ABSTRACT

In this paper, there is an introduction in chapter one, there are motivation, modes

of operation, analysis of helix and modified helices in chapter two, there are helical

antenna wave dispersion and radiation resistance in chapter three about helical

antenna. We can see an example for helical antenna in chapter four. In chapter five,

there are five topics. First one is feed impedance, second is polarization, third is

summary, fourth is conclusions and the last one is references.

1

CHAPTER ONEINTRODUCTION

A helical antenna is an antenna consisting of a conducting wire wound in the

form of a helix. In most cases, helical antennas are mounted over a ground plane.

Helical antennas can operate in one of two principal modes: normal (broadside) mode

or axial (or end-fire) mode.

A helical antenna is a specialized antenna that emits and responds to

electromagnetic fields with rotating (circular) polarization. These antennas are

commonly used at earth-based stations in satellite communications systems. This type

of antenna is designed for use with an unbalanced feed line such as coaxial cable. The

center conductor of the cable is connected to the helical element, and the shield of the

cable is connected to the reflector. To the casual observer, a helical antenna appears as

one or more "springs" or helixes mounted against a flat reflecting screen. The length of

the helical element is one wavelength or greater. The reflector is a circular or square

metal mesh or sheet whose cross dimension (diameter or edge) measures at least 3/4

wavelength. The helical element has a radius of 1/8 to 1/4 wavelengths, and a pitch of

1/4 to 1/2 wavelength. The minimum dimensions depend on the lowest frequency at

which the antenna is to be used. If the helix or reflector is too small (the frequency is

too low), the efficiency is severely degraded. Maximum radiation and response occur

along the axis of the helix. Helical antennas are commonly connected together in so-

called bays of two, four, or occasionally more elements with a common reflector. The

entire assembly can be rotated in the horizontal (azimuth) and vertical (elevation)

planes, so the system can be aimed toward a particular satellite. If the satellite is not in

a geostationary orbit, the azimuth and elevation rotators can be operated by a

computerized robot that is programmed to follow the course of the satellite across the

sky.

The helical antenna has a long history and has been the object of much study

and development over the last half century since its invention in 1946 [Kraus, 1976].

It is an interesting antenna with unique characteristics, being capable of high gain,

wide bandwidth, and circular polarization. As a result, it has been used in a wide range

2

of applications including satellite communications, radio astronomy, and wireless

networking. This dissertation presents a fundamental advancement of the basic axial

mode helix design. This new form of helix antenna, called the Stub Loaded Helix

(SLH) antenna, offers the advantage of a significant reduction in helix antenna size

with only a relatively small corresponding reduction in performance. The performance

reduction in many applications is not relevant and the application requirements are still

satisfied. The result is a new antenna design that offers the performance characteristics

and advantages of the conventional axial mode helix but in a much more compact

physical size envelope. The original aspects of the work described in this dissertation

are covered by U.S. patent #5,986,621. All intellectual properties related to this patent

are controlled and administered by Virginia Tech Intellectual Properties, Inc.

The helical antenna is a hybrid of two simple radiating elements, the dipole and

loop antennas. A helix becomes a linear antenna when its diameter approaches zero or

pitch angle goes to 90 o . On the other hand, a helix of fixed diameter can be seen as a

loop antenna when the spacing between the turns vanishes (a 0o ) .

Helical antennas have been widely used as simple and practical radiators over

the last five decades due to their remarkable and unique properties. The rigorous

analysis of a helix is extremely complicated. Therefore, radiation properties of the

helix, such as gain, far-field pattern, axial ratio, and input impedance have been

investigated using experimental methods, approximate analytical techniques, and

numerical analyses. Basic radiation properties of helical antennas are reviewed in this

chapter.

The geometry of a conventional helix is shown in Figure 2.1a. The parameters

that describe a helix are summarized below.

