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.

12

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.

13

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.

15

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.

22

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.

26

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.

28

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.