitude of the electric-field vector; specifically, the figure traced as a
function of time by the extremity of the vector at a fixed location in space, and the
sense in which it is traced, as observed along the direction of propagation.”
Polarization is the curve traced by the end point of the arrow (vector) representing the
instantaneous electric field. The field must be observed along the direction of
propagation.
Polarisation may be classified as linear, circular or elliptical. If the vector that
describes the electric field at a point in space as a function of time is always directed
along a line, the field is said to be linearly polarized. In general, the figure that the
electric field traces is an ellipse, and the field is said to be elliptically polarized.
Linear and circular polarizations are special cases of elliptical and they can be
obtained when the ellipse becomes a straight line or a circle, respectively. The figure
of the electric field is traced in a clockwise (CW) or counter clockwise (CCW) sense.
The ratio of orthogonal components of the radiating field is known as axial ratio.
It is important to note that, other than the antenna impedance bandwidth, the antenna
bandwidth can be defined for other parameters such as polarization or axial ratio.
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2.2.6 Directivity, Gain and Efficiency
The ratio of the radiation intensity U in a given direction from the antenna to the
radiation intensity of an isotropic antenna U0 is known as the directivity D of an
antenna [5]. In mathematical form, it can be written as (2.5)
(2.5)
where Prad is the total radiated power. If the direction is not specified, the direction of
maximum intensity is used to describe the antenna directivity.
Another useful parameter for describing the antenna radiation characteristics is
antenna gain G. Its definition is closely related to the directivity. Unlike directivity,
which only describes the directional properties of the antenna, the antenna gain is a
measure that takes into account the radiation efficiency erad as well as the directivity.
Using the equivalent circuit of the antenna in (2.1) the radiation efficiency of the
antenna is the ratio of power delivered to the radiation resistance Rr to the power
delivered to the total antenna resistance, that is Ra=Rr+Rl. So, the radiation efficiency
can be written as (2.6) and the antenna gain can then be calculated using (2.7).
(2.6)
(2.7)
2.3 Fundamental Parameters of Helical Antenna
J. D. Kraus introduced the helical antenna in 1947 [9]. In his IEEE Antennas and
Propagation Society Centennial address in 1984 he said, “With mankind‟s activities
expanding in to space, the need for antennas will grow to an unprecedented degree.
Antennas will provide the vital links to and from everything out there. The future of
antennas reaches to the stars”[10].
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In 1946 Kraus attended a lecture on travelling-wave tubes [10], in this tube an
electron is fired down the inside of a wire helix for amplification of waves travelling
along the helix. The helix is only a small fraction of wavelength in diameter and acts
as a guiding structure. After the lecture, Kraus asked the visitor for the possibility of
helix as an antenna, but the speaker replied that it wouldn‟t work. In spite of the
negative reply, Kraus tried helix as an antenna and succeeded. It took years of
extensive measurements and calculations to understand helical antenna. Kraus
published many articles on helical antenna.
2.3.1 Geometry
The helix with a ground plane, the combination being energized by a coaxial
transmission line as shown in Fig. 2.4. The outer conductor terminates in the ground
plane and the inner conductor connects to the end of the helix.
The following symbols are used to describe the helix and ground plane as shown in
Fig. 2.4 [11]
D = diameter of helix
S= spacing between turns (centre-to-centre)
Fig. 2.4 Helical antenna and associated dimensions.
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α = pitch angle = tan(S/πD)
L =length of one turn
n =number of turns
A = axial length = nS
d = diameter of helix conductor
g =distance of helix proper from ground plane
G = ground plane diameter.
If one turn of a helix is unrolled on a flat plane, the circumference (πD), spacing (S),
turn length (L), and pitch angle (α) are related by a triangle as shown in Fig. 2.4.
2.3.2 Helical Antenna Impedance
With axial feed the terminal impedance (resistive) given within 20 percent of
variation [10] given by eq. (2.8)
(2.8)
While with peripheral feed, Baker [12] gives its value within 10 percent of variation
by given by eq. (2.9)
(2.9)
These relations have the restrictions that 0.8 ≤ C/λ ≤ 1.2, 12o ≤ α ≤ 1.2 and number of
turns equal to or greater than four. With a suitable matching section, the terminal
impedance (resistive) can made any desired value from less than 50 Ω to more than
150 Ω.