D diameter of helix

S spacing between turns

N number of turns

C circumference of helix πD

A total axial length NS

a pitch angle

3

If one turn of the helix is unrolled, as shown in Figure 2.1(b), the relationships

between S, C, a and the length of wire per turn, L , are obtained as:

S L sin a C tan a

L=(S2+C2)12 (S2+π2 D2)

12

Figure 1.1 A sketch of a typical helical antenna

4

CHAPTER TWO

SURVEY OF HELICAL ANTENNAS

2.1 Motivation

The original motivation for this work came from the desire to develop a reduced

size helix antenna for use in satellite communications links for both earth terminals

and on space platforms. Although technological trends are toward the use of higher

frequencies in the microwave and millimeter regions where greater bandwidths are

available, there are still a number of satellite systems that utilize the VHF and UHF

frequency bands. The most prominent of these is the U.S. Navy FLTSATCOM system

which utilizes a network of geosynchronous satellites to provide worldwide coverage

to bases, ships, and mobile ground forces.

At VHF and UHF frequencies, the physical dimensions of a conventional axial

mode helix can be large enough to present difficulties, particularly for mobile forces

and on the ever 2 increasingly crowded top sides of today's naval ships. A typical helix

for FLTSATCOM applications can have a helix diameter on the order of one foot

(30.5 cm) and an axial length of 12 feet (4 meters) or greater with a ground plane on

the order of 4 feet (1.3 meters). Mounting and pointing of such a large structure

presents mechanical problems. Any reduction in antenna size without significantly

impacting performance would be very desirable.

In every aspect of wireless communications today, there is a desire to minimize

antenna size. The technological progress that has produced significant advances in the

miniaturization of components and circuitry has not been mirrored by corresponding

advancements in antenna miniaturization, for a very fundamental reason. Solid state

components are only now approaching structure sizes that are comparable to the

wavelength of an electron. Most antennas operate in the size regime where their

physical dimensions are on the order of the wavelength of operation. Much theoretical

5

work over the years, as well empirical results, indicate that antenna size reduction

results in compromises of some key performance characteristics, most notably

efficiency and bandwidth. It is the goal and art of engineering to minimize and

optimize these compromises to provide a solution that meets the requirements of each

specific application. It is hoped that the Stub Loaded Helix antenna has achieved an

appropriate balance between performance and compromises in order to be considered

a useful contribution.

2.2 Modes of Operation

2.2.1 Transmission Modes

An infinitely long helix may be modeled as a transmission line or waveguide

supporting a finite number of modes. If the length of one turn of the helix is small

compared to the wavelength, L λ , the lowest transmission mode, called the T0

mode, occurs. Figure 2.2a shows the charge distribution for this mode.

When the helix circumference, C , is of the order of about one wavelength

(C 1λ) , the second-order transmission mode, referred to as the T1 mode, occurs. The

charge distribution associated with the T1 mode can be seen in Figure 2.2b. Higher-

order modes can be obtained by increasing of the ratio of circumference to wavelength

and varying the pitch angle.

2.2.2 Radiation Modes

When the helix is limited in length, it radiates and can be used as an antenna.

There are two radiation modes of important practical applications, the normal mode

and the axial mode. Important properties of normal-mode and axial-mode helixes are

summarized below.

6

Figure 2.1 (a) Geometry of helical antenna; (b) Unrolled turn of helical antenna

Figure 2.2 Instantaneous charge distribution for transmission modes: (a) The lowest-order mode

(T0); (b) The second-order mode (T1)

7

2.2.2.1 Normal Mode

For a helical antenna with dimensions much smaller than wavelength (NL

λ) , the current may be assumed to be of uniform magnitude and with a constant

phase along the helix . The maximum radiation occurs in the plane perpendicular to

the helix axis, as shown in Figure 2.3a. This mode of operation is referred to as the

“normal mode”. In general, the radiation field of this mode is elliptically polarized in

all directions. But, under particular conditions, the radiation field can be circularly

polarized. Because of it small size compared to the wavelength, the normal-mode helix

has low efficiency and narrow bandwidth.

2.2.2.2 Axial Mode

When the circumference of a helix is of the order of one wavelength, it radiates

with the maximum power density in the direction of its axis, as seen in Figure 2.3b.

This radiation mode is referred to as “axial mode”. The radiation field of this mode is

nearly circularly polarized about the axis. The sense of polarization is related to the

sense of the helix winding.

In addition to circular polarization, this mode is found to operate over a wide

range of frequencies. When the circumference (C ) and pitch angle (a ) are in the

ranges of 3/ 4 < C / λ < 4 /3 and 12º a 15º , the radiation characteristics of the

axial-mode helix remain relatively constant. As stated in, “if the impedance and the

pattern of an antenna do not change significantly over about one octave ( f u/ f l = 2 ) or

more, we will classify it as a broadband antenna”. It is noted that the ratio of the upper

frequency to the lower frequency of the axial-mode helix is equal to

f u

f l=4 /3

3/4=1.78. This is close to the definition of broadband antennas. For the reason

that the axial-mode helix possesses a

8

C≪ λ C ≈ λ

Figure 2.3 Radiation patterns of helix: (a) Normal mode; (b) Axial mode

number of interesting properties, including wide bandwidth and circularly polarized

radiation, it has found many important applications in communication systems.

9

2.3 Analysis of Helix

Unlike the dipole and loop antennas, the helix has a complicated geometry.

There are no exact solutions that describe the behavior of a helix. However, using

experimental methods and approximate analytical or numerical techniques, it is

possible to study the radiation properties of this antenna with sufficient accuracy. This

section briefly discusses the analysis of normal-mode and axial-mode helices.

2.3.1 Normal-Mode Helix

The analysis of a normal-mode helix is based on a uniform current distribution

over the length of the helix. Furthermore, the helix may be modeled as a series of

small loop and short dipole antennas as shown in Figure 2.4. The length of the short

dipole is the same as the spacing between turns of the helix, while the diameter of the

loop is the same as the helix diameter.

Since the helix dimensions are much smaller than wavelength, the far-field

pattern is independent of the number of turns. It is possible to calculate the total far-

field of the normal-mode helix by combining the fields of a small loop and a short

dipole connected in series. Doing so, the result for the electric field is expressed as

E= j ƞk I 0 e− jkr

4 πrsinθ¿), (2.1)

where k=2πλ is the propagation constant, ƞ = √ μ

ε is the intrinsic impedance of the

medium, and I0 is a current amplitude. As noted in (2.1), the θ and ∅components of

the field are in phase quadrature. Generally, the polarization of this mode is elliptical

with an axial ratio given by

AR=|Eθ||E∅|

= 2 Sλπ2 D2 , (2.2)

10

The normal-mode helix will be circularly polarized if the condition AR 1 is

satisfied.

As seen from (2.2), this condition is satisfied if the diameter of the helix and the

spacing between the turns are related as

C¿√2Sλ (2.3)

It is noted that the polarization of this mode is the same in all directions except along

the z-axis where the field is zero. It is also seen from (2.1) that the maximum radiation

occurs at θ 90º ; that is, in a plane normal to the helix axis.

2.3.2 Axial-Mode Helix

Unlike the case of a normal-mode helix, simple analytical solutions for the axial

mode helix do not exist. Thus, radiation properties and current distributions are

obtained using experimental and approximate analytical or numerical methods.

The current distribution of a typical axial-mode helix is shown in Figure 2.5. As

noted, the current distribution can be divided into two regions. Near the feed region,

the current attenuates smoothly to a minimum, while the current amplitude over the

remaining length of the helix is relatively uniform. Since the near-feed region is small

compared to the length of the helix, the current can be approximated as a travelling

wave of constant amplitude. Using this approximation, the far-field pattern of the

axial-mode helix can be analytically determined. There are two methods for the

analysis of far field pattern. In the first method, an N-turn helix is considered as an

array of N elements with an element spacing equal to S . The total field pattern is then

obtained by multiplying the pattern of one turn of the helix by the array factor. The

result is

11

F (θ)=cₒ . cosθsin (N Ψ

2)

sin(Ψ2)

, (2.4)

where cₒ is a constant coefficient and 𝛹 kS.cosθ a . Here, a is the phase shift

between successive elements and is given as

α=−2 π− πN (2.5)

In (2.4), cosθ is the element pattern and sin (N Ψ

2)

sin (Ψ2)

is the array factor for a uniform

array of N equally-spaced elements. As noted from (2.5), the Hansen-Woodyard

condition is satisfied. This condition is necessary in order to achieve agreement

between the measured and calculated patterns.