Fig. 2.5 Helical antenna feed finger.
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2.3.3 Impedance Matching
Impedance of helical antenna remains constant over wide range of frequency.
Generally, helical antenna feed through a 50 Ω coaxial line [11]. The two-section
wide-band quarter wave transformers may be used for impedance matching. To
operate the antenna with a commercially available type, such as standard 50 Ω cable,
requires a transformer between the antenna and the cable for maximum power
transfer. Each transformer section is about one-quarter wavelength long at the centre
frequency. The section adjacent to the antenna terminal has characteristic impedance
higher than the other. These impedances differ somewhat from the optimum values
for such a transformer, but were chosen as the best compromise with the wire and
tubing sizes available.
Another method of impedance matching for helical antenna is the feed finger method
as shown in Fig.2.5. It has a tapered metallic part, which connects the helix to the
centre conductor of the coaxial transmission line. Random use of arbitrary shapes for
the feed finger results in a very widely divergent set of impedance data at the
transmission line termination. A feed finger which has been found to provide the most
broad-band impedance matches to the helix. The VSWR is a maximum of 1.2 over a
26 per cent band [13].
Fig. 2.6 Metal strip bonded to helix conductor near feed point reduces input impedance to 50 Ω.
17
In 1977 John D. Kraus, suggested a method for impedance matching to 50 Ω [14]. On
a helical beam antenna feed on-axis a thin metal strip was bonded to the helix
conductor between the feed point and the beginning of the helix proper as shown in
Fig. 2.6. Dimensions and adjustments are not critical but, by way of example, a metal
strip 70 mm wide was effective for a helix wound of 13-mm diameter tubing
operating on a 1.3 m wavelength.
2.3.4 Wide Band Characteristics
The helix diameter Dλ and spacing Sλ in free-space wavelengths change, as the
frequency varies but the pitch angle (α) remains constant. The relation of Dλ, Sλ and α
as a function of frequency [11] is conveniently illustrated by a diameter-spacing chart
as shown in Fig. 2.7. The dimensions of any uniform helix are defined by a point on
the chart. Let us consider a helix of pitch angle equal to 10o. At zero frequency,
Dλ = Sλ = 0. With increase in frequency, the co-ordinates (Dλ , Sλ) of the point giving
the helix spacing and diameter increase, but their ratio is constant so that the point
moves along the constant-pitch-angle line for 10o. Designating the lower and upper
frequency limits of the frequency range of the beam mode as F1 and F2,
Fig. 2.7 Diameter-spacing chart for helices showing range of dimensions associated with a
frequency band.
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respectively, the corresponding range in spacing and diameter is given by a line
between the points for F1 and F2 on the 10o line. The center frequency of the range is
F0 and is taken arbitrarily such that or . The
dimensions of the helices to be described are given in free-space wavelengths at this
center frequency F0.
The pattern contour in Fig. 2.8 indicates the approximate region of satisfactory
patterns. A satisfactory pattern is considered to be one with a major lobe in the axial
direction and with relatively small minor lobes. Inside the pattern contour of Fig. 2.8
the patterns are of this type, and have beamwidths from 30o to 60
o. Inside the
impedance contour in Fig. 2.8 [11] the terminal impedance is relatively constant
(between 100 Ω and 150 Ω), and is nearly a pure resistance. A third contour in Fig. 2.8
is for the axial ratio measured in the direction of the helix axis. Inside contour axial
ratio is less than 1.25. From a consideration of the three-contours it is apparent that
too small or too large a pitch angle is undesirable. An "optimum" pitch angle appears
to be about 14o. There is nothing critical about this value. In fact, the properties of
helices of pitch angles of 14o ± 2
o degrees differ little.
Fig. 2.8 Diameter-spacing chart for helices with contours showing regions of stable pattern shape,
and terminal impedance, and of low axial ratio, for helices of fixed physical length.