In a second method, the total field is directly calculated by integrating the

contributions of the current elements from one end of the helix to another. The current

is assumed to be a travelling wave of constant amplitude. The current distribution at an

arbitrary point on the helix is written as

I(l) = Iₒ.exp(-jg∅ ' ¿ I , (2.6)

Where

l the length of wire from the beginning of the helix to an arbitrary point

g = wL˕

pc ∅ ' m

LT = the total length of the helix

12

p phase velocity of wave propagation along the helix relative to the

helix

relative to the velocity of light , c

Figure 2.4 Approximating the geometry of normal-mode helix

Figure 2.5 Measured current distribution on axial-mode helix

=1

sinα+[ (2N+1)N ] ( λcosα)

C

¿according to Hansen-Woodyard condition)

= 2πN

13

∅ azimuthal coordinate of an arbitrary point

I unit vector along the wire

x sin ∅ ' yˆ cos∅ ' zˆ sina

The magnetic vector potential at an arbitrary point in space is obtained as

A(r) = μₐIₒ . exp (− jkr)

4 πr ∫0

∅ ' m

exp [ ju . cos (∅−∅ ')]exp(jd∅ ' ¿ Id∅ '

(2.7)

Where

u ka sinθ

a radius of the helix

d B g

B ka cosθ tana

Finally, the far-field components of the electric field, Eθ and EФ , can be expressed as

Eθ = jw[(AX cos∅+¿ AY sin∅ )cosθ + AZ sinθ ] ,

(2.8)

Eθ=-jw(AY cos∅ -AXsin∅ ) . (2.9)

2.3.3 Empirical Relations for Radiation Properties of Axial-Mode Helix

Approximate expressions for radiation properties of an axial-mode helix have

also been obtained empirically. A summary of the empirical formulas for radiation

characteristics is presented below. These formulas are valid when 12º a 15º ,

34<C λ<

43∧N >3 .

An approximate directivity expression is given as

D=C λ2NS , (2.10)

14

C λand Sλ are, respectively, the circumference and spacing between turns of the helix

normalized to the free space wavelength (λ) . Since the axial-mode helix is nearly

lossless, the directivity and the gain expressions are approximately the same.

In 1980, King and Wong reported that Kraus’s gain formula (2.10) overestimates

the actual gain and proposed a new gain expression using a much larger experimental

data base. The new expression is given as

Gp=8.3( πDλp )√

N+2−1

( NSλ p )

0.8[ tan 12.5o

tanα ]√N2 , (2.11)

where λ p is the free-space wavelength at peak gain.

In 1995, Emerson proposed a simple empirical expression for the maximum gain

based on numerical modeling of the helix. This expression gives the maximum gain in

dB as a function of length normalized to wavelength (LT = LT

λ¿ .

Gmax (dB )=¿10.25 + 1.22LT - 0.0726LT2 . (2.12)

Equation (2.12), when compared with the results from experimental and theoretical

analyses, gives the gain reasonably accurately.

Half-Power Beam width

The empirical formula for the half-power beam width is

HPBW = 52

C λ√NSλ (degrees) .

(2.13)

A more accurate formula was later presented by King and Wong using a larger

experimental data base. This result is

15

HPBW = 61.5( 2 N

N+5 )0.6

( πDλ )

√N4 ( NS

λ )0.7 ( tanα

tan 12.5o )√N4 ( degrees ) . (2.14)

Input Impedance

Since the current distribution on the axial-mode helix is assumed to be a

travelling wave of constant amplitude (Section 2.3.2), its terminal impedance is nearly

purely resistive and is constant with frequency. The empirical formula for the input

impedance is

R 140C λ (ohms).

(2.15)

The input impedance, however, is sensitive to feed geometry. Our numerical modeling

of the helix indicated that (2.15) is at best a crude approximation of the input

impedance.

Bandwidth

Based on the work of King and Wong, an empirical expression for gain

bandwidth, as a frequency ratio, has been developed:

f U

f L≈1.07 ( 0.91

GGP

)4

(3√N ) , (2.16)

where f U and f L are the upper and lower frequencies, respectively, GPis the peak gain

from equation (2.11), and G is the gain drop with respect to the peak gain.

16

2.3.4 Optimum Performance of Helix

Many different configurations of the helix have been examined in search of an

optimum performance entailing largest gain, widest bandwidth, and/or an axial ratio

closest to unity. The helix parameters that result in an optimum performance are

summarized in Table 2.1. There are some helices with parameters outside the ranges in

Table 2.1 that exhibit unique properties. However, such designs are not regarded as

optimum, because not all radiation characteristics meet desired specifications. A

summary of the effects of various parameters on the performance of helix is presented

below.