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2.3.5 Directivity and Gain
Approximate directivity relation for helical antenna is given in (2.10)
(2.10)
This calculation discards the effect of minor lobes and the details of the pattern shape.
A more realistic relation is in (2.11)
(2.11)
Restrictions are that (2.10) and (2.11) apply only for 0.8 ≤ C/λ ≤ 1.15, 12o ≤ α ≤ 1.2 and
number of turns greater than three.
The measured gain of King and Wong [15] for 12.8o axial mode helical antenna are
presented in Fig. 2.9 as a function of helical length (Lλ = nSλ) and frequency. Although
higher gains are obtained by an increased number of turns, the bandwidth tends to
become smaller. Highest gains occur at 10 to 20 percent above the centre frequency
for which Cλ = 1. Although the gains in Fig. 2.9 tend to be less than calculated from
(2.11), they were measured on helices with 0.08 λ diameter axial metal tubes.
Fig. 2.9 Calculated (solid) and measured (dashed) gain curves of axial mode helical antenna as a
function relative frequency for different no of turns for a pitch angle of 12.8o.
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Although pitch angles as small as 2o, as noted by MacLean and Kouyoumjian [16]
and as large as 25o, as noted by Kraus, can be used, angles of 12
o to 14
o are optimum.
King and Wong [15] found that on helices with metal axial tubes, smaller pitch angles
(near 12o) resulted in a slightly higher (1 dB) gain but a narrower bandwidth than
larger angles (near 14o).
2.3.6 Radiation Pattern and Axial Ratio
One of the outstanding characteristics of the axial mode of radiation of a helical
antenna is the circularly polarized radiation obtained. A 6-turn 14o right-handed
helical antenna is considered for study of radiation pattern [11]. The overall axial
length (A + g) of the antenna is 118 cm, and the ground-plane diameter (G) is 60 cm.
The centre frequency is 400 MHz with F1 =300 MHz and F2=500 MHz. The measured
radiation (electric field) patterns are presented in Fig. 2.10 for frequencies from 225
MHz to 600 MHz. The solid curves show the patterns of the horizontally polarized
component, and the dashed curves, the patterns of the vertically polarized component.
All patterns are adjusted to the same maximum value.
It is evident from these patterns that the axial mode of radiation occurs for frequencies
between about 290 and 500 MHz. This mode is characterized by patterns with a large
major lobe in the axial direction and relatively small minor lobes. At frequencies less
than 290 MHz the maximum radiation is in general not in the axial direction and
minor lobes although few in number are large. At frequencies above 500 MHz, the
minor lobes become both large and numerous.
The Fig. 2.11 [11] shows the half-power beamwidths and axial ratio. In the uppermost
section of the figure, the half-power beamwidth of the patterns for both the vertical
and horizontal components are presented as a function of frequency in MHz. These
data are taken from Fig. 2.10 [11].
Between 300 MHz and 500 MHz the half-power beamwidth ranges from about 60o to
40o. Based on pattern integration, the directivity or power gain of the 6-turn 14
o helix
over a nondirectional circularly polarized antenna varies from about 10.4 dB at 300
MHz to about 14 dB at 500 MHz. Between 300 MHz and 500 MHz, the axial ratio in
the direction of the helix axis varies from 1.05 to 1.5, being less than 1.2 for most of
the range. From a practical standpoint, this represents a relatively small deviation
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Fig. 2.10 Measured azimuth electric field patterns of the 6-tturn, 14- degree helix for 290 MHz to
500 MHz.
Fig. 2.11 Measured half-power beamwidths of the horizontal and vertical electric field
components and axial ratio in the direction of the helix axis.
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from circular polarization. Between 300 MHz and 500 MHz, the SWR varies from
1.03 to 1.4. Considered altogether, these patterns, polarization and impedance
characteristics represent a remarkably good performance over a wide frequency range,
especially since the antenna is merely a simple geometric form with no compensating
devices attached except a transformer to convert the 130 Ω terminal resistance to the
value of the transmission line 53 Ω.
2.4 Helical Antenna Modes of Radiation
The helix is a fundamental form of antenna in which loops and straight wires are
limiting cases. When the helix is small compared to the wavelength, radiation is
maximum, normal to the helix axis. Depending on the helix geometry, the radiation
may be elliptically plane or circularly polarized. When the helix circumference is
about one wavelength, radiation may be maximum in the direction of the helix axis
and circularly polarized or nearly so. This mode of radiation is called the axial or
beam mode of radiation [17] and may be dominant over a wide frequency range with
desirable pattern, impedance and polarization characteristics. The radiation pattern is
maintained in the axial mode over wide frequency ranges because of a natural
adjustment of the phase velocity of wave propagation on the helix.
Fig. 2.12 Circumference versus spacing chart for helical antenna showing regions for normal
radiation mode (shaded) and axial or beam mode radiation.
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The terminal impedance is relatively constant over the same frequency range because
of the large initial attenuation of waves on the helix. The dimensions of a helix are
very conveniently illustrated by a diameter versus spacing chart as shown in Fig. 2.12
[17]. On this chart, the dimensions of a helix may be expressed either in rectangular
co-ordinates by the spacing Sλ and circumference πDλ or in polar co-ordinates by the
length of one turn Lλ and in the pitch angle α.
The electromagnetic field around a helix may be regarded from two points of view, as
(1) A field which is guided along the helix and (2) A field which radiates. It is
assumed that an electromagnetic wave may be propagated without attenuation along
an infinite helix in much the same manner as along an infinite transmission line or
waveguide. This propagation may be described by the transmission mode, a variety of
different modes being possible. On the other hand, a field which radiates may be
described by the radiation pattern of the antenna. It will be convenient to classify the
general form of the pattern in terms of the direction in which the radiation is
maximum. Although an infinite variety of patterns is possible, two kinds are of
particular interest. In one, the direction of the maximum radiation is normal to the
helix axis. This is referred to as the normal radiation model or in shorthand notation,
as the Rn mode. In the other, the direction of maximum radiation is in the direction of
the helix axis. This is referred to as the axial or beam radiation mode or in shorthand
notation as the Ra mode.
The lowest transmission mode for a helical conductor has adjacent regions of positive
and negative charge separated by many turns. This mode will be designated as the To
mode and the instantaneous charge distribution is suggested by Fig. 2.13(a). The To
mode is important when the length of one turn is small compared to the wavelength
L << λ, and is the mode commonly occurring on low-frequency inductors [17]. It is
also the dominant mode in the travelling-wave tube. Since the adjacent regions of
positive and negative charge are separated by an appreciable axial distance, a
substantial axial component of the electric field is present and in the travelling-wave
tube, this field interacts with the electron stream. If the criterion Lλ < 1/2 is arbitrarily
selected as a boundary for the To transmission mode, the region of helix dimensions
for which this mode is important is shown by the shaded area in Fig. 2.12.
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Fig. 2.13 Approximate charge distribution on helices for different transmission modes.
Theoretically it is of interest to examine some of the possible radiation patterns
associated with the To transmission mode. Only the simplest radiation case will be
considered. This occurs when the helix is very short so that nL << λ and the
assumption is made that the current on the helix is uniform in magnitude and in-phase
along its length. Referring to Fig. 2.13(a), the length is much less between adjacent
regions of maximum positive and negative charge. Theoretically, it is possible to
approximate this condition with a standing wave on a small end-loaded helix. The
terminal impedance of such a small helix would be sensitive to frequency and the
radiation efficiency would be low. However, let us assume that appreciable radiation
can be obtained. The maximum radiation is then normal to the helix axis for all helix
dimensions provided only that nL << λ. Hence, this condition is referred to as a
normal radiation mode Rn. The transmission mode and radiation pattern for very small
helices by combining the To transmission mode and the Rn radiation mode
designations as ToRn. This designation is applied to the region of helix dimensions
near the origin in Fig. 2.12.