Table 2.1 Parameter ranges for optimum performance of helix

Circumference

As shown in Figure 2.6, it is noted that the optimum circumference for achieving

the peak gain is around 1.1λ and is relatively independent of the length of the helix.

Other results show that the peak gain smoothly drops as the diameter of the helix

decreases (Figure 2.7). Since other parameters of the helix also affect its properties, a

circumference of 1.1λ is viewed as a good estimate for an optimum performance.

Pitch Angle

17

Keeping the circumference and the length of a helix fixed, the gain increases

smoothly when the pitch angle is reduced, as seen in Figure 2.8. However, the

reduction

Figure 2.6 Gain of helix for different lengths as function of normalized circumference (Cλ )

18

Figure 2.7 Peak gain of various diameter as D and a varied (circles), D fixed and a varied

of pitch angle is limited by the bandwidth performance. That is, a narrower bandwidth

is obtained for a helix with a smaller pitch angle. For this reason, it has been generally

agreed that the optimal pitch angle for the axial-mode helix is about12.5O.

Number of Turns

Many properties, such as gain, axial ratio, and beam width, are affected by the

number of turns. Figure 2.9 shows the variation of gain versus the number of turns. It

is noted that as the number of turns increases, the gain increases too. The increase in

gain is simply explained using the uniformly excited equally-spaced array theory.

However, the gain does not increase linearly with the number of turns, and, for very

large number of turns, adding more turns has little effect. Also, as shown in Figure

2.10, the beam width becomes narrower for larger number of turns. Although adding

more turns improves the gain, it makes the helix larger, heavier, and more costly.

Practical helices have between 6 and 16 turns. If high gain is required, array of helices

may be used.

Conductor Diameter

19

This parameter does not significantly affect the radiation properties of the helix.

For larger conductor diameters, slightly wider bandwidths are obtained. Also, thicker

conductors can be used for supporting a longer antenna.

Ground Plain

The effect of ground plain on radiation characteristics of the helix is negligible

since the backward traveling waves incident upon it are very weak. Nevertheless, a

ground plane with a diameter of one-half wavelength at the lowest frequency is

usually recommended.

Figure 2.8 Gain versus frequency of 30.8-inch length and 4.3-inch diameter helix for different

pitch angles.

20

Figure 2.9 Gain versus frequency for 5 to 35-turn helical antennas with 4.23-inch diameter

Figure 2.10 Radiation patterns for various helical turns of helices with a 12o and C 10cm. at 3Hz GHz.

21

2.4 Modified Helices

Various modifications of the conventional helical antenna have been proposed

for the purpose of improving its radiation characteristics. A summary of these

modifications is presented below.

2.4.1 Helical Antenna with Tapered End

Nakano and Yamauchi have proposed a modified helix in which the open end

section is tapered as illustrated in Figure 2.11. This structure provides significant

improvement in the axial ratio over a wide bandwidth. According to them, the axial

ratio improves as the cone angle θtis increased. For a helix with pitch angle of 12.5o

and 6 turns followed by few tapered turns, they obtained an axial ratio of 1:1.3 over a

frequency range of 2.6 to 3.5 GHz.

2.4.2 Printed Resonant Quadrifilar Helix

Printed resonant quadrifilar helix is a modified form of the resonant quadrifilar

helix antenna first proposed by Kings. The structure of this helix consists of 4 micro

strips printed spirally around a cylindrical surface. The feed end is connected to the

opposite radial strips as seen in Figure 2.12. The advantage of this antenna is a broad

beam radiation pattern (half-power beam width 145o). Additionally, its compact

size and light weight are attractive to many applications especially for GPS system.

2.4.3 Stub-Loaded Helix

To reduce the size of a helix operating in the axial mode, a novel geometry

referred to as stub-loaded helix has been recently proposed. Each turn contains four

stubs as illustrated in Figure 2.13. The stub-loaded helix provides comparable

radiation properties to the conventional helix with the same number of turns, while

offering an approximately 4:1 reduction in the physical size.

2.4.4 Monopole-Helix Antenna

22

This antenna consists of a helix and a monopole, as shown in Figure 2.14 . The

purpose of this modified antenna is to maintain operation at two different frequencies,

applicable to dual-band cellular phone systems operating in two different frequency

bands (900 MHz for GSM and 1800 MHz for DCS1800).