A first-order transmission mode designated T1 has adjacent regions of maximum
positive and negative electric charge approximately one-half turn apart or near the
opposite ends of a diameter, as suggested in Fig. 2.13(b) for the case of a small pitch
angle. This mode is important when the length of one turn is of the order of the
wavelength (L ≈ λ). It is found that the radiation from helices of this turn length and of
a number of turns (n > 1) is usually maximum in the direction of the helix axis and is
circularly polarized or nearly so. This type of radiation pattern is referred to as the
axial or beam mode of radiation Ra. This radiation mode occurs for a wide range of
25
helix dimensions and being associated with the T1 transmission mode, the combined
designation appropriate to this region of helix dimensions is T1Ra.
Still higher-order transmission modes, designated T2, T3, etc. will have the
approximate charge distributions suggested in the one-turn views of Fig. 2.13(c) for
the case of a small pitch angle. For these modes to exist, the length of one turn must
generally be at least one wavelength. The normal Rn and axial Ra radiation modes are
special cases for the radiation patterns of helical antennas. In the general case, the
maximum radiation is neither at θ = 0o nor at θ = 90
o but at some intermediate value,
the pattern being conical or multi lobed in form.
2.4.1 Normal Mode of Radiation
The direction of maximum radiation is always normal to the helix axis when the helix
is small (nL<<λ). Referring to Fig. 2.14(a), the helix is coincident with the polar or y
axis. At a large distance r from the helix, the electric field may have in general two
components and as shown [17].
Two limiting cases of the small helix are:
(1) The short electric dipole of Fig. 2.12(b), α = 90o, and
(2) The small loop of Fig. 2.12(c), α = 0o.
Fig. 2.14 Relation of field components to helix, dipole and loop.
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In the case of the short electric dipole, everywhere and the distant electric
field has only component. On the other hand, with the small loop
everywhere and the distant electric field has only component. By the retarded
potential method, it may be shown that at a large distance from a short electric
dipole is given by (2.12).
(2.12)
where
s = length of short dipole
ω = 2πf
r = distance from origin
c = velocity of light (in free space)
ε = dielectric constant of medium (free space)
and [I] = retarded value of the current =I0 e[j ω (t- r/)c ]
In an analogous way, at a large distance from a short magnetic dipole or from the
equivalent small loop is given in (2.13)
(2.13)
where
A = area of loop =
[I] = retarded value of the current on the loop.
If , a helix may be considered as a combination of a series of loops and linear
conductors as illustrated in Fig. 2.15. Each turn is assumed to consist of a short dipole
of length S connected in series with a small loop of diameter D. Further, the current
on the helix of Fig. 2.15 is assumed to be uniform and in phase over the entire length.
The required end loading is not shown. Provided where the length of one turn
is now given by L = S + πD, far field pattern will be independent of number of turns.
27
Fig. 2.15 Equivalent form of small helix.
Hence, to simplify the analysis, only a single turn will be considered. The electric
field components at a large distance are then given by (2.9) and (2.10).
The operator j in (2.9) and its absence in (2.10) indicate that and are in time
phase quadrature. Taking the ratio of the magnitudes of and , we have
(2.14)
Introducing the relation between the area and diameter of the loop (2.11)
becomes
(2.15)
In the general case, both and have values and the electric field is elliptically
polarized. Since and are in time phase quadrature, either the major or the
minor axis of the polarization ellipse will lie in a plane through the polar or y axis as
shown in Fig. 2.14(a). Let us assume that the y axis is vertical and that observations of
the field are confined to the equatorial or x-z plane. The ratio of the major to minor
axes of the polarization ellipse is conveniently designated as the axial ratio. Let us
define the axial ratio in this case as given in (2.16)
(2.16)
Thus in the extreme case when , the axial ratio is infinite the polarization
ellipse becomes a straight vertical line indicating linear vertical polarization.
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Table 2.1 Conditions for normal mode polarization.
Sr. No. Condition Type of Polarization
1 S=0
α=0o
Linear (horizontal) polarization
2 S >0
Elliptical Polarization with major axis of polarization
ellipse horizontal
3 Circular Polarization
4 Elliptical polarization with major axis of polarization
ellipse vertical
5
α=90o
Linear Vertical polarization
At the other extreme, when , the axial ratio is zero and the polarization ellipse
becomes a straight horizontal line indicating linear horizontal polarization.
An interesting special case occurs for an axial ratio of unity . This is the
case for circular polarization. Setting the axial ratio in (2.12) equal to 1, we have
(2.17)
For this case, the polarization ellipse becomes a circle. The radiation is circularly
polarized not only in all directions in the x-z plane but in all directions in space except
the direction of the ±y axis, where the field is zero.
The five conditions of Table 2.1 [17] are suggested by the polarization ellipses at the
five positions along the constant-L (turn-length). The fact that the linear polarization
is horizontal for the loop and vertical for linear conductors assumes, of course that the
axis of the helix is vertical as in Fig. 2.13.
2.4.2 Axial Mode of Radiation
The preceding section deals mainly with small helices . For this condition,
the lowest T0 transmission mode is dominant and any radiation is in the normal Rn
mode. When the circumference of the helix is increased to about one wavelength
, the first-order T1 transmission mode becomes important and over a
29
considerable range of helix dimensions, the radiation may be in the axial Ra or beam
mode [17].
An outstanding characteristic of the axial or beam mode of radiation is the ease with
which it is produced. In fact, owing to the extremely noncritical nature of the helix
dimensions in this mode, a helical beam antenna is one of the simplest types of
antenna that is possible to build.
In transmission modes, it is assumed that the helix is infinite in extent. In discussing
radiation modes, the helix must be finite. For convenience, the finite helix is assumed
to be in the first approximation a section of an infinite helix. Thus, the observed
current distribution on a helix may be resolved into the current distribution for an
outward traveling wave and a current distribution for an inward traveling wave of
considerably smaller magnitude, as in Fig. 2.16. Each wave is characterized by an
initial region of relatively rapid attenuation, which is followed, by a region in which
the current is relatively constant in value.
The helical antenna is radiating in the axial mode. This large attenuation of the
reflected wave on the helical conductor results in the relatively uniform current
distribution over the central region of long helices. The marked attenuation of both the
outgoing and reflected waves also accounts for the relatively stable terminal
impedance of a helical antenna radiating in the axial mode, since relatively little
energy reflected from the open end of the helix reaches the input.
Fig. 2.16 Current distribution of helical antenna in axial mode.
30
The SWR of current at the input terminals is given by (2.18)
(2.18)
Since I2 is small compared to I0 (see Fig. 2.16), the SWR at the input terminals is
nearly unity, the same as for a transmission line terminated in approximately its
characteristic impedance.
When the helix is radiating in the axial mode, the phase velocity of wave propagation
on the helix is such as to make the component electric fields from each turn of the
helix add nearly in phase, in the direction of the helix axis. The tendency for this to
occur is sufficiently strong that the phase velocity adjusts itself to produce this result.
This natural adjustment of the phase velocity is one of the important characteristics of
wave transmission in the T1 mode on a helix. It is fact this accounts for the persistence
of axial-mode Ra radiation patterns over such a wide frequency range. The phase
velocity of wave propagation along a helical conductor is approximately equal to the
velocity of light in free space, when the frequency is too low for the axial Ra mode of
radiation. As the frequency is increased, there is a frequency range in which the phase
velocity is decreased. In this same frequency range, the radiation is observed to be in
the axial Ra mode and the current distribution changes from that due to two nearly
equal but oppositely directed traveling waves to essentially a single outgoing traveling
wave and a small reflected wave as in Fig. 2.16.
2.5 Summary
Antennas are essential parts of a radio link. To understand the functioning of antenna,
it is essential to understand the fundamental parameters of antenna. The antenna
fundamental parameters and their interdependency are discussed in detail. The helix is
a fundamental form of antenna in which loops and straight wires are limiting cases.
The helix geometry, axial and normal radiation modes are discussed in this chapter.
Apart from radiation modes, gain and bandwidth of the antenna are the important
parameters of the helical antenna. The various classical and advance techniques for
gain and bandwidth improvement are discussed in the next chapter.
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