Figure 2.11 Tapered helical antenna configuration.

23

Figure 2.12 12

turn half-wavelength printed resonant quadrifilar helix .

Figure 2.13 Stub-loaded helix configuration .

24

Figure 2.14 Monopole-helix antenna .

CHAPTER THREE

3.1 Helical Antenna Current Density

To calculate the current density of the helical antenna a simplified geometry was

assumed with infinitely thin wire and a single complete loop around the tube at either

end to complete the circuit. Thus the generalized antenna model used to calculate the

current density consists of two helical windings, each making one rotation in a

distance λ and displaced by 0.5 × λ . The total length of the antenna is L, and the

radius of the antenna is α . This is the simplified antenna configuration employed by

the numerical model when making a comparison with the experimental results in

section 3.2. With the origin in the middle of the antenna the θ component of the

current density can be written as

25

(3.1)

where θ0 = L

2β , β=λ

2π , and F is defined by equation 2.4 Equation (2.17) can be

Fourier transformed into the more useful coordinates of the azimuthal mode number

m, and the wave number k.

(3.2)

This has the property

(3.3)

When the parallel wave number is close to the peak in the current density

spectrum, the azimuthal wave number is predominately m = |1|. This antenna has

positive helicity, in the positive k direction m = +1 is dominant, while in the negative k

direction m = -1 is predominant. The dominance of m = +1 in the positive k direction

is shown in figure 3.1(b). Figure 3.1(a) shows how the k spectra becomes more

selective as the length of the antenna is increased. The total length of the antenna used

for Basil was L = 1.5 × λ=0.27 m, where λ=0.18 m.

3.2 Helical Antenna Wave Dispersion and Radiation Resistance

26

A helical antenna was constructed in the hope of producing plasma with the m =

-1 azimuthal mode. It would be expected that if a plasma were produced in the k‖ < 0

direction that the wave mode responsible for the plasma production would be m = 1. It

was immediately clear from the light emission that the helical antenna only produced

plasma in the direction of positive azimuthal modes. Measurements in both directions

of the wave were taken by reversing the direction of the static magnetic field.

Azimuthal magnetic wave field measurements confirmed that the mode in the

direction of strong plasma was m = 1. The plasma extended a short

Figure 3.1 The current density spectrum of the simple helical antenna, r = 0.0225 m,

λ = 0.18 m. (a) Axial spectra for azimuthal mode number m = +1 for different antenna

lengths, L , L = 2 × λ (dotted), L = 1.5 × λ(solid), L = 1 × λ(dashed), and L = 0.5 × λ

(dot-dash). (b) Azimuthal mode number spectra for parallel wave number 35 m−1 , and

L = 1.5 × λ .

27

Distance, approximately 10cm, in the negative k direction as can be seen in

figure 3.2(a). Measurements of the azimuthal fields in this plasma revealed a low

amplitude m = +1 mode probably coupled by the end sections of the antenna. The

wave propagating in the direction of right hand rotation of the antenna travels from

under the antenna along the discharge.

The measured dispersion shown in figure 3.3(a) gives an indication of the higher

selectivity of the helical antenna, with a smaller range of parallel wavelengths being

observed than with the double saddle coil antenna. It was found that attempts to

significantly vary the wavelength by increasing the power resulted in unstable

discharges. An example of this is shown in figure 3.4, which shows the ion saturation

current of a Langmuir probe in a fix position as a function of time for increasing

power. As the power is increased the discharge becomes unstable. However, eventual

an equilibrium condition is established where further increases in power do not

increase the on axis density significantly. Thus, for a helical antenna with a total

length equal to, or larger than the wavelength of the antenna, the operating regime is

limited to the region of the preferred parallel wavelength of the antenna.

Figure 3.3(b) compares the measured radiation resistance with that calculated by

the numerical model which used the measured radial density profiles shown in figure

3.5. The radiation resistance measured for the helical antenna is more peaked than that

of the double saddle coil, which is consistent with the higher selectivity of the helical

antenna as indicated by the current density spectrum. The radiation resistance reaches

a maximum at approximately ne

B0≈ 50× 1019 m−3 T−1, which from the dispersion curve

correspondstok‖=40rads m−1. This is in agreement with figure 3.1 where the current

density

28

Figure 3.2 Longitudinal measurements of (a) electron density (b) and temperature on

axis (c) axial magnetic wavefield amplitudes and (c) phase and (d) 3 azimuthal magnetic

wave field amplitudes and (e) phase 30msec into an Argon discharge with a helical antenna

at a static field of 960 Gauss and filling pressure of 30mTorr.

The position of the antenna is indicated by the vertical dashed lines and the end of the

static field coils by the solid line.

29

Figure 3.3 Comparison of measured and calculated dispersion and radiation resistance

of the helicon wave launched by the helical antenna in argo.

30

Figure 3.4 Power scan with a helical antenna, B0= 576 Gauss, pressure = 30 mTorr.

Spectrum reaches a maximum at approximately the same value. It also agrees with the

numerical model which also reaches a maximum at approximately the same value.

It is noticeable that the radiation resistance of the helical antenna is much higher

than the double saddle coil antenna. However there is a significant discrepancy

between the measured and calculated radiation resistance for the higher values of nc

B0.

As discussed in section the results from the numerical model can be strongly

influenced by systematic errors in the density profiles. This is especially the case with

the helical antenna which has a higher selectivity of parallel wavelength. However,

Kamenski demonstrated that by altering the maximum in the density profiles only

slightly higher radiation resistances could be obtained, which are not as high as the

experimental results. The peak value of the radiation resistance for the helical antenna

31

is 4 times higher than for the double saddle coil antenna. Below the peak the radiation

resistance drops off sharply, consistent with the current density spectrum and is in

reasonable agreement with the model. Above the peak there appears a systematic

discrepancy between the measured and model results which is not presently

understood.

In figure 3.2, which show longitudinal measurements for neon and krypton, it is

clear that the plasma extends in the direction of left hand rotation of the antenna

beyond the region of power deposition by the wave. This is due to ionization by

electrons travelling from the region of power deposition. As expected the distance the

plasma extends in this direction is strongly dependent on the gas, with the collision

cross section, and thus the mean free path of the electrons being a function of the gas

type and filling pressure. In an measurement at similar conditions to those in figure

3.2, but with a filling pressure of 13mTorr, the plasma extended 35cm past the antenna

compared to

Figure 3.5 Radial density profiles of Argon plasmas produced with a helical antenna as

a function of applied field.

32

10cm as in the figure, demonstrating the dependence on pressure. Also noticeable in

the axial density profiles is the peak in the density near the end of the discharge where

the plasma reaches the end of the field. This is believed to be due to depletion of

neutrals along the length of the discharge and supply of neutrals from the end of the

tube and will be studied.

By comparing the radial density profiles obtained with the helical antenna (see

figure 3.5 and those obtained with the double saddle coil antenna it can be seen that

the densities obtained in both cases are similar in magnitude. However, comparing the

corresponding plots of power coupled to the plasma for the helical antenna profiles

and double saddle coil antenna profiles (see figure 3.4) it is clear that the power

required to produce discharges of similar densities was much lower for the helical

antenna. This is not surprising, as with only half the plasma, the plasma losses have

also been halved. Thus if a plasma on only one side of the antenna is sufficient the

helical antenna is far more efficient, but has a less flexible operating regime.

33

CHAPTER FOUR

EXAMPLE FOR HELICAL ANTENNA

A helical antenna operating in the normal mode has N turns with diameter 2b

and interturn spacing s. Both 2b and s are very small in comparison to λ /N and

are adjusted to radiate circularly polarized waves.

Find :

(a) its directive gain and directivity,

(b) its radiation resistance.

(Sol.)

(a) E=

N ωμ0 I4 π

( e− jβR

R)[ aθ js+ aϕ βπ b2 ]sin θ

, H= 1

η0aR×E= NβI

4 π( e− jβR

R)[ aφ js−aθ βπ b2 ]sin θ

Circularly polarized: s =βπb 2

U=R2 aR⋅Pav=R2 aR

12

Re [ E×H ]=β2η0

16 π 2 (NIs )2sin2θ

Pr=∫0

2 π ∫0

πU sin θdθdφ=

β2 η0

bπ(NIs )2⇒GD=

4 πUP r

=32

sin2θ,

D=GD(π2)=1 .5

(b)

Rr=2 P r

I 2 =η0 (NIs )2

3π=40(Nβ2 πb2 )2

34

CHAPTER FIVE

5.1 Feed impedance

A typical helical antenna has an input impedance of around 140 ohms. Kraus3

gives a nominal impedance of Z = 140C with axial feed. This is a resistive

impedance only at one frequency, probably near the center frequency. Matching the

impedance to 50 ohms over a broad bandwidth would be more difficult than simply

matching it well for a ham band. A simple quarter-wave matching section with a Zo ~

84 ohms should do the trick for a single band. The matching section10 is often part of

the helix: a quarter-wave of wire close to the ground plane before the first turn starts.

It could also be on the other side of the ground plane, to separate impedance matching

from the radiating element.

5.2 Polarization

Circular polarization has two possible senses: right-hand (RHCP) and lefthand

(LHCP). Since a helix cannot switch polarization, it is important to get it right: by the

IEEE definition3, RHCP results when the helix is wound as though it were to fit in the

threads of a large screw with normal right-hand threads. Note that the classical optics

definition of polarization is opposite to the IEEE definition. More important for a feed

is that the sense of the polarization reverses on reflection, so that for a dish to radiate

RHCP polarization requires a feed with LHCP. For EME, reflection from the moon

also reverses circular polarization, so that the echo returns with polarization reversed

from the transmitted polarization. A helical feed used for EME would not be able to

receive its own echoes because of cross-polarization loss.

35

5.3 Summary

The helical antenna is an excellent feed for circular polarization. It is broadband

and dimensions are not critical, and the patterns are well-suited to illumination of

offset dishes. It is a particularly good feed for small offset dishes for satellite

applications.

36

CONCLUSION

A helical antenna for the capsule endoscope is designed. To encase the system in

the capsule module and to obtain the omni-directional radiation pattem, the small sized

normal mode helical antenna is designed. To enhance the bandwidth of the antenna for

transmitting the high data rate information, the end of the helix is connected to the

ground. From the measured return loss and the radiation pattem, it is found that the

designed antenna is suitable to use for the capsule endoscope. The shape and the size

of the ground conductor can significantly influence the helical antenna performance.

The ground conductor in the form of truncated cone has the highest favorable impact

on the antenna gain, which was demonstrated both computationally and

experimentally. The geometrical parameters of the conical ground conductor were

optimized with the goal to maximize the antenna gain. The details of the optimization

procedure were outlined. The obtained optimal parameters (cone diameters and height)

are in good agreement with those used in our computations and experiments. The

performed optimization of the conical ground conductor improves the antenna

performance.

37

Referances

1.] http://ourworld.compuserve.com/homepages/demerson/helix.htm or

2. ] http://www.tuc.nrao.edu/~demerson/helixgain/helix.htm

3. ] http://www.zeland.com

4. ] http://www.ansoft.com

5. ] http://www.qsl.net/wb6tpu/swindex.html

6. ] http://en.wikipedia.org/wiki/Helical_antenna

7.]http://related:scholar.lib.vt.edu/theses/available/etd-02102000

19330046/unrestricted/07chapter2.PDF 2. Survey of Helical Antennas

38

References Types

1. ] Kraus, J.D., (W8JK), “A Helical-Beam Antenna Without a Ground Plane,” IEEE

Antennas and Propagation Magazine, April 1995, p. 45.

2. ] Kraus, J.D., Antennas, McGraw-Hill, 1950.

3. ] Kraus, J.D. & Marhefka, R.J., Antennas: for All Applications, third edition,

McGraw-Hill, 2002.

4. ] Emerson, D., AA7FV, “The Gain of the Axial-Mode Helix Antenna,” Antenna

Compendium Volume 4, ARRL, 1995, pp. 64-68.

5. ] Kraus, J.D., “A 50-Ohm Impedance for Helical Beam Antennas,” IEEE

Transactions on Antennas and Propagation, November 1977, p. 913

6. ] J. D. Kraus, “Helical beam antennas,” Electronics, vol. 20, pp. 109-111, April

1947.

7. ] H. E. King and J. L. Wong, “Characteristics of 1 to 8 wavelength uniform helical

antennas”, IEEE Trans. Antennas Propagat., vol. 28, pp. 291-296, March 1980.

39